Stephen Wolfram: Fundamental Theory of Physics, Life, and the Universe
物理与宇宙学技术与编程太空与探索数学AI 与机器学习
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AI 智能总结
斯蒂芬·沃尔弗拉姆谈物理基本理论与宇宙
这是 Lex Fridman 与 Wolfram Research 创始人 Stephen Wolfram 的第二次对话。Wolfram 深入阐述了他的 Wolfram 物理项目——试图用简单的计算规则推导出物理学的所有基本定律，以及这对我们理解宇宙、时间和意识的深刻含义。
Wolfram物理项目计算宇宙时间意识统一物理理论细胞自动机
Stephen Wolfram 是英国-美国计算机科学家、数学家和物理学家，Wolfram Research 创始人兼 CEO，创造了 Mathematica、Wolfram Alpha 和 Wolfram Language，著有《一种新科学》，是计算科学领域最具原创性的思想家之一。
📌 核心观点
- Wolfram 物理项目：Wolfram 提出宇宙可以用极其简单的计算规则（超图重写规则）来描述，从这些规则中可以推导出广义相对论和量子力学。这是一个雄心勃勃的统一物理理论尝试。
- 计算等价原理：Wolfram 的核心哲学是「计算等价原理」——几乎所有足够复杂的系统都具有相同的计算能力，这意味着宇宙、大脑和简单的细胞自动机在某种意义上是等价的。
- 时间的本质：在 Wolfram 的框架中，时间是计算的进行，宇宙的历史是一个不断展开的计算过程。这对时间旅行、因果关系和自由意志有深刻的含义。
- 意识与计算：Wolfram 认为意识可能是某种特定类型的计算过程，但他对意识的「困难问题」保持谦逊，承认这可能超出了纯粹计算框架的解释能力。
- Wolfram Alpha 与 ChatGPT：Wolfram 讨论了 Wolfram Alpha（基于规则的知识引擎）与 ChatGPT（基于统计学习的语言模型）的根本区别，以及两者如何互补。
✨ 金句摘录
Wolfram：宇宙可能只是一个极其简单的计算规则在运行——从这个规则中可以推导出所有的物理定律。
Wolfram：计算等价原理告诉我们，几乎所有足够复杂的系统都具有相同的计算能力——宇宙和大脑在某种意义上是等价的。
Wolfram：时间是计算的进行——宇宙的历史是一个不断展开的计算过程。
📋 章节目录
暂无章节信息
🔑 关键词
spacephysicsuniversequantumtheorycomputationalgraphmathematicsdongoingrulecausalmathematicalsciencedoingmechanicsrelativityhypergraphgeneralmodel
💬 精彩语录
暂无语录
🎙️ 完整对话（6329 条）
Lex Fridman (00:00.000)
The following is a conversation with Stephen Wolfram,
Lex Fridman (00:02.800)
his second time on the podcast.
Lex Fridman (00:05.080)
He's a computer scientist, mathematician,
Lex Fridman (00:07.240)
theoretical physicist, and the founder and CEO
Lex Fridman (00:10.640)
of Wolfram Research, a company behind Mathematica,
Stephen Wolfram (00:14.400)
Wolfram Alpha, Wolfram Language,
Lex Fridman (00:16.680)
and the new Wolfram Physics Project.
Stephen Wolfram (00:19.200)
He's the author of several books,
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including A New Kind of Science, and the new book,
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A Project to Find the Fundamental Theory of Physics.
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This second round of our conversation is primarily focused
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on this latter endeavor of searching for the physics
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of our universe in simple rules that do their work
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on hypergraphs and eventually generate the infrastructure
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from which space, time, and all of modern physics can emerge.
Stephen Wolfram (00:45.420)
Quick summary of the sponsors,
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SimpliSafe, Sunbasket, and Masterclass.
Stephen Wolfram (00:50.240)
Please check out these sponsors in the description
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to get a discount and to support this podcast.
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As a side note, let me say that to me,
Lex Fridman (00:58.680)
the idea that seemingly infinite complexity can arise
Stephen Wolfram (01:02.040)
from very simple rules and initial conditions
Lex Fridman (01:05.080)
is one of the most beautiful and important
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mathematical and philosophical mysteries in science.
Lex Fridman (01:10.440)
I find that both cellular automata
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and the hypergraph data structure
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that Stephen and team are currently working on
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to be the kind of simple, clear mathematical playground
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within which fundamental ideas about intelligence,
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consciousness, and the fundamental laws of physics
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can be further developed in totally new ways.
Stephen Wolfram (01:31.680)
In fact, I think I'll try to make a video or two
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about the most beautiful aspects of these models
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in the coming weeks, especially, I think,
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trying to describe how fellow curious minds like myself
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can jump in and explore them either just for fun
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or potentially for publication of new innovative research
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in math, computer science, and physics.
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But honestly, I think the emerging complexity
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in these hypergraphs can capture the imagination
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of everyone, even if you're someone
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who never really connected with mathematics.
Lex Fridman (02:04.040)
That's my hope, at least, to have these conversations
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that inspire everyone to look up to the skies
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and into our own minds in awe of our amazing universe.
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Let me also mention that this is the first time
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I ever recorded a podcast outdoors
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as a kind of experiment to see if this is an option
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in times of COVID.
Stephen Wolfram (02:25.360)
I'm sorry if the audio is not great.
Lex Fridman (02:27.840)
I did my best and promise to keep improving
Lex Fridman (02:30.580)
and learning as always.
Lex Fridman (02:32.640)
If you enjoy this thing, subscribe on YouTube,
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review it with Five Stars and Apple Podcast,
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follow on Spotify, support on Patreon,
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or connect with me on Twitter at Lex Friedman.
Lex Fridman (02:42.880)
As usual, I'll do a few minutes of ads now
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and no ads in the middle.
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I tried to make these interesting,
Lex Fridman (02:48.440)
but I do give you timestamps, so you're welcome to skip,
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but still, please do check out the sponsors
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by clicking the links in the description.
Lex Fridman (02:56.600)
It's the best way to support this podcast.
Stephen Wolfram (02:59.560)
Also, let me say, even though I'm talking way too much,
Lex Fridman (03:02.800)
that I did a survey and it seems like over 90% of people
Stephen Wolfram (03:06.580)
either enjoy these ad reads somehow magically
Lex Fridman (03:09.880)
or don't mind them, at least.
Stephen Wolfram (03:11.800)
That honestly just warms my heart
Lex Fridman (03:14.320)
that people are that supportive.
Stephen Wolfram (03:16.160)
This show is sponsored by SimpliSafe,
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a home security company.
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Go to SimpliSafe.com to get a free HD camera.
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It's simple, no contracts, 15 bucks a month, easy setup.
Stephen Wolfram (03:28.120)
Even I figured it out.
Lex Fridman (03:29.600)
I have it set up in my apartment.
Stephen Wolfram (03:31.600)
Of course, I also welcome intruders.
Lex Fridman (03:34.280)
One of my favorite movies is Leon or The Professional
Stephen Wolfram (03:38.300)
with Jean Reno, Gary Oldman,
Lex Fridman (03:40.580)
and the brilliant young Natalie Portman.
Stephen Wolfram (03:43.380)
If you haven't seen the movie,
Lex Fridman (03:44.280)
he's a hit man with a minimalist life that resembles my own.
Stephen Wolfram (03:48.800)
In fact, when I was younger, the idea of being a hit man
Lex Fridman (03:52.600)
or targeting evil in a skilled way,
Stephen Wolfram (03:56.420)
which is how I thought about it, really appealed to me.
Lex Fridman (03:59.640)
The skill of it, the planning, the craftsmanship.
Stephen Wolfram (04:03.720)
In another life, perhaps,
Lex Fridman (04:05.280)
if I didn't love engineering and science so much,
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I could see myself being something like a Navy SEAL.
Lex Fridman (04:10.760)
And in general, I love the idea of serving my country,
Stephen Wolfram (04:14.080)
of serving society by contributing my skill
Lex Fridman (04:16.700)
in some small way.
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Anyway, go to Simplisafe.com slash Lex
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to get a free HD camera and to support this podcast.
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They're a new sponsor, and this is a trial run,
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so you know what to do.
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This show is also sponsored by Sun Basket,
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a meal delivery service.
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Visit SunBasket.com slash Lex
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and use code LEX to get $30 off your order
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and to support this podcast.
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This is the last read of the trial they're doing,
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so this is the time to get them if you're considering it.
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And if you do, it'll help ensure
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that they decide to support this podcast long term.
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Their meals are healthy and delicious,
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a nice break from the minimalist meals of meat
Lex Fridman (04:56.960)
and vegetables that I usually eat.
Stephen Wolfram (04:59.640)
Maybe on a personal note,
Lex Fridman (05:00.840)
one of my favorite things to do is watch people cook,
Stephen Wolfram (05:03.720)
especially people who love cooking,
Lex Fridman (05:05.800)
and hang out with people over amazing meals.
Stephen Wolfram (05:09.080)
I still tend to be strict in my diet no matter what,
Lex Fridman (05:11.640)
even in fancy restaurants,
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but it brings me joy to see friends and family indulge
Lex Fridman (05:17.140)
something like a cake that has way too many calories
Stephen Wolfram (05:20.760)
or ice cream or whatever.
Lex Fridman (05:22.640)
My mom, in fact, for much of my life,
Stephen Wolfram (05:24.920)
made this cake called an anthill on my birthday
Lex Fridman (05:27.760)
that brings me a lot of joy and way too many calories.
Stephen Wolfram (05:32.500)
I was thinking of doing a video with my mom as she makes it.
Lex Fridman (05:36.480)
I thought it'd be a fun thing to do together.
Stephen Wolfram (05:39.500)
Anyway, go to SunBasket.com slash Lex and use code LEX.
Lex Fridman (05:44.020)
Do it now.
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So they signed a longterm contract for this podcast.
Lex Fridman (05:48.200)
This show is also sponsored by Masterclass.
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Sign up at masterclass.com slash LEX.
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180 bucks a year, you get an all access pass
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to watch lessons from Chris Hadfield,
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and many more brilliant world experts.
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Masterclass has been a really special sponsor.
Lex Fridman (06:10.260)
They believe in this podcast in a way that gives me strength
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and motivation to take intellectual risks.
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I'm thinking of doing a few solo podcast episodes
Stephen Wolfram (06:18.880)
on difficult topics, especially in history,
Lex Fridman (06:22.240)
like the rise and fall of the Third Reich or Stalin, Putin,
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and many other difficult topics that I'm fascinated by.
Lex Fridman (06:29.560)
I have a worldview that seeks inspiring positive insights,
Stephen Wolfram (06:33.120)
even and perhaps especially from periods of tragedy and evil
Lex Fridman (06:38.240)
that perhaps some folks may find value in.
Stephen Wolfram (06:40.800)
If I can only learn to convey the ideas in my mind
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as clearly as I think them.
Stephen Wolfram (06:45.800)
I think deeply and rigorously and precisely,
Lex Fridman (06:50.520)
but to be honest, have trouble speaking in a way
Stephen Wolfram (06:53.520)
that reflects that rigor of thought.
Lex Fridman (06:56.800)
So it really does mean a lot, the love and support I get
Stephen Wolfram (07:00.160)
as I try to get better at this thing,
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at this talking thing.
Stephen Wolfram (07:03.880)
Anyway, go to masterclass.com slash LEX to get a discount
Lex Fridman (07:07.400)
and to support this podcast.
Lex Fridman (07:09.400)
And now finally, here's my conversation with Stephen Wolfram.
Lex Fridman (07:14.800)
You said that there are moments in history of physics
Lex Fridman (07:17.420)
and maybe mathematical physics or even mathematics
Lex Fridman (07:20.200)
where breakthroughs happen
Lex Fridman (07:22.460)
and then a flurry of progress follows.
Lex Fridman (07:24.800)
So if you look back through the history of physics,
Lex Fridman (07:28.320)
what moments stand out to you as important such breakthroughs
Lex Fridman (07:32.240)
where a flurry of progress follows?
Lex Fridman (07:34.560)
So the big famous one was 1920s,
Lex Fridman (07:36.880)
the invention of quantum mechanics,
Stephen Wolfram (07:38.960)
where in about five or 10 years,
Lex Fridman (07:41.960)
lots of stuff got figured out.
Stephen Wolfram (07:43.720)
That's now quantum mechanics.
Lex Fridman (07:45.040)
Can you mention the people involved?
Stephen Wolfram (07:46.600)
Yeah, it was kind of the Schrodinger, Heisenberg,
Lex Fridman (07:50.640)
Einstein had been a key figure, originally Planck,
Stephen Wolfram (07:53.900)
then Dirac was a little bit later.
Lex Fridman (07:56.560)
That was something that happened at that time,
Lex Fridman (07:58.160)
that's sort of before my time, right?
Lex Fridman (08:00.440)
In my time was in the 1970s,
Stephen Wolfram (08:04.040)
there was this sort of realization
Lex Fridman (08:06.320)
that quantum field theory was actually going to be useful
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in physics and QCD, quantum thermodynamics theory
Lex Fridman (08:13.040)
of quarks and gluons and so on was really getting started.
Lex Fridman (08:16.080)
And there was again, sort of big flurry of things
Lex Fridman (08:19.800)
happened then, I happened to be a teenager at that time
Lex Fridman (08:22.440)
and happened to be really involved in physics.
Lex Fridman (08:26.540)
And so I got to be part of that, which was really cool.
Stephen Wolfram (08:29.760)
Who were the key figures
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aside from your young selves at that time?
Lex Fridman (08:33.880)
You know, who won the Nobel Prize for QCD, okay?
Lex Fridman (08:37.040)
People, David Gross, Frank Wilczek, you know, David Politzer.
Stephen Wolfram (08:41.440)
The people who are the sort of the slightly older generation,
Lex Fridman (08:44.000)
Dick Feynman, Murray Gellman, people like that,
Stephen Wolfram (08:48.520)
who were Steve Weinberg, Gerhard Hoft, he's younger,
Lex Fridman (08:52.760)
he's in the younger group actually.
Lex Fridman (08:54.800)
But these are all, you know, characters who were involved.
Lex Fridman (08:59.240)
I mean, it's funny because those are all people
Stephen Wolfram (09:02.540)
who are kind of in my time and I know them
Lex Fridman (09:05.040)
and they don't seem like sort of historical,
Stephen Wolfram (09:08.820)
you know, iconic figures.
Lex Fridman (09:10.140)
They seem more like everyday characters, so to speak.
Lex Fridman (09:14.480)
And so it's always, you know, when you look at history
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from long afterwards, it always seems like
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everything happened instantly.
Lex Fridman (09:24.120)
And that's usually not the case.
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There was usually a long buildup,
Lex Fridman (09:27.360)
but usually there's, you know,
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there's some methodological thing happens
Lex Fridman (09:30.920)
and then there's a whole bunch of low hanging fruit
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to be picked.
Lex Fridman (09:33.800)
And that usually lasts five or 10 years.
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You know, we see it today with machine learning
Lex Fridman (09:38.760)
and, you know, deep learning neural nets and so on.
Stephen Wolfram (09:42.640)
You know, methodological advance,
Lex Fridman (09:44.440)
things actually started working in, you know, 2011, 2012
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and so on.
Lex Fridman (09:48.440)
And, you know, there's been this sort of rapid
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picking of low hanging fruit, which is probably, you know,
Lex Fridman (09:56.520)
some significant fraction of the way done, so to speak.
Lex Fridman (10:00.080)
Do you think there's a key moment?
Lex Fridman (10:01.600)
Like if I had to really introspect,
Stephen Wolfram (10:03.120)
like what was the key moment
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for the deep learning, quote unquote, revolution?
Stephen Wolfram (10:08.040)
I mean.
Lex Fridman (10:08.860)
It's probably the AlexNet business.
Stephen Wolfram (10:10.120)
AlexNet with ImageNet.
Lex Fridman (10:11.480)
So is there something like that with physics
Stephen Wolfram (10:13.840)
where, so deep learning neural networks
Lex Fridman (10:18.080)
have been around for a long time.
Stephen Wolfram (10:19.880)
Absolutely, since the 1940s, yeah.
Lex Fridman (10:22.000)
There's a bunch of little pieces that came together
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and then all of a sudden everybody's eyes lit up.
Lex Fridman (10:27.480)
Like, wow, there's something here.
Stephen Wolfram (10:29.820)
Like even just looking at your own work,
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just your thinking about the universe,
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that there's simple rules can create complexity.
Lex Fridman (10:40.120)
You know, at which point was there a thing
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where your eyes light up?
Lex Fridman (10:45.120)
It's like, wait a minute, there's something here.
Stephen Wolfram (10:46.520)
Is it the very first idea
Lex Fridman (10:49.480)
or is it some moment along the line of implementations
Lex Fridman (10:53.360)
and experiments and so on?
Lex Fridman (10:54.640)
There's a couple of different stages to this.
Stephen Wolfram (10:56.380)
I mean, one is the think about the world computationally.
Lex Fridman (11:01.080)
Can we use programs instead of equations
Lex Fridman (11:03.880)
to make models of the world?
Lex Fridman (11:05.880)
That's something that I got interested in
Stephen Wolfram (11:07.760)
in the beginning of the 1980s.
Lex Fridman (11:10.400)
I did a bunch of computer experiments.
Stephen Wolfram (11:13.040)
When I first did them, I didn't really,
Lex Fridman (11:15.820)
I could see some significance to them,
Lex Fridman (11:17.520)
but it took me a few years to really say,
Lex Fridman (11:20.000)
wow, there's a big important phenomenon here
Stephen Wolfram (11:22.880)
that lets sort of complex things arise
Lex Fridman (11:25.400)
from very simple programs.
Stephen Wolfram (11:27.360)
That kind of happened back in 1984 or so.
Lex Fridman (11:30.560)
Then, you know, a bunch of other years go by,
Stephen Wolfram (11:33.000)
then I start actually doing a lot
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of much more systematic computer experiments and things
Lex Fridman (11:37.720)
and find out that the, you know,
Lex Fridman (11:39.280)
this phenomenon that I could only have said occurs
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in one particular case
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is actually something incredibly general.
Lex Fridman (11:45.120)
And then that led me to this thing called
Lex Fridman (11:46.560)
principle of computational equivalence.
Lex Fridman (11:48.680)
And that was a long story.
Lex Fridman (11:51.120)
And then, you know, as part of that process,
Stephen Wolfram (11:53.920)
I was like, okay, you can make simple programs,
Lex Fridman (11:56.880)
can make models of complicated things.
Lex Fridman (11:59.240)
What about the whole universe?
Lex Fridman (12:00.720)
That's our sort of ultimate example of a complicated thing.
Lex Fridman (12:03.760)
And so I got to thinking, you know,
Lex Fridman (12:05.080)
could we use these ideas to study fundamental physics?
Stephen Wolfram (12:10.240)
You know, I happen to know a lot about,
Lex Fridman (12:11.960)
you know, traditional fundamental physics.
Stephen Wolfram (12:14.160)
My first, you know, I had a bunch of ideas
Lex Fridman (12:17.320)
about how to do this in the early 1990s.
Stephen Wolfram (12:19.360)
I made a bunch of technical progress.
Lex Fridman (12:21.080)
I figured out a bunch of things
Stephen Wolfram (12:22.120)
I thought were pretty interesting.
Lex Fridman (12:23.880)
You know, I wrote about them back in 2002.
Stephen Wolfram (12:26.600)
With the new kind of science
Lex Fridman (12:27.800)
in the cellular automata world.
Lex Fridman (12:29.200)
And there's echoes in the cellular automata world
Lex Fridman (12:32.200)
with your new Wolfram physics project.
Stephen Wolfram (12:36.680)
We'll get to all that.
Lex Fridman (12:37.640)
Allow me to sort of romanticize a little more
Stephen Wolfram (12:40.280)
on the philosophy of science.
Lex Fridman (12:43.280)
So Thomas Kuhn, philosopher of science,
Stephen Wolfram (12:45.600)
describes that, you know, the progress in science
Lex Fridman (12:49.440)
is made with these paradigm shifts.
Lex Fridman (12:52.160)
And so to link on the sort of original line of discussion,
Lex Fridman (12:56.920)
do you agree with this view
Stephen Wolfram (12:58.120)
that there is revolutions in science
Lex Fridman (13:01.520)
that just kind of flip the table?
Lex Fridman (13:03.400)
What happens is it's a different way
Lex Fridman (13:05.920)
of thinking about things.
Stephen Wolfram (13:07.000)
It's a different methodology for studying things.
Lex Fridman (13:09.920)
And that opens stuff up.
Stephen Wolfram (13:11.720)
There's this idea of,
Lex Fridman (13:15.400)
he's a famous biographer,
Lex Fridman (13:16.840)
but I think it's called the innovators.
Lex Fridman (13:19.640)
There's a biographer of Steve Jobs, of Albert Einstein.
Stephen Wolfram (13:22.680)
He also wrote a book,
Lex Fridman (13:23.640)
I think it's called the innovators,
Stephen Wolfram (13:24.800)
where he discusses how a lot of the innovations
Lex Fridman (13:30.240)
in the history of computing has been done by groups.
Stephen Wolfram (13:33.840)
There's a complicated group dynamic going on,
Lex Fridman (13:37.320)
but there's also a romanticized notion
Stephen Wolfram (13:39.360)
that the individual is at the core of the revolution.
Lex Fridman (13:42.800)
Like where does your sense fall?
Stephen Wolfram (13:45.280)
Is ultimately like one person responsible
Lex Fridman (13:49.880)
for these revolutions that creates the spark
Stephen Wolfram (13:52.680)
or one or two, whatever,
Lex Fridman (13:54.600)
or is it just the big mush and mess and chaos
Lex Fridman (13:58.760)
of people interacting, of personalities interacting?
Lex Fridman (14:01.360)
I think it ends up being like many things,
Stephen Wolfram (14:03.120)
there's leadership and there ends up being,
Lex Fridman (14:05.360)
it's a lot easier for one person to have a crisp new idea
Stephen Wolfram (14:08.080)
than it is for a big committee to have a crisp new idea.
Lex Fridman (14:10.840)
And I think, but I think it can happen
Stephen Wolfram (14:13.720)
that you have a great idea,
Lex Fridman (14:16.440)
but the world isn't ready for it.
Lex Fridman (14:19.120)
And you can, I mean, this has happened to me plenty, right?
Lex Fridman (14:24.040)
It's, you have an idea, it's actually a pretty good idea,
Lex Fridman (14:27.200)
but things aren't ready,
Lex Fridman (14:29.240)
either you're not really ready for it,
Stephen Wolfram (14:31.680)
or the ambient world isn't ready for it.
Lex Fridman (14:34.480)
And it's hard to get the thing to get traction.
Stephen Wolfram (14:37.880)
It's kind of interesting.
Lex Fridman (14:38.720)
I mean, when I look at a new kind of science,
Stephen Wolfram (14:41.720)
you're now living inside the history,
Lex Fridman (14:43.640)
so you can't tell the story of these decades,
Lex Fridman (14:46.680)
but it seems like the new kind of science
Lex Fridman (14:49.640)
has not had the revolutionary impact
Stephen Wolfram (14:55.200)
I would think it might.
Lex Fridman (14:59.120)
Like, it feels like at some point, of course it might be,
Lex Fridman (15:02.640)
but it feels at some point people will return to that book
Lex Fridman (15:07.120)
and say, that was something special here.
Stephen Wolfram (15:09.600)
This was incredible.
Lex Fridman (15:10.880)
What happened?
Lex Fridman (15:11.840)
Or do you think that's already happened?
Lex Fridman (15:13.560)
Oh, yeah, it's happened, except that people aren't,
Stephen Wolfram (15:16.400)
the sort of the heroism of it may not be there,
Lex Fridman (15:19.480)
but what's happened is for 300 years,
Stephen Wolfram (15:22.760)
people basically said,
Lex Fridman (15:24.520)
if you want to make a model of things in the world,
Stephen Wolfram (15:27.040)
mathematical equations are the best place to go.
Lex Fridman (15:29.760)
Last 15 years, doesn't happen.
Stephen Wolfram (15:32.480)
New models that get made of things
Lex Fridman (15:34.600)
most often are made with programs, not with equations.
Lex Fridman (15:38.600)
Now, was that sort of going to happen anyway?
Lex Fridman (15:42.320)
Was that a consequence of my particular work
Lex Fridman (15:45.600)
and my particular book?
Lex Fridman (15:47.240)
It's hard to know for sure.
Stephen Wolfram (15:48.800)
I mean, I am always amazed at the amounts of feedback
Lex Fridman (15:51.560)
that I get from people where they say,
Stephen Wolfram (15:52.960)
oh, by the way, I started doing this whole line of research
Lex Fridman (15:56.080)
because I read your book, blah, blah, blah, blah, blah.
Stephen Wolfram (15:58.520)
It's like, well, can you tell that
Lex Fridman (15:59.920)
from the academic literature?
Lex Fridman (16:01.880)
Was there a chain of academic references?
Lex Fridman (16:04.520)
Probably not.
Stephen Wolfram (16:05.800)
One of the interesting side effects of publishing
Lex Fridman (16:09.040)
in the way you did this tome
Stephen Wolfram (16:11.920)
is it serves as an education tool and an inspiration
Lex Fridman (16:15.320)
to hundreds of thousands, millions of people,
Lex Fridman (16:19.200)
but because it's not a single,
Lex Fridman (16:21.680)
it's not a chain of papers with spiffy titles,
Stephen Wolfram (16:25.200)
it doesn't create a splash of citations.
Lex Fridman (16:29.320)
It's had plenty of citations, but it's, you know,
Stephen Wolfram (16:31.440)
I think that people think of it as probably more,
Lex Fridman (16:36.440)
you know, conceptual inspiration than kind of a,
Stephen Wolfram (16:41.640)
you know, this is a line from here to here to here
Lex Fridman (16:43.880)
in our particular field.
Stephen Wolfram (16:45.440)
I think that the thing which I am disappointed by
Lex Fridman (16:49.520)
and which will eventually happen
Stephen Wolfram (16:51.440)
is this kind of study of the sort of pure computationalism,
Lex Fridman (16:55.840)
this kind of study of the abstract behavior
Stephen Wolfram (16:58.600)
of the computational universe.
Lex Fridman (17:00.520)
That should be a big thing that lots of people do.
Stephen Wolfram (17:03.960)
You mean in mathematics purely, almost like.
Lex Fridman (17:06.320)
It's like pure mathematics, but it isn't mathematics.
Lex Fridman (17:08.840)
But it isn't, it isn't.
Lex Fridman (17:10.440)
It's a new kind of mathematics.
Lex Fridman (17:12.320)
Is it a new title of the book?
Lex Fridman (17:14.360)
Yeah, right.
Stephen Wolfram (17:15.200)
That's why the book is called that.
Lex Fridman (17:17.040)
Right, that's not coincidental.
Stephen Wolfram (17:19.160)
Yeah.
Lex Fridman (17:20.160)
It's interesting that I haven't seen
Stephen Wolfram (17:22.840)
really rigorous investigation
Lex Fridman (17:24.960)
by thousands of people of this idea.
Stephen Wolfram (17:26.880)
I mean, you look at your competition around rule 30.
Lex Fridman (17:30.080)
I mean, that's fascinating.
Stephen Wolfram (17:31.320)
If you can say something.
Lex Fridman (17:34.320)
Right.
Lex Fridman (17:35.160)
Is there some aspect of this thing that could be predicted?
Lex Fridman (17:38.800)
That's the fundamental question of science.
Stephen Wolfram (17:40.960)
That's the core.
Lex Fridman (17:41.800)
Well, that has been a question of science.
Stephen Wolfram (17:42.880)
I think that is some people's view of what science is about
Lex Fridman (17:47.440)
and it's not clear that's the right view.
Stephen Wolfram (17:48.960)
In fact, as we live through this pandemic
Lex Fridman (17:51.520)
full of predictions and so on,
Stephen Wolfram (17:53.320)
it's an interesting moment to be pondering
Lex Fridman (17:55.360)
what science's actual role in those kinds of things is.
Stephen Wolfram (17:58.440)
Or you think it's possible that in science,
Lex Fridman (18:02.080)
clean, beautiful, simple prediction
Stephen Wolfram (18:04.920)
may not even be possible in real systems.
Lex Fridman (18:07.240)
That's the open question.
Stephen Wolfram (18:08.800)
I don't think it's open.
Lex Fridman (18:09.640)
I think that question is answered and the answer is no.
Stephen Wolfram (18:12.240)
Well, no, no.
Lex Fridman (18:13.120)
The answer could be just humans are not smart enough yet.
Stephen Wolfram (18:16.680)
Like we don't have the tools yet.
Lex Fridman (18:17.520)
No, that's the whole point.
Stephen Wolfram (18:18.680)
I mean, that's sort of the big discovery
Lex Fridman (18:20.680)
of this principle of computational equivalence of mine.
Lex Fridman (18:23.320)
And this is something which is kind of a follow on
Lex Fridman (18:26.880)
to Gödel's theorem, to Turing's work
Stephen Wolfram (18:28.920)
on the halting problem, all these kinds of things.
Lex Fridman (18:31.680)
That there is this fundamental limitation
Stephen Wolfram (18:34.720)
built into science,
Lex Fridman (18:36.360)
this idea of computational irreducibility
Stephen Wolfram (18:39.120)
that says that even though you may know the rules
Lex Fridman (18:42.480)
by which something operates,
Stephen Wolfram (18:44.160)
that does not mean that you can readily sort of
Lex Fridman (18:47.600)
be smarter than it and jump ahead
Lex Fridman (18:49.760)
and figure out what it's going to do.
Lex Fridman (18:51.640)
Yes, but do you think there's a hope
Lex Fridman (18:53.800)
for pockets of computational reducibility?
Lex Fridman (18:56.960)
Computational reducibility.
Lex Fridman (19:02.480)
And then a set of tools and mathematics
Lex Fridman (19:04.840)
that help you discover such pockets.
Stephen Wolfram (19:07.040)
That's where we live is in the pockets of reducibility.
Lex Fridman (19:10.160)
That's why, and this is one of the things
Stephen Wolfram (19:12.560)
that sort of come out of this physics project
Lex Fridman (19:14.080)
and actually something that, again,
Stephen Wolfram (19:15.480)
I should have realized many years ago, but didn't,
Lex Fridman (19:18.680)
is it could very well be that everything about the world
Stephen Wolfram (19:23.440)
is computationally reducible and completely unpredictable.
Lex Fridman (19:26.560)
But in our experience of the world,
Stephen Wolfram (19:29.720)
there is at least some amount of prediction we can make.
Lex Fridman (19:32.520)
And that's because we have sort of chosen a slice of,
Stephen Wolfram (19:36.560)
probably talk about this in much more detail,
Lex Fridman (19:38.320)
but I mean, we've kind of chosen a slice
Stephen Wolfram (19:39.920)
of how to think about the universe
Lex Fridman (19:41.760)
in which we can kind of sample
Stephen Wolfram (19:43.960)
a certain amount of computational reducibility.
Lex Fridman (19:46.640)
And that's sort of where we exist.
Lex Fridman (19:51.640)
And it may not be the whole story of how the universe is,
Lex Fridman (19:55.920)
but it is the part of the universe that we care about
Lex Fridman (19:59.240)
and we sort of operate in.
Lex Fridman (1:00:01.120)
the consequences of general relativity,
Lex Fridman (1:00:03.080)
but it's not, there's no, I mean,
Lex Fridman (1:00:05.720)
and some things are kind of squiggly and complicated.
Stephen Wolfram (1:00:09.400)
Like people believe, you know, energy is conserved.
Lex Fridman (1:00:12.120)
Okay, well, energy conservation doesn't really work
Stephen Wolfram (1:00:14.480)
in general activity in the same way as it ordinarily does.
Lex Fridman (1:00:16.840)
And it's all a big mathematical story
Stephen Wolfram (1:00:19.300)
of how you actually nail down something that is definitive
Lex Fridman (1:00:22.840)
that you can talk about it and not specific to the,
Stephen Wolfram (1:00:25.320)
you know, reference frames you're operating in
Lex Fridman (1:00:27.200)
and so on and so on and so on.
Lex Fridman (1:00:28.420)
But fundamentally, general relativity is a straight shot
Lex Fridman (1:00:31.360)
in the sense that you have this theory,
Stephen Wolfram (1:00:32.960)
you work out its consequences.
Lex Fridman (1:00:34.960)
And that theory is useful in terms of basic science
Lex Fridman (1:00:39.300)
and trying to understand the way black holes work,
Lex Fridman (1:00:41.220)
the way the creation of galaxies work,
Stephen Wolfram (1:00:43.580)
sort of all of these kinds of cosmological things,
Lex Fridman (1:00:45.840)
understanding what happened, like you said, at the Big Bang.
Stephen Wolfram (1:00:49.200)
Yeah. Like all those kinds of,
Lex Fridman (1:00:50.560)
well, no, not at the Big Bang actually, right?
Lex Fridman (1:00:52.800)
But the...
Lex Fridman (1:00:53.860)
Well, features of the expansion of the universe, yes.
Stephen Wolfram (1:00:55.880)
I mean, and there are lots of details
Lex Fridman (1:00:58.220)
where we don't quite know how it's working, you know,
Stephen Wolfram (1:00:59.920)
is there, you know, where's the dark matter,
Lex Fridman (1:01:02.040)
is there dark energy, you know, et cetera, et cetera, et cetera.
Lex Fridman (1:01:04.400)
But fundamentally, the, you know,
Lex Fridman (1:01:06.320)
the testable features of general relativity,
Stephen Wolfram (1:01:08.440)
it all works very beautifully.
Lex Fridman (1:01:10.080)
And it's in a sense, it is mathematically sophisticated,
Lex Fridman (1:01:13.720)
but it is not conceptually hard to understand in some sense.
Lex Fridman (1:01:17.160)
Okay. So that's general relativity.
Lex Fridman (1:01:18.720)
And what's its friendly neighbor, like you said,
Lex Fridman (1:01:21.240)
there's two theories, quantum mechanics.
Stephen Wolfram (1:01:22.800)
Right. So quantum mechanics,
Lex Fridman (1:01:24.320)
the sort of the way that that originated was,
Lex Fridman (1:01:28.240)
one question was, is the world continuous or is it discrete?
Lex Fridman (1:01:31.360)
You know, in ancient Greek times,
Stephen Wolfram (1:01:32.480)
people have been debating this.
Lex Fridman (1:01:34.000)
People debated it, you know, throughout history.
Lex Fridman (1:01:36.400)
Is light made of waves?
Lex Fridman (1:01:38.360)
Is it continuous? Is it discrete?
Stephen Wolfram (1:01:39.820)
Is it made of particles, corpuscles, whatever.
Lex Fridman (1:01:43.380)
You know, what had become clear in the 1800s is that atoms,
Stephen Wolfram (1:01:47.760)
that, you know, materials are made of discrete atoms.
Lex Fridman (1:01:51.360)
You know, when you take some water,
Stephen Wolfram (1:01:53.940)
the water is not a continuous fluid,
Lex Fridman (1:01:55.560)
even though it seems like a continuous fluid
Stephen Wolfram (1:01:57.360)
to us at our scale.
Lex Fridman (1:01:58.880)
But if you say, let's look at it,
Stephen Wolfram (1:02:00.760)
smaller and smaller and smaller and smaller scale,
Lex Fridman (1:02:02.480)
eventually you get down to these, you know,
Stephen Wolfram (1:02:04.400)
these molecules and then atoms.
Lex Fridman (1:02:06.320)
It's made of discrete things.
Lex Fridman (1:02:07.960)
The question is sort of how important is this discreteness?
Lex Fridman (1:02:10.960)
Just what's discrete, what's not discrete?
Lex Fridman (1:02:12.900)
Is energy discrete?
Lex Fridman (1:02:14.040)
Is, you know, what's discrete, what's not?
Lex Fridman (1:02:17.400)
And so.
Lex Fridman (1:02:18.240)
Does it have mass?
Stephen Wolfram (1:02:19.560)
Those kinds of questions.
Lex Fridman (1:02:20.880)
Yeah, yeah, right.
Stephen Wolfram (1:02:21.700)
Well, there's a question, I mean, for example,
Lex Fridman (1:02:23.640)
is mass discrete is an interesting question,
Stephen Wolfram (1:02:26.040)
which is now something we can address.
Lex Fridman (1:02:28.140)
But, you know, what happened in the coming up to the 1920s,
Stephen Wolfram (1:02:35.720)
there was this kind of mathematical theory developed
Lex Fridman (1:02:37.720)
that could explain certain kinds of discreteness
Stephen Wolfram (1:02:40.500)
in particularly in features of atoms and so on.
Lex Fridman (1:02:44.340)
And, you know, what developed was this mathematical theory
Stephen Wolfram (1:02:47.780)
that was the theory of quantum mechanics,
Lex Fridman (1:02:50.200)
theory of wave functions, Schrodinger's equation,
Stephen Wolfram (1:02:52.520)
things like this.
Lex Fridman (1:02:53.680)
That's a mathematical theory that allows you to calculate
Stephen Wolfram (1:02:57.320)
lots of features of the microscopic world,
Lex Fridman (1:02:59.260)
lots of things about how atoms work,
Stephen Wolfram (1:03:01.480)
et cetera, et cetera, et cetera.
Lex Fridman (1:03:03.000)
Now, the calculations all work just great.
Stephen Wolfram (1:03:05.760)
The question of what does it really mean
Lex Fridman (1:03:09.400)
is a complicated question.
Stephen Wolfram (1:03:11.300)
Now, I mean, to just explain a little bit historically,
Lex Fridman (1:03:14.280)
the, you know, the early calculations of things like atoms
Stephen Wolfram (1:03:17.040)
worked great in 1920s, 1930s and so on.
Lex Fridman (1:03:20.320)
There was always a problem.
Stephen Wolfram (1:03:21.400)
There were, in quantum field theory,
Lex Fridman (1:03:24.200)
which is a theory of, in quantum mechanics,
Stephen Wolfram (1:03:27.300)
you're dealing with a certain number of electrons
Lex Fridman (1:03:30.480)
and you fix the number of electrons.
Stephen Wolfram (1:03:31.940)
You say, I'm dealing with a two electron thing.
Lex Fridman (1:03:34.900)
In quantum field theory,
Stephen Wolfram (1:03:35.800)
you allow for particles being created and destroyed.
Lex Fridman (1:03:38.880)
So you can emit a photon that didn't exist before.
Stephen Wolfram (1:03:41.200)
You can absorb a photon, things like that.
Lex Fridman (1:03:43.440)
That's a more complicated,
Stephen Wolfram (1:03:44.560)
mathematically complicated theory.
Lex Fridman (1:03:46.280)
And it had all kinds of mathematical issues
Lex Fridman (1:03:47.960)
and all kinds of infinities that cropped up.
Lex Fridman (1:03:49.980)
And it was finally figured out more or less
Lex Fridman (1:03:51.400)
how to get rid of those.
Lex Fridman (1:03:52.920)
But there were only certain ways of doing the calculations
Lex Fridman (1:03:55.940)
and those didn't work for atomic nuclei among other things.
Lex Fridman (1:03:59.640)
And that led to a lot of development up until the 1960s
Stephen Wolfram (1:04:03.840)
of alternative ideas for how one could understand
Lex Fridman (1:04:07.160)
what was happening in atomic nuclei, et cetera,
Stephen Wolfram (1:04:09.080)
et cetera, et cetera.
Lex Fridman (1:04:10.120)
End result, in the end,
Stephen Wolfram (1:04:12.280)
the kind of most quotes obvious mathematical structure
Lex Fridman (1:04:16.000)
of quantum field theory seems to work.
Stephen Wolfram (1:04:18.360)
Although it's mathematically difficult to deal with,
Lex Fridman (1:04:20.680)
but you can calculate all kinds of things.
Stephen Wolfram (1:04:22.980)
You can calculate to a dozen decimal places,
Lex Fridman (1:04:26.140)
certain things, you can measure them.
Stephen Wolfram (1:04:27.800)
It all works.
Lex Fridman (1:04:28.640)
It's all beautiful.
Stephen Wolfram (1:04:29.600)
Now you say...
Lex Fridman (1:04:30.440)
The underlying fabric is the model
Stephen Wolfram (1:04:32.520)
of that particular theory is fields.
Lex Fridman (1:04:34.800)
Like you keep saying fields.
Stephen Wolfram (1:04:37.000)
Those are quantum fields.
Lex Fridman (1:04:37.940)
Those are different from classical fields.
Stephen Wolfram (1:04:40.400)
A field is something like you say,
Lex Fridman (1:04:44.640)
like you say the temperature field in this room.
Stephen Wolfram (1:04:46.920)
It's like there is a value of temperature
Lex Fridman (1:04:49.520)
at every point around the room.
Stephen Wolfram (1:04:51.360)
That's some, or you can say the wind field
Lex Fridman (1:04:53.980)
would be the vector direction of the wind at every point.
Stephen Wolfram (1:04:56.920)
It's continuous.
Lex Fridman (1:04:57.880)
Yes, and that's a classical field.
Stephen Wolfram (1:05:00.200)
The quantum field is a much more
Lex Fridman (1:05:01.360)
mathematically elaborate kind of thing.
Lex Fridman (1:05:04.280)
And I should explain that one of the pictures
Lex Fridman (1:05:06.400)
of quantum mechanics that's really important is,
Stephen Wolfram (1:05:09.360)
in classical physics, one believes
Lex Fridman (1:05:11.760)
that sort of definite things happen in the world.
Stephen Wolfram (1:05:13.800)
You pick up a ball, you throw it,
Lex Fridman (1:05:16.160)
the ball goes in a definite trajectory
Stephen Wolfram (1:05:17.980)
that has certain equations of motion.
Lex Fridman (1:05:20.200)
It goes in a parabola, whatever else.
Stephen Wolfram (1:05:22.240)
In quantum mechanics, the picture is
Lex Fridman (1:05:25.320)
definite things don't happen.
Stephen Wolfram (1:05:26.880)
Instead, sort of what happens is this whole
Lex Fridman (1:05:29.720)
sort of structure of all many different paths being followed
Lex Fridman (1:05:34.840)
and we can calculate certain aspects of what happens,
Lex Fridman (1:05:37.840)
certain probabilities of different outcomes and so on.
Lex Fridman (1:05:40.560)
And you say, well, what really happened?
Lex Fridman (1:05:42.440)
What's really going on?
Stephen Wolfram (1:05:43.440)
What's the sort of, what's the underlying,
Lex Fridman (1:05:45.680)
what's the underlying story?
Lex Fridman (1:05:47.120)
How do we turn this mathematical theory
Lex Fridman (1:05:50.640)
that we can calculate things with
Stephen Wolfram (1:05:52.400)
into something that we can really understand
Lex Fridman (1:05:54.760)
and have a narrative about?
Lex Fridman (1:05:56.360)
And that's been really, really hard for quantum mechanics.
Lex Fridman (1:05:58.920)
My friend, Dick Feynman, always used to say,
Stephen Wolfram (1:06:01.500)
nobody understands quantum mechanics,
Lex Fridman (1:06:03.640)
even though he'd made his whole career
Stephen Wolfram (1:06:06.400)
out of calculating things about quantum mechanics.
Lex Fridman (1:06:10.160)
And so it's a little bit.
Stephen Wolfram (1:06:11.720)
Nevertheless, it's what the quantum field theory is very,
Lex Fridman (1:06:16.840)
very accurate at predicting a lot of the physical phenomena.
Lex Fridman (1:06:20.640)
So it works.
Lex Fridman (1:06:21.720)
Yeah.
Lex Fridman (1:06:22.560)
But there are things about it, it has certain,
Lex Fridman (1:06:25.240)
when we apply it, the standard model of particle physics,
Stephen Wolfram (1:06:27.780)
for example, we, which we apply to calculate
Lex Fridman (1:06:31.500)
all kinds of things that works really well.
Lex Fridman (1:06:33.440)
And you say, well, it has certain parameters.
Lex Fridman (1:06:34.880)
It has a whole bunch of parameters actually.
Lex Fridman (1:06:36.900)
You say, why is the, why does the muon particle exist?
Lex Fridman (1:06:41.540)
Why is it 206 times the mass of the electron?
Stephen Wolfram (1:06:44.880)
We don't know, no idea.
Lex Fridman (1:06:46.680)
But so the standard model of physics is one of the models
Stephen Wolfram (1:06:50.020)
that's very accurate for describing
Lex Fridman (1:06:51.720)
three of the fundamental forces of physics.
Lex Fridman (1:06:55.200)
And it's looking at the world of the very small.
Lex Fridman (1:06:58.240)
Right.
Lex Fridman (1:06:59.080)
And then there's back to the neighbor of gravity,
Lex Fridman (1:07:03.140)
of general relativity.
Stephen Wolfram (1:07:04.760)
So, and then in the context of a theory of everything,
Lex Fridman (1:07:07.660)
what's traditionally the task of the unification
Lex Fridman (1:07:13.560)
of these theories?
Lex Fridman (1:07:15.160)
And why is it hard?
Stephen Wolfram (1:07:16.000)
The issue is you try to use the methods
Lex Fridman (1:07:18.160)
of quantum field theory to talk about gravity
Lex Fridman (1:07:20.840)
and it doesn't work.
Lex Fridman (1:07:22.000)
Just like there are photons of light.
Lex Fridman (1:07:24.000)
So there are gravitons,
Lex Fridman (1:07:25.320)
which are sort of the particles of gravity.
Lex Fridman (1:07:27.960)
And when you try and compute sort of the properties
Lex Fridman (1:07:30.280)
of the particles of gravity,
Stephen Wolfram (1:07:32.680)
the kind of mathematical tricks that get used
Lex Fridman (1:07:36.040)
in working things out in quantum field theory don't work.
Lex Fridman (1:07:39.280)
And that's, so that's been a sort of fundamental issue.
Lex Fridman (1:07:43.000)
And when you think about black holes,
Stephen Wolfram (1:07:44.800)
which are a place where sort of the structure of space
Lex Fridman (1:07:48.960)
is, you know, has sort of rapid variation
Lex Fridman (1:07:52.800)
and you get kind of quantum effects mixed in
Lex Fridman (1:07:55.320)
with effects from general relativity,
Stephen Wolfram (1:07:57.520)
things get very complicated
Lex Fridman (1:07:58.720)
and there are apparent paradoxes and things like that.
Lex Fridman (1:08:01.320)
And people have, you know,
Lex Fridman (1:08:02.840)
there've been a bunch of mathematical developments
Stephen Wolfram (1:08:05.040)
in physics over the last, I don't know, 30 years or so,
Lex Fridman (1:08:08.600)
which have kind of picked away at those kinds of issues
Lex Fridman (1:08:11.560)
and got hints about how things might work.
Lex Fridman (1:08:15.200)
But it hasn't been, you know,
Lex Fridman (1:08:17.280)
and the other thing to realize is,
Lex Fridman (1:08:19.040)
as far as physics is concerned,
Stephen Wolfram (1:08:20.680)
it's just like here's general relativity,
Lex Fridman (1:08:22.840)
here's quantum field theory, you know, be happy.
Stephen Wolfram (1:08:25.840)
Yeah, so do you think there's a quantization of gravity,
Lex Fridman (1:08:28.760)
so quantum gravity, what do you think of efforts
Stephen Wolfram (1:08:31.100)
that people have tried to, yeah,
Lex Fridman (1:08:33.760)
what do you think in general of the efforts
Lex Fridman (1:08:36.340)
of the physics community to try to unify these laws?
Lex Fridman (1:08:39.600)
So I think what's, it's interesting.
Stephen Wolfram (1:08:41.320)
I mean, I would have said something very different
Lex Fridman (1:08:43.360)
before what's happened with our physics project.
Stephen Wolfram (1:08:46.400)
I mean, you know, the remarkable thing is
Lex Fridman (1:08:48.880)
what we've been able to do is to make
Stephen Wolfram (1:08:51.720)
from this very simple, structurally simple,
Lex Fridman (1:08:55.560)
underlying set of ideas,
Stephen Wolfram (1:08:57.960)
we've been able to build this, you know,
Lex Fridman (1:09:00.940)
very elaborate structure that's both very abstract
Lex Fridman (1:09:04.480)
and very sort of mathematically rich.
Lex Fridman (1:09:06.880)
And the big surprise, as far as I'm concerned,
Stephen Wolfram (1:09:09.240)
is that it touches many of the ideas that people have had.
Lex Fridman (1:09:12.960)
So in other words, things like string theory and so on,
Stephen Wolfram (1:09:15.520)
twister theory, it's like the, you know,
Lex Fridman (1:09:18.160)
we might've thought, I had thought we're out on a prong,
Stephen Wolfram (1:09:21.020)
we're building something that's computational,
Lex Fridman (1:09:22.640)
it's completely different from what other people have done.
Lex Fridman (1:09:25.060)
But actually it seems like what we've done
Lex Fridman (1:09:27.320)
is to provide essentially the machine code that, you know,
Stephen Wolfram (1:09:30.820)
these things are various features
Lex Fridman (1:09:33.080)
of domain specific languages, so to speak,
Stephen Wolfram (1:09:35.460)
that talk about various aspects of this machine code.
Lex Fridman (1:09:37.920)
And I think this is something that to me is very exciting
Stephen Wolfram (1:09:41.800)
because it allows one both for us to provide
Lex Fridman (1:09:45.540)
sort of a new foundation for what's been thought about there
Lex Fridman (1:09:48.440)
and for all the work that's been done in those areas
Lex Fridman (1:09:52.000)
to give us, you know, more momentum
Stephen Wolfram (1:09:55.760)
to be able to figure out what's going on.
Lex Fridman (1:09:57.140)
Now, you know, people have sort of hoped,
Stephen Wolfram (1:09:58.840)
oh, we're just gonna be able to get, you know,
Lex Fridman (1:10:01.200)
string theory to just answer everything.
Stephen Wolfram (1:10:03.400)
That hasn't worked out.
Lex Fridman (1:10:04.920)
And I think we now kind of can see a little bit about
Stephen Wolfram (1:10:07.920)
just sort of how far away certain kinds of things are
Lex Fridman (1:10:10.360)
from being able to explain things.
Stephen Wolfram (1:10:12.520)
Some things, one of the big surprises to me,
Lex Fridman (1:10:14.720)
actually I literally just got a message
Stephen Wolfram (1:10:16.600)
about one aspect of this is the, you know,
Lex Fridman (1:10:20.800)
it's turning out to be easier.
Stephen Wolfram (1:10:22.640)
I mean, this project has been so much easier
Lex Fridman (1:10:24.880)
than I could ever imagine it would be.
Stephen Wolfram (1:10:26.680)
That is, I thought we would be, you know,
Lex Fridman (1:10:29.720)
just about able to understand
Stephen Wolfram (1:10:31.360)
the first 10 to the minus 100 seconds of the universe.
Lex Fridman (1:10:34.120)
And, you know, it would be a hundred years
Stephen Wolfram (1:10:35.800)
before we get much further than that.
Lex Fridman (1:10:37.640)
It's just turned out, it actually wasn't that hard.
Stephen Wolfram (1:10:40.440)
I mean, we're not finished, but, you know.
Lex Fridman (1:10:42.480)
So you're seeing echoes of all the disparate theories
Stephen Wolfram (1:10:45.840)
of physics in this framework.
Lex Fridman (1:10:47.400)
Yes, yes.
Stephen Wolfram (1:10:48.440)
I mean, it's a very interesting, you know,
Lex Fridman (1:10:50.840)
sort of history of science like phenomenon.
Stephen Wolfram (1:10:53.300)
I mean, the best analogy that I can see
Lex Fridman (1:10:55.920)
is what happened with the early days
Stephen Wolfram (1:10:58.240)
of computability and computation theory.
Lex Fridman (1:11:00.600)
You know, Turing machines were invented in 1936.
Stephen Wolfram (1:11:03.520)
People sort of understand computation
Lex Fridman (1:11:06.040)
in terms of Turing machines,
Lex Fridman (1:11:07.280)
but actually there had been preexisting theories
Lex Fridman (1:11:09.920)
of computation, combinators, general recursive functions,
Stephen Wolfram (1:11:12.920)
Lambda calculus, things like this.
Lex Fridman (1:11:14.880)
But people hadn't, those hadn't been concrete enough
Stephen Wolfram (1:11:18.280)
that people could really wrap their arms around them
Lex Fridman (1:11:20.320)
and understand what was going on.
Lex Fridman (1:11:21.800)
And I think what we're gonna see in this case
Lex Fridman (1:11:23.480)
is that a bunch of these mathematical theories,
Stephen Wolfram (1:11:26.000)
including some very,
Lex Fridman (1:11:28.080)
I mean, one of the things that's really interesting
Stephen Wolfram (1:11:29.720)
is one of the most abstract things
Lex Fridman (1:11:31.840)
that's come out of sort of mathematics,
Stephen Wolfram (1:11:36.240)
higher category theory, things about infinity group voids,
Lex Fridman (1:11:39.680)
things like this, which to me always just seemed
Stephen Wolfram (1:11:41.640)
like they were floating off into the stratosphere,
Lex Fridman (1:11:44.160)
ionosphere of mathematics, turn out to be things
Stephen Wolfram (1:11:48.300)
which our sort of theory anchors down
Lex Fridman (1:11:52.000)
to something fairly definite and says are super relevant
Stephen Wolfram (1:11:56.240)
to the way that we can understand how physics works.
Lex Fridman (1:11:59.240)
Give me a sec.
Stephen Wolfram (1:12:00.080)
By the way, I just threw a hat on.
Lex Fridman (1:12:01.560)
You've said that with this metaphor analogy
Stephen Wolfram (1:12:06.400)
that the theory of everything is a big mountain
Lex Fridman (1:12:09.360)
and you have a sense that however far we are up the mountain,
Stephen Wolfram (1:12:14.360)
that the Wolfram physics model view of the universe
Lex Fridman (1:12:21.280)
is at least the right mountain.
Stephen Wolfram (1:12:22.600)
We're the right mountain, yes, without question.
Lex Fridman (1:12:25.440)
Which aspect of it is the right mountain?
Lex Fridman (1:12:27.880)
So for example, I mean, so there's so many aspects
Lex Fridman (1:12:31.000)
to just the way of the Wolfram physics project,
Stephen Wolfram (1:12:34.560)
the way it approaches the world that's clean, crisp,
Lex Fridman (1:12:39.560)
and unique and powerful, so there's a discreet nature to it,
Stephen Wolfram (1:12:45.320)
there's a hypergraph, there's a computational nature,
Lex Fridman (1:12:48.960)
there's a generative aspect, you start from nothing,
Stephen Wolfram (1:12:51.600)
you generate everything, do you think the actual model
Lex Fridman (1:12:56.920)
is actually a really good one,
Stephen Wolfram (1:12:58.320)
or do you think this general principle
Lex Fridman (1:13:00.160)
from simplicity generating complexity is the right,
Lex Fridman (1:13:02.880)
like what aspect of the mountain is the correct?
Lex Fridman (1:13:05.040)
Yeah, right, I think that the kind of the meta idea
Stephen Wolfram (1:13:10.080)
about using simple computational systems to do things,
Lex Fridman (1:13:14.080)
that's the ultimate big paradigm
Stephen Wolfram (1:13:18.080)
that is sort of super important.
Lex Fridman (1:13:21.560)
The details of the particular model are very nice and clean
Lex Fridman (1:13:25.560)
and allow one to actually understand what's going on.
Lex Fridman (1:13:27.880)
They are not unique, and in fact, we know that.
Stephen Wolfram (1:13:30.600)
We know that there's a very, very, very, very,
Lex Fridman (1:13:34.680)
there's a large number of different ways
Stephen Wolfram (1:13:37.160)
to describe essentially the same thing.
Lex Fridman (1:13:38.600)
I mean, I can describe things in terms of hypergraphs,
Stephen Wolfram (1:13:41.120)
I can describe them in terms of higher category theory,
Lex Fridman (1:13:43.520)
I can describe them in a bunch of different ways.
Stephen Wolfram (1:13:45.240)
They are in some sense all the same thing,
Lex Fridman (1:13:47.480)
but our sort of story about what's going on
Lex Fridman (1:13:50.240)
and the kind of cultural mathematical resonances
Lex Fridman (1:13:53.600)
are a bit different.
Lex Fridman (1:13:54.720)
And I think it's perhaps worth sort of saying a little bit
Lex Fridman (1:13:57.600)
about kind of the foundational ideas
Stephen Wolfram (1:14:00.600)
of these models and things.
Lex Fridman (1:14:04.800)
Great, so can you maybe, can we like rewind?
Stephen Wolfram (1:14:09.920)
We've talked about it a little bit,
Lex Fridman (1:14:11.120)
but can you say like what the central idea is
Lex Fridman (1:14:14.080)
of the Wolfram Physics Project?
Lex Fridman (1:14:16.680)
Right, so the question is we're interested
Stephen Wolfram (1:14:19.200)
in finding sort of simple computational rule
Lex Fridman (1:14:21.920)
that describes our whole universe.
Lex Fridman (1:14:24.040)
Can we just pause on that?
Lex Fridman (1:14:25.480)
It's just so beautiful, that's such a beautiful idea
Stephen Wolfram (1:14:30.920)
that we can generate our universe
Lex Fridman (1:14:32.440)
from a data structure, a simple structure,
Stephen Wolfram (1:14:39.400)
simple set of rules, and we can generate our entire universe.
Lex Fridman (1:14:42.680)
Yes, that's the idea. That's awe inspiring.
Lex Fridman (1:14:44.840)
Right, but so the question is how do you actualize that?
Lex Fridman (1:14:50.480)
What might this rule be like?
Lex Fridman (1:14:52.560)
And so one thing you quickly realize is
Lex Fridman (1:14:55.160)
if you're gonna pack everything about our universe
Stephen Wolfram (1:14:57.200)
into this tiny rule, not much that we are familiar with
Lex Fridman (1:15:01.240)
in our universe will be obvious in that rule.
Lex Fridman (1:15:05.000)
So you don't get to fit all these parameters of the universe,
Lex Fridman (1:15:07.920)
all these features of, you know, this is how space works,
Stephen Wolfram (1:15:10.080)
this is how time works, et cetera, et cetera, et cetera.
Lex Fridman (1:15:12.000)
You don't get to fit that all in.
Stephen Wolfram (1:15:13.080)
It all has to be sort of packed in to this thing,
Lex Fridman (1:15:16.680)
something much smaller, much more basic,
Stephen Wolfram (1:15:18.640)
much lower level machine code, so to speak, than that.
Lex Fridman (1:15:22.040)
And all the stuff that we're familiar with
Stephen Wolfram (1:15:23.520)
has to kind of emerge from the operation.
Lex Fridman (1:15:26.240)
So the rule in itself,
Stephen Wolfram (1:15:27.840)
because of the computational reducibility,
Lex Fridman (1:15:30.440)
is not gonna tell you the story.
Stephen Wolfram (1:15:32.320)
It's not gonna give you the answer to,
Lex Fridman (1:15:36.600)
it's not gonna let you predict
Lex Fridman (1:15:38.360)
what you're gonna have for lunch tomorrow,
Lex Fridman (1:15:40.600)
and it's not going to let you predict
Stephen Wolfram (1:15:42.160)
basically anything about your life, about the universe.
Lex Fridman (1:15:44.800)
Right, and you're not going to be able to see in that rule,
Stephen Wolfram (1:15:47.880)
oh, there's the three
Lex Fridman (1:15:49.160)
for the number of dimensions of space and so on.
Stephen Wolfram (1:15:51.240)
That's not gonna be there.
Lex Fridman (1:15:52.080)
Spacetime is not going to be obviously.
Stephen Wolfram (1:15:54.560)
Right, so the question is then,
Lex Fridman (1:15:55.720)
what is the universe made of?
Stephen Wolfram (1:15:57.760)
That's a basic question.
Lex Fridman (1:16:00.200)
And we've had some assumptions
Stephen Wolfram (1:16:01.640)
about what the universe is made of
Lex Fridman (1:16:02.960)
for the last few thousand years
Stephen Wolfram (1:16:04.840)
that I think in some cases just turn out not to be right.
Lex Fridman (1:16:08.680)
And the most important assumption
Stephen Wolfram (1:16:11.040)
is that space is a continuous thing.
Lex Fridman (1:16:13.960)
That is that you can, if you say,
Stephen Wolfram (1:16:17.040)
let's pick a point in space.
Lex Fridman (1:16:19.200)
We're gonna do geometry.
Stephen Wolfram (1:16:20.120)
We're gonna pick a point.
Lex Fridman (1:16:21.520)
We can pick a point absolutely anywhere in space.
Stephen Wolfram (1:16:24.320)
Precise numbers we can specify of where that point is.
Lex Fridman (1:16:28.080)
In fact, Euclid who kind of wrote down
Stephen Wolfram (1:16:30.320)
the original kind of axiomatization of geometry
Lex Fridman (1:16:32.960)
back in 300 BC or so,
Stephen Wolfram (1:16:36.000)
his very first definition, he says,
Lex Fridman (1:16:38.320)
a point is that which has no part.
Stephen Wolfram (1:16:40.640)
A point is this indivisible infinitesimal thing.
Lex Fridman (1:16:47.520)
Okay, so we might've said that about material objects.
Stephen Wolfram (1:16:50.440)
We might've said that about water, for example.
Lex Fridman (1:16:52.880)
We might've said water is a continuous thing
Stephen Wolfram (1:16:54.800)
that we can just pick any point we want in some water,
Lex Fridman (1:16:59.160)
but actually we know it isn't true.
Stephen Wolfram (1:17:00.760)
We know that water is made of molecules that are discrete.
Lex Fridman (1:17:04.120)
And so the question, one fundamental question
Lex Fridman (1:17:06.560)
is what is space made of?
Lex Fridman (1:17:08.360)
And so one of the things that's sort of a starting point
Stephen Wolfram (1:17:10.880)
for what I've done is to think of space as a discrete thing,
Lex Fridman (1:17:15.600)
to think of there being sort of atoms of space
Stephen Wolfram (1:17:18.560)
just as there are atoms of material things,
Lex Fridman (1:17:20.600)
although very different kinds of atoms.
Lex Fridman (1:17:23.120)
And by the way, I mean, this idea,
Lex Fridman (1:17:25.000)
you know, there were ancient Greek philosophers
Stephen Wolfram (1:17:27.200)
who had this idea.
Lex Fridman (1:17:28.360)
There were, you know, Einstein actually thought
Stephen Wolfram (1:17:30.280)
this is probably how things would work out.
Lex Fridman (1:17:31.840)
I mean, he said, you know, repeatedly he thought
Stephen Wolfram (1:17:34.320)
that's the way it would work out.
Lex Fridman (1:17:35.520)
We don't have the mathematical tools in our time,
Stephen Wolfram (1:17:38.680)
which was 1940s, 1950s and so on to explore this.
Lex Fridman (1:17:42.520)
Like the way he thought,
Stephen Wolfram (1:17:44.120)
you mean that there is something very, very small
Lex Fridman (1:17:48.280)
and discrete that's underlying space.
Stephen Wolfram (1:17:52.240)
Yes.
Lex Fridman (1:17:53.080)
And that means that, so, you know, the mathematical theory,
Stephen Wolfram (1:17:56.600)
mathematical theories in physics assume that space
Lex Fridman (1:17:59.960)
can be described just as a continuous thing.
Stephen Wolfram (1:18:02.400)
You can just pick coordinates
Lex Fridman (1:18:04.000)
and the coordinates can have any values.
Lex Fridman (1:18:06.000)
And that's how you define space.
Lex Fridman (1:18:07.840)
Space is this just sort of background sort of theater
Stephen Wolfram (1:18:11.680)
on which the universe operates.
Lex Fridman (1:18:13.600)
But can we draw a distinction between space
Stephen Wolfram (1:18:17.240)
as a thing that could be described by three values,
Lex Fridman (1:18:22.280)
coordinates, and how you're,
Lex Fridman (1:18:25.400)
are you using the word space more generally when you say?
Lex Fridman (1:18:29.320)
No, I'm just talking about space
Stephen Wolfram (1:18:30.960)
as in what we experience in the universe.
Lex Fridman (1:18:34.320)
So that you think this 3D aspect of it is fundamental.
Stephen Wolfram (1:18:38.440)
No, I don't think that 3D is fundamental at all, actually.
Lex Fridman (1:18:40.840)
I think that the thing that has been assumed
Stephen Wolfram (1:18:45.160)
is that space is this continuous thing
Lex Fridman (1:18:48.200)
where you can just describe it by,
Stephen Wolfram (1:18:49.480)
let's say three numbers, for instance.
Lex Fridman (1:18:51.320)
But most important thing about that
Stephen Wolfram (1:18:53.160)
is that you can describe it by precise numbers
Lex Fridman (1:18:56.080)
because you can pick any point in space
Lex Fridman (1:18:58.200)
and you can talk about motions,
Lex Fridman (1:18:59.640)
any infinitesimal motion in space.
Lex Fridman (1:19:01.800)
And that's what continuous means.
Lex Fridman (1:19:03.320)
That's what continuous means.
Stephen Wolfram (1:19:04.240)
That's what, you know, Newton invented calculus
Lex Fridman (1:19:06.120)
to describe these kind of continuous small variations
Lex Fridman (1:19:08.600)
and so on.
Lex Fridman (1:19:09.440)
That was, that's kind of a fundamental idea
Stephen Wolfram (1:19:11.400)
from Euclid on that's been a fundamental idea about space.
Lex Fridman (1:19:15.360)
And so.
Lex Fridman (1:19:16.200)
Is that right or wrong?
Lex Fridman (1:19:18.800)
It's not right.
Stephen Wolfram (1:19:20.000)
It's not right.
Lex Fridman (1:19:20.960)
It's right at the level of our experience most of the time.
Stephen Wolfram (1:19:25.720)
It's not right at the level of the machine code,
Lex Fridman (1:19:27.760)
so to speak.
Lex Fridman (1:19:28.920)
And so.
Lex Fridman (1:19:29.760)
Machine code.
Stephen Wolfram (1:19:31.040)
Yeah, of the simulation.
Lex Fridman (1:19:32.200)
That's right.
Stephen Wolfram (1:19:33.040)
That's right.
Lex Fridman (1:19:33.880)
They're the very lowest level of the fabric of the universe,
Stephen Wolfram (1:19:36.960)
at least under the Wolfram physics model
Lex Fridman (1:19:41.960)
is your senses is discrete.
Stephen Wolfram (1:19:44.240)
Right.
Lex Fridman (1:19:45.080)
So now what does that mean?
Lex Fridman (1:19:46.320)
So it means what is space then?
Lex Fridman (1:19:49.160)
So in models, the basic idea is you say
Stephen Wolfram (1:19:54.160)
there are these sort of atoms of space.
Lex Fridman (1:19:56.400)
They're these points that represent,
Stephen Wolfram (1:19:59.080)
you know, represent places in space,
Lex Fridman (1:20:02.040)
but they're just discrete points.
Lex Fridman (1:20:03.960)
And the only thing we know about them
Lex Fridman (1:20:06.120)
is how they're connected to each other.
Stephen Wolfram (1:20:08.000)
We don't know where they are.
Lex Fridman (1:20:09.480)
They don't have coordinates.
Stephen Wolfram (1:20:10.520)
We don't get to say this is a position, such and such.
Lex Fridman (1:20:12.920)
It's just, here's a big bag of points.
Stephen Wolfram (1:20:15.280)
Like in our universe,
Lex Fridman (1:20:16.120)
there might be 10 to the 100 of these points.
Lex Fridman (1:20:18.440)
And all we know is this point is connected
Lex Fridman (1:20:21.640)
to this other point.
Lex Fridman (1:20:22.480)
So it's like, you know,
Lex Fridman (1:20:23.480)
all we have is the friend network, so to speak.
Stephen Wolfram (1:20:25.560)
We don't have, you know, people's, you know,
Lex Fridman (1:20:27.960)
physical addresses.
Stephen Wolfram (1:20:29.120)
All we have is the friend network of these points.
Lex Fridman (1:20:31.560)
Yeah.
Stephen Wolfram (1:20:32.400)
The underlying nature of reality is kind of like a Facebook.
Lex Fridman (1:20:35.240)
We don't know their location, but we have the friends.
Stephen Wolfram (1:20:37.240)
Yeah, yeah, right.
Lex Fridman (1:20:38.080)
We know which point is connected to which other points.
Lex Fridman (1:20:41.960)
And that's all we know.
Lex Fridman (1:20:43.480)
And so you might say, well,
Lex Fridman (1:20:44.320)
how on earth can you get something
Lex Fridman (1:20:46.040)
which is like our experience of, you know,
Lex Fridman (1:20:49.200)
what seems like continuous space?
Lex Fridman (1:20:50.560)
Well, the answer is,
Stephen Wolfram (1:20:51.640)
by the time you have 10 to the 100 of these things,
Lex Fridman (1:20:54.520)
those connections can work in such a way
Stephen Wolfram (1:20:57.840)
that on a large scale,
Lex Fridman (1:20:59.720)
it will seem to be like continuous space
Stephen Wolfram (1:21:02.320)
in let's say three dimensions
Lex Fridman (1:21:03.800)
or some other number of dimensions
Stephen Wolfram (1:21:05.240)
or 2.6 dimensions or whatever else.
Lex Fridman (1:21:07.760)
Because they're much, much, much, much larger.
Lex Fridman (1:21:10.360)
So like the number of relationships here we're talking about
Lex Fridman (1:21:15.200)
is just a humongous amount.
Lex Fridman (1:21:16.480)
So the kind of thing you're talking about
Lex Fridman (1:21:18.880)
is very, very, very small relative
Stephen Wolfram (1:21:20.640)
to our experience of daily life.
Lex Fridman (1:21:22.720)
Right, so I mean, you know,
Stephen Wolfram (1:21:23.760)
we don't know exactly the size,
Lex Fridman (1:21:25.080)
but maybe 10 to the minus,
Stephen Wolfram (1:21:30.400)
maybe around 10 to the minus 100 meters.
Lex Fridman (1:21:32.760)
So, you know, the size of, to give a comparison,
Stephen Wolfram (1:21:34.960)
the size of a proton is 10 to the minus 15 meters.
Lex Fridman (1:21:38.480)
And so this is something incredibly tiny compared to that.
Lex Fridman (1:21:42.440)
And the idea that from that would emerge
Lex Fridman (1:21:45.960)
the experience of continuous space is mind blowing.
Lex Fridman (1:21:51.040)
Well, what's your intuition why that's possible?
Lex Fridman (1:21:53.520)
Like, first of all, I mean, we'll get into it,
Lex Fridman (1:21:57.480)
but I don't know if we will
Lex Fridman (1:21:59.320)
through the medium of conversation,
Lex Fridman (1:22:01.840)
but the construct of hypergraphs is just beautiful.
Lex Fridman (1:22:06.400)
Right.
Stephen Wolfram (1:22:07.240)
Cellular automata are beautiful.
Lex Fridman (1:22:08.200)
We'll talk about it.
Lex Fridman (1:22:09.040)
But this thing about, you know,
Lex Fridman (1:22:11.120)
continuity arising from discrete systems
Stephen Wolfram (1:22:14.160)
is in today's world is actually not so surprising.
Lex Fridman (1:22:17.240)
I mean, you know, your average computer screen, right?
Stephen Wolfram (1:22:19.480)
Every computer screen is made of discrete pixels.
Lex Fridman (1:22:21.920)
Yet we have the, you know,
Stephen Wolfram (1:22:23.680)
we have the idea that we're seeing
Lex Fridman (1:22:25.440)
these continuous pictures.
Stephen Wolfram (1:22:27.000)
I mean, it's, you know,
Lex Fridman (1:22:27.840)
the fact that on a large scale,
Stephen Wolfram (1:22:29.480)
continuity can arise from lots of discrete elements.
Lex Fridman (1:22:33.120)
This is at some level unsurprising now.
Stephen Wolfram (1:22:35.640)
Wait, wait, wait, wait, wait, wait.
Lex Fridman (1:22:37.000)
But the pixels have a very definitive structure
Stephen Wolfram (1:22:42.360)
of neighbors on a computer screen.
Lex Fridman (1:22:46.000)
Right.
Stephen Wolfram (1:22:46.840)
There's no concept of spatial,
Lex Fridman (1:22:50.520)
of space inherent in the underlying fabric of reality.
Stephen Wolfram (1:22:55.760)
Right, right, right.
Lex Fridman (1:22:56.600)
So the point is that, but there are cases where there are.
Lex Fridman (1:22:59.920)
So for example, let's just imagine you have a square grid.
Lex Fridman (1:23:03.400)
Okay, and at every point on the grid,
Stephen Wolfram (1:23:05.360)
you have one of these atoms of space
Lex Fridman (1:23:07.680)
and it's connected to four other,
Stephen Wolfram (1:23:09.480)
four other atoms of space on the, you know,
Lex Fridman (1:23:11.440)
Northeast, Southwest corners, right?
Stephen Wolfram (1:23:14.480)
There you have something where if you zoom out from that,
Lex Fridman (1:23:17.600)
it's like a computer screen.
Stephen Wolfram (1:23:19.040)
Yeah, so the relationship creates the spatial,
Lex Fridman (1:23:23.240)
like the relationship creates a constraint,
Stephen Wolfram (1:23:26.720)
which then in an emergent sense creates a like,
Lex Fridman (1:23:33.080)
yeah, like basically a spatial coordinate for that thing.
Stephen Wolfram (1:23:37.720)
Yeah, right.
Lex Fridman (1:23:38.560)
Even though the individual point doesn't have a space.
Stephen Wolfram (1:23:40.560)
Even though the individual point doesn't know anything,
Lex Fridman (1:23:42.320)
it just knows what its neighbors are.
Stephen Wolfram (1:23:45.000)
On a large scale, it can be described by saying,
Lex Fridman (1:23:48.840)
oh, it looks like it's a, you know,
Stephen Wolfram (1:23:50.960)
this grid is zoomed out grid.
Lex Fridman (1:23:52.800)
You can say, well, you can describe these different points
Stephen Wolfram (1:23:54.920)
by saying they have certain positions,
Lex Fridman (1:23:56.480)
coordinates, et cetera.
Stephen Wolfram (1:23:57.840)
Now, in the sort of real setup,
Lex Fridman (1:23:59.920)
it's more complicated than that.
Stephen Wolfram (1:24:00.920)
It isn't just a square grid or something.
Lex Fridman (1:24:03.040)
It's something much more dynamic and complicated,
Stephen Wolfram (1:24:05.720)
which we'll talk about.
Lex Fridman (1:24:07.200)
But so, you know, the first idea,
Stephen Wolfram (1:24:10.800)
the first key idea is, you know,
Lex Fridman (1:24:12.720)
what's the universe made of?
Stephen Wolfram (1:24:13.840)
It's made of atoms of space basically
Lex Fridman (1:24:15.720)
with these connections between them.
Lex Fridman (1:24:17.760)
What kind of connections do they have?
Lex Fridman (1:24:19.320)
Well, so the simplest kind of thing you might say is,
Stephen Wolfram (1:24:23.000)
we've got something like a graph
Lex Fridman (1:24:25.200)
where every atom of space,
Stephen Wolfram (1:24:28.440)
where we have these edges that go between,
Lex Fridman (1:24:31.200)
these connections that go between atoms of space.
Stephen Wolfram (1:24:33.120)
We're not saying how long these edges are.
Lex Fridman (1:24:34.960)
We're just saying there is a connection
Stephen Wolfram (1:24:36.360)
from this place, from this atom to this atom.
Lex Fridman (1:24:39.080)
Just a quick pause,
Stephen Wolfram (1:24:40.600)
because there's a lot of very people that listen to this.
Lex Fridman (1:24:44.520)
Just to clarify, because I did a poll actually,
Lex Fridman (1:24:46.920)
what do you think a graph is a long time ago?
Lex Fridman (1:24:49.640)
And it's kind of funny how few people
Stephen Wolfram (1:24:52.080)
know the term graph outside of computer science.
Lex Fridman (1:24:55.920)
It's good.
Stephen Wolfram (1:24:56.760)
Let's call it a network.
Lex Fridman (1:24:57.600)
I think that's it.
Stephen Wolfram (1:24:58.440)
Let's call it a network is better.
Lex Fridman (1:24:59.280)
So, but every time, I like the word graph though.
Lex Fridman (1:25:00.920)
So let's define, let's just say that a graph
Lex Fridman (1:25:03.880)
will use terms nodes and edges maybe.
Lex Fridman (1:25:06.680)
And it's just the nodes represent some abstract entity
Lex Fridman (1:25:11.600)
and then the edges represent relationships
Stephen Wolfram (1:25:13.960)
between those entities.
Lex Fridman (1:25:14.840)
Right, exactly.
Lex Fridman (1:25:15.880)
So that's what a graph says.
Lex Fridman (1:25:16.800)
Sorry, so there you go.
Lex Fridman (1:25:18.480)
So that's the basic structure.
Lex Fridman (1:25:20.600)
That is the simplest case of a basic structure.
Stephen Wolfram (1:25:23.360)
Actually, it tends to be better to think about hypergraphs.
Lex Fridman (1:25:27.840)
So a hypergraph is just, instead of saying
Stephen Wolfram (1:25:31.560)
there are connections between pairs of things,
Lex Fridman (1:25:34.600)
we say there are connections between any number of things.
Lex Fridman (1:25:37.160)
So there might be ternary edges.
Lex Fridman (1:25:39.200)
So instead of just having two points
Stephen Wolfram (1:25:42.920)
are connected by an edge,
Lex Fridman (1:25:44.520)
you say three points are all associated with a hyperedge,
Stephen Wolfram (1:25:48.320)
are all connected by a hyperedge.
Lex Fridman (1:25:50.200)
That's just, at some level, that's a detail.
Stephen Wolfram (1:25:54.120)
It's a detail that happens to make the, for me,
Lex Fridman (1:25:57.880)
sort of in the history of this project,
Stephen Wolfram (1:26:00.000)
the realization that you could do things that way
Lex Fridman (1:26:02.320)
broke out of certain kinds of arbitrariness
Stephen Wolfram (1:26:04.360)
that I felt that there was in the model
Lex Fridman (1:26:06.080)
before I had seen how this worked.
Stephen Wolfram (1:26:07.880)
I mean, a hypergraph can be mapped to a graph.
Lex Fridman (1:26:12.440)
It's just a convenient representation.
Stephen Wolfram (1:26:14.360)
Mathematical speaking.
Lex Fridman (1:26:15.320)
That's correct. That's correct.
Lex Fridman (1:26:16.920)
But so then, so, okay, so the first question,
Lex Fridman (1:26:19.680)
the first idea of these models of ours is
Stephen Wolfram (1:26:22.720)
space is made of these connected sort of atoms of space.
Lex Fridman (1:26:26.520)
The next idea is space is all there is.
Stephen Wolfram (1:26:29.800)
There's nothing except for this space.
Lex Fridman (1:26:31.840)
So in traditional ideas in physics,
Stephen Wolfram (1:26:33.880)
people have said there's space, it's kind of a background.
Lex Fridman (1:26:36.960)
And then there's matter, all these particles, electrons,
Lex Fridman (1:26:39.200)
all these other things, which exist in space, right?
Lex Fridman (1:26:43.360)
But in this model, one of the key ideas is
Stephen Wolfram (1:26:46.200)
there's nothing except space.
Lex Fridman (1:26:48.400)
So in other words, everything that exists in the universe
Stephen Wolfram (1:26:52.160)
is a feature of this hypergraph.
Lex Fridman (1:26:54.640)
So how can that possibly be?
Stephen Wolfram (1:26:55.920)
Well, the way that works is
Lex Fridman (1:26:58.040)
that there are certain structures in this hypergraph
Stephen Wolfram (1:27:01.640)
where you say that little twisty knotted thing,
Lex Fridman (1:27:05.760)
we don't know exactly how this works yet,
Lex Fridman (1:27:07.240)
but we have sort of idea about how it works mathematically.
Lex Fridman (1:27:10.960)
This sort of twisted knotted thing,
Stephen Wolfram (1:27:13.000)
that's the core of an electron.
Lex Fridman (1:27:14.840)
This thing over there that has this different form,
Stephen Wolfram (1:27:17.360)
that's something else.
Lex Fridman (1:27:18.520)
So the different peculiarities of the structure
Stephen Wolfram (1:27:21.040)
of this graph are the very things
Lex Fridman (1:27:24.800)
that we think of as the particles inside the space,
Lex Fridman (1:27:29.000)
but in fact, it's just a property of the space.
Lex Fridman (1:27:31.760)
Mind blowing, first of all, that it's mind blowing,
Lex Fridman (1:27:34.960)
and we'll probably talk in its simplicity and beauty.
Lex Fridman (1:27:38.520)
Yes, I think it's very beautiful.
Stephen Wolfram (1:27:40.480)
I mean, this is, I'm...
Lex Fridman (1:27:41.320)
But okay, but that's space,
Lex Fridman (1:27:43.080)
and then there's another concept
Lex Fridman (1:27:44.560)
we didn't really kind of mention,
Lex Fridman (1:27:45.880)
but you think it of computation as a transformation.
Lex Fridman (1:27:50.480)
Let's talk about time in a second.
Stephen Wolfram (1:27:51.680)
Let's just, I mean, on the subject of space,
Lex Fridman (1:27:55.360)
there's this question of kind of what,
Stephen Wolfram (1:27:57.680)
there's this idea, there is this hypergraph,
Lex Fridman (1:27:59.880)
it represents space,
Lex Fridman (1:28:01.760)
and it represents everything that's in space.
Lex Fridman (1:28:03.640)
The features of that hypergraph,
Stephen Wolfram (1:28:05.320)
you can say certain features in this part we do know,
Lex Fridman (1:28:08.320)
certain features of the hypergraph
Stephen Wolfram (1:28:09.680)
represent the presence of energy, for example,
Lex Fridman (1:28:11.800)
or the presence of mass or momentum,
Lex Fridman (1:28:13.960)
and we know what the features of the hypergraph
Lex Fridman (1:28:16.080)
that represent those things are,
Lex Fridman (1:28:17.920)
but it's all just the same hypergraph.
Lex Fridman (1:28:20.320)
So one thing you might ask is,
Stephen Wolfram (1:28:22.040)
you know, if you just look at this hypergraph and you say,
Lex Fridman (1:28:24.280)
and we're gonna talk about sort of what the hypergraph does,
Lex Fridman (1:28:27.160)
but if you say, you know,
Lex Fridman (1:28:28.600)
how much of what's going on in this hypergraph
Stephen Wolfram (1:28:31.320)
is things we know and care about,
Lex Fridman (1:28:34.040)
like particles and atoms and electrons
Lex Fridman (1:28:36.520)
and all this kind of thing,
Lex Fridman (1:28:37.560)
and how much is just the background of space?
Lex Fridman (1:28:40.880)
So it turns out, so far as in one rough estimate of this,
Lex Fridman (1:28:45.440)
everything that we care about in the universe
Stephen Wolfram (1:28:47.880)
is only one part in 10 to the 120
Lex Fridman (1:28:50.800)
of what's actually going on.
Stephen Wolfram (1:28:52.040)
The vast majority of what's happening
Lex Fridman (1:28:54.040)
is purely things that maintain the structure of space.
Stephen Wolfram (1:28:57.360)
That, in other words, that the things that are
Lex Fridman (1:28:59.760)
the features of space that are the things
Stephen Wolfram (1:29:03.280)
that we consider notable,
Lex Fridman (1:29:04.640)
like the presence of particles and so on,
Stephen Wolfram (1:29:06.480)
that's a tiny little piece of froth
Lex Fridman (1:29:08.760)
on the top of all this activity
Stephen Wolfram (1:29:10.680)
that mostly is just intended to,
Lex Fridman (1:29:13.560)
you know, mostly, I can't say intended,
Stephen Wolfram (1:29:15.160)
there's no intention here,
Lex Fridman (1:29:16.480)
that just maintains the structure of space.
Stephen Wolfram (1:29:20.600)
Let me load that in.
Lex Fridman (1:29:24.160)
It just makes me feel so good as a human being.
Stephen Wolfram (1:29:27.880)
To be the froth on the one in a 10 to the 120
Lex Fridman (1:29:31.800)
or something of, well.
Lex Fridman (1:29:33.120)
And also just humbling how,
Lex Fridman (1:29:37.960)
in this mathematical framework,
Lex Fridman (1:29:39.880)
how much work needs to be done
Lex Fridman (1:29:41.400)
on the infrastructure of our universe.
Stephen Wolfram (1:29:44.840)
Right, to maintain the infrastructure of our universe
Lex Fridman (1:29:46.840)
is a lot of work.
Stephen Wolfram (1:29:47.960)
We are merely writing a little tiny things
Lex Fridman (1:29:51.560)
on top of that infrastructure.
Lex Fridman (1:29:53.360)
But you were just starting to talk a little bit about,
Lex Fridman (1:29:57.480)
we talked about space,
Stephen Wolfram (1:29:59.800)
that represents all the stuff that's in the universe.
Lex Fridman (1:30:03.280)
The question is, what does that stuff do?
Lex Fridman (1:30:06.080)
And for that, we have to start talking about time
Lex Fridman (1:30:09.200)
and what is time and so on.
Stephen Wolfram (1:30:11.440)
And, you know, one of the basic idea of this model
Lex Fridman (1:30:15.240)
is time is the progression of computation.
Lex Fridman (1:30:18.000)
So in other words, we have a structure of space
Lex Fridman (1:30:21.040)
and there is a rule that says
Lex Fridman (1:30:23.000)
how that structure of space will change.
Lex Fridman (1:30:25.120)
And it's the application,
Stephen Wolfram (1:30:26.160)
the repeated application of that rule
Lex Fridman (1:30:28.480)
that defines the progress of time.
Lex Fridman (1:30:32.400)
And what does the rule look like
Lex Fridman (1:30:34.040)
in the space of hypergraphs?
Stephen Wolfram (1:30:36.000)
Right, so what the rule says is something like,
Lex Fridman (1:30:38.640)
if you have a little tiny piece of hypergraph
Stephen Wolfram (1:30:40.440)
that looks like this,
Lex Fridman (1:30:42.200)
then it will be transformed into a piece of hypergraph
Stephen Wolfram (1:30:44.720)
that looks like this.
Lex Fridman (1:30:46.640)
So that's all it says.
Stephen Wolfram (1:30:47.880)
It says you pick up these elements of space
Lex Fridman (1:30:51.280)
and you can think of these edges,
Stephen Wolfram (1:30:54.360)
these hyper edges as being relations
Lex Fridman (1:30:56.040)
between elements in space.
Stephen Wolfram (1:30:57.720)
You might pick up these two relations
Lex Fridman (1:31:01.200)
between elements in space.
Lex Fridman (1:31:03.280)
And we're not saying where those elements are
Lex Fridman (1:31:04.840)
or what they are,
Lex Fridman (1:31:05.680)
but every time there's a certain arrangement
Lex Fridman (1:31:07.520)
of elements in space,
Stephen Wolfram (1:31:09.240)
then arrangement in the sense of the way they're connected,
Lex Fridman (1:31:12.200)
then we transform it into some other arrangement.
Lex Fridman (1:31:14.640)
So there's a little tiny pattern
Lex Fridman (1:31:16.280)
and you transform it into another little pattern.
Stephen Wolfram (1:31:18.520)
That's right.
Lex Fridman (1:31:19.360)
And then because of this,
Stephen Wolfram (1:31:20.840)
I mean, again, it's kind of similar to cellular automata
Lex Fridman (1:31:23.280)
in that like on paper, the rule looks like super simple.
Stephen Wolfram (1:31:26.840)
It's like, yeah, okay.
Lex Fridman (1:31:30.480)
Yeah, right, from this, the universe can be born.
Lex Fridman (1:31:33.680)
But like once you start applying it,
Lex Fridman (1:31:36.720)
beautiful structure starts being,
Stephen Wolfram (1:31:39.040)
potentially can be created.
Lex Fridman (1:31:41.000)
And what you're doing is you're applying that rule
Stephen Wolfram (1:31:43.560)
to different parts,
Lex Fridman (1:31:45.400)
like anytime you match it within the hypergraph.
Lex Fridman (1:31:49.320)
And then one of the like incredibly beautiful
Lex Fridman (1:31:53.160)
and interesting things to think about
Stephen Wolfram (1:31:55.640)
is the order in which you apply that rule,
Lex Fridman (1:31:59.280)
because that pattern appears all over the place.
Stephen Wolfram (1:32:02.000)
Right, so this is a big complicated thing,
Lex Fridman (1:32:04.400)
very hard to wrap one's brain around, okay?
Lex Fridman (1:32:06.200)
So you say the rule is every time you see this little pattern
Lex Fridman (1:32:10.680)
transform it in this way.
Lex Fridman (1:32:12.520)
But yet, as you look around the space
Lex Fridman (1:32:15.800)
that represents the universe,
Stephen Wolfram (1:32:17.400)
there may be zillions of places
Lex Fridman (1:32:18.760)
where that little pattern occurs.
Lex Fridman (1:32:20.600)
So what it says is just do this,
Lex Fridman (1:32:24.440)
apply this rule wherever you feel like.
Lex Fridman (1:32:26.920)
And what is extremely non trivial is,
Lex Fridman (1:32:31.360)
well, okay, so this is happening sort of
Stephen Wolfram (1:32:33.520)
in computer science terms, sort of asynchronously,
Lex Fridman (1:32:35.920)
you're just doing it wherever you feel like doing it.
Lex Fridman (1:32:39.000)
And the only constraint is
Lex Fridman (1:32:41.120)
that if you're going to apply the rule somewhere,
Stephen Wolfram (1:32:43.880)
the things to which you apply the rule,
Lex Fridman (1:32:46.760)
the little elements to which you apply the rule,
Stephen Wolfram (1:32:50.080)
if they have to be,
Lex Fridman (1:32:54.200)
okay, well, you can think of each application of the rule
Stephen Wolfram (1:32:56.560)
as being kind of an event that happens in the universe.
Lex Fridman (1:32:59.840)
And the input to an event has to be ready
Stephen Wolfram (1:33:04.760)
for the event to occur.
Lex Fridman (1:33:06.240)
That is, if one event occurred,
Stephen Wolfram (1:33:08.240)
if one transformation occurred,
Lex Fridman (1:33:10.000)
and it produced a particular atom of space,
Stephen Wolfram (1:33:12.720)
then that atom of space has to already exist
Lex Fridman (1:33:17.200)
before another transformation that's going to apply
Stephen Wolfram (1:33:20.880)
to that atom of space can occur.
Lex Fridman (1:33:23.240)
So that's like the prerequisite for the event.
Stephen Wolfram (1:33:25.840)
That's right, that's right.
Lex Fridman (1:33:26.920)
So that defines a kind of,
Stephen Wolfram (1:33:30.520)
this sort of set of causal relationships between events.
Lex Fridman (1:33:33.840)
It says, this event has to have happened before this event.
Lex Fridman (1:33:38.000)
But that is...
Lex Fridman (1:33:40.200)
But that's not a very limiting constraint.
Stephen Wolfram (1:33:42.960)
No, it's not.
Lex Fridman (1:33:44.080)
And what's interesting...
Stephen Wolfram (1:33:44.960)
You still get the zillion,
Lex Fridman (1:33:47.200)
that's a technical term, options.
Stephen Wolfram (1:33:49.760)
That's correct.
Lex Fridman (1:33:50.680)
But, okay, so this is where things get a little bit more
Stephen Wolfram (1:33:53.760)
elaborate, but...
Lex Fridman (1:33:54.600)
But they're mind blowing, so...
Stephen Wolfram (1:33:56.640)
Right, but so what happens is,
Lex Fridman (1:33:59.120)
so the first thing you might say is,
Stephen Wolfram (1:34:01.160)
you know, let's...
Lex Fridman (1:34:02.520)
Well, okay, so this question about the freedom
Stephen Wolfram (1:34:04.800)
of which event you do when.
Lex Fridman (1:34:07.200)
Well, let me sort of state an answer and then explain it.
Stephen Wolfram (1:34:10.200)
Okay, the validity of special relativity
Lex Fridman (1:34:14.120)
is a consequence of the fact that in some sense,
Stephen Wolfram (1:34:17.000)
it doesn't matter in what order you do
Lex Fridman (1:34:19.240)
these underlying things, so long as they respect
Stephen Wolfram (1:34:22.160)
this kind of set of causal relationships.
Lex Fridman (1:34:25.400)
So...
Lex Fridman (1:34:26.240)
And that's the part that's in a certain sense
Lex Fridman (1:34:30.640)
is a really important one,
Lex Fridman (1:34:31.800)
but the fact that it sometimes doesn't matter,
Lex Fridman (1:34:35.640)
that's a...
Stephen Wolfram (1:34:37.080)
I don't know what to...
Lex Fridman (1:34:37.920)
That's another, like, beautiful thing.
Stephen Wolfram (1:34:38.760)
Well, okay, so there's this idea
Lex Fridman (1:34:40.520)
of what I call causal invariance.
Stephen Wolfram (1:34:42.560)
Causal invariance, exactly.
Lex Fridman (1:34:44.080)
So that's a...
Stephen Wolfram (1:34:44.920)
Really, really powerful idea.
Lex Fridman (1:34:46.240)
Right, it's a powerful idea,
Stephen Wolfram (1:34:47.640)
which has actually arisen in different forms
Lex Fridman (1:34:50.080)
many times in the history of mathematics,
Stephen Wolfram (1:34:52.040)
mathematical logic, even computer science,
Lex Fridman (1:34:54.880)
has many different names.
Stephen Wolfram (1:34:56.800)
I mean, our particular version of it
Lex Fridman (1:34:58.200)
is a little bit tighter than other versions,
Lex Fridman (1:35:00.240)
but it's basically the same idea.
Lex Fridman (1:35:01.480)
Here's how to think about that idea.
Lex Fridman (1:35:03.680)
So imagine that...
Lex Fridman (1:35:05.440)
Well, let's talk about it in terms of math for a second.
Stephen Wolfram (1:35:08.120)
Let's say you're doing algebra and you're told,
Lex Fridman (1:35:10.600)
you know, multiply out this series of polynomials
Lex Fridman (1:35:14.280)
that are multiplied together, okay?
Lex Fridman (1:35:16.800)
You say, well, which order should I do that in?
Stephen Wolfram (1:35:19.120)
Say, well, do I multiply the third one by the fourth one
Lex Fridman (1:35:21.480)
and then do it by the first one?
Lex Fridman (1:35:22.640)
Or do I do the fifth one by the sixth one and then do that?
Lex Fridman (1:35:25.920)
Well, it turns out it doesn't matter.
Stephen Wolfram (1:35:27.800)
You can multiply them out in any order,
Lex Fridman (1:35:29.720)
you'll always get the same answer.
Stephen Wolfram (1:35:31.560)
That's a property...
Lex Fridman (1:35:33.760)
If you think about kind of making a kind of network
Stephen Wolfram (1:35:36.240)
that represents in what order you do things,
Lex Fridman (1:35:38.720)
you'll get different orders
Stephen Wolfram (1:35:40.680)
for different ways of multiplying things out,
Lex Fridman (1:35:42.760)
but you'll always get the same answer.
Stephen Wolfram (1:35:44.880)
Same thing if you...
Lex Fridman (1:35:45.720)
Let's say you're sorting.
Stephen Wolfram (1:35:46.680)
You've got a bunch of A's and B's.
Lex Fridman (1:35:48.880)
They're in random, some random order,
Stephen Wolfram (1:35:50.280)
you know, BAA, BBBAA, whatever.
Lex Fridman (1:35:53.400)
And you have a little rule that says,
Lex Fridman (1:35:55.240)
every time you see BA, flip it around to AB, okay?
Lex Fridman (1:36:00.000)
Eventually you apply that rule enough times,
Stephen Wolfram (1:36:02.280)
you'll have sorted the string
Lex Fridman (1:36:03.800)
so that it's all the A's first and then all the B's.
Stephen Wolfram (1:36:07.400)
Again, there are many different orders
Lex Fridman (1:36:10.040)
in which you can do that to many different sort of places
Stephen Wolfram (1:36:13.200)
where you can apply that update.
Lex Fridman (1:36:15.280)
In the end, you'll always get the string sorted the same way.
Stephen Wolfram (1:36:18.520)
I know with sorting the string, it sounds obvious.
Lex Fridman (1:36:22.320)
That's to me surprising
Stephen Wolfram (1:36:24.680)
that there is in complicated systems,
Lex Fridman (1:36:28.320)
obviously with a string,
Lex Fridman (1:36:29.840)
but in a hypergraph that the application of the rule,
Lex Fridman (1:36:33.760)
asynchronous rule can lead to the same results sometimes.
Stephen Wolfram (1:36:36.720)
Yes, yes, that is not obvious.
Lex Fridman (1:36:39.080)
And it was something that, you know,
Stephen Wolfram (1:36:40.720)
I sort of discovered that idea for these kinds of systems
Lex Fridman (1:36:44.080)
and back in the 1990s.
Lex Fridman (1:36:45.520)
And for various reasons, I was not satisfied
Lex Fridman (1:36:50.360)
by how sort of fragile finding that particular property was.
Lex Fridman (1:36:54.320)
And let me just make another point,
Lex Fridman (1:36:56.360)
which is that it turns out that even if the underlying rule
Stephen Wolfram (1:37:01.120)
does not have this property of causal invariance,
Lex Fridman (1:37:03.880)
it can turn out that every observation
Stephen Wolfram (1:37:06.200)
made by observers of the rule can,
Lex Fridman (1:37:09.240)
they can impose what amounts to causal invariance
Stephen Wolfram (1:37:12.680)
on the rule.
Lex Fridman (1:37:13.880)
We can explain that.
Stephen Wolfram (1:37:14.720)
It's a little bit more complicated.
Lex Fridman (1:37:15.560)
I mean, technically that has to do with this idea
Stephen Wolfram (1:37:18.000)
of completions, which is something that comes up
Lex Fridman (1:37:20.160)
in term rewriting systems,
Stephen Wolfram (1:37:21.760)
automated theorem proving systems and so on.
Lex Fridman (1:37:24.040)
But let's ignore that for a second.
Stephen Wolfram (1:37:26.320)
We can come to that later.
Lex Fridman (1:37:27.560)
But is it useful to talk about observation?
Stephen Wolfram (1:37:29.840)
Not yet.
Lex Fridman (1:37:30.680)
Not yet.
Stephen Wolfram (1:37:31.720)
It's so great.
Lex Fridman (1:37:33.160)
So there's some concept of causal invariance
Stephen Wolfram (1:37:35.560)
as you apply these rules in an asynchronous way,
Lex Fridman (1:37:39.480)
you can think of those transformations as events.
Lex Fridman (1:37:42.200)
So there's this hypergraph that represents space
Lex Fridman (1:37:44.400)
and all of these events happening in the space
Lex Fridman (1:37:47.000)
and the graph grows in interesting complicated ways.
Lex Fridman (1:37:50.440)
And eventually the froth arises of what we experience
Stephen Wolfram (1:37:54.560)
as human existence.
Lex Fridman (1:37:56.200)
So that's it.
Stephen Wolfram (1:37:57.440)
That's some version of the picture,
Lex Fridman (1:37:58.920)
but let's explain a little bit more.
Stephen Wolfram (1:38:00.800)
Exactly.
Lex Fridman (1:38:01.640)
What's a little more detail like?
Stephen Wolfram (1:38:03.600)
Right.
Lex Fridman (1:38:04.440)
Well, so one thing that is sort of surprising
Stephen Wolfram (1:38:06.760)
in this theory is one of the sort of achievements
Lex Fridman (1:38:10.080)
of 20th century physics was kind of bringing
Stephen Wolfram (1:38:12.000)
space and time together.
Lex Fridman (1:38:13.880)
That was, you know, special relativity.
Stephen Wolfram (1:38:15.720)
People talk about space time, this sort of unified thing
Lex Fridman (1:38:19.320)
where space and time kind of a mixed
Lex Fridman (1:38:21.880)
and there's a nice mathematical formalism
Lex Fridman (1:38:24.680)
that in which, you know, space and time sort of appear
Stephen Wolfram (1:38:28.040)
as part of the space time continuum,
Lex Fridman (1:38:30.760)
the space time, you know, four vectors and things like this.
Stephen Wolfram (1:38:34.480)
You know, we talk about time as the fourth dimension
Lex Fridman (1:38:37.320)
and all these kinds of things.
Stephen Wolfram (1:38:38.800)
It's, you know, and it seems like the theory of relativity
Lex Fridman (1:38:42.200)
sort of says space and time are fundamentally
Stephen Wolfram (1:38:44.040)
the same kind of thing.
Lex Fridman (1:38:45.400)
So one of the things that took a while to understand
Stephen Wolfram (1:38:48.680)
in this approach of mine is that in my kind of approach,
Lex Fridman (1:38:54.880)
space and time are really not fundamentally
Stephen Wolfram (1:38:56.680)
the same kind of thing.
Lex Fridman (1:38:57.520)
Space is the extension of this hypergraph.
Stephen Wolfram (1:39:00.480)
Time is the kind of progress of this inexorable computation
Lex Fridman (1:39:04.440)
of these rules getting applied to the hypergraph.
Lex Fridman (1:39:07.040)
So it's, they seem like very different kinds of things.
Lex Fridman (1:39:10.000)
And so that at first seems like
Lex Fridman (1:39:12.760)
how can that possibly be right?
Lex Fridman (1:39:14.160)
How can that possibly be Lorentz invariant?
Stephen Wolfram (1:39:16.440)
That's the term for things being, you know,
Lex Fridman (1:39:18.840)
following the rules of special relativity.
Stephen Wolfram (1:39:21.600)
Well, it turns out that when you have causal invariants
Lex Fridman (1:39:26.120)
that, and let's see, we can, it's worth explaining
Stephen Wolfram (1:39:30.120)
a little bit how this works.
Lex Fridman (1:39:31.000)
It's a little bit elaborate,
Lex Fridman (1:39:32.440)
but the basic point is that even though space and time
Lex Fridman (1:39:38.960)
sort of come from very different places,
Stephen Wolfram (1:39:41.640)
it turns out that the rules of sort of space time
Lex Fridman (1:39:45.360)
that special relativity talks about come out of this model
Stephen Wolfram (1:39:51.080)
when you're looking at large enough systems.
Lex Fridman (1:39:53.680)
So a way to think about this, you know,
Stephen Wolfram (1:39:56.080)
in terms of when you're looking at large enough systems,
Lex Fridman (1:39:59.480)
the part of that story is when you look at some fluid
Stephen Wolfram (1:40:03.800)
like water, for example, there are equations
Lex Fridman (1:40:06.280)
that govern the flow of water.
Stephen Wolfram (1:40:08.920)
Those equations are things that apply on a large scale.
Lex Fridman (1:40:12.720)
If you look at the individual molecules,
Stephen Wolfram (1:40:14.400)
they don't know anything about those equations.
Lex Fridman (1:40:16.280)
It's just the sort of the large scale effect
Stephen Wolfram (1:40:19.360)
of those molecules turns out to follow those equations.
Lex Fridman (1:40:22.800)
And it's the same kind of thing happening in our models.
Stephen Wolfram (1:40:25.960)
I know this might be a small point,
Lex Fridman (1:40:27.960)
but it might be a very big one.
Stephen Wolfram (1:40:29.600)
We've been talking about space and time
Lex Fridman (1:40:32.560)
at the lowest level of the model, which is space.
Stephen Wolfram (1:40:35.960)
The hypergraph time is the evolution of this hypergraph.
Lex Fridman (1:40:39.860)
But there's also space time that we think about
Lex Fridman (1:40:43.160)
and general relativity for your special relativity.
Lex Fridman (1:40:47.400)
Like how do you go from the lowest source code
Stephen Wolfram (1:40:54.080)
of space and time as we're talking about
Lex Fridman (1:40:55.960)
to the more traditional terminology of space and time?
Lex Fridman (1:40:58.720)
So the key thing is this thing we call the causal graph.
Lex Fridman (1:41:01.840)
So the causal graph is the graph
Stephen Wolfram (1:41:03.760)
of causal relationships between events.
Lex Fridman (1:41:06.660)
So every one of these little updating events,
Stephen Wolfram (1:41:08.980)
every one of these little transformations
Lex Fridman (1:41:10.320)
of the hypergraph happens somewhere in the hypergraph,
Stephen Wolfram (1:41:13.360)
happens at some stage in the computation.
Lex Fridman (1:41:16.800)
That's an event.
Stephen Wolfram (1:41:18.240)
That event has a causal relationship to other events
Lex Fridman (1:41:22.280)
in the sense that if another event needs as its input,
Stephen Wolfram (1:41:27.360)
the output from the first event,
Lex Fridman (1:41:29.440)
there will be a causal relationship
Stephen Wolfram (1:41:31.140)
of the future event will depend on the past event.
Lex Fridman (1:41:35.220)
So you can say it has a causal connection.
Lex Fridman (1:41:37.960)
And so you can make this graph
Lex Fridman (1:41:39.760)
of causal relationships between events.
Stephen Wolfram (1:41:42.440)
That graph of causal relationships,
Lex Fridman (1:41:44.240)
causal invariance implies that that graph is unique.
Stephen Wolfram (1:41:47.680)
It doesn't matter even though you think,
Lex Fridman (1:41:51.280)
oh, I'm, let's say we were sorting a string, for example,
Stephen Wolfram (1:41:54.160)
I did that particular transposition of characters
Lex Fridman (1:41:57.720)
at this time, then I did that one, then I did this one.
Stephen Wolfram (1:42:00.180)
Turns out if you look at the network of connections
Lex Fridman (1:42:03.000)
between those updating events, that network is the same.
Stephen Wolfram (1:42:06.680)
It's the, if you were to, the structure.
Lex Fridman (1:42:11.040)
So in other words, if you were to draw that,
Stephen Wolfram (1:42:13.360)
if you were to put that network on a picture
Lex Fridman (1:42:15.440)
of where you're doing all the updating,
Stephen Wolfram (1:42:17.100)
the places where you put the nodes of the network
Lex Fridman (1:42:20.080)
will be different, but the way the nodes are connected
Stephen Wolfram (1:42:22.440)
will always be the same.
Lex Fridman (1:42:23.560)
So, but the causal graph is, I don't know,
Stephen Wolfram (1:42:27.320)
it's kind of an observation, it's not enforced,
Lex Fridman (1:42:31.080)
it's just emergent from a set of events.
Stephen Wolfram (1:42:33.760)
It's a feature of, okay, so what it is is.
Lex Fridman (1:42:36.440)
The characteristic, I guess, of the way events happen.
Stephen Wolfram (1:42:38.860)
Right, it's an event can't happen
Lex Fridman (1:42:40.800)
until its input is ready.
Lex Fridman (1:42:42.520)
And so that creates this network of causal relationships.
Lex Fridman (1:42:46.360)
And that's the causal graph.
Lex Fridman (1:42:48.280)
And the thing that the next thing to realize is,
Lex Fridman (1:42:51.560)
okay, we, when you're going to observe
Lex Fridman (1:42:54.480)
what happens in the universe,
Lex Fridman (1:42:56.400)
you have to sort of make sense of this causal graph.
Stephen Wolfram (1:42:59.560)
So, and you are an observer who yourself
Lex Fridman (1:43:02.840)
is part of this causal graph.
Lex Fridman (1:43:05.040)
And so that means, so let me give you an example
Lex Fridman (1:43:07.520)
of how that works.
Lex Fridman (1:43:08.360)
So imagine we have a really weird theory of physics
Lex Fridman (1:43:11.160)
of the world where it says this updating process,
Stephen Wolfram (1:43:15.100)
there's only gonna be one update at every moment in time.
Lex Fridman (1:43:18.180)
And there's just gonna be like a Turing machine.
Stephen Wolfram (1:43:19.720)
It has a little head that runs around
Lex Fridman (1:43:21.520)
and just is always just updating one thing at a time.
Lex Fridman (1:43:23.680)
So you say, I have a theory of physics
Lex Fridman (1:43:26.040)
and the theory of physics says,
Stephen Wolfram (1:43:27.480)
there's just this one little place where things get updated.
Lex Fridman (1:43:30.440)
You say, that's completely crazy because,
Stephen Wolfram (1:43:32.960)
it's plainly obvious that things are being updated
Lex Fridman (1:43:35.860)
sort of at the same time.
Stephen Wolfram (1:43:37.120)
Async obviously, yeah, at the same time, yeah.
Lex Fridman (1:43:39.280)
But the fact is that the thing is that if I'm talking to you
Lex Fridman (1:43:44.240)
and you seem to be being updated as I'm being updated,
Lex Fridman (1:43:47.200)
but if there's just this one little head
Stephen Wolfram (1:43:48.960)
that's running around updating things,
Lex Fridman (1:43:51.000)
I will not know whether you've been updated or not
Stephen Wolfram (1:43:53.440)
until I'm updated.
Lex Fridman (1:43:55.440)
So in other words, draw this causal graph
Stephen Wolfram (1:43:58.640)
of the causal relationship between the updatings in you
Lex Fridman (1:44:01.000)
and the updatings in me,
Stephen Wolfram (1:44:02.440)
it'll still be the same causal graph,
Lex Fridman (1:44:04.400)
whether even though the underlying sort of story
Stephen Wolfram (1:44:07.120)
of what happens is, oh, there's just this one little thing
Lex Fridman (1:44:10.120)
and it goes and updates in different places in the universe.
Lex Fridman (1:44:12.840)
So is that clear or is that a hypothesis?
Lex Fridman (1:44:18.040)
Is that clear that there's a unique causal graph?
Stephen Wolfram (1:44:21.440)
If there's causal invariance, there's unique causal graph.
Lex Fridman (1:44:24.880)
So it's okay to think of what we're talking about
Stephen Wolfram (1:44:28.060)
as a hypergraph and the operations on it
Lex Fridman (1:44:30.600)
as a kind of touring machine with a single head,
Stephen Wolfram (1:44:32.960)
like a single guy running around updating stuff.
Lex Fridman (1:44:37.120)
Is that safe to intuitively think of it this way?
Stephen Wolfram (1:44:40.520)
Let me think about that for a second.
Lex Fridman (1:44:41.680)
Yes, I think so.
Stephen Wolfram (1:44:42.560)
I think there's nothing, it doesn't matter.
Lex Fridman (1:44:44.800)
I mean, you can say, okay, there is one,
Stephen Wolfram (1:44:47.980)
the reason I'm pausing for a second is that I'm wondering,
Lex Fridman (1:44:52.880)
well, when you say running around,
Stephen Wolfram (1:44:55.840)
depends how far it jumps every time it runs.
Lex Fridman (1:44:57.960)
Yeah, yeah, that's right.
Lex Fridman (1:44:59.160)
But I mean like one operation at a time.
Lex Fridman (1:45:02.000)
Yeah, you can think of it as one operation at a time.
Stephen Wolfram (1:45:03.760)
It's easier for the human brain to think of it that way
Lex Fridman (1:45:06.680)
as opposed to simultaneous.
Stephen Wolfram (1:45:08.240)
Well, maybe it's not, okay, but the thing is
Lex Fridman (1:45:10.720)
that's not how we experience the world.
Lex Fridman (1:45:12.720)
What we experience is we look around,
Lex Fridman (1:45:15.760)
everything seems to be happening
Stephen Wolfram (1:45:17.880)
at successive moments in time everywhere in space.
Lex Fridman (1:45:21.000)
Yes.
Stephen Wolfram (1:45:21.840)
That is the, and that's partly a feature
Lex Fridman (1:45:23.880)
of our particular construction.
Stephen Wolfram (1:45:25.580)
I mean, that is the speed of light is really fast
Lex Fridman (1:45:28.480)
compared to, you know, we look around, you know,
Stephen Wolfram (1:45:30.680)
I can see maybe a hundred feet away right now.
Lex Fridman (1:45:33.800)
You know, it's the, my brain does not process very much
Stephen Wolfram (1:45:38.800)
in the time it takes light to go a hundred feet.
Lex Fridman (1:45:41.280)
The brain operates at a scale of hundreds of milliseconds
Stephen Wolfram (1:45:44.040)
or something like that, I don't know.
Lex Fridman (1:45:45.320)
Right.
Lex Fridman (1:45:46.160)
And speed of light is much faster.
Lex Fridman (1:45:47.600)
Right, you know, light goes,
Stephen Wolfram (1:45:49.160)
in a billionth of a second light has gone afoot.
Lex Fridman (1:45:51.000)
So it goes a billion feet every second.
Stephen Wolfram (1:45:53.720)
There's certain moments through this conversation
Lex Fridman (1:45:56.480)
where I imagine the absurdity of the fact
Stephen Wolfram (1:46:01.200)
that there's two descendants of apes modeled by a hypergraph
Lex Fridman (1:46:05.080)
that are communicating with each other
Lex Fridman (1:46:06.400)
and experiencing this whole thing
Lex Fridman (1:46:09.160)
as a real time simultaneous update with,
Stephen Wolfram (1:46:13.440)
I'm taking in photons from you right now,
Lex Fridman (1:46:15.440)
but there's something much, much deeper going on here.
Stephen Wolfram (1:46:19.160)
Right, it does have a.
Lex Fridman (1:46:20.000)
It's paralyzing sometimes to just.
Stephen Wolfram (1:46:22.560)
Yes.
Lex Fridman (1:46:23.400)
To remember that.
Stephen Wolfram (1:46:24.220)
Right, no, I mean, you know, it's a, you know.
Lex Fridman (1:46:26.400)
Sorry.
Stephen Wolfram (1:46:27.240)
Yes, yes, no.
Lex Fridman (1:46:28.080)
As a small little tangent, I just remembered
Stephen Wolfram (1:46:30.800)
that we're talking about,
Lex Fridman (1:46:32.360)
I mean, about the fabric of reality.
Stephen Wolfram (1:46:37.080)
Right, so we've got this causal graph
Lex Fridman (1:46:40.080)
that represents the sort of causal relationships
Stephen Wolfram (1:46:41.920)
between all these events in the universe.
Lex Fridman (1:46:43.760)
That causal graph kind of is a representation of space time,
Lex Fridman (1:46:47.680)
but our experience of it requires
Lex Fridman (1:46:50.800)
that we pick reference frames.
Stephen Wolfram (1:46:52.960)
This is kind of a key idea.
Lex Fridman (1:46:54.200)
Einstein had this idea that what that means is
Stephen Wolfram (1:46:57.440)
we have to say, what are we going to pick
Lex Fridman (1:47:01.040)
as being the sort of what we define
Lex Fridman (1:47:04.540)
as simultaneous moments in time?
Lex Fridman (1:47:07.680)
So for example, we can say, you know,
Lex Fridman (1:47:11.400)
how do we set our clocks?
Lex Fridman (1:47:13.040)
You know, if we've got a spacecraft landing on Mars,
Stephen Wolfram (1:47:16.420)
you know, do we say that, you know,
Lex Fridman (1:47:17.840)
what time is it landing at?
Stephen Wolfram (1:47:19.480)
Was it, you know, even though there's a 20 minute
Lex Fridman (1:47:21.640)
speed of light delay or something, you know,
Lex Fridman (1:47:23.760)
what time do we say it landed at?
Lex Fridman (1:47:25.340)
How do we set up sort of time coordinates for the world?
Lex Fridman (1:47:30.020)
And that turns out to be that there's kind of
Lex Fridman (1:47:32.400)
this arbitrariness to how we set these reference frames
Stephen Wolfram (1:47:35.960)
that defines sort of what counts as simultaneous.
Lex Fridman (1:47:39.200)
And what is the essence of special relativity
Stephen Wolfram (1:47:42.020)
is to think about reference frames going at different speeds
Lex Fridman (1:47:45.880)
and to think about sort of how they assign,
Lex Fridman (1:47:48.760)
what counts as space, what counts as time and so on.
Lex Fridman (1:47:52.320)
That's all a bit technical, but the basic bottom line is
Stephen Wolfram (1:47:55.680)
that this causal invariance property,
Lex Fridman (1:47:58.920)
that means that it's always the same causal graph,
Stephen Wolfram (1:48:01.800)
independent of how you slice it with these reference frames,
Lex Fridman (1:48:04.760)
you'll always sort of see the same physical processes go on.
Lex Fridman (1:48:07.840)
And that's basically why special relativity works.
Lex Fridman (1:48:10.380)
So there's something like special relativity,
Stephen Wolfram (1:48:14.620)
like everything around space and time
Lex Fridman (1:48:17.680)
that fits this idea of the causal graph.
Stephen Wolfram (1:48:22.900)
Right, well, you know, one way to think about it is
Lex Fridman (1:48:24.900)
given that you have a basic structure
Stephen Wolfram (1:48:27.280)
that just involves updating things in these,
Lex Fridman (1:48:31.040)
you know, connected updates and looking at
Stephen Wolfram (1:48:33.280)
the causal relationships between connected updates,
Lex Fridman (1:48:35.640)
that's enough when you unravel the consequences of that,
Stephen Wolfram (1:48:39.760)
that together with the fact that there are lots
Lex Fridman (1:48:41.500)
of these things and that you can take a continuum limit
Lex Fridman (1:48:43.880)
and so on implies special relativity.
Lex Fridman (1:48:46.900)
And so that, it's kind of not a big deal
Stephen Wolfram (1:48:51.000)
because it's kind of a, you know,
Lex Fridman (1:48:52.920)
it was completely unobvious when you started off
Stephen Wolfram (1:48:56.520)
with saying, we've got this graph,
Lex Fridman (1:48:57.860)
it's being updated in time, et cetera, et cetera, et cetera,
Stephen Wolfram (1:49:00.200)
that just looks like nothing to do with special relativity.
Lex Fridman (1:49:03.280)
And yet you get that.
Lex Fridman (1:49:05.040)
And what, I mean, then the thing,
Lex Fridman (1:49:08.080)
I mean, this was stuff that I figured out back in the 1990s.
Stephen Wolfram (1:49:11.160)
The next big thing you get is general relativity.
Lex Fridman (1:49:16.200)
And so in this hypergraph,
Stephen Wolfram (1:49:18.920)
the sort of limiting structure,
Lex Fridman (1:49:20.700)
when you have a very big hypergraph,
Stephen Wolfram (1:49:22.440)
you can think of as being just like, you know,
Lex Fridman (1:49:24.480)
water seems continuous on a large scale.
Lex Fridman (1:49:27.040)
So this hypergraph seems continuous on a large scale.
Lex Fridman (1:49:30.140)
One question is, you know,
Lex Fridman (1:49:31.660)
how many dimensions of space does it correspond to?
Lex Fridman (1:49:35.200)
So one question you can ask is,
Stephen Wolfram (1:49:36.440)
if you've just got a bunch of points
Lex Fridman (1:49:38.000)
and they're connected together,
Lex Fridman (1:49:39.480)
how do you deduce what effective dimension of space
Lex Fridman (1:49:43.160)
that bundle of points corresponds to?
Lex Fridman (1:49:46.000)
And that's pretty easy to explain.
Lex Fridman (1:49:47.680)
So basically if you say you've got a point
Lex Fridman (1:49:50.520)
and you look at how many neighbors does that point have?
Lex Fridman (1:49:52.760)
Okay, imagine it's on a square grid.
Stephen Wolfram (1:49:54.680)
Then it'll have four neighbors.
Lex Fridman (1:49:56.260)
Go another level out.
Lex Fridman (1:49:58.280)
How many neighbors do you get then?
Lex Fridman (1:50:00.000)
What you realize is as you go more and more levels out,
Stephen Wolfram (1:50:02.800)
as you go more and more distance on the graph out,
Lex Fridman (1:50:05.920)
you're capturing something which is essentially a circle
Stephen Wolfram (1:50:09.700)
in two dimensions so that, you know,
Lex Fridman (1:50:11.920)
the number of the area of a circle is pi R squared.
Lex Fridman (1:50:14.720)
So it's the number of points that you get to
Lex Fridman (1:50:18.400)
goes up like the distance you've gone squared.
Lex Fridman (1:50:21.540)
And in general, in D dimensional space,
Lex Fridman (1:50:24.440)
it's R to the power D.
Stephen Wolfram (1:50:25.940)
It's the number of points you get to
Lex Fridman (1:50:28.680)
if you go R steps on the graph grows like
Stephen Wolfram (1:50:32.720)
the number of steps you go to the power of the dimension.
Lex Fridman (1:50:35.560)
And that's a way that you can estimate
Stephen Wolfram (1:50:37.760)
the effective dimension of one of these graphs.
Lex Fridman (1:50:39.960)
So what does that grow to?
Lex Fridman (1:50:41.080)
So how does the dimension grow?
Lex Fridman (1:50:42.540)
There's a, I mean, obviously the visual aspect
Stephen Wolfram (1:50:45.900)
of these hypergraphs,
Lex Fridman (1:50:47.380)
they're often visualized in three dimensions.
Stephen Wolfram (1:50:50.120)
Right.
Lex Fridman (1:50:50.960)
So there's a certain kind of structure,
Stephen Wolfram (1:50:54.640)
like you said, there's, I mean, a circle, a sphere,
Lex Fridman (1:50:58.880)
there's a planar aspect to it,
Stephen Wolfram (1:51:02.360)
to this graph to where it kind of,
Lex Fridman (1:51:04.680)
it almost starts creating a surface,
Stephen Wolfram (1:51:06.760)
like a complicated surface, but a surface.
Lex Fridman (1:51:09.120)
So how does that connect to effective dimension?
Stephen Wolfram (1:51:11.880)
Okay, so if you can lay out the graph
Lex Fridman (1:51:14.400)
in such a way that the points in the graph that,
Stephen Wolfram (1:51:18.880)
you know, the points that are neighbors on the graph
Lex Fridman (1:51:21.360)
are neighbors as you lay them out,
Lex Fridman (1:51:23.520)
and you can do that in two dimensions,
Lex Fridman (1:51:25.680)
then it's gonna approximate a two dimensional thing.
Stephen Wolfram (1:51:28.360)
If you can't do that in two dimensions,
Lex Fridman (1:51:29.760)
if everything would have to fold over a lot
Stephen Wolfram (1:51:31.240)
in two dimensions,
Lex Fridman (1:51:32.240)
then it's not approximating a two dimensional thing.
Stephen Wolfram (1:51:34.080)
Maybe you can lay it out in three dimensions.
Lex Fridman (1:51:36.200)
Maybe you have to lay it out in five dimensions
Stephen Wolfram (1:51:38.640)
to have it be the case
Lex Fridman (1:51:39.640)
that it sort of smoothly lays out like that.
Stephen Wolfram (1:51:42.000)
Well, but okay, so I apologize
Lex Fridman (1:51:44.720)
for the different tangent questions,
Lex Fridman (1:51:46.060)
but you know, there's an infinity number of possible rules.
Lex Fridman (1:51:51.320)
So we have to look for rules
Stephen Wolfram (1:51:54.600)
that create the kind of structures
Lex Fridman (1:51:58.520)
that are reminiscent for,
Stephen Wolfram (1:52:01.560)
that have echoes of the different physics theories in them.
Lex Fridman (1:52:05.080)
So what kind of rules,
Stephen Wolfram (1:52:06.600)
is there something simple to be said
Lex Fridman (1:52:08.240)
about the kind of rules that you have found beautiful,
Lex Fridman (1:52:12.080)
that you have found powerful?
Lex Fridman (1:52:13.480)
Right, so I mean, what, you know,
Stephen Wolfram (1:52:15.400)
one of the features of computational irreducibility is,
Lex Fridman (1:52:18.760)
it's very, you can't say in advance,
Stephen Wolfram (1:52:21.980)
what's gonna happen with any particular,
Lex Fridman (1:52:23.960)
you can't say, I'm gonna pick these rules
Stephen Wolfram (1:52:26.000)
from this part of rule space, so to speak,
Lex Fridman (1:52:28.900)
because they're gonna be the ones that are gonna work.
Stephen Wolfram (1:52:30.960)
That's, you can make some statements along those lines,
Lex Fridman (1:52:33.360)
but you can't generally say that.
Stephen Wolfram (1:52:35.200)
Now, you know, the state of what we've been able to do
Lex Fridman (1:52:38.280)
is, you know, different properties of the universe,
Stephen Wolfram (1:52:40.680)
like dimensionality, you know, integer dimensionality,
Lex Fridman (1:52:44.600)
features of other features of quantum mechanics,
Stephen Wolfram (1:52:47.960)
things like that.
Lex Fridman (1:52:48.960)
At this point, what we've got is,
Stephen Wolfram (1:52:50.600)
we've got rules that any one of those features,
Lex Fridman (1:52:55.380)
we can get a rule that has that feature.
Stephen Wolfram (1:52:58.080)
Yeah, so the.
Lex Fridman (1:52:58.920)
We don't have the sort of, the final,
Stephen Wolfram (1:53:00.720)
here's a rule which has all of these features,
Lex Fridman (1:53:02.640)
we do not have that yet.
Lex Fridman (1:53:03.680)
So if I were to try to summarize
Lex Fridman (1:53:06.960)
the Wolfram physics project, which is, you know,
Stephen Wolfram (1:53:11.380)
something that's been in your brain for a long time,
Lex Fridman (1:53:13.920)
but really has just exploded in activity,
Stephen Wolfram (1:53:17.280)
you know, only just months ago.
Lex Fridman (1:53:19.160)
Yes.
Lex Fridman (1:53:20.040)
So it's an evolving thing, and next week,
Lex Fridman (1:53:23.480)
I'll try to publish this conversation
Stephen Wolfram (1:53:24.920)
as quickly as possible, because by the time it's published,
Lex Fridman (1:53:27.840)
already new things will probably have come out.
Lex Fridman (1:53:29.640)
So if I were to summarize it,
Lex Fridman (1:53:33.180)
we've talked about the basics of,
Stephen Wolfram (1:53:35.940)
there's a hypergraph that represents space,
Lex Fridman (1:53:38.360)
there is transformations in that hypergraph
Stephen Wolfram (1:53:42.360)
that represents time.
Lex Fridman (1:53:44.720)
The progress of time.
Stephen Wolfram (1:53:45.560)
The progress of time, there's a causal graph
Lex Fridman (1:53:47.840)
that's a characteristic of this,
Lex Fridman (1:53:49.640)
and the basic process of science,
Lex Fridman (1:53:53.720)
of, yeah, of science within the Wolfram physics model
Stephen Wolfram (1:53:58.640)
is to try different rules and see which properties
Lex Fridman (1:54:02.560)
of physics that we know of, known physical theories,
Stephen Wolfram (1:54:06.120)
are, appear within the graphs that emerge from that rule.
Lex Fridman (1:54:10.700)
That's what I thought it was going to be.
Stephen Wolfram (1:54:12.400)
Uh oh, okay.
Lex Fridman (1:54:13.660)
So what is it?
Stephen Wolfram (1:54:16.080)
It turns out we can do a lot better than that.
Lex Fridman (1:54:18.200)
It turns out that using kind of mathematical ideas,
Stephen Wolfram (1:54:21.400)
we can say, and computational ideas,
Lex Fridman (1:54:25.140)
we can make general statements,
Lex Fridman (1:54:28.400)
and those general statements turn out to correspond
Lex Fridman (1:54:31.520)
to things that we know from 20th century physics.
Stephen Wolfram (1:54:34.080)
In other words, the idea of you just try a bunch of rules
Lex Fridman (1:54:36.940)
and see what they do,
Stephen Wolfram (1:54:37.780)
that's what I thought we were gonna have to do.
Lex Fridman (1:54:40.240)
But in fact, we can say, given causal invariance
Lex Fridman (1:54:43.760)
and computational irreducibility, we can derive,
Lex Fridman (1:54:47.480)
and this is where it gets really pretty interesting,
Stephen Wolfram (1:54:49.480)
we can derive special relativity,
Lex Fridman (1:54:51.120)
we can derive general relativity,
Stephen Wolfram (1:54:52.920)
we can derive quantum mechanics.
Lex Fridman (1:54:55.140)
And that's where things really start to get exciting,
Stephen Wolfram (1:54:58.280)
is, you know, it wasn't at all obvious to me
Lex Fridman (1:55:01.340)
that even if we were completely correct,
Lex Fridman (1:55:03.360)
and even if we had, you know, this is the rule,
Lex Fridman (1:55:05.240)
you know, even if we found the rule,
Stephen Wolfram (1:55:06.920)
to be able to say, yes, it corresponds
Lex Fridman (1:55:08.940)
to things we already know,
Stephen Wolfram (1:55:10.360)
I did not expect that to be the case.
Lex Fridman (1:55:12.660)
And...
Lex Fridman (1:55:13.500)
So for somebody who is a simple mind
Lex Fridman (1:55:16.920)
and definitely not a physicist, not even close,
Lex Fridman (1:55:19.460)
what does derivation mean in this case?
Lex Fridman (1:55:22.760)
Okay, so let me, this is an interesting question.
Stephen Wolfram (1:55:26.940)
Okay, so there's, so one thing...
Lex Fridman (1:55:29.160)
In the context of computational irreducibility.
Stephen Wolfram (1:55:31.880)
Yeah, yeah, right, right.
Lex Fridman (1:55:32.920)
So what you have to do, let me go back to, again,
Stephen Wolfram (1:55:36.840)
the mundane example of fluids and water
Lex Fridman (1:55:39.000)
and things like that, right?
Lex Fridman (1:55:40.400)
So you have a bunch of molecules bouncing around.
Lex Fridman (1:55:44.040)
You can say, just as a piece of mathematics,
Stephen Wolfram (1:55:47.340)
I happen to do this from cellular automata
Lex Fridman (1:55:49.260)
back in the mid 1980s, you can say,
Stephen Wolfram (1:55:52.160)
just as a matter of mathematics,
Lex Fridman (1:55:54.200)
you can say the continuum limit
Stephen Wolfram (1:55:57.240)
of these little molecules bouncing around
Lex Fridman (1:55:59.240)
is the Navier Stokes equations.
Stephen Wolfram (1:56:01.640)
That's just a piece of mathematics.
Lex Fridman (1:56:03.260)
It's not, it doesn't rely on...
Stephen Wolfram (1:56:06.640)
You have to make certain assumptions
Lex Fridman (1:56:08.480)
that you have to say there's enough randomness
Stephen Wolfram (1:56:10.880)
in the way the molecules bounce around
Lex Fridman (1:56:12.400)
that certain statistical averages work,
Stephen Wolfram (1:56:14.240)
et cetera, et cetera, et cetera.
Lex Fridman (1:56:15.680)
Okay, it is a very similar derivation
Stephen Wolfram (1:56:18.320)
to derive, for example, the Einstein equations.
Lex Fridman (1:56:21.220)
Okay, so the way that works, roughly,
Stephen Wolfram (1:56:23.720)
the Einstein equations are about curvature of space.
Lex Fridman (1:56:26.740)
Curvature of space, I talked about sort of
Lex Fridman (1:56:29.080)
how you can figure out dimension of space.
Lex Fridman (1:56:31.840)
There's a similar kind of way of figuring out
Stephen Wolfram (1:56:34.260)
if you just sort of say, you know,
Lex Fridman (1:56:37.240)
you're making a larger and larger ball
Stephen Wolfram (1:56:39.040)
or larger and larger, if you draw a circle
Lex Fridman (1:56:40.920)
on the surface of the earth, for example,
Stephen Wolfram (1:56:42.940)
you might think the area of a circle is pi r squared,
Lex Fridman (1:56:45.980)
but on the surface of the earth,
Stephen Wolfram (1:56:47.940)
because it's a sphere, it's not flat,
Lex Fridman (1:56:50.560)
the area of a circle isn't precisely pi r squared.
Stephen Wolfram (1:56:53.360)
As the circle gets bigger, the area is slightly smaller
Lex Fridman (1:56:56.240)
than you would expect from the formula pi r squared
Stephen Wolfram (1:56:58.160)
as a little correction term that depends on the ratio
Lex Fridman (1:57:01.040)
of the size of the circle to the radius of the earth.
Stephen Wolfram (1:57:03.700)
Okay, so it's the same basic thing,
Lex Fridman (1:57:05.680)
allows you to measure from one of these hypergraphs
Lex Fridman (1:57:08.240)
what is its effective curvature.
Lex Fridman (1:57:11.240)
And that's...
Lex Fridman (1:57:12.080)
So the little piece of mathematics
Lex Fridman (1:57:15.440)
that explains special general relativity
Stephen Wolfram (1:57:20.960)
can map nicely to describe fundamental property
Lex Fridman (1:57:25.400)
of the hypergraphs, the curvature of the hypergraphs.
Lex Fridman (1:57:27.560)
So special relativity is about the relationship
Lex Fridman (1:57:31.280)
of time to space.
Stephen Wolfram (1:57:32.720)
General relativity is about curvature
Lex Fridman (1:57:35.280)
and this space represented by this hypergraph.
Lex Fridman (1:57:38.600)
So what is the curvature of a hypergraph?
Lex Fridman (1:57:40.760)
Okay, so first I have to explain,
Lex Fridman (1:57:43.120)
what we're explaining is,
Lex Fridman (1:57:44.680)
first thing you have to have is a notion of dimension.
Stephen Wolfram (1:57:47.120)
You don't get to talk about curvature of things.
Lex Fridman (1:57:49.280)
If you say, oh, it's a curved line,
Lex Fridman (1:57:51.800)
but I don't know what a line is yet.
Lex Fridman (1:57:53.800)
So...
Lex Fridman (1:57:54.640)
Yeah, what is the dimension of a hypergraph then?
Lex Fridman (1:57:56.960)
From where, we've talked about effective dimension, but...
Stephen Wolfram (1:58:00.580)
Right, that's what this is about.
Lex Fridman (1:58:03.080)
What this is about is, you have your hypergraph,
Stephen Wolfram (1:58:05.180)
it's got a trillion nodes in it.
Lex Fridman (1:58:07.380)
What is it roughly like?
Lex Fridman (1:58:08.740)
Is it roughly like a grid, a two dimensional grid?
Lex Fridman (1:58:11.460)
Is it roughly like all those nodes are arranged online?
Lex Fridman (1:58:15.240)
What's it roughly like?
Lex Fridman (1:58:16.740)
And there's a pretty simple mathematical way
Stephen Wolfram (1:58:19.600)
to estimate that by just looking at this thing
Lex Fridman (1:58:23.960)
I was describing, this sort of the size of a ball
Stephen Wolfram (1:58:26.340)
that you construct in the hypergraph.
Lex Fridman (1:58:28.240)
That's a, you just measure that,
Stephen Wolfram (1:58:29.800)
you can just compute it on a computer for a given hypergraph
Lex Fridman (1:58:33.000)
and you can say, oh, this thing is wiggling around,
Lex Fridman (1:58:35.160)
but it's roughly corresponds to two or something like that,
Lex Fridman (1:58:38.240)
or roughly corresponds to 2.6 or whatever.
Lex Fridman (1:58:41.440)
So that's how you have a notion of dimension
Lex Fridman (1:58:44.080)
in these hypergraphs.
Stephen Wolfram (1:58:45.640)
Curvature is something a little bit beyond that.
Lex Fridman (1:58:48.600)
If you look at how the size of this ball increases
Stephen Wolfram (1:58:52.120)
as you increase its radius,
Lex Fridman (1:58:53.960)
curvature is a correction
Stephen Wolfram (1:58:55.400)
to the size increase associated with dimension.
Lex Fridman (1:58:58.920)
It's a sort of a second order term
Stephen Wolfram (1:59:01.120)
in determining the size.
Lex Fridman (1:59:03.360)
Just like the area of a circle is roughly pi R squared.
Lex Fridman (1:59:07.000)
So it goes up like R squared.
Lex Fridman (1:59:08.520)
The two is because it's in two dimensions,
Lex Fridman (1:59:11.080)
but when that circle is drawn on a big sphere,
Lex Fridman (1:59:14.440)
the actual formula is pi R squared times one minus
Stephen Wolfram (1:59:19.400)
R squared over A squared and some coefficient.
Lex Fridman (1:59:22.640)
So in other words, there's a correction to,
Lex Fridman (1:59:25.000)
and that correction term, that gives you curvature.
Lex Fridman (1:59:28.240)
And that correction term
Stephen Wolfram (1:59:29.720)
is what makes this hypergraph correspond,
Lex Fridman (1:59:32.880)
have the potential to correspond to curved space.
Stephen Wolfram (1:59:35.840)
Now, the next question is, is that curvature,
Lex Fridman (1:59:38.480)
is the way that curvature works
Stephen Wolfram (1:59:40.400)
the way that Einstein's equations for general relativity,
Lex Fridman (1:59:43.800)
is it the way they say it should work?
Lex Fridman (1:59:46.040)
And the answer is yes.
Lex Fridman (1:59:49.160)
And so how does that work?
Stephen Wolfram (1:59:54.560)
The calculation of the curvature of this hypergraph
Lex Fridman (1:59:57.240)
for some set of rules?
Stephen Wolfram (1:59:59.760)
No, it doesn't matter what the rules are.
Lex Fridman (20:01.000)
And that's, you know, in science,
Stephen Wolfram (20:03.600)
that's been sort of a very special case of that.
Lex Fridman (20:05.720)
That is science has chosen to talk a lot about places
Stephen Wolfram (20:09.360)
where there is this computational reducibility
Lex Fridman (20:12.120)
that it can find, you know,
Stephen Wolfram (20:13.640)
the motion of the planets can be more or less predicted.
Lex Fridman (20:16.400)
You know, something about the weather
Stephen Wolfram (20:19.080)
is much harder to predict.
Lex Fridman (20:20.640)
Something about, you know, other kinds of things
Stephen Wolfram (20:22.760)
that are much harder to predict.
Lex Fridman (20:25.160)
And it's, these are, but science has tended to,
Stephen Wolfram (20:29.160)
you know, concentrate itself on places
Lex Fridman (20:31.040)
where its methods have allowed successful prediction.
Lex Fridman (20:35.080)
So you think rule 30, if we could linger on it,
Lex Fridman (20:39.160)
because it's just such a beautiful, simple formulation
Stephen Wolfram (20:41.600)
of the essential concept underlying
Lex Fridman (20:43.520)
all the things we're talking about.
Lex Fridman (20:45.000)
Do you think there's pockets of reducibility
Lex Fridman (20:47.240)
inside rule 30?
Lex Fridman (20:48.480)
Yes, that is the question of how big are they?
Lex Fridman (20:51.600)
What will they allow you to say?
Lex Fridman (20:53.120)
And so on.
Lex Fridman (20:53.960)
And that's, and figuring out where those pockets are,
Stephen Wolfram (20:56.960)
I mean, in a sense, that's the, that's sort of a,
Lex Fridman (21:00.480)
you know, that is an essential thing
Stephen Wolfram (21:02.640)
that one would like to do in science.
Lex Fridman (21:05.760)
But it's also, the important thing to realize
Stephen Wolfram (21:08.800)
that has not been, you know, is that science,
Lex Fridman (21:13.760)
if you just pick an arbitrary thing,
Lex Fridman (21:15.400)
you say, what's the answer to this question?
Lex Fridman (21:18.120)
That question may not be one
Stephen Wolfram (21:20.200)
that has a computationally reducible answer.
Lex Fridman (21:22.880)
That question, if you choose, you know,
Stephen Wolfram (21:26.360)
if you walk along the series of questions
Lex Fridman (21:28.880)
and you've got one that's reducible
Lex Fridman (21:30.280)
and you get to another one that's nearby
Lex Fridman (21:31.680)
and it's reducible too,
Stephen Wolfram (21:33.000)
if you stick to that kind of stick to the land,
Lex Fridman (21:36.080)
so to speak, then you can go down this chain
Stephen Wolfram (21:39.640)
of sort of reducible, answerable things.
Lex Fridman (21:41.960)
But if you just say, I'm just pick a question at random,
Stephen Wolfram (21:44.440)
I'm gonna have my computer pick a question at random.
Lex Fridman (21:47.400)
Most likely it's gonna be reducible.
Stephen Wolfram (21:49.280)
Most likely it will be reducible.
Lex Fridman (21:50.960)
And what we're thrown in the world, so to speak,
Stephen Wolfram (21:54.720)
we, you know, when we engineer things,
Lex Fridman (21:56.440)
we tend to engineer things to sort of keep
Stephen Wolfram (21:58.320)
in the zone of reducibility.
Lex Fridman (22:00.280)
When we're throwing things by the natural world,
Stephen Wolfram (22:02.280)
for example, not at all certain
Lex Fridman (22:05.520)
that we will be kept in this kind of zone of reducibility.
Lex Fridman (22:08.680)
Can we talk about this pandemic then?
Lex Fridman (22:11.240)
Sure.
Stephen Wolfram (22:12.080)
For a second, is a, so how do we,
Lex Fridman (22:16.000)
there's obviously huge amount of economic pain
Stephen Wolfram (22:18.920)
that people are feeling.
Lex Fridman (22:19.800)
There's a huge incentive and medical pain,
Stephen Wolfram (22:23.960)
health, just all kind of psychological.
Lex Fridman (22:26.760)
There's a huge incentive to figure this out,
Stephen Wolfram (22:28.760)
to walk along the trajectory of reducible, of reducibility.
Lex Fridman (22:34.440)
There's a lot of disparate data.
Stephen Wolfram (22:38.040)
You know, people understand generally how viruses spread,
Lex Fridman (22:40.520)
but it's very complicated
Stephen Wolfram (22:43.240)
because there's a lot of uncertainty.
Lex Fridman (22:45.320)
There's a, there could be a lot of variability also,
Stephen Wolfram (22:49.320)
like so many, obviously a nearly infinite number
Lex Fridman (22:52.920)
of variables that represent human interaction.
Lex Fridman (22:57.920)
And so you have to figure out,
Lex Fridman (22:59.920)
from the perspective of reducibility,
Stephen Wolfram (23:02.680)
figure out which variables are really important
Lex Fridman (23:06.600)
in this kind of, from an epidemiological perspective.
Lex Fridman (23:10.600)
So why aren't we, you kind of said
Lex Fridman (23:13.800)
that we're clearly failing.
Stephen Wolfram (23:15.960)
Well, I think it's a complicated thing.
Lex Fridman (23:17.320)
So, I mean, you know, when this pandemic started up,
Stephen Wolfram (23:20.200)
you know, I happened to be in the middle
Lex Fridman (23:21.800)
of being about to release this whole physics project thing,
Lex Fridman (23:24.800)
but I thought, you know.
Lex Fridman (23:25.640)
The timing is just cosmically absurd.
Stephen Wolfram (23:28.280)
A little bit bizarre, but you know,
Lex Fridman (23:30.440)
but I thought, you know,
Stephen Wolfram (23:31.360)
I should do the public service thing of, you know,
Lex Fridman (23:33.960)
trying to understand what I could about the pandemic.
Stephen Wolfram (23:36.000)
And, you know, we'd been curating data about it
Lex Fridman (23:38.160)
and all that kind of thing.
Stephen Wolfram (23:39.280)
But, you know, so I started looking at the data
Lex Fridman (23:41.680)
and started looking at modeling
Lex Fridman (23:43.600)
and I decided it's just really hard.
Lex Fridman (23:46.000)
You need to know a lot of stuff that we don't know
Stephen Wolfram (23:48.240)
about human interactions.
Lex Fridman (23:49.840)
It's actually clear now that there's a lot of stuff
Stephen Wolfram (23:51.600)
we didn't know about viruses
Lex Fridman (23:53.480)
and about the way immunity works and so on.
Lex Fridman (23:56.000)
And it's, you know, I think what will come out in the end
Lex Fridman (23:58.840)
is there's a certain amount of what happens
Stephen Wolfram (24:02.000)
that we just kind of have to trace each step
Lex Fridman (24:04.320)
and see what happens.
Stephen Wolfram (24:05.800)
There's a certain amount of stuff
Lex Fridman (24:06.960)
where there's going to be a big narrative
Stephen Wolfram (24:08.280)
about this happened because, you know, of T cell immunity.
Lex Fridman (24:12.240)
This could happen because there's this whole giant
Stephen Wolfram (24:14.320)
sort of field of asymptomatic viral stuff out there.
Lex Fridman (24:18.640)
You know, there will be a narrative
Lex Fridman (24:20.120)
and that narrative, whenever there's a narrative,
Lex Fridman (24:22.400)
that's kind of a sign of reducibility.
Lex Fridman (24:24.600)
But when you just say,
Lex Fridman (24:26.000)
let's from first principles figure out what's going on,
Stephen Wolfram (24:28.880)
then you can potentially be stuck
Lex Fridman (24:30.880)
in this kind of a mess of irreducibility
Stephen Wolfram (24:33.720)
where you just have to simulate each step
Lex Fridman (24:35.680)
and you can't do that unless you know details about,
Stephen Wolfram (24:38.240)
you know, human interaction networks
Lex Fridman (24:40.120)
and so on and so on and so on.
Stephen Wolfram (24:41.360)
The thing that has been very sort of frustrating to see
Lex Fridman (24:46.440)
is the mismatch between people's expectations
Stephen Wolfram (24:48.920)
about what science can deliver
Lex Fridman (24:50.760)
and what science can actually deliver, so to speak.
Stephen Wolfram (24:53.680)
Because people have this idea that, you know, it's science.
Lex Fridman (24:56.760)
So there must be a definite answer
Lex Fridman (24:58.480)
and we must be able to know that answer.
Lex Fridman (25:00.520)
And, you know, this is, it is both, you know,
Stephen Wolfram (25:05.040)
when you've, after you've played around
Lex Fridman (25:07.600)
with sort of little programs in the computational universe,
Stephen Wolfram (25:10.080)
you don't have that intuition anymore.
Lex Fridman (25:11.840)
You know, it's, I always, I'm always fond of saying,
Stephen Wolfram (25:14.520)
you know, the computational animals
Lex Fridman (25:17.040)
are always smarter than you are.
Stephen Wolfram (25:18.240)
That is, you know, you look at one of these things
Lex Fridman (25:20.240)
and it's like, it can't possibly do such and such a thing.
Stephen Wolfram (25:23.240)
Then you run it and it's like, wait a minute,
Lex Fridman (25:25.280)
it's doing that thing.
Lex Fridman (25:26.200)
How does that work?
Lex Fridman (25:27.520)
Okay, now I can go back and understand it.
Lex Fridman (25:29.320)
But that's the brave thing about science
Lex Fridman (25:31.520)
is that in the chaos of the irreducible universe,
Stephen Wolfram (25:35.880)
we nevertheless persist to find those pockets.
Lex Fridman (25:38.600)
That's kind of the whole point.
Stephen Wolfram (25:40.240)
That's like, you say that the limits of science,
Lex Fridman (25:43.000)
but that, you know, yes, it's highly limited,
Lex Fridman (25:46.800)
but there's a hope there.
Lex Fridman (25:48.800)
And like, there's so many questions I want to ask here.
Lex Fridman (25:51.960)
So one, you said narrative, which is really interesting.
Lex Fridman (25:54.160)
So obviously from a, at every level of society,
Stephen Wolfram (25:58.040)
you look at Twitter, everybody's constructing narratives
Lex Fridman (26:00.400)
about the pandemic, about not just the pandemic,
Lex Fridman (26:03.120)
but all the cultural tension that we're going through.
Lex Fridman (26:06.000)
So there's narratives,
Lex Fridman (26:07.000)
but they're not necessarily connected
Lex Fridman (26:10.200)
to the underlying reality of these systems.
Lex Fridman (26:17.400)
So our human narratives, I don't even know if they're,
Lex Fridman (26:22.440)
I don't like those pockets of reducibility
Stephen Wolfram (26:25.360)
because we're, it's like constructing things
Lex Fridman (26:29.480)
that are not actually representative of reality,
Lex Fridman (26:33.360)
and thereby not giving us like good solutions
Lex Fridman (26:36.360)
to how to predict the system.
Stephen Wolfram (26:39.520)
Look, it gets complicated because, you know,
Lex Fridman (26:41.120)
people want to say, explain the pandemic to me,
Stephen Wolfram (26:43.840)
explain what's going to happen.
Lex Fridman (26:45.320)
In the future.
Lex Fridman (26:46.360)
Yes, but also, can you explain it?
Lex Fridman (26:48.200)
Is there a story to tell?
Lex Fridman (26:49.520)
What already happened in the past?
Lex Fridman (26:51.440)
Yeah, or what's going to happen,
Lex Fridman (26:53.040)
but I mean, you know, it's similar to sort of
Lex Fridman (26:55.280)
explaining things in AI or in any computational system.
Stephen Wolfram (26:58.560)
It's like, you know, explain what happened.
Lex Fridman (27:00.960)
Well, it could just be this happened
Stephen Wolfram (27:03.000)
because of this detail and this detail and this detail,
Lex Fridman (27:05.240)
and a million details,
Lex Fridman (27:06.880)
and there isn't a big story to tell.
Lex Fridman (27:08.600)
There's no kind of big arc of the story that says,
Stephen Wolfram (27:12.000)
oh, it's because, you know, there's a viral field
Lex Fridman (27:14.480)
that has these properties
Lex Fridman (27:15.640)
and people start showing symptoms.
Lex Fridman (27:17.680)
You know, when the seasons change,
Stephen Wolfram (27:20.040)
people will show symptoms
Lex Fridman (27:21.000)
and people don't even understand, you know,
Stephen Wolfram (27:22.480)
seasonal variation of flu, for example.
Lex Fridman (27:24.640)
It's something where, you know,
Stephen Wolfram (27:28.480)
there could be a big story,
Lex Fridman (27:29.920)
or it could be just a zillion little details that mount up.
Stephen Wolfram (27:33.800)
See, but, okay, let's pretend that this pandemic,
Lex Fridman (27:38.200)
like the coronavirus, resembles something
Lex Fridman (27:41.080)
like the 1D rule 30 cellular automata, okay?
Lex Fridman (27:45.840)
So, I mean, that's how epidemiologists model virus spread.
Stephen Wolfram (27:51.880)
Indeed, yes.
Lex Fridman (27:52.720)
They sometimes use cellular automata, yes.
Stephen Wolfram (27:54.320)
Yeah, and okay, so you could say it's simplistic,
Lex Fridman (27:57.280)
but okay, let's say it's representative
Stephen Wolfram (28:00.520)
of actually what happens.
Lex Fridman (28:02.320)
You know, the dynamic of,
Stephen Wolfram (28:06.240)
you have a graph,
Lex Fridman (28:07.480)
it probably is closer to the hypergraph model.
Stephen Wolfram (28:09.760)
It is, yes.
Lex Fridman (28:10.600)
It's actually, that's another funny thing.
Stephen Wolfram (28:13.280)
As we were getting ready to release this physics project,
Lex Fridman (28:15.320)
we realized that a bunch of things we'd worked out
Stephen Wolfram (28:17.200)
about foliations of causal graphs and things
Lex Fridman (28:20.680)
were directly relevant to thinking about contact tracing.
Stephen Wolfram (28:23.520)
Yeah, exactly.
Lex Fridman (28:24.360)
And interactions with cell phones and so on,
Stephen Wolfram (28:25.920)
which is really weird.
Lex Fridman (28:27.200)
But like, it just feels like,
Stephen Wolfram (28:29.680)
it feels like we should be able to get
Lex Fridman (28:31.000)
some beautiful core insight about the spread
Stephen Wolfram (28:34.960)
of this particular virus
Lex Fridman (28:36.720)
on the hypergraph of human civilization, right?
Stephen Wolfram (28:40.040)
I tried, I didn't manage to figure it out.
Lex Fridman (28:42.360)
But you're one person.
Stephen Wolfram (28:43.520)
Yeah, but I mean, I think actually it's a funny thing
Lex Fridman (28:46.240)
because it turns out the main model,
Stephen Wolfram (28:48.360)
you know, this SIR model,
Lex Fridman (28:49.960)
I only realized recently was invented by the grandfather
Stephen Wolfram (28:53.280)
of a good friend of mine from high school.
Lex Fridman (28:55.160)
So that was just a, you know, it's a weird thing, right?
Stephen Wolfram (28:58.800)
The question is, you know, okay, so you know,
Lex Fridman (29:02.240)
on this graph of how humans are connected,
Stephen Wolfram (29:04.400)
you know something about what happens
Lex Fridman (29:05.880)
if this happens and that happens.
Stephen Wolfram (29:07.520)
That graph is made in complicated ways
Lex Fridman (29:09.680)
that depends on all sorts of issues
Stephen Wolfram (29:11.480)
that where we don't have the data
Lex Fridman (29:13.120)
about how human society works well enough
Stephen Wolfram (29:15.200)
to be able to make that graph.
Lex Fridman (29:17.160)
There's actually, one of my kids did a study
Stephen Wolfram (29:20.480)
of sort of what happens on different kinds of graphs
Lex Fridman (29:23.320)
and how robust are the results, okay?
Stephen Wolfram (29:25.720)
His basic answer is there are a few general results
Lex Fridman (29:28.760)
that you can get that are quite robust.
Stephen Wolfram (29:30.720)
Like, you know, a small number of big gatherings
Lex Fridman (29:33.080)
is worse than a large number of small gatherings, okay?
Stephen Wolfram (29:36.280)
That's quite robust.
Lex Fridman (29:37.680)
But when you ask more detailed questions,
Stephen Wolfram (29:40.120)
it seemed like it just depends.
Lex Fridman (29:42.960)
It depends on details.
Stephen Wolfram (29:44.200)
In other words, it's kind of telling you in that case,
Lex Fridman (29:47.240)
you know, the irreducibility matters, so to speak.
Stephen Wolfram (29:49.760)
It's not, there's not gonna be this kind of one
Lex Fridman (29:53.040)
sort of master theorem that says,
Lex Fridman (29:55.040)
and therefore this is how things are gonna work.
Lex Fridman (29:57.520)
Yeah, but there's a certain kind of,
Stephen Wolfram (29:59.040)
from a graph perspective,
Lex Fridman (2:00:01.800)
So long as they have causal invariance
Lex Fridman (2:00:03.360)
and computational irreducibility,
Lex Fridman (2:00:05.440)
and they lead to finite dimensional space,
Stephen Wolfram (2:00:09.360)
noninfinite dimensional space.
Lex Fridman (2:00:11.600)
Noninfinite dimensional.
Stephen Wolfram (2:00:13.600)
It can grow infinitely,
Lex Fridman (2:00:14.760)
but it can't be infinite dimensional.
Lex Fridman (2:00:16.560)
So what is a infinitely dimensional hypergraph look like?
Lex Fridman (2:00:19.840)
So that means, for example, so in a tree,
Stephen Wolfram (2:00:22.600)
you start from one root of the tree,
Lex Fridman (2:00:25.400)
it doubles, doubles again, doubles again, doubles again.
Lex Fridman (2:00:28.360)
And that means if you ask the question,
Lex Fridman (2:00:30.720)
starting from a given point,
Lex Fridman (2:00:32.360)
how many points do you get to?
Lex Fridman (2:00:34.160)
Remember, in like a circle,
Stephen Wolfram (2:00:35.360)
you get to R squared, the two there.
Lex Fridman (2:00:37.840)
On a tree, you get to, for example, two to the R.
Stephen Wolfram (2:00:41.240)
It's exponential dimensional, so to speak,
Lex Fridman (2:00:43.320)
or infinite dimensional.
Lex Fridman (2:00:44.360)
Do you have a sense of, in the space of all possible rules,
Lex Fridman (2:00:48.480)
how many lead to infinitely dimensional hypergraphs?
Stephen Wolfram (2:00:53.720)
Is that? No.
Lex Fridman (2:00:55.280)
Okay.
Lex Fridman (2:00:56.120)
Is that an important thing to know?
Lex Fridman (2:00:57.920)
Yes, it's an important thing to know.
Stephen Wolfram (2:00:59.520)
I would love to know the answer to that.
Lex Fridman (2:01:01.560)
But it gets a little bit more complicated
Stephen Wolfram (2:01:03.520)
because, for example, it's very possibly the case
Lex Fridman (2:01:05.720)
that in our physical universe,
Stephen Wolfram (2:01:07.440)
that the universe started infinite dimensional.
Lex Fridman (2:01:10.000)
And it only, as the Big Bang,
Stephen Wolfram (2:01:13.800)
it was very likely infinite dimensional.
Lex Fridman (2:01:16.080)
And as the universe sort of expanded and cooled,
Stephen Wolfram (2:01:21.280)
its dimension gradually went down.
Lex Fridman (2:01:23.720)
And so one of the bizarre possibilities,
Stephen Wolfram (2:01:25.400)
which actually there are experiments you can do
Lex Fridman (2:01:27.120)
to try and look at this,
Stephen Wolfram (2:01:28.520)
the universe can have dimension fluctuations.
Lex Fridman (2:01:31.000)
So in other words,
Stephen Wolfram (2:01:31.840)
we think we live in a three dimensional universe,
Lex Fridman (2:01:33.400)
but actually there may be places
Stephen Wolfram (2:01:35.600)
where it's actually 3.01 dimensional,
Lex Fridman (2:01:37.920)
or where it's 2.99 dimensional.
Lex Fridman (2:01:40.520)
And it may be that in the very early universe,
Lex Fridman (2:01:43.320)
it was actually infinite dimensional,
Lex Fridman (2:01:45.200)
and it's only a late stage phenomenon
Lex Fridman (2:01:47.200)
that we end up getting three dimensional space.
Lex Fridman (2:01:49.240)
But from your perspective of the hypergraph,
Lex Fridman (2:01:51.920)
one of the underlying assumptions you kind of implied,
Lex Fridman (2:01:55.240)
but you have a sense, a hope set of assumptions
Lex Fridman (2:01:59.640)
that the rules that underlie our universe,
Stephen Wolfram (2:02:03.120)
or the rule that underlies our universe is static.
Lex Fridman (2:02:08.200)
Is that one of the assumptions
Lex Fridman (2:02:10.160)
you're currently operating under?
Lex Fridman (2:02:11.840)
Yes, but there's a footnote to that,
Stephen Wolfram (2:02:14.840)
which we should get to,
Lex Fridman (2:02:15.680)
because it requires a few more steps.
Stephen Wolfram (2:02:17.560)
Well, actually then, let's backtrack to the curvature,
Lex Fridman (2:02:19.920)
because we're talking about as long as it's finite dimensional.
Stephen Wolfram (2:02:25.320)
Finite dimensional computational irreducibility
Lex Fridman (2:02:28.000)
and causal invariance,
Stephen Wolfram (2:02:29.680)
then it follows that the large scale structure
Lex Fridman (2:02:35.800)
will follow Einstein's equations.
Lex Fridman (2:02:37.880)
And now let me again, qualify that a little bit more,
Lex Fridman (2:02:40.720)
there's a little bit more complexity to it.
Stephen Wolfram (2:02:43.120)
The, okay, so Einstein's equations in their simplest form
Lex Fridman (2:02:48.120)
apply to the vacuum, no matter, just the vacuum.
Lex Fridman (2:02:51.720)
And they say, in particular, what they say is,
Lex Fridman (2:02:54.200)
if you have, so there's this term GD6,
Stephen Wolfram (2:02:58.520)
that's a term that means shortest path,
Lex Fridman (2:03:00.920)
comes from measuring the shortest paths on the Earth.
Lex Fridman (2:03:03.680)
So you look at a bunch of, a bundle of GD6,
Lex Fridman (2:03:07.600)
a bunch of shortest paths,
Stephen Wolfram (2:03:09.520)
it's like the paths that photons
Lex Fridman (2:03:11.040)
would take between two points.
Stephen Wolfram (2:03:13.040)
Then the statement of Einstein's equations,
Lex Fridman (2:03:14.960)
it's basically a statement about a certain the,
Stephen Wolfram (2:03:18.040)
that as you look at a bundle of GD6,
Lex Fridman (2:03:20.360)
the structure of space has to be such that,
Stephen Wolfram (2:03:22.920)
although the cross sectional area of this bundle may,
Lex Fridman (2:03:27.800)
although the actual shape of the cross section may change,
Stephen Wolfram (2:03:30.000)
the cross sectional area does not.
Lex Fridman (2:03:31.800)
That's a version, that's the most simple minded version
Stephen Wolfram (2:03:35.280)
of R mu nu minus a half R G mu nu equals zero,
Lex Fridman (2:03:38.960)
which is the more mathematical version
Stephen Wolfram (2:03:41.040)
of Einstein's equations.
Lex Fridman (2:03:42.440)
It's a statement of the thing called the Ritchie tensor
Stephen Wolfram (2:03:45.360)
is equal to zero.
Lex Fridman (2:03:46.840)
That's Einstein's equations for the vacuum.
Stephen Wolfram (2:03:50.080)
Okay, so we get that as a result of this model,
Lex Fridman (2:03:54.400)
but footnote, big footnote,
Stephen Wolfram (2:03:57.840)
because all the matter in the universe
Lex Fridman (2:04:00.280)
is the stuff we actually care about.
Stephen Wolfram (2:04:01.680)
The vacuum is not stuff we care about.
Lex Fridman (2:04:03.560)
So the question is, how does matter come into this?
Lex Fridman (2:04:06.440)
And for that, you have to understand what energy is
Lex Fridman (2:04:09.720)
in these models.
Lex Fridman (2:04:11.120)
And one of the things that we realized, you know,
Lex Fridman (2:04:15.280)
late last year was that there's a very simple interpretation
Lex Fridman (2:04:20.360)
of energy in these models, okay?
Lex Fridman (2:04:22.560)
And energy is basically, well, intuitively,
Stephen Wolfram (2:04:28.000)
it's the amount of activity in these hypergraphs
Lex Fridman (2:04:32.720)
and the way that that remains over time.
Lex Fridman (2:04:36.840)
So a little bit more formally,
Lex Fridman (2:04:38.640)
you can think about this causal graph
Stephen Wolfram (2:04:41.560)
as having these edges that represent causal relationships.
Lex Fridman (2:04:44.880)
You can think about, oh boy,
Stephen Wolfram (2:04:46.120)
there's one more concept that we didn't get to.
Lex Fridman (2:04:47.920)
It's the notion of space like hypersurfaces.
Lex Fridman (2:04:51.800)
So this is not as scary as it sounds.
Lex Fridman (2:04:55.800)
It's a common notion in general activity.
Stephen Wolfram (2:04:59.720)
The notion is you are defining what is a possibly,
Lex Fridman (2:05:04.720)
where in space time might be a particular moment in time.
Lex Fridman (2:05:13.960)
So in other words, what is a consistent set of places
Lex Fridman (2:05:18.200)
where you can say, this is happening now, so to speak.
Lex Fridman (2:05:21.760)
And you make the series of sort of slices
Lex Fridman (2:05:25.600)
through the space time, through this causal graph
Stephen Wolfram (2:05:29.200)
to represent sort of what we consider
Lex Fridman (2:05:32.000)
to be successive moments in time.
Stephen Wolfram (2:05:34.680)
It's somewhat arbitrary because you can deform that
Lex Fridman (2:05:37.720)
if you're going at a different speed in a special activity,
Stephen Wolfram (2:05:39.880)
you tip those things, there are different kinds
Lex Fridman (2:05:44.520)
of deformations, but only certain deformations
Stephen Wolfram (2:05:46.800)
are allowed by the structure of the causal graph.
Lex Fridman (2:05:48.400)
Anyway, be that as it may, the basic point is
Stephen Wolfram (2:05:52.360)
there is a way of figuring out,
Lex Fridman (2:05:54.880)
you say, what is the energy associated
Lex Fridman (2:05:57.120)
with what's going on in this hypergraph?
Lex Fridman (2:06:00.400)
And the answer is there is a precise definition of that.
Lex Fridman (2:06:04.360)
And it is the formal way to say it is,
Lex Fridman (2:06:06.840)
it's the flux of causal edges
Stephen Wolfram (2:06:08.560)
through space like hypersurfaces.
Lex Fridman (2:06:10.680)
The slightly less formal way to say it,
Stephen Wolfram (2:06:12.280)
it's basically the amount of activity.
Lex Fridman (2:06:14.480)
See, the reason it gets tricky is you might say
Stephen Wolfram (2:06:18.000)
it's the amount of activity per unit volume
Lex Fridman (2:06:21.000)
in this hypergraph, but you haven't defined what volume is.
Lex Fridman (2:06:25.280)
So it's a little bit, you have to be a little more careful.
Lex Fridman (2:06:27.520)
But this hypersurface gives some more formalism to that.
Stephen Wolfram (2:06:30.600)
Yeah, yeah, it gives a way to connect that.
Lex Fridman (2:06:32.840)
But intuitive, we should think about as the just activity.
Stephen Wolfram (2:06:36.400)
Right, so the amount of activity that kind of remains
Lex Fridman (2:06:39.640)
in one place in the hypergraph corresponds to energy.
Stephen Wolfram (2:06:42.800)
The amount of activity that is kind of where an activity here
Lex Fridman (2:06:45.800)
affects an activity somewhere else,
Stephen Wolfram (2:06:48.160)
corresponds to momentum.
Lex Fridman (2:06:50.480)
And so one of the things that's kind of cool
Stephen Wolfram (2:06:53.840)
is that I'm trying to think about
Lex Fridman (2:06:55.600)
how to say this intuitively.
Stephen Wolfram (2:06:56.680)
The mathematics is easy,
Lex Fridman (2:06:57.720)
but the intuitive version, I'm not sure.
Lex Fridman (2:06:59.800)
But basically the way that things sort of stay
Lex Fridman (2:07:01.640)
in the same place and have activity
Stephen Wolfram (2:07:03.960)
is associated with rest mass.
Lex Fridman (2:07:05.920)
And so one of the things that you get to derive
Stephen Wolfram (2:07:08.080)
is E equals MC squared.
Lex Fridman (2:07:10.800)
That is a consequence of this interpretation of energy
Stephen Wolfram (2:07:14.840)
in terms of the way the causal graph works,
Lex Fridman (2:07:18.040)
which is the whole thing is sort of a consequence
Stephen Wolfram (2:07:20.160)
of this whole story about updates and hypergraphs and so on.
Lex Fridman (2:07:23.720)
So can you linger on that a little bit?
Lex Fridman (2:07:26.280)
How do we get E equals MC squared?
Lex Fridman (2:07:28.840)
So where does the mass come from?
Stephen Wolfram (2:07:31.280)
Okay, okay.
Lex Fridman (2:07:32.240)
I mean, is there an intuitive, it's okay.
Stephen Wolfram (2:07:35.000)
First of all, you're pretty deep
Lex Fridman (2:07:37.720)
in the mathematical explorations of this thing right now.
Stephen Wolfram (2:07:41.600)
We're in a very, we're in a flux currently.
Lex Fridman (2:07:45.920)
So maybe you haven't even had time
Stephen Wolfram (2:07:47.960)
to think about intuitive explanations, but.
Lex Fridman (2:07:51.680)
Yeah, I mean, this one is, look, roughly what's happening,
Stephen Wolfram (2:07:56.320)
that derivation is actually rather easy.
Lex Fridman (2:07:58.400)
And everybody, and I've been saying
Stephen Wolfram (2:07:59.840)
we should pay more attention to this derivation
Lex Fridman (2:08:01.600)
because it's such, you know,
Stephen Wolfram (2:08:02.480)
cause people care about this one.
Lex Fridman (2:08:04.320)
But everybody says, it's just easy.
Stephen Wolfram (2:08:05.880)
It's easy.
Lex Fridman (2:08:07.200)
So there's some concept of energy
Stephen Wolfram (2:08:09.320)
that can be intuitively thought of as the activity,
Lex Fridman (2:08:12.880)
the flux, the level of changes that are occurring
Stephen Wolfram (2:08:16.760)
based on the transformations within a certain volume,
Lex Fridman (2:08:19.400)
however the heck do you find the volume.
Stephen Wolfram (2:08:21.240)
Okay, so, and then mass.
Lex Fridman (2:08:23.560)
Well, mass is associated with kind of the energy
Stephen Wolfram (2:08:28.560)
that does not cause you to,
Lex Fridman (2:08:30.440)
that does not somehow propagate through time.
Stephen Wolfram (2:08:34.000)
Yeah, I mean, one of the things that was not obvious
Lex Fridman (2:08:35.960)
in the usual formulation of special relativity
Stephen Wolfram (2:08:38.400)
is that space and time are connected in a certain way.
Lex Fridman (2:08:42.800)
Energy and momentum are also connected in a certain way.
Stephen Wolfram (2:08:46.280)
The fact that the connection of energy to momentum
Lex Fridman (2:08:49.080)
is analogous to the connection to space
Stephen Wolfram (2:08:50.800)
between space and time
Lex Fridman (2:08:52.400)
is not self evident in ordinary relativity.
Stephen Wolfram (2:08:54.920)
It is a consequence of this, of the way this model works.
Lex Fridman (2:08:58.360)
It's an intrinsic consequence of the way this model works.
Lex Fridman (2:09:00.960)
And it's all to do with that,
Lex Fridman (2:09:02.800)
with unraveling that connection
Stephen Wolfram (2:09:05.240)
that ends up giving you this relationship
Lex Fridman (2:09:07.720)
between energy and, well, it's energy, momentum, mass,
Stephen Wolfram (2:09:12.480)
they're all connected.
Lex Fridman (2:09:13.760)
And so like, that's hence the general relativity.
Stephen Wolfram (2:09:19.560)
You have a sense that it appears to be baked in
Lex Fridman (2:09:24.600)
to the fundamental properties
Stephen Wolfram (2:09:27.000)
of the way these hypergraphs are evolved.
Lex Fridman (2:09:29.320)
Well, I didn't yet get to,
Lex Fridman (2:09:30.360)
so I got as far as special relativity and equals MC squared.
Lex Fridman (2:09:33.680)
The one last step is, in general relativity,
Stephen Wolfram (2:09:37.320)
the final connection is energy and mass
Lex Fridman (2:09:41.800)
cause curvature in space.
Lex Fridman (2:09:44.440)
And that's something that when you understand
Lex Fridman (2:09:47.720)
this interpretation of energy,
Lex Fridman (2:09:49.760)
and you kind of understand the correspondence
Lex Fridman (2:09:52.080)
to curvature and hypergraphs,
Stephen Wolfram (2:09:54.000)
then you can finally sort of, the big final answer is,
Lex Fridman (2:09:57.640)
you derive the full version of Einstein's equations
Stephen Wolfram (2:10:00.440)
for space, time and matter.
Lex Fridman (2:10:03.320)
And that's some.
Stephen Wolfram (2:10:04.480)
Is that, have you, that last piece with curvature,
Lex Fridman (2:10:09.520)
have, is that, have you arrived there yet?
Stephen Wolfram (2:10:12.320)
Oh yeah, we're there, yes.
Lex Fridman (2:10:13.760)
And here's the way that we,
Stephen Wolfram (2:10:15.480)
here's how we're really, really going to know
Lex Fridman (2:10:17.200)
we've arrived, okay?
Stephen Wolfram (2:10:18.480)
So, you know, we have the mathematical derivation,
Lex Fridman (2:10:20.720)
it's all fine, but, you know,
Stephen Wolfram (2:10:22.720)
mathematical derivations, okay.
Lex Fridman (2:10:25.000)
So one thing that's sort of a,
Stephen Wolfram (2:10:27.720)
you know, we're taking this limit
Lex Fridman (2:10:29.240)
of what happens when you, the limit,
Stephen Wolfram (2:10:31.160)
you have to look at things which are large
Lex Fridman (2:10:32.920)
compared to the size of an elementary length,
Stephen Wolfram (2:10:35.240)
small compared to the whole size of the universe,
Lex Fridman (2:10:37.440)
large compared to certain kinds of fluctuations,
Stephen Wolfram (2:10:40.480)
blah, blah, blah.
Lex Fridman (2:10:41.600)
There's a, there's a, there's a tower
Stephen Wolfram (2:10:43.360)
of many, many of these mathematical limits
Lex Fridman (2:10:45.160)
that have to be taken.
Lex Fridman (2:10:46.440)
So if you're a pure mathematician saying,
Lex Fridman (2:10:48.720)
where's the precise proof?
Stephen Wolfram (2:10:50.520)
It's like, well, there are all these limits,
Lex Fridman (2:10:52.480)
we can, you know, we can try each one of them
Stephen Wolfram (2:10:54.880)
computationally and we could say, yeah, it really works,
Lex Fridman (2:10:57.520)
but the formal mathematics is really hard to do.
Stephen Wolfram (2:11:00.560)
I mean, for example, in the case of deriving
Lex Fridman (2:11:03.120)
the equations of fluid dynamics from molecular dynamics,
Stephen Wolfram (2:11:06.200)
that derivation has never been done.
Lex Fridman (2:11:09.000)
There is no rigorous version of that derivation.
Stephen Wolfram (2:11:11.360)
So, so that could be.
Lex Fridman (2:11:12.200)
Because you can't do the limits?
Stephen Wolfram (2:11:13.760)
Yeah, because you can't do the limits.
Lex Fridman (2:11:15.920)
But so the limits allow you to try to describe
Stephen Wolfram (2:11:18.320)
something general about the system
Lex Fridman (2:11:20.280)
and very, very particular kinds of limits that you need
Stephen Wolfram (2:11:22.520)
to take with these very.
Lex Fridman (2:11:23.640)
Right, and the limits will definitely work
Stephen Wolfram (2:11:26.000)
the way we think they work.
Lex Fridman (2:11:27.200)
And we can do all kinds of computer experiments.
Stephen Wolfram (2:11:28.760)
It's just a hard derivation.
Lex Fridman (2:11:29.760)
Yeah, it's just, it's just the mathematical structure
Stephen Wolfram (2:11:32.760)
kind of, you know, ends up running right into
Lex Fridman (2:11:35.240)
computational irreducibility.
Lex Fridman (2:11:37.080)
And you end up with a bunch of, a bunch of difficulty there.
Lex Fridman (2:11:39.560)
But here's the way that we're getting really confident
Stephen Wolfram (2:11:42.320)
that we know completely what we're talking about,
Lex Fridman (2:11:43.960)
which is when people study things like black hole mergers,
Lex Fridman (2:11:47.880)
using Einstein's equations, what do they actually do?
Lex Fridman (2:11:51.000)
Well, they actually use Mathematica or a whole bunch
Stephen Wolfram (2:11:52.800)
to analyze the equations and so on.
Lex Fridman (2:11:54.440)
But in the end, they do numerical relativity,
Stephen Wolfram (2:11:57.360)
which means they take these nice mathematical equations
Lex Fridman (2:12:01.440)
and they break them down so that they can run them
Stephen Wolfram (2:12:03.280)
on a computer.
Lex Fridman (2:12:04.360)
And they break them down into something
Stephen Wolfram (2:12:05.920)
which is actually a discrete approximation
Lex Fridman (2:12:07.680)
to these equations.
Stephen Wolfram (2:12:08.920)
Then they run them on a computer, they get results.
Lex Fridman (2:12:11.560)
Then you look at the gravitational waves
Lex Fridman (2:12:12.880)
and you see if they match, okay?
Lex Fridman (2:12:14.840)
It turns out that our model gives you a direct way
Stephen Wolfram (2:12:18.240)
to do numerical relativity.
Lex Fridman (2:12:19.800)
So in other words, instead of saying,
Stephen Wolfram (2:12:21.120)
you start from these continuum equations from Einstein,
Lex Fridman (2:12:23.960)
you break them down into these discrete things,
Stephen Wolfram (2:12:26.280)
you run them on a computer,
Lex Fridman (2:12:27.600)
you say, we're doing it the other way around.
Stephen Wolfram (2:12:28.920)
We're starting from these discrete things
Lex Fridman (2:12:30.680)
that come from our model.
Lex Fridman (2:12:31.880)
And we're just running big versions on the computer.
Lex Fridman (2:12:34.520)
And, you know, what we're saying is,
Lex Fridman (2:12:37.080)
and this is how things will work.
Lex Fridman (2:12:39.560)
So the way I'm calling this is proof by compilation,
Lex Fridman (2:12:43.760)
so to speak, that is, in other words,
Lex Fridman (2:12:46.480)
you're taking something where, you know,
Stephen Wolfram (2:12:49.320)
we've got this description of a black hole system.
Lex Fridman (2:12:52.320)
And what we're doing is we're showing that the, you know,
Lex Fridman (2:12:56.120)
what we get by just running our model agrees
Lex Fridman (2:12:59.320)
with what you would get by doing the computation
Stephen Wolfram (2:13:02.720)
from the Einstein equations.
Lex Fridman (2:13:04.320)
As a small tangent or actually a very big tangent,
Lex Fridman (2:13:08.360)
but proof by compilation is a beautiful concept.
Lex Fridman (2:13:15.200)
In a sense, the way of doing physics with this model
Stephen Wolfram (2:13:21.400)
is by running it or compiling it.
Lex Fridman (2:13:26.040)
And have you thought about,
Lex Fridman (2:13:29.800)
and these things can be very large,
Lex Fridman (2:13:32.000)
is there a totally new possibilities of computing hardware
Lex Fridman (2:13:37.000)
and computing software,
Lex Fridman (2:13:38.960)
which allows you to perform this kind of compilation?
Stephen Wolfram (2:13:42.200)
Well, algorithms, software, hardware.
Lex Fridman (2:13:44.920)
So first comment is these models seem to give one
Stephen Wolfram (2:13:49.440)
a lot of intuition about distributed computing,
Lex Fridman (2:13:52.480)
a lot of different intuition about how to think
Stephen Wolfram (2:13:54.680)
about parallel computation.
Lex Fridman (2:13:56.640)
And that particularly comes from the quantum mechanics
Stephen Wolfram (2:13:58.960)
side of things, which we didn't talk about much yet.
Lex Fridman (2:14:01.880)
But the question of what, you know,
Stephen Wolfram (2:14:04.720)
given our current computer hardware,
Lex Fridman (2:14:07.760)
how can we most efficiently simulate things?
Stephen Wolfram (2:14:10.120)
That's actually partly a story of the model itself,
Lex Fridman (2:14:12.920)
because the model itself has deep parallelism in it.
Stephen Wolfram (2:14:16.160)
The ways that we are simulating it,
Lex Fridman (2:14:17.760)
we're just starting to be able to use that deep parallelism
Stephen Wolfram (2:14:21.080)
to be able to be more efficient
Lex Fridman (2:14:22.600)
in the way that we simulate things.
Lex Fridman (2:14:24.400)
But in fact, the structure of the model itself
Lex Fridman (2:14:27.880)
allows us to think about parallel computation
Stephen Wolfram (2:14:30.280)
in different ways.
Lex Fridman (2:14:31.520)
And one of my realizations is that, you know,
Lex Fridman (2:14:34.600)
so it's very hard to get in your brain
Lex Fridman (2:14:37.000)
how you deal with parallel computation.
Lex Fridman (2:14:38.520)
And you're always worrying about, you know,
Lex Fridman (2:14:40.240)
if multiple things can happen on different computers
Stephen Wolfram (2:14:42.720)
at different times, oh, what happens
Lex Fridman (2:14:44.640)
if this thing happens before that thing?
Lex Fridman (2:14:46.440)
And we've really got, you know,
Lex Fridman (2:14:47.520)
we have these race conditions where something can race
Stephen Wolfram (2:14:49.720)
to get to the answer before another thing.
Lex Fridman (2:14:51.800)
And you get all tangled up because you don't know
Stephen Wolfram (2:14:54.040)
which thing is gonna come in first.
Lex Fridman (2:14:55.960)
And usually when you do parallel computing,
Stephen Wolfram (2:14:58.320)
there's a big obsession to lock things down
Lex Fridman (2:15:00.480)
to the point where you've had locks and mutexes
Lex Fridman (2:15:03.920)
and God knows what else,
Lex Fridman (2:15:05.240)
where you've arranged it so that there can only be
Stephen Wolfram (2:15:09.600)
one sequence of things that can happen.
Lex Fridman (2:15:11.560)
So you don't have to think about
Stephen Wolfram (2:15:12.640)
all the different kinds of things that can happen.
Lex Fridman (2:15:14.760)
Well, in these models, physics is throwing us into,
Stephen Wolfram (2:15:18.200)
forcing us to think about all these possible things
Lex Fridman (2:15:20.240)
that can happen.
Lex Fridman (2:15:21.240)
But these models together with what we know from physics
Lex Fridman (2:15:24.640)
is giving us new ways to think about
Stephen Wolfram (2:15:26.520)
all possible things happening,
Lex Fridman (2:15:28.560)
about all these different things happening in parallel.
Lex Fridman (2:15:30.680)
And so I'm guessing...
Lex Fridman (2:15:31.680)
They have built in protection for some of the parallelism.
Stephen Wolfram (2:15:34.640)
Well, causal invariance is the built in protection.
Lex Fridman (2:15:37.280)
Causal invariance is what means that
Stephen Wolfram (2:15:39.720)
even though things happen in different orders,
Lex Fridman (2:15:41.680)
it doesn't matter in the end.
Stephen Wolfram (2:15:43.440)
As a person who struggled with concurrent programming
Lex Fridman (2:15:46.520)
in like Java,
Stephen Wolfram (2:15:50.240)
with all the basic concepts of concurrent programming,
Lex Fridman (2:15:53.760)
that if there could be built up
Stephen Wolfram (2:15:55.760)
a strong mathematical framework for causal invariance,
Lex Fridman (2:16:00.080)
that's so liberating.
Lex Fridman (2:16:01.760)
And that could be not just liberating,
Lex Fridman (2:16:03.680)
but really powerful for massively distributed computation.
Stephen Wolfram (2:16:08.320)
Absolutely.
Lex Fridman (2:16:09.160)
No, I mean, what's eventual consistency
Stephen Wolfram (2:16:11.800)
in distributed databases
Lex Fridman (2:16:14.000)
is essentially the causal invariance idea.
Stephen Wolfram (2:16:16.160)
Yeah. Okay.
Lex Fridman (2:16:17.000)
So that's...
Lex Fridman (2:16:17.840)
But have you thought about,
Lex Fridman (2:16:22.160)
like really large simulations?
Stephen Wolfram (2:16:26.000)
Yeah. I mean, I'm also thinking about,
Lex Fridman (2:16:28.080)
look, the fact is I've spent much of my life
Lex Fridman (2:16:30.400)
as a language designer, right?
Lex Fridman (2:16:31.640)
So I can't possibly not think about,
Lex Fridman (2:16:34.360)
what does this mean for designing languages
Lex Fridman (2:16:37.240)
for parallel computation?
Stephen Wolfram (2:16:38.320)
In fact, another thing that's one of these...
Lex Fridman (2:16:41.640)
I'm always embarrassed at how long it's taken me
Stephen Wolfram (2:16:44.400)
to figure stuff out.
Lex Fridman (2:16:45.680)
But back in the 1980s,
Stephen Wolfram (2:16:47.360)
I worked on trying to make up languages
Lex Fridman (2:16:49.600)
for parallel computation.
Stephen Wolfram (2:16:50.960)
I thought about doing graph rewriting.
Lex Fridman (2:16:53.080)
I thought about doing these kinds of things,
Lex Fridman (2:16:54.440)
but I couldn't see how to actually make the connections
Lex Fridman (2:16:57.160)
to actually do something useful.
Stephen Wolfram (2:16:59.320)
I think now physics is kind of showing us
Lex Fridman (2:17:02.520)
how to make those things useful.
Lex Fridman (2:17:04.200)
And so my guess is that in time,
Lex Fridman (2:17:06.320)
we'll be talking about, we do parallel programming.
Stephen Wolfram (2:17:09.000)
We'll be talking about programming
Lex Fridman (2:17:10.360)
in a certain reference frame,
Stephen Wolfram (2:17:12.080)
just as we think about thinking about physics
Lex Fridman (2:17:14.120)
in a certain reference frame.
Stephen Wolfram (2:17:15.080)
It's a certain coordination of what's going on.
Lex Fridman (2:17:17.640)
We say, we're gonna program in this reference frame.
Stephen Wolfram (2:17:19.960)
Oh, let's change the reference frame
Lex Fridman (2:17:21.280)
to this reference frame.
Lex Fridman (2:17:22.680)
And then our program will seem different
Lex Fridman (2:17:25.240)
and we'll have a different way to think about it.
Lex Fridman (2:17:27.120)
But it's still the same program underneath.
Lex Fridman (2:17:28.960)
So let me ask on this topic,
Stephen Wolfram (2:17:30.760)
cause I put out that I'm talking to you.
Lex Fridman (2:17:32.360)
I got way more questions than I can deal with,
Lex Fridman (2:17:34.560)
but what pops to mind is a question somebody asked
Lex Fridman (2:17:37.520)
on Reddit I think is, please ask Dr. Wolfram,
Lex Fridman (2:17:42.560)
what are the specs of the computer running the universe?
Lex Fridman (2:17:46.200)
So we're talking about specs of hardware and software
Stephen Wolfram (2:17:51.480)
for simulations of a large scale thing.
Lex Fridman (2:17:54.080)
What about a scale that is comparative
Stephen Wolfram (2:17:57.520)
to something that eventually leads
Lex Fridman (2:17:59.720)
to the two of us talking and about?
Stephen Wolfram (2:18:01.560)
Right, right, right.
Lex Fridman (2:18:02.400)
So actually I did try to estimate that.
Lex Fridman (2:18:05.080)
And we actually have to go a couple more stages
Lex Fridman (2:18:07.280)
before we can really get to that answer
Stephen Wolfram (2:18:08.680)
because we're talking about this thing.
Lex Fridman (2:18:14.200)
This is what happens when you build these abstract systems
Lex Fridman (2:18:16.920)
and you're trying to explain the universe,
Lex Fridman (2:18:19.560)
they're quite a number of levels deep, so to speak.
Lex Fridman (2:18:23.640)
But the...
Lex Fridman (2:18:25.520)
You mean conceptually or like literally?
Stephen Wolfram (2:18:27.280)
Cause you're talking about small objects
Lex Fridman (2:18:28.800)
and there's 10 to the 120 something.
Stephen Wolfram (2:18:31.600)
Yeah, right.
Lex Fridman (2:18:33.840)
It is conceptually deep.
Lex Fridman (2:18:35.120)
And one of the things that's happening sort of structurally
Lex Fridman (2:18:37.920)
in this project is, you know, there were ideas,
Stephen Wolfram (2:18:40.600)
there's another layer of ideas,
Lex Fridman (2:18:41.760)
there's another layer of ideas
Stephen Wolfram (2:18:43.240)
to get to the different things that correspond to physics.
Lex Fridman (2:18:46.960)
They're just different layers of ideas.
Lex Fridman (2:18:49.280)
And they are, you know, it's actually probably,
Lex Fridman (2:18:52.360)
if anything, getting harder to explain this project
Stephen Wolfram (2:18:54.480)
cause I'm realizing that the fraction of way through
Lex Fridman (2:18:56.520)
that I am so far and explaining this to you is less than,
Stephen Wolfram (2:18:59.760)
than, you know, it might be because we know more now,
Lex Fridman (2:19:02.840)
you know, every week basically we know a little bit more.
Lex Fridman (2:19:06.200)
And like...
Lex Fridman (2:19:07.040)
Those are just layers on the initial fundamental structure.
Stephen Wolfram (2:19:10.480)
Yes, but the layers are, you know,
Lex Fridman (2:19:12.640)
you might be asking me, you know,
Lex Fridman (2:19:14.320)
how do we get the difference between fermions and bosons,
Lex Fridman (2:19:18.680)
the difference between particles
Stephen Wolfram (2:19:19.880)
that can be all in the same state
Lex Fridman (2:19:21.760)
and particles that exclude each other, okay.
Stephen Wolfram (2:19:24.080)
Last three days, we've kind of figured that out.
Lex Fridman (2:19:26.600)
Okay.
Stephen Wolfram (2:19:27.440)
But, and it's very interesting.
Lex Fridman (2:19:29.440)
It's very cool.
Lex Fridman (2:19:31.080)
And it's very...
Lex Fridman (2:19:32.040)
And those are some kind of properties at a certain level,
Stephen Wolfram (2:19:35.800)
layer of abstraction on the graph.
Lex Fridman (2:19:37.880)
Yes, yes.
Lex Fridman (2:19:38.720)
And there's, but the layers of abstraction are kind of,
Lex Fridman (2:19:41.640)
they're compounding.
Stephen Wolfram (2:19:42.760)
Stacking up.
Lex Fridman (2:19:43.600)
So it's difficult, but...
Lex Fridman (2:19:45.320)
But okay.
Lex Fridman (2:19:46.160)
But the specs nevertheless remain the same.
Stephen Wolfram (2:19:47.920)
Okay, the specs underneath.
Lex Fridman (2:19:49.560)
So I have an estimate.
Lex Fridman (2:19:50.960)
So the question is, what are the units?
Lex Fridman (2:19:52.440)
So we've got these different fundamental constants
Stephen Wolfram (2:19:54.840)
about the world.
Lex Fridman (2:19:56.160)
So one of them is the speed of light, which is the...
Lex Fridman (2:19:58.520)
So the thing that's always the same
Lex Fridman (2:20:00.200)
in all these different ways of thinking about the universe
Stephen Wolfram (2:20:02.720)
is the notion of time, because time is computation.
Lex Fridman (2:20:06.200)
And so there's an elementary time,
Stephen Wolfram (2:20:08.080)
which is sort of the amount of time that we ascribe
Lex Fridman (2:20:12.240)
to elapsing in a single computational step.
Stephen Wolfram (2:20:16.160)
Yeah.
Lex Fridman (2:20:17.000)
Okay.
Lex Fridman (2:20:17.840)
So that's the elementary time.
Lex Fridman (2:20:18.680)
So then there's an elementary...
Stephen Wolfram (2:20:19.520)
That's a parameter or whatever.
Lex Fridman (2:20:20.440)
That's a constant.
Stephen Wolfram (2:20:21.880)
It's whatever we define it to be,
Lex Fridman (2:20:23.360)
because I mean, we don't, you know...
Lex Fridman (2:20:25.360)
I mean, it's all relative, right?
Lex Fridman (2:20:26.840)
It doesn't matter.
Stephen Wolfram (2:20:27.680)
Yes, it doesn't matter what it is,
Lex Fridman (2:20:28.520)
because we could be, it could be slower.
Stephen Wolfram (2:20:30.360)
It's just a number which we use to convert that
Lex Fridman (2:20:33.840)
to seconds, so to speak,
Stephen Wolfram (2:20:35.000)
because we are experiencing things
Lex Fridman (2:20:37.160)
and we say this amount of time has elapsed, so to speak.
Lex Fridman (2:20:39.880)
But we're within this thing.
Lex Fridman (2:20:41.400)
Absolutely.
Lex Fridman (2:20:42.240)
So it doesn't matter, right?
Lex Fridman (2:20:43.680)
But what does matter is the ratio,
Lex Fridman (2:20:46.000)
what we can, the ratio of the spatial distance
Lex Fridman (2:20:49.520)
and this hypergraph to this moment of time.
Stephen Wolfram (2:20:54.320)
Again, that's an arbitrary thing,
Lex Fridman (2:20:55.800)
but we measure that in meters per second, for example,
Lex Fridman (2:20:58.720)
and that ratio is the speed of light.
Lex Fridman (2:21:00.880)
So the ratio of the elementary distance
Lex Fridman (2:21:03.160)
to the elementary time is the speed of light, okay?
Lex Fridman (2:21:06.640)
Perfect.
Lex Fridman (2:21:07.480)
And so there's another,
Lex Fridman (2:21:08.320)
there are two other levels of this, okay?
Lex Fridman (2:21:11.360)
So there is a thing which we can talk about,
Lex Fridman (2:21:13.880)
which is the maximum entanglement speed,
Stephen Wolfram (2:21:16.520)
which is a thing that happens at another level
Lex Fridman (2:21:19.320)
in this whole sort of story
Stephen Wolfram (2:21:20.680)
of how these things get constructed.
Lex Fridman (2:21:22.840)
That's a sort of maximum speed in quantum,
Stephen Wolfram (2:21:24.840)
in the space of quantum states.
Lex Fridman (2:21:26.920)
Just as the speed of light
Stephen Wolfram (2:21:28.040)
is a maximum speed in physical space,
Lex Fridman (2:21:30.200)
this is a maximum speed in the space of quantum states.
Stephen Wolfram (2:21:32.680)
There's another level which is associated
Lex Fridman (2:21:35.000)
with what we call ruleal space,
Stephen Wolfram (2:21:36.600)
which is another one of these maximum speeds.
Lex Fridman (2:21:39.120)
We'll get to this.
Lex Fridman (2:21:40.360)
So these are limitations on the system
Lex Fridman (2:21:42.120)
that are able to capture the kind of physical universe
Stephen Wolfram (2:21:45.280)
which we live in.
Lex Fridman (2:21:46.280)
The quantum mechanical.
Stephen Wolfram (2:21:47.120)
There are inevitable features of having a rule
Lex Fridman (2:21:51.800)
that has only a finite amount of information in the rule.
Lex Fridman (2:21:54.600)
So long as you have a rule that only involves
Lex Fridman (2:21:57.280)
a bounded amount, a limited amount of,
Stephen Wolfram (2:22:01.560)
only involving a limited number of elements,
Lex Fridman (2:22:03.280)
limited number of relations,
Stephen Wolfram (2:22:04.760)
it is inevitable that there are these speed constraints.
Lex Fridman (2:22:07.320)
We knew about the one for speed of light.
Stephen Wolfram (2:22:08.800)
We didn't know about the one for maximum entanglement speed,
Lex Fridman (2:22:11.440)
which is actually something that is possibly measurable,
Stephen Wolfram (2:22:14.040)
particularly in black hole systems and things like this.
Lex Fridman (2:22:17.000)
Anyway, this is long, long story short.
Stephen Wolfram (2:22:19.600)
You're asking what the processing specs of the universe,
Lex Fridman (2:22:23.120)
of the sort of computation of the universe.
Stephen Wolfram (2:22:25.120)
There's a question of even what are the units
Lex Fridman (2:22:27.400)
of some of these measurements, okay?
Lex Fridman (2:22:29.000)
So the units I'm using are Wolfram language instructions
Lex Fridman (2:22:31.960)
per second, okay?
Stephen Wolfram (2:22:33.280)
Because you gotta have some,
Lex Fridman (2:22:34.840)
what computation are you doing?
Stephen Wolfram (2:22:37.000)
There gotta be some kind of frame of reference.
Lex Fridman (2:22:38.360)
Right, right.
Stephen Wolfram (2:22:39.200)
So, because it turns out in the end,
Lex Fridman (2:22:41.800)
there will be, there's sort of an arbitrariness
Stephen Wolfram (2:22:44.240)
in the language that you use to describe the universe.
Lex Fridman (2:22:46.960)
So in those terms, I think it's like 10 to the 500,
Stephen Wolfram (2:22:51.600)
Wolfram language operations per second, I think,
Lex Fridman (2:22:54.320)
is the, I think it's of that order.
Stephen Wolfram (2:22:56.480)
You know, basically.
Lex Fridman (2:22:57.320)
So that's the scale of the computation.
Lex Fridman (2:22:58.760)
What about memory?
Lex Fridman (2:22:59.920)
If there's an interesting thing to say
Stephen Wolfram (2:23:01.360)
about storage and memory.
Lex Fridman (2:23:02.720)
Well, there's a question of how many sort of atoms
Lex Fridman (2:23:04.360)
of space might there be?
Lex Fridman (2:23:06.280)
You know, maybe 10 to the 400.
Stephen Wolfram (2:23:08.680)
We don't know exactly how to estimate these numbers.
Lex Fridman (2:23:11.320)
I mean, this is based on some, I would say,
Stephen Wolfram (2:23:14.680)
somewhat rickety way of estimating things.
Lex Fridman (2:23:17.960)
You know, when there start to be able to be experiments done,
Stephen Wolfram (2:23:20.240)
if we're lucky, there will be experiments
Lex Fridman (2:23:21.840)
that can actually nail down some of these numbers.
Lex Fridman (2:23:24.160)
And because of computation reducibility,
Lex Fridman (2:23:27.920)
there's not much hope for very efficient compression,
Stephen Wolfram (2:23:31.520)
like very efficient representation
Lex Fridman (2:23:34.080)
of this atom space? Good question.
Stephen Wolfram (2:23:35.680)
I mean, there's probably certain things, you know,
Lex Fridman (2:23:37.960)
the fact that we can deduce anything,
Lex Fridman (2:23:40.560)
okay, the question is how deep does the reducibility go?
Lex Fridman (2:23:44.560)
Right. Okay.
Lex Fridman (2:23:45.400)
And I keep on being surprised
Lex Fridman (2:23:46.600)
that it's a lot deeper than I thought.
Stephen Wolfram (2:23:48.560)
Okay, and so one of the things is that,
Lex Fridman (2:23:52.120)
that there's a question of sort of how much
Stephen Wolfram (2:23:53.840)
of the whole of physics do we have to be able to get
Lex Fridman (2:23:57.480)
in order to explain certain kinds of phenomena?
Stephen Wolfram (2:23:59.280)
Like for example, if we want to study quantum interference,
Lex Fridman (2:24:02.840)
do we have to know what an electron is?
Stephen Wolfram (2:24:05.800)
Turns out I thought we did, turns out we don't.
Lex Fridman (2:24:08.480)
I thought to know what energy is,
Stephen Wolfram (2:24:10.400)
we would have to know what electrons were.
Lex Fridman (2:24:12.320)
We don't.
Lex Fridman (2:24:13.160)
So you get a lot of really powerful shortcuts.
Lex Fridman (2:24:15.560)
Right.
Stephen Wolfram (2:24:16.400)
There's a bunch of sort of bulk information about the world.
Lex Fridman (2:24:19.240)
The thing that I'm excited about last few days, okay,
Stephen Wolfram (2:24:22.960)
is the idea of fermions versus bosons, fundamental idea
Lex Fridman (2:24:27.560)
that I mean, it's the reason we have matter
Stephen Wolfram (2:24:29.800)
that doesn't just self destruct,
Lex Fridman (2:24:31.920)
is because of the exclusion principle
Stephen Wolfram (2:24:33.800)
that means that two electrons can never be
Lex Fridman (2:24:36.360)
in the same quantum state.
Stephen Wolfram (2:24:38.280)
Is it useful for us to maybe first talk
Lex Fridman (2:24:41.000)
about how quantum mechanics fits
Lex Fridman (2:24:44.240)
into the Wolfram physics model?
Lex Fridman (2:24:46.480)
Yes.
Stephen Wolfram (2:24:47.320)
Let's go there.
Lex Fridman (2:24:48.160)
So we talked about general relativity.
Stephen Wolfram (2:24:49.680)
Now, what have you found from quantum mechanics
Lex Fridman (2:24:56.960)
within and outside of the Wolfram physics?
Stephen Wolfram (2:24:59.920)
Right, so I mean, the key idea of quantum mechanics
Lex Fridman (2:25:04.200)
that sort of the typical interpretation
Stephen Wolfram (2:25:06.600)
is classical physics says a definite thing happens.
Lex Fridman (2:25:09.960)
Quantum physics says there's this whole set of paths
Stephen Wolfram (2:25:12.880)
of things that might happen.
Lex Fridman (2:25:14.600)
And we are just observing some overall probability
Stephen Wolfram (2:25:17.760)
of how those paths work.
Lex Fridman (2:25:19.680)
Okay, so when you think about our hypergraphs
Lex Fridman (2:25:22.480)
and all these little updates that are going on,
Lex Fridman (2:25:24.680)
there's a very remarkable thing to realize,
Stephen Wolfram (2:25:27.040)
which is if you say, well,
Lex Fridman (2:25:29.240)
which particular sequence of updates should you do?
Stephen Wolfram (2:25:32.360)
Say, well, it's not really defined.
Lex Fridman (2:25:33.760)
You can do any of a whole collection
Stephen Wolfram (2:25:35.400)
of possible sequences of updates.
Lex Fridman (2:25:37.440)
Okay, that set of possible sequences of updates
Stephen Wolfram (2:25:42.000)
defines yet another kind of graph
Lex Fridman (2:25:44.240)
that we call a multiway graph.
Lex Fridman (2:25:46.120)
And a multiway graph just is a graph
Lex Fridman (2:25:48.680)
where at every node, there is a choice
Stephen Wolfram (2:25:52.800)
of several different possible things that could happen.
Lex Fridman (2:25:55.320)
So for example, you go this way, you go that way.
Stephen Wolfram (2:25:57.720)
Those are two different edges in the multiway graph.
Lex Fridman (2:26:00.920)
And you're building up the set of possibilities.
Lex Fridman (2:26:02.640)
So actually, like, for example, I just made the one,
Lex Fridman (2:26:04.880)
the multiway graph for tic tac toe, okay?
Lex Fridman (2:26:07.400)
So tic tac toe, you start off with some board
Lex Fridman (2:26:11.000)
that, you know, is everything is blank,
Lex Fridman (2:26:12.280)
and then somebody can put down an X somewhere,
Lex Fridman (2:26:15.240)
an O somewhere, and then there are different possibilities.
Stephen Wolfram (2:26:18.200)
At each stage, there are different possibilities.
Lex Fridman (2:26:20.320)
And so you build up this multiway graph
Stephen Wolfram (2:26:22.760)
of all those possibilities.
Lex Fridman (2:26:23.760)
Now notice that even in tic tac toe,
Stephen Wolfram (2:26:25.960)
you have the feature that there can be something
Lex Fridman (2:26:28.160)
where you have two different things that happen
Lex Fridman (2:26:31.000)
and then those branches merge
Lex Fridman (2:26:33.400)
because you end up with the same shape,
Stephen Wolfram (2:26:35.280)
you know, the same configuration of the board,
Lex Fridman (2:26:37.440)
even though you got there in two different ways.
Lex Fridman (2:26:40.000)
So the thing that's sort of an inevitable feature
Lex Fridman (2:26:42.840)
of our models is that just like quantum mechanics suggests,
Stephen Wolfram (2:26:47.360)
definite things don't happen.
Lex Fridman (2:26:48.880)
Instead, you get this whole multiway graph
Stephen Wolfram (2:26:50.880)
of all these possibilities.
Lex Fridman (2:26:52.760)
Okay, so then the question is, so, okay,
Lex Fridman (2:26:55.680)
so that's sort of a picture of what's going on.
Lex Fridman (2:26:58.320)
Now you say, okay, well, quantum mechanics
Stephen Wolfram (2:27:00.520)
has all these features of, you know,
Lex Fridman (2:27:02.720)
all this mathematical structure and so on.
Lex Fridman (2:27:04.880)
How do you get that mathematical structure?
Lex Fridman (2:27:07.160)
Okay, a couple of things to say.
Lex Fridman (2:27:08.880)
So quantum mechanics is actually, in a sense,
Lex Fridman (2:27:11.680)
two different theories glued together.
Stephen Wolfram (2:27:13.960)
Quantum mechanics is the theory
Lex Fridman (2:27:15.680)
of how quantum amplitudes work
Stephen Wolfram (2:27:18.120)
that more or less give you the probabilities
Lex Fridman (2:27:19.440)
of things happening.
Lex Fridman (2:27:20.720)
And it's the theory of quantum measurement,
Lex Fridman (2:27:22.800)
which is the theory of how we actually
Stephen Wolfram (2:27:25.200)
conclude definite things.
Lex Fridman (2:27:27.000)
Because the mathematics just gives you
Stephen Wolfram (2:27:29.080)
these quantum amplitudes, which are more or less
Lex Fridman (2:27:30.760)
probabilities of things happening,
Lex Fridman (2:27:32.480)
but yet we actually observe definite things in the world.
Lex Fridman (2:27:36.920)
Quantum measurement has always been a bit mysterious.
Stephen Wolfram (2:27:39.120)
It's always been something where people just say,
Lex Fridman (2:27:41.160)
well, the mathematics says this,
Lex Fridman (2:27:42.400)
but then you do a measurement,
Lex Fridman (2:27:43.480)
and there are philosophical arguments
Stephen Wolfram (2:27:45.120)
about what the measurement is.
Lex Fridman (2:27:46.600)
But it's not something where there's a theory
Stephen Wolfram (2:27:48.800)
of the measurement.
Lex Fridman (2:27:49.720)
Somebody on Reddit also asked,
Stephen Wolfram (2:27:53.080)
please ask Stephen to tell his story
Lex Fridman (2:27:56.800)
of the double slit experiment.
Stephen Wolfram (2:27:59.840)
Okay, yeah, I can.
Lex Fridman (2:28:01.160)
Is that, does that make sense?
Stephen Wolfram (2:28:02.880)
Oh yeah, it makes sense.
Lex Fridman (2:28:03.960)
Absolutely makes sense.
Lex Fridman (2:28:05.000)
Why, is this like a good way to discuss?
Lex Fridman (2:28:07.760)
A little bit.
Stephen Wolfram (2:28:08.600)
Let me go, let me explain a couple of things first.
Lex Fridman (2:28:10.560)
So the structure of quantum mechanics
Stephen Wolfram (2:28:13.840)
is mathematically quite complicated.
Lex Fridman (2:28:16.240)
One of the features, let's see,
Stephen Wolfram (2:28:18.600)
well, how to describe this.
Lex Fridman (2:28:20.520)
Okay, so first point is there's this multiway graph
Stephen Wolfram (2:28:23.800)
of all these different paths of things
Lex Fridman (2:28:26.880)
that can happen in the world.
Lex Fridman (2:28:28.760)
And the important point is that these,
Lex Fridman (2:28:32.600)
you can have branchings and you can have mergings.
Stephen Wolfram (2:28:35.600)
Okay, so this property turns out causal invariance
Lex Fridman (2:28:39.680)
is the statement that the number of mergings
Stephen Wolfram (2:28:43.360)
is equal to the number of branchings.
Lex Fridman (2:28:45.520)
Yeah.
Lex Fridman (2:28:46.360)
So in other words, every time there's a branch,
Lex Fridman (2:28:48.720)
eventually there will also be a merge.
Stephen Wolfram (2:28:50.640)
In other words, every time there were two possibilities
Lex Fridman (2:28:52.600)
for what might've happened, eventually those will merge.
Stephen Wolfram (2:28:55.120)
Beautiful concept by the way, but yeah, yeah, yeah.
Lex Fridman (2:28:57.400)
So that idea, okay, so then, so that's one thing
Lex Fridman (2:29:03.920)
and that's closely related to the sort of objectivity
Lex Fridman (2:29:07.680)
in quantum mechanics.
Stephen Wolfram (2:29:08.520)
The fact that we believe definite things happen,
Lex Fridman (2:29:10.720)
it's because although there are all these different paths,
Stephen Wolfram (2:29:13.200)
in some sense, because of causal invariance,
Lex Fridman (2:29:15.600)
they all imply the same thing.
Stephen Wolfram (2:29:17.640)
I'm cheating a little bit in saying that,
Lex Fridman (2:29:19.400)
but that's roughly the essence of what's going on.
Stephen Wolfram (2:29:22.120)
Okay, next thing to think about
Lex Fridman (2:29:24.560)
is you have this multiway graph,
Stephen Wolfram (2:29:27.440)
it has all these different possible things
Lex Fridman (2:29:28.840)
that are happening.
Stephen Wolfram (2:29:30.040)
Now we ask, this multiway graph
Lex Fridman (2:29:32.440)
is sort of evolving with time.
Stephen Wolfram (2:29:34.120)
Over time, it's branching, it's merging,
Lex Fridman (2:29:36.680)
it's doing all these things, okay?
Stephen Wolfram (2:29:39.840)
Question we can ask is if we slice it at a particular time,
Lex Fridman (2:29:44.680)
what do we see?
Lex Fridman (2:29:46.120)
And that slice represents in a sense,
Lex Fridman (2:29:48.840)
something to do with the state of the universe
Stephen Wolfram (2:29:51.240)
at a particular time.
Lex Fridman (2:29:53.080)
So in other words, we've got this multiway graph
Stephen Wolfram (2:29:55.080)
of all these possibilities,
Lex Fridman (2:29:56.680)
and then we're asking, okay, we take the slice,
Stephen Wolfram (2:30:01.320)
this slice represents, okay,
Lex Fridman (2:30:04.440)
each of these different paths
Stephen Wolfram (2:30:05.640)
corresponds to a different quantum possibility
Lex Fridman (2:30:07.760)
for what's happening.
Stephen Wolfram (2:30:09.320)
When we take the slice, we're saying,
Lex Fridman (2:30:11.440)
what are the set of quantum possibilities
Lex Fridman (2:30:13.120)
that exist at a particular time?
Lex Fridman (2:30:14.960)
And when you say slice, you slice the graph
Lex Fridman (2:30:17.640)
and then there's a bunch of leaves.
Lex Fridman (2:30:19.720)
A bunch of leaves.
Stephen Wolfram (2:30:20.560)
Those represent the state of things.
Lex Fridman (2:30:23.440)
Right, but then, okay, so the important thing
Stephen Wolfram (2:30:26.240)
that you are quickly picking up on
Lex Fridman (2:30:29.040)
is that what matters is kind of
Lex Fridman (2:30:31.960)
how these leaves are related to each other.
Lex Fridman (2:30:34.600)
So a good way to tell how leaves are related
Stephen Wolfram (2:30:37.560)
is just to say on the step before
Lex Fridman (2:30:39.920)
do they have a common ancestor?
Lex Fridman (2:30:42.160)
So two leaves might be,
Lex Fridman (2:30:43.960)
they might have just branched from one thing
Stephen Wolfram (2:30:45.800)
or they might be far away,
Lex Fridman (2:30:47.920)
way far apart in this graph
Stephen Wolfram (2:30:50.720)
where to get to a common ancestor,
Lex Fridman (2:30:52.320)
maybe you have to go all the way back
Stephen Wolfram (2:30:53.400)
to the beginning of the graph,
Lex Fridman (2:30:54.240)
all the way back to the beginning.
Lex Fridman (2:30:55.080)
So there's some kind of measure of distance.
Lex Fridman (2:30:57.160)
Right, but what you get is by making the slice,
Stephen Wolfram (2:31:02.000)
we call it branchial space, the space of branches.
Lex Fridman (2:31:05.880)
And in this branchial space,
Stephen Wolfram (2:31:08.360)
you have a graph that represents the relationships
Lex Fridman (2:31:11.240)
between these quantum states in branchial space.
Stephen Wolfram (2:31:14.640)
You have this notion of distance in branchial space.
Lex Fridman (2:31:18.000)
Okay, so.
Stephen Wolfram (2:31:18.840)
It's connected to quantum entanglement.
Lex Fridman (2:31:20.880)
Yes, yes, it's basically,
Stephen Wolfram (2:31:23.520)
the distance in branchial space
Lex Fridman (2:31:25.640)
is kind of an entanglement distance.
Lex Fridman (2:31:27.840)
So this.
Lex Fridman (2:31:28.680)
That's a very nice model.
Stephen Wolfram (2:31:29.880)
Right, it is very nice, it's very beautiful.
Lex Fridman (2:31:33.240)
I mean, it's so clean.
Stephen Wolfram (2:31:35.520)
I mean, it's really, and it tells one,
Lex Fridman (2:31:38.920)
okay, so anyway, so then this branchial space
Stephen Wolfram (2:31:42.840)
has this sort of map of the entanglements
Lex Fridman (2:31:46.080)
between quantum states.
Lex Fridman (2:31:47.760)
So in physical space, we have,
Lex Fridman (2:31:50.360)
so you can say, take, let's say the causal graph,
Lex Fridman (2:31:54.680)
and we can slice that at a particular time,
Lex Fridman (2:31:57.800)
and then we get this map
Stephen Wolfram (2:31:58.840)
of how things are laid out in physical space.
Lex Fridman (2:32:01.400)
When we do the same kind of thing,
Stephen Wolfram (2:32:02.720)
there's a thing called the multiway causal graph,
Lex Fridman (2:32:04.840)
which is the analog of a causal graph
Stephen Wolfram (2:32:06.360)
for the multiway system.
Lex Fridman (2:32:07.760)
We slice that, we get essentially the relationships
Stephen Wolfram (2:32:11.360)
between things, not in physical space,
Lex Fridman (2:32:13.720)
but in the space of quantum states.
Stephen Wolfram (2:32:15.720)
It's like which quantum state
Lex Fridman (2:32:17.040)
is similar to which other quantum state.
Stephen Wolfram (2:32:19.360)
Okay, so now I think next thing to say
Lex Fridman (2:32:22.280)
is just to mention how quantum measurement works.
Lex Fridman (2:32:24.800)
So quantum measurement has to do with reference frames
Lex Fridman (2:32:27.560)
in branchial space.
Stephen Wolfram (2:32:29.760)
So, okay, so measurement in physical space,
Lex Fridman (2:32:33.720)
it matters whether how we assign spatial position
Lex Fridman (2:32:38.720)
and how we define coordinates in space and time.
Lex Fridman (2:32:42.520)
And that's how we make measurements in ordinary space.
Lex Fridman (2:32:45.360)
Are we making a measurement based on us sitting still here?
Lex Fridman (2:32:48.240)
Are we traveling at half the speed of light
Lex Fridman (2:32:49.880)
and making measurements that way?
Lex Fridman (2:32:51.600)
These are different reference frames
Stephen Wolfram (2:32:53.080)
in which we're making our measurements.
Lex Fridman (2:32:54.760)
And the relationship between different events
Lex Fridman (2:32:57.840)
and different points in space and time
Lex Fridman (2:33:00.760)
will be different depending on what reference frame we're in.
Stephen Wolfram (2:33:04.200)
Okay, so then we have this idea
Lex Fridman (2:33:06.480)
of quantum observation frames,
Stephen Wolfram (2:33:08.880)
which are the analog of reference frames,
Lex Fridman (2:33:11.040)
but in branchial space.
Lex Fridman (2:33:13.040)
And so what happens is what we realize
Lex Fridman (2:33:15.880)
is that a quantum measurement is the observer
Stephen Wolfram (2:33:19.960)
is sort of arbitrarily determining this reference frame.
Lex Fridman (2:33:23.000)
The observer is saying, I'm going to understand the world
Stephen Wolfram (2:33:26.840)
by saying that space and time are coordinated this way.
Lex Fridman (2:33:30.560)
I'm gonna understand the world by saying
Stephen Wolfram (2:33:32.600)
that quantum states and time are coordinated in this way.
Lex Fridman (2:33:36.520)
And essentially what happens is
Stephen Wolfram (2:33:38.280)
that the process of quantum measurement
Lex Fridman (2:33:40.920)
is a process of deciding how you slice up
Stephen Wolfram (2:33:44.920)
this multiway system in these quantum observation frames.
Lex Fridman (2:33:48.560)
So in a sense, the observer, the way the observer enters
Stephen Wolfram (2:33:51.760)
is by their choice of these quantum observation frames.
Lex Fridman (2:33:55.600)
And what happens is that the observer,
Stephen Wolfram (2:33:58.880)
because, okay, this is again,
Lex Fridman (2:34:00.480)
another stack of other concepts, but anyway,
Stephen Wolfram (2:34:03.120)
because the observer is computationally bounded,
Lex Fridman (2:34:06.200)
there is a limit to the type of quantum observation frames
Stephen Wolfram (2:34:08.880)
that they can construct.
Lex Fridman (2:34:09.960)
Interesting, okay, so there's some constraints,
Stephen Wolfram (2:34:12.600)
some limit on the choice of observation frames.
Lex Fridman (2:34:17.760)
Right, and by the way, I just want to mention
Stephen Wolfram (2:34:19.960)
that there's a, I mean, it's bizarre,
Lex Fridman (2:34:21.840)
but there's a hierarchy of these things.
Lex Fridman (2:34:23.640)
So in thermodynamics,
Lex Fridman (2:34:27.440)
the fact that we believe entropy increases,
Stephen Wolfram (2:34:29.600)
we believe things get more disordered,
Lex Fridman (2:34:31.480)
is a consequence of the fact
Stephen Wolfram (2:34:32.520)
that we can't track each individual molecule.
Lex Fridman (2:34:34.280)
If we could track every single molecule,
Stephen Wolfram (2:34:36.160)
we could run every movie in reverse, so to speak,
Lex Fridman (2:34:38.240)
and we would not see that things are getting more disordered.
Lex Fridman (2:34:42.200)
But it's because we are computationally bounded,
Lex Fridman (2:34:44.800)
we can only look at these big blobs
Stephen Wolfram (2:34:46.720)
of what all these molecules collectively do,
Lex Fridman (2:34:49.560)
that we think that things are,
Stephen Wolfram (2:34:52.280)
that we describe it in terms of entropy increasing
Lex Fridman (2:34:54.920)
and so on.
Lex Fridman (2:34:55.800)
And it's the same phenomenon, basically,
Lex Fridman (2:34:58.560)
and also a consequence of computational irreducibility
Stephen Wolfram (2:35:01.520)
that causes us to basically be forced to conclude
Lex Fridman (2:35:04.800)
that definite things happen in the world,
Stephen Wolfram (2:35:06.920)
even though there's this quantum,
Lex Fridman (2:35:08.720)
this set of all these different quantum processes
Stephen Wolfram (2:35:10.680)
that are going on.
Lex Fridman (2:35:11.880)
So, I mean, I'm skipping a little bit,
Lex Fridman (2:35:15.400)
but that's a rough picture.
Lex Fridman (2:35:18.560)
And in the evolution of the Wolfram Physics Project,
Stephen Wolfram (2:35:21.880)
where do you feel we stand on some of the puzzles
Lex Fridman (2:35:24.280)
that are along the way?
Stephen Wolfram (2:35:25.120)
See, you're skipping along a bunch of stuff.
Lex Fridman (2:35:28.080)
It's amazing how much these things are unraveling.
Stephen Wolfram (2:35:30.440)
I mean, you know, these things, look,
Lex Fridman (2:35:32.480)
it used to be the case that I would agree with Dick Feynman,
Lex Fridman (2:35:35.640)
nobody understands quantum mechanics, including me, okay?
Lex Fridman (2:35:38.840)
I'm getting to the point where I think
Stephen Wolfram (2:35:40.120)
I actually understand quantum mechanics.
Lex Fridman (2:35:41.560)
My exercise, okay, is can I explain quantum mechanics
Stephen Wolfram (2:35:45.720)
for real at the level of kind of middle school
Lex Fridman (2:35:48.800)
type explanation?
Lex Fridman (2:35:50.320)
And I'm getting closer, it's getting there.
Lex Fridman (2:35:52.600)
I'm not quite there, I've tried it a few times,
Lex Fridman (2:35:54.960)
and I realized that there are things
Lex Fridman (2:35:57.640)
where I have to start talking about
Stephen Wolfram (2:35:59.080)
elaborate mathematical concepts and so on.
Lex Fridman (2:36:00.920)
But I think, and you've got to realize
Stephen Wolfram (2:36:03.000)
that it's not self evident that we can explain
Lex Fridman (2:36:06.280)
at an intuitively graspable level,
Stephen Wolfram (2:36:09.240)
something which, about the way the universe works,
Lex Fridman (2:36:12.400)
the universe wasn't built for our understanding,
Lex Fridman (2:36:14.760)
so to speak.
Lex Fridman (2:36:16.280)
But I think then, okay, so another important idea
Stephen Wolfram (2:36:21.720)
is this idea of branchial space, which I mentioned,
Lex Fridman (2:36:25.280)
this sort of space of quantum states.
Stephen Wolfram (2:36:27.400)
It is, okay, so I mentioned Einstein's equations
Lex Fridman (2:36:31.240)
describing the effect of mass and energy
Stephen Wolfram (2:36:37.400)
on trajectories of particles, on GD6.
Lex Fridman (2:36:40.840)
The curvature of physical space is associated
Stephen Wolfram (2:36:44.920)
with the presence of energy,
Lex Fridman (2:36:47.040)
according to Einstein's equations, okay?
Lex Fridman (2:36:49.400)
So it turns out that, rather amazingly,
Lex Fridman (2:36:51.920)
the same thing is true in branchial space.
Lex Fridman (2:36:54.880)
So it turns out the presence of energy
Lex Fridman (2:36:57.360)
or more accurately Lagrangian density,
Stephen Wolfram (2:36:59.440)
which is a kind of relativistic invariant version of energy,
Lex Fridman (2:37:03.200)
the presence of that causes essentially deflection of GD6
Lex Fridman (2:37:08.560)
in this branchial space, okay?
Lex Fridman (2:37:11.160)
So you might say, so what?
Stephen Wolfram (2:37:12.560)
Well, it turns out that the sort of the best formulation
Lex Fridman (2:37:17.040)
we have of quantum mechanics,
Stephen Wolfram (2:37:18.800)
this Feynman path integral,
Lex Fridman (2:37:21.360)
is a thing that describes quantum processes
Stephen Wolfram (2:37:26.200)
in terms of mathematics that can be interpreted as,
Lex Fridman (2:37:31.480)
well, in quantum mechanics, the big thing
Stephen Wolfram (2:37:33.880)
is you get these quantum amplitudes,
Lex Fridman (2:37:35.360)
which are complex numbers that represent,
Stephen Wolfram (2:37:38.280)
when you combine them together,
Lex Fridman (2:37:39.400)
represent probabilities of things happening.
Lex Fridman (2:37:41.560)
And so the big story has been,
Lex Fridman (2:37:42.840)
how do you derive these quantum amplitudes?
Lex Fridman (2:37:45.320)
And people think these quantum amplitudes,
Lex Fridman (2:37:47.480)
they have a complex number,
Stephen Wolfram (2:37:49.160)
has a real part and an imaginary part.
Lex Fridman (2:37:51.200)
You can also think of it as a magnitude and a phase.
Lex Fridman (2:37:53.920)
And people have sort of thought these quantum amplitudes
Lex Fridman (2:37:57.160)
have magnitude and phase, and you compute those together.
Stephen Wolfram (2:38:00.040)
Turns out that the magnitude and the phase
Lex Fridman (2:38:03.680)
come from completely different places.
Stephen Wolfram (2:38:06.120)
The magnitude comes, okay, so how do you compute things
Lex Fridman (2:38:10.080)
in quantum mechanics?
Stephen Wolfram (2:38:10.920)
Roughly, I'm telling you, I'm getting there
Lex Fridman (2:38:13.360)
to be able to do this at a middle school level,
Lex Fridman (2:38:15.080)
but I'm not there yet.
Lex Fridman (2:38:17.720)
Roughly what happens is you're asking,
Stephen Wolfram (2:38:20.440)
does this state in quantum mechanics
Lex Fridman (2:38:24.160)
evolve to this other state in quantum mechanics?
Lex Fridman (2:38:27.080)
And you can think about that like a particle traveling
Lex Fridman (2:38:30.600)
or something traveling through physical space,
Lex Fridman (2:38:33.240)
but instead it's traveling through branchial space.
Lex Fridman (2:38:36.160)
And so what's happening is, does this quantum state evolve
Lex Fridman (2:38:38.920)
to this other quantum state?
Lex Fridman (2:38:39.920)
It's like saying, does this object move
Lex Fridman (2:38:42.160)
from this place in space to this other place in space?
Lex Fridman (2:38:45.160)
Okay, now the way that these quantum amplitudes
Stephen Wolfram (2:38:49.360)
characterize kind of to what extent the thing
Lex Fridman (2:38:54.000)
will successfully reach some particular point
Stephen Wolfram (2:38:56.400)
in branchial space, just like in physical space,
Lex Fridman (2:38:58.560)
you could say, oh, it had a certain velocity
Lex Fridman (2:39:00.720)
and it went in this direction.
Lex Fridman (2:39:02.400)
In branchial space, there's a similar kind of concept.
Stephen Wolfram (2:39:05.160)
Is there a nice way to visualize for me now
Lex Fridman (2:39:08.280)
mentally branchial space?
Stephen Wolfram (2:39:10.560)
It's just, you have this hypergraph,
Lex Fridman (2:39:13.720)
sorry, you have this multiway graph.
Stephen Wolfram (2:39:15.720)
It's this big branching thing, branching and merging thing.
Lex Fridman (2:39:18.440)
But I mean, like moving through that space,
Stephen Wolfram (2:39:21.800)
I'm just trying to understand what that looks like.
Lex Fridman (2:39:25.920)
You know, that space is probably exponential dimensional,
Stephen Wolfram (2:39:29.280)
which makes it again, another can of worms
Lex Fridman (2:39:32.280)
in understanding what's going on.
Stephen Wolfram (2:39:33.880)
That space as in an ordinary space,
Lex Fridman (2:39:36.920)
this hypergraph, the spatial hypergraph
Stephen Wolfram (2:39:39.160)
limits to something which is like a manifold,
Lex Fridman (2:39:42.600)
like something like three dimensional space.
Stephen Wolfram (2:39:45.040)
Almost certainly the multiway graph limits
Lex Fridman (2:39:48.720)
to a Hilbert space, which is something that,
Stephen Wolfram (2:39:52.360)
I mean, it's just a weird exponential dimensional space.
Lex Fridman (2:39:55.560)
And by the way, you can ask, I mean,
Stephen Wolfram (2:39:57.400)
there are much weirder things that go on.
Lex Fridman (2:39:58.880)
For example, one of the things I've been interested in
Stephen Wolfram (2:40:00.720)
is the expansion of the universe in branchial space.
Lex Fridman (2:40:03.920)
So we know the universe is expanding in physical space,
Lex Fridman (2:40:07.080)
but the universe is probably also expanding
Lex Fridman (2:40:09.200)
in branchial space.
Lex Fridman (2:40:10.920)
So that means the number of quantum states
Lex Fridman (2:40:13.280)
of the universe is increasing with time.
Stephen Wolfram (2:40:15.760)
The diameter of the thing is growing.
Lex Fridman (2:40:17.880)
Right, so that means that the,
Lex Fridman (2:40:19.480)
and by the way, this is related
Lex Fridman (2:40:22.760)
to whether quantum computing can ever work.
Lex Fridman (2:40:28.200)
Why?
Lex Fridman (2:40:29.040)
Okay, so let me explain why.
Lex Fridman (2:40:30.440)
So let's talk about, okay, so first of all,
Lex Fridman (2:40:32.840)
just to finish the thought about quantum amplitudes,
Stephen Wolfram (2:40:35.320)
that the incredibly beautiful thing,
Lex Fridman (2:40:37.320)
but I'm just very excited about this.
Stephen Wolfram (2:40:40.680)
The fine path integral is this formula.
Lex Fridman (2:40:44.640)
It says that the amplitude, the quantum amplitude
Stephen Wolfram (2:40:47.360)
is E to the I S over H bar,
Lex Fridman (2:40:49.480)
where S is the thing called the action.
Lex Fridman (2:40:51.560)
And it, okay, so that can be thought of
Lex Fridman (2:40:55.720)
as representing a deflection of the angle
Stephen Wolfram (2:40:59.280)
of this path in the multiway graph.
Lex Fridman (2:41:02.200)
So it's a deflection of a geodesic in the multiway path
Stephen Wolfram (2:41:05.040)
that is caused by this thing called the action,
Lex Fridman (2:41:06.960)
which is essentially associated with energy, okay?
Lex Fridman (2:41:10.040)
And so this is a deflection of a path in branchial space
Lex Fridman (2:41:13.760)
that is described by this path integral,
Stephen Wolfram (2:41:15.520)
which is the thing that is the mathematical essence
Lex Fridman (2:41:17.760)
of quantum mechanics.
Stephen Wolfram (2:41:19.440)
Turns out that deflection is,
Lex Fridman (2:41:22.760)
the deflection of geodesics in branchial space
Stephen Wolfram (2:41:25.240)
follows the exact same mathematical setup
Lex Fridman (2:41:28.720)
as the deflection of geodesics in physical space,
Stephen Wolfram (2:41:31.880)
except the deflection of geodesics in physical space
Lex Fridman (2:41:34.280)
is described with Einstein's equations.
Stephen Wolfram (2:41:36.480)
The deflection of geodesics in branchial space
Lex Fridman (2:41:38.600)
is defined by the Feynman path integral,
Lex Fridman (2:41:40.880)
and they are the same.
Lex Fridman (2:41:42.800)
In other words, they are mathematically the same.
Lex Fridman (2:41:45.760)
So that means that general relativity
Lex Fridman (2:41:48.360)
is a story of essentially motion in physical space.
Stephen Wolfram (2:41:53.200)
Quantum mechanics is a story of essentially motion
Lex Fridman (2:41:55.560)
in branchial space.
Lex Fridman (2:41:57.320)
And the underlying equation for those two things,
Lex Fridman (2:42:01.360)
although it's presented differently
Stephen Wolfram (2:42:02.560)
because one's interested in different things
Lex Fridman (2:42:04.160)
in branchial space than physical space,
Lex Fridman (2:42:06.080)
but the underlying equation is the same.
Lex Fridman (2:42:08.720)
So in other words, it's just these two theories,
Stephen Wolfram (2:42:13.440)
which are those two sort of pillars
Lex Fridman (2:42:14.600)
of 20th century physics,
Stephen Wolfram (2:42:16.320)
which have seemed to be off in different directions,
Lex Fridman (2:42:19.080)
are actually facets of the exact same theory.
Stephen Wolfram (2:42:24.280)
That's exciting to see where that evolves
Lex Fridman (2:42:26.960)
and exciting that that just is there.
Stephen Wolfram (2:42:29.120)
Right, I mean, to me,
Lex Fridman (2:42:31.000)
look, having spent some part of my early life
Stephen Wolfram (2:42:34.480)
working in the context of these theories
Lex Fridman (2:42:37.040)
of 20th century physics,
Stephen Wolfram (2:42:39.400)
it's, they just, they seem so different.
Lex Fridman (2:42:41.960)
And the fact that they're really the same
Stephen Wolfram (2:42:44.080)
is just really amazing.
Lex Fridman (2:42:46.480)
Actually, you mentioned double slit experiment, okay?
Lex Fridman (2:42:49.120)
So the double slit experiment
Lex Fridman (2:42:50.280)
is an interference phenomenon where you say there are,
Stephen Wolfram (2:42:54.360)
you can have a photon or an electron,
Lex Fridman (2:42:56.600)
and you say there are these two slits
Stephen Wolfram (2:42:58.240)
that could have gone through either one,
Lex Fridman (2:43:00.320)
but there is this interference pattern
Stephen Wolfram (2:43:02.560)
where there's destructive interference,
Lex Fridman (2:43:05.080)
where you might've said in classical physics,
Stephen Wolfram (2:43:07.200)
oh, well, if there are two slits,
Lex Fridman (2:43:09.000)
then there's a better chance
Stephen Wolfram (2:43:10.440)
that it gets through one or the other of them.
Lex Fridman (2:43:12.120)
But in quantum mechanics,
Stephen Wolfram (2:43:13.240)
there's this phenomenon of destructive interference
Lex Fridman (2:43:15.720)
that means that even though there are two slits,
Stephen Wolfram (2:43:18.120)
two can lead to nothing,
Lex Fridman (2:43:20.240)
as opposed to two leading to more
Stephen Wolfram (2:43:22.560)
than, for example, one slit.
Lex Fridman (2:43:25.240)
And what happens in this model,
Lex Fridman (2:43:27.480)
and we've just been understanding this
Lex Fridman (2:43:29.040)
in the last few weeks, actually,
Stephen Wolfram (2:43:30.760)
is that what essentially happens
Lex Fridman (2:43:34.400)
is that the double slit experiment
Stephen Wolfram (2:43:38.040)
is a story of the interface
Lex Fridman (2:43:39.360)
between branchial space and physical space.
Lex Fridman (2:43:41.960)
And what's essentially happening
Lex Fridman (2:43:43.080)
is that the destructive interference
Stephen Wolfram (2:43:45.520)
is the result of the two possible paths
Lex Fridman (2:43:48.520)
associated with photons going through those two slits
Stephen Wolfram (2:43:51.200)
winding up at opposite ends of branchial space.
Lex Fridman (2:43:53.960)
And so that's why there's sort of nothing there
Stephen Wolfram (2:43:57.120)
when you look at it,
Lex Fridman (2:43:58.440)
is because these two different sort of branches
Stephen Wolfram (2:44:02.120)
couldn't get merged together
Lex Fridman (2:44:03.920)
to produce something that you can measure
Stephen Wolfram (2:44:06.240)
in physical space.
Lex Fridman (2:44:07.680)
Is there a lot to be understood about branchial space?
Stephen Wolfram (2:44:10.680)
I guess, mathematically speaking.
Lex Fridman (2:44:13.920)
Yes, it's a very beautiful mathematical thing.
Lex Fridman (2:44:16.400)
And it's very, I mean, by the way,
Lex Fridman (2:44:18.280)
this whole theory is just amazingly rich
Stephen Wolfram (2:44:22.000)
in terms of the mathematics that it says should exist.
Lex Fridman (2:44:24.920)
Okay, so for example,
Stephen Wolfram (2:44:26.120)
calculus is a story of infinitesimal change
Lex Fridman (2:44:30.320)
in integer dimensional space,
Stephen Wolfram (2:44:32.000)
one dimensional, two dimensional, three dimensional space.
Lex Fridman (2:44:34.880)
We need a theory of infinitesimal change
Stephen Wolfram (2:44:37.960)
in fractional dimensional and dynamic dimensional space.
Lex Fridman (2:44:41.440)
No such theory exists.
Lex Fridman (2:44:42.640)
So there's tools of mathematics that are needed here.
Lex Fridman (2:44:45.280)
Right.
Lex Fridman (2:44:46.120)
And this is a motivation for that actually.
Lex Fridman (2:44:47.040)
Right, and there are indications
Lex Fridman (2:44:50.320)
and we can do computer experiments
Lex Fridman (2:44:51.760)
and we can see how it's gonna come out,
Lex Fridman (2:44:53.560)
but we need to, the actual mathematics doesn't exist.
Lex Fridman (2:44:58.040)
And in branchial space, it's actually even worse.
Stephen Wolfram (2:45:00.720)
There's even more sort of layers of mathematics that are,
Lex Fridman (2:45:04.720)
we can see how it works roughly
Stephen Wolfram (2:45:06.240)
by doing computer experiments,
Lex Fridman (2:45:07.960)
but to really understand it,
Stephen Wolfram (2:45:10.120)
we need more sort of mathematical sophistication.
Lex Fridman (2:45:13.320)
So quantum computers.
Stephen Wolfram (2:45:14.880)
Okay, so the basic idea of quantum computers,
Lex Fridman (2:45:17.800)
the promise of quantum computers
Stephen Wolfram (2:45:19.960)
is quantum mechanics does things in parallel.
Lex Fridman (2:45:23.640)
And so you can sort of intrinsically do computations
Stephen Wolfram (2:45:26.960)
in parallel.
Lex Fridman (2:45:27.880)
And somehow that can be much more efficient
Stephen Wolfram (2:45:30.160)
than just doing them one after another.
Lex Fridman (2:45:33.280)
And I actually worked on quantum computing a bit
Stephen Wolfram (2:45:36.240)
with Dick Feynman back in 1981, two, three,
Lex Fridman (2:45:40.680)
that kind of timeframe.
Lex Fridman (2:45:41.800)
And we...
Lex Fridman (2:45:42.640)
It's a fascinating image.
Stephen Wolfram (2:45:43.680)
You and Feynman working on quantum computers.
Lex Fridman (2:45:46.600)
Well, we tried to work,
Stephen Wolfram (2:45:47.880)
the big thing we tried to do was invent a randomness chip
Lex Fridman (2:45:51.040)
that would generate randomness at a high speed
Stephen Wolfram (2:45:53.800)
using quantum mechanics.
Lex Fridman (2:45:55.480)
And the discovery that that wasn't really possible
Stephen Wolfram (2:45:58.920)
was part of the story of,
Lex Fridman (2:46:01.520)
we never really wrote anything about it.
Stephen Wolfram (2:46:03.000)
I think maybe he wrote some stuff,
Lex Fridman (2:46:04.240)
but we didn't write stuff about what we figured out
Stephen Wolfram (2:46:07.520)
about sort of the fact that it really seemed like
Lex Fridman (2:46:10.080)
the measurement process in quantum mechanics
Stephen Wolfram (2:46:12.320)
was a serious damper on what was possible to do
Lex Fridman (2:46:15.680)
in sort of the possible advantages of quantum mechanics
Stephen Wolfram (2:46:19.600)
for computing.
Lex Fridman (2:46:20.760)
But anyway, so the sort of the promise of quantum computing
Stephen Wolfram (2:46:24.800)
is let's say you're trying to factor an integer.
Lex Fridman (2:46:28.320)
Well, you can, instead of,
Stephen Wolfram (2:46:30.040)
when you factor an integer, you might say,
Lex Fridman (2:46:31.560)
well, does this factor work?
Lex Fridman (2:46:32.720)
Does this factor work?
Lex Fridman (2:46:33.560)
Does this factor work?
Stephen Wolfram (2:46:35.680)
In ordinary computing,
Lex Fridman (2:46:37.160)
it seems like we pretty much just have to try
Stephen Wolfram (2:46:39.120)
all these different factors,
Lex Fridman (2:46:41.680)
kind of one after another.
Lex Fridman (2:46:43.160)
But in quantum mechanics, you might have the idea,
Lex Fridman (2:46:45.200)
oh, you can just sort of have the physics,
Lex Fridman (2:46:48.360)
try all of them in parallel, okay?
Lex Fridman (2:46:51.320)
And there's this algorithm, Shor's algorithm,
Stephen Wolfram (2:46:56.120)
which allows you,
Lex Fridman (2:46:58.760)
according to the formalism of quantum mechanics,
Stephen Wolfram (2:47:01.080)
to do everything in parallel
Lex Fridman (2:47:02.400)
and to do it much faster than you can on a classical computer.
Stephen Wolfram (2:47:05.320)
Okay, the only little footnote is
Lex Fridman (2:47:08.120)
you have to figure out what the answer is.
Stephen Wolfram (2:47:09.920)
You have to measure the result.
Lex Fridman (2:47:12.000)
So the quantum mechanics internally has figured out
Stephen Wolfram (2:47:13.960)
all these different branches,
Lex Fridman (2:47:15.520)
but then you have to pull all these branches together
Lex Fridman (2:47:17.880)
to say, and the classical answer is this, okay?
Lex Fridman (2:47:21.040)
The standard theory of quantum mechanics
Stephen Wolfram (2:47:22.600)
does not tell you how to do that.
Lex Fridman (2:47:24.200)
It tells you how the branching works,
Lex Fridman (2:47:26.160)
but it doesn't tell you the process
Lex Fridman (2:47:27.880)
of corralling all these things together.
Lex Fridman (2:47:30.240)
And that process, which intuitively you can see
Lex Fridman (2:47:32.800)
is gonna be kind of tricky,
Lex Fridman (2:47:34.400)
but our model actually does tell you
Lex Fridman (2:47:37.080)
how that process of pulling things together works.
Lex Fridman (2:47:40.200)
And the answer seems to be, we're not absolutely sure.
Lex Fridman (2:47:42.880)
We've only got to two times three so far
Stephen Wolfram (2:47:46.720)
which is kind of in this factorization
Lex Fridman (2:47:50.520)
in quantum computers.
Lex Fridman (2:47:51.360)
But we can, what seems to be the case
Lex Fridman (2:47:55.440)
is that the advantage you get from the parallelization
Stephen Wolfram (2:47:58.520)
from quantum mechanics is lost
Lex Fridman (2:48:01.200)
from the amount that you have to spend
Stephen Wolfram (2:48:03.520)
pulling together all those parallel threads
Lex Fridman (2:48:05.320)
to get to a classical answer at the end.
Stephen Wolfram (2:48:07.680)
Now, that phenomenon is not unrelated
Lex Fridman (2:48:10.280)
to various decoherence phenomena
Stephen Wolfram (2:48:11.880)
that are seen in practical quantum computers and so on.
Lex Fridman (2:48:14.320)
I mean, I should say as a very practical point,
Stephen Wolfram (2:48:16.760)
I mean, it's like, should people stop bothering
Lex Fridman (2:48:19.080)
to do quantum computing research?
Stephen Wolfram (2:48:20.760)
No, because what they're really doing
Lex Fridman (2:48:23.120)
is they're trying to use physics
Stephen Wolfram (2:48:25.240)
to get to a new level of what's possible in computing.
Lex Fridman (2:48:28.720)
And that's a completely valid activity.
Stephen Wolfram (2:48:30.920)
Whether you can really put, you know,
Lex Fridman (2:48:33.400)
whether you can say,
Stephen Wolfram (2:48:34.240)
oh, you can solve an NP complete problem.
Lex Fridman (2:48:36.000)
You can reduce exponential time to polynomial time.
Stephen Wolfram (2:48:39.120)
You know, we're not sure.
Lex Fridman (2:48:40.600)
And I'm suspecting the answer is no,
Lex Fridman (2:48:43.080)
but that's not relevant to the practical speed ups
Lex Fridman (2:48:46.080)
you can get by using different kinds of technologies,
Stephen Wolfram (2:48:48.520)
different kinds of physics to do basic computing.
Lex Fridman (2:48:52.320)
But you're saying, I mean,
Stephen Wolfram (2:48:53.680)
some of the models you're playing with,
Lex Fridman (2:48:55.280)
the indication is that to get all the sheep back together
Stephen Wolfram (2:49:02.640)
and, you know, to corral everything together,
Lex Fridman (2:49:05.960)
to get the actual solution to the algorithm is...
Stephen Wolfram (2:49:10.120)
You lose all the...
Lex Fridman (2:49:10.960)
You lose all of the...
Stephen Wolfram (2:49:12.240)
By the way, I mean, so again, this question,
Lex Fridman (2:49:14.400)
do we actually know what we're talking about
Lex Fridman (2:49:16.600)
about quantum computing and so on?
Lex Fridman (2:49:18.240)
So again, we're doing proof by compilation.
Lex Fridman (2:49:22.440)
So we have a quantum computing framework
Lex Fridman (2:49:24.880)
in Wolfram language,
Lex Fridman (2:49:26.080)
and which is, you know,
Lex Fridman (2:49:26.920)
a standard quantum computing framework
Stephen Wolfram (2:49:28.360)
that represents things in terms of the standard,
Lex Fridman (2:49:31.080)
you know, formalism of quantum mechanics.
Lex Fridman (2:49:32.840)
And we have a compiler that simply compiles
Lex Fridman (2:49:36.920)
the representation of quantum gates into multiway systems.
Stephen Wolfram (2:49:41.520)
So, and in fact, the message that I got
Lex Fridman (2:49:43.920)
was from somebody who's working on the project
Stephen Wolfram (2:49:46.000)
who has managed to compile one of the sort of
Lex Fridman (2:49:50.360)
a core formalism based on category theory
Lex Fridman (2:49:53.200)
and core quantum formalism into multiway systems.
Lex Fridman (2:49:57.520)
So this is...
Lex Fridman (2:49:58.360)
When you say multiway system, these multiway graphs?
Lex Fridman (2:50:00.160)
Yes.
Lex Fridman (2:50:01.000)
So you're compiling...
Lex Fridman (2:50:02.000)
Yeah, okay, that's awesome.
Lex Fridman (2:50:03.200)
And then you can do all kinds of experiments
Lex Fridman (2:50:05.200)
on that multiway graph.
Stephen Wolfram (2:50:06.280)
Right, but the point is that what we're saying is
Lex Fridman (2:50:08.640)
the thing we've got this representation
Stephen Wolfram (2:50:10.400)
of let's say Shor's algorithm
Lex Fridman (2:50:12.000)
in terms of standard quantum gates.
Lex Fridman (2:50:14.040)
And it's just a pure matter of sort of computation
Lex Fridman (2:50:17.480)
to just say that is equivalent.
Stephen Wolfram (2:50:19.240)
We will get the same result as running this multiway system.
Lex Fridman (2:50:23.360)
Can you do complexity analysis on that multiway system?
Stephen Wolfram (2:50:26.640)
Well, that's what we've been trying to do, yes.
Lex Fridman (2:50:28.600)
We're getting there.
Stephen Wolfram (2:50:29.440)
We haven't done that yet.
Lex Fridman (2:50:30.280)
I mean, there's a pretty good indication
Stephen Wolfram (2:50:32.520)
of how that's gonna work out.
Lex Fridman (2:50:33.480)
We've done, as I say, our computer experiments.
Stephen Wolfram (2:50:36.280)
We've unimpressively gotten to about two times three
Lex Fridman (2:50:39.440)
in terms of factorization,
Stephen Wolfram (2:50:41.080)
which is kind of about how far people have got
Lex Fridman (2:50:43.120)
with physical quantum computers as well.
Lex Fridman (2:50:45.440)
But yes, we will be able to do...
Lex Fridman (2:50:48.040)
We definitely will be able to do complexity analysis
Lex Fridman (2:50:50.480)
and we will be able to know.
Lex Fridman (2:50:51.800)
So the one remaining hope for quantum computing
Stephen Wolfram (2:50:55.240)
really, really working at this formal level
Lex Fridman (2:50:58.200)
of quantum brand exponential stuff being done
Stephen Wolfram (2:51:01.120)
in polynomial time and so on.
Lex Fridman (2:51:03.080)
The one hope, which is very bizarre,
Stephen Wolfram (2:51:05.280)
is that you can kind of piggyback
Lex Fridman (2:51:09.000)
on the expansion of branchial space.
Lex Fridman (2:51:11.240)
So here's how that might work.
Lex Fridman (2:51:13.480)
So you think, you know, energy conservation,
Stephen Wolfram (2:51:17.160)
standard thing in high school physics,
Lex Fridman (2:51:18.720)
energy is conserved, right?
Lex Fridman (2:51:20.600)
But now you imagine, you think about energy
Lex Fridman (2:51:23.640)
in the context of cosmology
Lex Fridman (2:51:25.000)
and the context of the whole universe.
Lex Fridman (2:51:26.920)
It's a much more complicated story.
Stephen Wolfram (2:51:28.680)
The expansion of the universe kind of violates
Lex Fridman (2:51:30.800)
energy conservation.
Lex Fridman (2:51:32.520)
And so for example, if you imagine you've got two galaxies,
Lex Fridman (2:51:35.000)
they're receding from each other very quickly.
Stephen Wolfram (2:51:37.080)
They've got two big central black holes.
Lex Fridman (2:51:39.400)
You connect a spring between these two central black holes.
Stephen Wolfram (2:51:43.040)
Not easy to do in practice,
Lex Fridman (2:51:44.640)
but let's imagine you could do it.
Stephen Wolfram (2:51:46.600)
Now that spring is being pulled apart.
Lex Fridman (2:51:49.200)
It's getting more potential energy in the spring
Stephen Wolfram (2:51:52.400)
as a result of the expansion of the universe.
Lex Fridman (2:51:55.120)
So in a sense, you are piggybacking on the expansion
Stephen Wolfram (2:51:59.040)
that exists in the universe
Lex Fridman (2:52:00.520)
and the sort of violation of energy conservation
Stephen Wolfram (2:52:03.120)
that's associated with that cosmological expansion
Lex Fridman (2:52:05.840)
to essentially get energy.
Stephen Wolfram (2:52:07.160)
You're essentially building a perpetual motion machine
Lex Fridman (2:52:09.680)
by using the expansion of the universe.
Lex Fridman (2:52:12.400)
And that is a physical version of that.
Lex Fridman (2:52:15.280)
It is conceivable that the same thing can be done
Stephen Wolfram (2:52:17.640)
in branchial space to essentially mine the expansion
Lex Fridman (2:52:22.640)
of the universe in branchial space
Stephen Wolfram (2:52:24.880)
as a way to get sort of quantum computing for free,
Lex Fridman (2:52:29.880)
so to speak, just from the expansion of the universe
Stephen Wolfram (2:52:32.280)
in branchial space.
Lex Fridman (2:52:33.520)
Now, the physical space version is kind of absurd
Lex Fridman (2:52:35.840)
and involves springs between black holes and so on.
Lex Fridman (2:52:39.520)
It's conceivable that the branchial space version
Stephen Wolfram (2:52:42.080)
is not as absurd
Lex Fridman (2:52:43.560)
and that it's actually something you can reach
Stephen Wolfram (2:52:45.840)
with physical things you can build in labs and so on.
Lex Fridman (2:52:48.600)
We don't know yet.
Stephen Wolfram (2:52:49.680)
Okay, so like you were saying,
Lex Fridman (2:52:51.320)
the branch of space might be expanding
Lex Fridman (2:52:54.040)
and there might be something that could be exploited.
Lex Fridman (2:52:57.120)
Right, in the same kind of way
Stephen Wolfram (2:52:59.040)
that you can exploit that expansion of the universe
Lex Fridman (2:53:03.720)
in principle, in physical space.
Stephen Wolfram (2:53:06.560)
You just have like a glimmer of hope.
Lex Fridman (2:53:08.520)
Right, I think that the,
Stephen Wolfram (2:53:09.640)
look, I think the real answer is going to be
Lex Fridman (2:53:11.800)
that for practical purposes,
Stephen Wolfram (2:53:13.960)
the official brand that says you can do exponential things
Lex Fridman (2:53:18.240)
in polynomial time is probably not gonna work.
Stephen Wolfram (2:53:20.480)
For people curious to kind of learn more,
Lex Fridman (2:53:22.320)
so this is more like, it's not middle school,
Stephen Wolfram (2:53:24.680)
we're gonna go to elementary school for a second.
Lex Fridman (2:53:27.880)
Maybe middle school, let's go to middle school.
Lex Fridman (2:53:31.320)
So if I were to try to maybe write a pamphlet
Lex Fridman (2:53:38.280)
of like Wolfram physics project for dummies,
Stephen Wolfram (2:53:42.760)
AKA for me, or maybe make a video on the basics,
Lex Fridman (2:53:47.280)
but not just the basics of the physics project,
Lex Fridman (2:53:51.240)
but the basics plus the most beautiful central ideas.
Lex Fridman (2:53:59.280)
How would you go about doing that?
Lex Fridman (2:54:01.200)
Could you help me out a little bit?
Lex Fridman (2:54:02.720)
Yeah, yeah, I mean, as a really practical matter,
Stephen Wolfram (2:54:05.760)
we have this kind of visual summary picture that we made,
Lex Fridman (2:54:10.280)
which I think is a pretty good,
Stephen Wolfram (2:54:12.320)
when I've tried to explain this to people
Lex Fridman (2:54:14.520)
and it's a pretty good place to start.
Stephen Wolfram (2:54:17.120)
As you got this rule, you apply the rule,
Lex Fridman (2:54:19.800)
you're building up this big hypergraph,
Stephen Wolfram (2:54:22.760)
you've got all these possibilities,
Lex Fridman (2:54:24.560)
you're kind of thinking about that
Stephen Wolfram (2:54:25.960)
in terms of quantum mechanics.
Lex Fridman (2:54:27.680)
I mean, that's a decent place to start.
Lex Fridman (2:54:30.640)
So basically the things we've talked about,
Lex Fridman (2:54:33.000)
which is space represented as a hypergraph,
Stephen Wolfram (2:54:37.120)
transformation of that space is kind of time.
Lex Fridman (2:54:40.760)
Yes.
Lex Fridman (2:54:41.600)
And then...
Lex Fridman (2:54:43.040)
Structure of that space,
Stephen Wolfram (2:54:45.080)
the curvature of that space has gravity.
Lex Fridman (2:54:47.840)
That can be explained without going anywhere
Stephen Wolfram (2:54:49.440)
near quantum mechanics.
Lex Fridman (2:54:51.240)
I would say that's actually easier to explain
Stephen Wolfram (2:54:53.120)
than special relativity.
Lex Fridman (2:54:55.200)
Oh, so going into general, so go into curvature.
Stephen Wolfram (2:54:58.440)
Yeah, I mean, special relativity,
Lex Fridman (2:54:59.880)
I think it's a little bit elaborate to explain.
Lex Fridman (2:55:03.520)
And honestly, you only care about it
Lex Fridman (2:55:05.600)
if you know about special relativity,
Stephen Wolfram (2:55:06.840)
if you know how special relativity
Lex Fridman (2:55:08.000)
is ordinarily derived and so on.
Lex Fridman (2:55:09.920)
So general relativity is easier.
Lex Fridman (2:55:11.800)
Is easier, yes.
Lex Fridman (2:55:12.800)
And then what about quantum?
Lex Fridman (2:55:13.800)
What's the easiest way to reveal...
Stephen Wolfram (2:55:16.320)
I think the basic point is just this.
Lex Fridman (2:55:19.320)
This fact that there are all these different branches,
Stephen Wolfram (2:55:22.160)
that there's this kind of map of how the branches work.
Lex Fridman (2:55:25.320)
And that, I mean, I think actually the recent things
Stephen Wolfram (2:55:30.600)
that we have about the double slit experiment
Lex Fridman (2:55:32.280)
are pretty good, because you can actually see this.
Stephen Wolfram (2:55:34.920)
You can see how the double slit phenomenon arises
Lex Fridman (2:55:39.080)
from just features of these graphs.
Stephen Wolfram (2:55:41.360)
Now, having said that,
Lex Fridman (2:55:43.880)
there is a little bit of sleight of hand there
Stephen Wolfram (2:55:47.080)
because the true story of the way
Lex Fridman (2:55:49.880)
that double slit thing works
Stephen Wolfram (2:55:51.800)
depends on the coordination of branchial space
Lex Fridman (2:55:55.080)
that, for example, in our internal team,
Stephen Wolfram (2:55:57.800)
there is still a vigorous battle going on
Lex Fridman (2:56:00.200)
about how that works.
Lex Fridman (2:56:01.560)
And what's becoming clear is...
Lex Fridman (2:56:04.320)
I mean, what's becoming clear
Stephen Wolfram (2:56:05.880)
is that it's mathematically really quite interesting.
Lex Fridman (2:56:08.840)
I mean, that is that there's a...
Stephen Wolfram (2:56:10.720)
It involves essentially putting space filling curves.
Lex Fridman (2:56:13.120)
You'll basically have a thing
Stephen Wolfram (2:56:14.120)
which is naturally two dimensional,
Lex Fridman (2:56:15.840)
and you're sort of mapping it into one dimension
Stephen Wolfram (2:56:18.800)
with a space filling curve.
Lex Fridman (2:56:20.000)
And it's like, why is it this space filling curve
Lex Fridman (2:56:21.640)
and another space filling curve?
Lex Fridman (2:56:23.360)
And that becomes a story about Riemann surfaces and things,
Lex Fridman (2:56:26.560)
and it's quite elaborate.
Lex Fridman (2:56:29.200)
But there's a more, a little bit sleight of hand way
Stephen Wolfram (2:56:32.640)
of doing it where it's surprisingly direct.
Lex Fridman (2:56:36.680)
It's...
Lex Fridman (2:56:37.520)
So a question that might be difficult to answer,
Lex Fridman (2:56:42.520)
but for several levels of people,
Lex Fridman (2:56:46.120)
could you give me advice on how we can learn more?
Lex Fridman (2:56:50.360)
Specifically, there is people that are completely outside
Lex Fridman (2:56:54.640)
and just curious and are captivated
Lex Fridman (2:56:57.080)
by the beauty of hypergraphs, actually.
Lex Fridman (2:57:00.880)
So people that just wanna explore, play around with this.
Lex Fridman (2:57:04.040)
Second level is people from, say, people like me
Stephen Wolfram (2:57:09.040)
who somehow got a PhD in computer science,
Lex Fridman (2:57:12.720)
but are not physicists.
Lex Fridman (2:57:14.240)
But fundamentally, the work you're doing
Lex Fridman (2:57:16.600)
is of computational nature.
Lex Fridman (2:57:18.720)
So it feels very accessible.
Lex Fridman (2:57:20.480)
So what can a person like that do to learn enough physics
Stephen Wolfram (2:57:27.480)
or not to be able to, one, explore the beauty of it,
Lex Fridman (2:57:31.640)
and two, the final level of contribute something
Stephen Wolfram (2:57:36.640)
of a level of even publishable,
Lex Fridman (2:57:40.280)
like strong, interesting ideas.
Lex Fridman (2:57:43.240)
So at all those layers, complete beginner,
Lex Fridman (2:57:46.200)
a CS person, and the CS person that wants to publish.
Stephen Wolfram (2:57:49.560)
I mean, I think that, I've written a bunch of stuff,
Lex Fridman (2:57:53.120)
a person called Jonathan Gorod,
Stephen Wolfram (2:57:54.440)
who's been a key person working on this project,
Lex Fridman (2:57:56.160)
has also written a bunch of stuff.
Lex Fridman (2:57:58.040)
And some other people started writing things too.
Lex Fridman (2:58:00.800)
And he's a physicist.
Stephen Wolfram (2:58:02.120)
Physicist.
Lex Fridman (2:58:02.960)
Well, he's, I would say, a mathematical physicist.
Stephen Wolfram (2:58:05.240)
Mathematical.
Lex Fridman (2:58:06.080)
Mathematical physicist.
Stephen Wolfram (2:58:06.920)
He's pretty mathematically sophisticated.
Lex Fridman (2:58:08.800)
He regularly outmathematicizes me.
Stephen Wolfram (2:58:11.640)
Yeah, strong mathematical physicist.
Lex Fridman (2:58:14.720)
Yeah, I looked at some of the papers.
Stephen Wolfram (2:58:16.560)
Right, but so, I mean,
Lex Fridman (2:58:19.440)
I wrote this kind of original announcement blog post
Stephen Wolfram (2:58:22.440)
about this project, which people seem to have found.
Lex Fridman (2:58:25.480)
I've been really happy, actually, that people who,
Stephen Wolfram (2:58:30.880)
people seem to have grokked key points from that,
Lex Fridman (2:58:34.760)
much deeper key points, people seem to have grokked
Stephen Wolfram (2:58:37.400)
than I thought they would grokk.
Lex Fridman (2:58:39.520)
And that's a kind of a long blog post
Stephen Wolfram (2:58:41.600)
that explains some of the things we talked about,
Lex Fridman (2:58:43.120)
like the hypergraph and the basic rules.
Lex Fridman (2:58:45.360)
And I don't, does it, I forget,
Lex Fridman (2:58:47.920)
it doesn't have any quantum mechanics in here.
Stephen Wolfram (2:58:49.880)
It does. It does.
Lex Fridman (2:58:51.920)
But we know a little bit more since that blog post
Stephen Wolfram (2:58:54.720)
that probably clarifies,
Lex Fridman (2:58:56.480)
but that blog post does a pretty decent job.
Stephen Wolfram (2:58:59.560)
And, you know, talking about things like, again,
Lex Fridman (2:59:02.160)
something we didn't mention,
Stephen Wolfram (2:59:03.000)
the fact that the uncertainty principle
Lex Fridman (2:59:04.960)
is a consequence of curvature in branchial space.
Lex Fridman (2:59:07.760)
How much physics should a person know
Lex Fridman (2:59:10.120)
to be able to understand the beauty of this framework
Lex Fridman (2:59:14.480)
and to contribute something novel?
Lex Fridman (2:59:16.880)
Okay, so I think that those are different questions.
Lex Fridman (2:59:20.200)
So, I mean, I think that the, why does this work?
Lex Fridman (2:59:23.840)
Why does this make any sense?
Stephen Wolfram (2:59:27.440)
To really know that,
Lex Fridman (2:59:28.480)
you have to know a fair amount of physics, okay?
Lex Fridman (2:59:32.040)
And for example, have a decent understanding.
Lex Fridman (2:59:33.520)
When you say, why does this work?
Stephen Wolfram (2:59:35.040)
You're referring to the connection between this model
Lex Fridman (2:59:38.480)
and general relativity, for example.
Stephen Wolfram (2:59:40.600)
You have to understand something about general relativity.
Lex Fridman (2:59:43.160)
There's also a side of this where just
Stephen Wolfram (2:59:45.240)
as the pure mathematical framework is fascinating.
Lex Fridman (2:59:47.880)
Yes.
Stephen Wolfram (2:59:48.720)
If you throw the physics out completely.
Lex Fridman (2:59:50.360)
Then it's quite accessible to, I mean, you know,
Stephen Wolfram (2:59:52.520)
I wrote this sort of long technical introduction
Lex Fridman (2:59:55.280)
to the project, which seems to have been very accessible
Stephen Wolfram (2:59:58.480)
to people who are, you know, who understand computation
Lex Fridman (30:01.480)
the certain kind of dynamic to human interaction.
Lex Fridman (30:04.720)
So like large groups and small groups,
Lex Fridman (30:08.640)
I think it matters who the groups are.
Stephen Wolfram (30:10.520)
For example, you could imagine large,
Lex Fridman (30:12.600)
depends how you define large,
Lex Fridman (30:13.720)
but you can imagine groups of 30 people,
Lex Fridman (30:17.120)
as long as they are cliques or whatever.
Stephen Wolfram (30:22.440)
Right.
Lex Fridman (30:23.280)
As long as the outgoing degree of that graph is small
Stephen Wolfram (30:27.640)
or something like that,
Lex Fridman (30:28.480)
like you can imagine some beautiful underlying rule
Stephen Wolfram (30:31.360)
of human dynamic interaction where I can still be happy,
Lex Fridman (30:34.640)
where I can have a conversation with you
Lex Fridman (30:36.520)
and a bunch of other people that mean a lot to me in my life
Lex Fridman (30:39.640)
and then stay away from the bigger, I don't know,
Stephen Wolfram (30:42.560)
not going to a Miley Cyrus concert or something like that
Lex Fridman (30:45.600)
and figuring out mathematically some nice.
Stephen Wolfram (30:49.840)
See, this is an interesting thing.
Lex Fridman (30:51.080)
So I mean, this is the question of what you're describing
Stephen Wolfram (30:54.760)
is kind of the problem of the many situations
Lex Fridman (30:59.320)
where you would like to get away
Stephen Wolfram (31:00.600)
from computational irreducibility.
Lex Fridman (31:02.040)
A classic one in physics is thermodynamics.
Stephen Wolfram (31:05.080)
The second law of thermodynamics,
Lex Fridman (31:06.840)
the law that says entropy tends to increase things
Stephen Wolfram (31:09.880)
that start orderly tend to get more disordered,
Lex Fridman (31:13.240)
or which is also the thing that says,
Stephen Wolfram (31:15.040)
given that you have a bunch of heat,
Lex Fridman (31:16.640)
it's hard, heat is the microscopic motion of molecules,
Stephen Wolfram (31:19.800)
it's hard to turn that heat into systematic mechanical work.
Lex Fridman (31:23.600)
It's hard to just take something being hot
Lex Fridman (31:26.240)
and turn that into, oh, all the atoms are gonna line up
Lex Fridman (31:29.840)
in the bar of metal and the piece of metal
Stephen Wolfram (31:31.520)
is gonna shoot in some direction.
Lex Fridman (31:33.600)
That's essentially the same problem
Stephen Wolfram (31:35.800)
as how do you go from this computationally irreducible
Lex Fridman (31:40.040)
mess of things happening
Lex Fridman (31:41.680)
and get something you want out of it.
Lex Fridman (31:43.560)
It's kind of mining, you're kind of,
Stephen Wolfram (31:45.760)
now, actually I've understood in recent years
Lex Fridman (31:48.320)
that the story of thermodynamics
Stephen Wolfram (31:50.880)
is actually precisely a story of computational irreducibility,
Lex Fridman (31:54.400)
but it is a, it is already an analogy.
Stephen Wolfram (31:58.600)
You can kind of see that as can you take the,
Lex Fridman (32:02.080)
what you're asking to do there
Stephen Wolfram (32:03.560)
is you're asking to go from the kind of,
Lex Fridman (32:07.840)
the mess of all these complicated human interactions
Lex Fridman (32:10.080)
and all this kind of computational processes going on
Lex Fridman (32:12.360)
and you say, I want to achieve
Stephen Wolfram (32:14.120)
this particular thing out of it.
Lex Fridman (32:15.240)
I want to kind of extract from the heat of what's happening.
Stephen Wolfram (32:18.680)
I want to kind of extract this useful piece
Lex Fridman (32:22.160)
of sort of mechanical work that I find helpful.
Stephen Wolfram (32:25.240)
I mean.
Lex Fridman (32:26.080)
Do you have a hope for the pandemic?
Lex Fridman (32:27.320)
So we'll talk about physics,
Lex Fridman (32:28.600)
but for the pandemic, can that be extracted?
Lex Fridman (32:31.320)
Do you think?
Lex Fridman (32:32.160)
What's your intuition?
Stephen Wolfram (32:33.120)
The good news is the curves basically,
Lex Fridman (32:36.520)
for reasons we don't understand,
Stephen Wolfram (32:38.480)
the curves, the clearly measurable mortality curves
Lex Fridman (32:42.560)
and so on for the Northern Hemisphere have gone down.
Stephen Wolfram (32:46.360)
Yeah, but the bad news is that it could be a lot worse
Lex Fridman (32:50.320)
for future viruses.
Lex Fridman (32:51.640)
And what this pandemic revealed is we're highly unprepared
Lex Fridman (32:55.200)
for the discovery of the pockets of reducibility
Stephen Wolfram (32:59.840)
within a pandemic that's much more dangerous.
Lex Fridman (33:02.560)
Well, my guess is the specific risk of viral pandemics,
Stephen Wolfram (33:07.400)
you know, that the pure virology
Lex Fridman (33:10.400)
and immunology of the thing,
Stephen Wolfram (33:12.760)
this will cause that to advance to the point
Lex Fridman (33:14.720)
where this particular risk
Stephen Wolfram (33:16.640)
is probably considerably mitigated.
Lex Fridman (33:19.040)
But is the structure of modern society robust
Lex Fridman (33:25.160)
to all kinds of risks?
Lex Fridman (33:26.920)
Well, the answer is clearly no.
Lex Fridman (33:29.160)
And it's surprising to me the extent to which people,
Lex Fridman (33:34.120)
as I say, it's kind of scary actually
Lex Fridman (33:37.320)
how much people believe in science.
Lex Fridman (33:39.360)
That is people say, oh, you know,
Stephen Wolfram (33:41.560)
because the science says this, that and the other,
Lex Fridman (33:43.160)
we'll do this and this and this,
Stephen Wolfram (33:44.320)
even though from a sort of common sense point of view,
Lex Fridman (33:46.760)
it's a little bit crazy and people are not prepared
Lex Fridman (33:50.440)
and it doesn't really work in society
Lex Fridman (33:52.600)
as it is for people to say,
Stephen Wolfram (33:53.600)
well, actually we don't really know how the science works.
Lex Fridman (33:56.520)
People say, well, tell us what to do.
Lex Fridman (33:58.600)
Yeah, because then, yeah, what's the alternative?
Lex Fridman (34:01.600)
For the masses, it's difficult to sit,
Stephen Wolfram (34:04.960)
it's difficult to meditate on computational reducibility.
Lex Fridman (34:08.560)
It's difficult to sit,
Stephen Wolfram (34:10.280)
it's difficult to enjoy a good dinner meal
Lex Fridman (34:13.120)
while knowing that you know nothing about the world.
Stephen Wolfram (34:15.600)
Well, I think this is a place where, you know,
Lex Fridman (34:17.800)
this is what politicians and political leaders do
Stephen Wolfram (34:21.160)
for a living, so to speak,
Lex Fridman (34:22.120)
is you've got to make some decision about what to do.
Lex Fridman (34:24.880)
And it's...
Lex Fridman (34:25.840)
Tell some narrative that while amidst the mystery
Lex Fridman (34:29.760)
and knowing not much about the past or the future,
Lex Fridman (34:33.760)
still telling a narrative that somehow gives people hope
Stephen Wolfram (34:37.240)
that we know what the heck we're doing.
Lex Fridman (34:39.200)
Yeah, and get society through the issue.
Stephen Wolfram (34:41.520)
You know, even though, you know,
Lex Fridman (34:43.440)
the idea that we're just gonna, you know,
Stephen Wolfram (34:45.560)
sort of be able to get the definitive answer from science
Lex Fridman (34:48.600)
and it's gonna tell us exactly what to do.
Stephen Wolfram (34:50.600)
Unfortunately, you know, it's interesting
Lex Fridman (34:54.360)
because let me point out that if that was possible,
Stephen Wolfram (34:56.880)
if science could always tell us what to do,
Lex Fridman (34:59.200)
then in a sense, our, you know,
Stephen Wolfram (35:01.920)
that would be a big downer for our lives.
Lex Fridman (35:03.960)
If science could always tell us
Lex Fridman (35:05.080)
what the answer is gonna be,
Lex Fridman (35:06.760)
it's like, well, you know,
Stephen Wolfram (35:08.720)
it's kind of fun to live one's life
Lex Fridman (35:10.120)
and just sort of see what happens.
Stephen Wolfram (35:11.720)
If one could always just say,
Lex Fridman (35:12.960)
let me check my science.
Stephen Wolfram (35:15.080)
Oh, I know, you know,
Lex Fridman (35:16.760)
the result of everything is gonna be 42.
Stephen Wolfram (35:18.320)
I don't need to live my life and do what I do.
Lex Fridman (35:21.000)
It's just, we already know the answer.
Stephen Wolfram (35:23.000)
It's actually good news in a sense
Lex Fridman (35:24.840)
that there is this phenomenon
Stephen Wolfram (35:25.960)
of computational irreducibility
Lex Fridman (35:27.640)
that doesn't allow you to just sort of jump through time
Lex Fridman (35:30.760)
and say, this is the answer, so to speak.
Lex Fridman (35:33.680)
And that's, so that's a good thing.
Stephen Wolfram (35:35.160)
The bad thing is it doesn't allow you to jump through time
Lex Fridman (35:38.120)
and know what the answer is.
Stephen Wolfram (35:39.640)
It's scary.
Lex Fridman (35:40.960)
Do you think we're gonna be okay as a human civilization?
Stephen Wolfram (35:44.160)
You said, we don't know.
Lex Fridman (35:46.120)
Absolutely.
Lex Fridman (35:47.920)
Do you think we'll prosper or destroy ourselves?
Lex Fridman (35:53.920)
In general?
Stephen Wolfram (35:54.760)
In general.
Lex Fridman (35:55.720)
I'm an optimist.
Stephen Wolfram (35:57.760)
No, I think that, you know,
Lex Fridman (35:59.200)
it'll be interesting to see, for example,
Stephen Wolfram (36:01.000)
with this, you know, pandemic,
Lex Fridman (36:02.480)
I, you know, to me, you know,
Stephen Wolfram (36:05.720)
when you look at like organizations, for example,
Lex Fridman (36:08.320)
you know, having some kind of perturbation,
Stephen Wolfram (36:10.920)
some kick to the system,
Lex Fridman (36:12.840)
usually the end result of that is actually quite good.
Stephen Wolfram (36:16.120)
You know, unless it kills the system,
Lex Fridman (36:17.720)
it's actually quite good usually.
Lex Fridman (36:19.520)
And I think in this case, you know, people,
Lex Fridman (36:22.280)
I mean, my impression, you know,
Stephen Wolfram (36:23.840)
it's a little weird for me because, you know,
Lex Fridman (36:25.400)
I've been a remote tech CEO for 30 years.
Stephen Wolfram (36:28.000)
It doesn't, you know, this is bizarrely, you know,
Lex Fridman (36:30.720)
and the fact that, you know, like this coming to see you here
Stephen Wolfram (36:33.920)
is the first time in six months that I've been like,
Lex Fridman (36:39.160)
you know, in a building other than my house, okay?
Stephen Wolfram (36:41.360)
So, you know, I'm a kind of ridiculous outlier
Lex Fridman (36:46.160)
in these kinds of things.
Lex Fridman (36:47.040)
But overall, your sense is when you shake up the system
Lex Fridman (36:50.920)
and throw in chaos that you challenge the system,
Stephen Wolfram (36:55.200)
we humans emerge better.
Lex Fridman (36:57.720)
Seems to be that way.
Lex Fridman (36:58.800)
Who's to know?
Lex Fridman (36:59.640)
I think that, you know, people, you know,
Stephen Wolfram (37:01.920)
my sort of vague impression is that people are sort of,
Lex Fridman (37:05.040)
you know, oh, what's actually important?
Lex Fridman (37:07.280)
You know, what is worth caring about and so on?
Lex Fridman (37:10.400)
And that seems to be something that perhaps is more,
Stephen Wolfram (37:14.280)
you know, emergent in this kind of situation.
Lex Fridman (37:16.840)
It's so fascinating that on the individual level,
Stephen Wolfram (37:19.840)
we have our own complex cognition.
Lex Fridman (37:22.320)
We have consciousness, we have intelligence,
Stephen Wolfram (37:24.080)
we're trying to figure out little puzzles.
Lex Fridman (37:25.960)
And then that somehow creates this graph
Stephen Wolfram (37:28.280)
of collective intelligence.
Lex Fridman (37:30.280)
Well, we figure out, and then you throw in these viruses
Stephen Wolfram (37:33.920)
of which there's millions different, you know,
Lex Fridman (37:36.600)
there's entire taxonomy and the viruses are thrown
Stephen Wolfram (37:39.360)
into the system of collective human intelligence.
Lex Fridman (37:42.640)
And when little humans figure out what to do about it,
Stephen Wolfram (37:45.680)
we get like, we tweet stuff about information.
Lex Fridman (37:48.680)
There's doctors as conspiracy theorists.
Lex Fridman (37:50.720)
And then we play with different information.
Lex Fridman (37:53.120)
I mean, the whole of it is fascinating.
Stephen Wolfram (37:55.680)
I am like you also very optimistic,
Lex Fridman (37:58.080)
but you said the computational reducibility.
Stephen Wolfram (38:04.120)
There's always a fear of the darkness
Lex Fridman (38:06.440)
of the uncertainty before us.
Stephen Wolfram (38:09.760)
Yeah, I know. And it's scary.
Lex Fridman (38:11.120)
I mean, the thing is, if you knew everything,
Stephen Wolfram (38:13.400)
it will be boring.
Lex Fridman (38:15.280)
And it would be, and then, and worse than boring,
Lex Fridman (38:19.720)
so to speak.
Lex Fridman (38:20.560)
It would reveal the pointlessness, so to speak.
Lex Fridman (38:24.120)
And in a sense, the fact that there is
Lex Fridman (38:26.540)
this computational irreducibility,
Stephen Wolfram (38:28.000)
it's like as we live our lives, so to speak,
Lex Fridman (38:30.360)
something is being achieved.
Stephen Wolfram (38:31.660)
We're computing what our lives, you know,
Lex Fridman (38:35.520)
what happens in our lives.
Stephen Wolfram (38:36.900)
That's funny.
Lex Fridman (38:37.740)
So the computational reducibility is kind of like,
Stephen Wolfram (38:40.520)
it gives the meaning to life.
Lex Fridman (38:41.980)
It is the meaning of life.
Stephen Wolfram (38:43.360)
Computational reducibility is the meaning of life.
Lex Fridman (38:45.720)
There you go.
Stephen Wolfram (38:46.560)
It gives it meaning, yes.
Lex Fridman (38:47.480)
I mean, it's what causes it to not be something
Stephen Wolfram (38:51.580)
where you can just say, you know,
Lex Fridman (38:53.540)
you went through all those steps to live your life,
Lex Fridman (38:55.760)
but we already knew what the answer was.
Lex Fridman (38:58.560)
Hold on one second.
Stephen Wolfram (38:59.400)
I'm going to use my handy Wolfram Alpha sunburn
Lex Fridman (39:03.120)
computation thing, so long as I can get network here.
Stephen Wolfram (39:06.120)
There we go.
Lex Fridman (39:08.240)
Oh, actually, you know what?
Stephen Wolfram (39:09.460)
It says sunburn unlikely.
Lex Fridman (39:11.460)
This is a QA moment.
Stephen Wolfram (39:12.680)
This is a good moment.
Lex Fridman (39:16.720)
Okay, well, let me just check what it thinks.
Stephen Wolfram (39:20.560)
See why it thinks that.
Lex Fridman (39:22.000)
It doesn't seem like my intuition.
Stephen Wolfram (39:23.540)
This is one of these cases where we can,
Lex Fridman (39:25.360)
the question is, do we trust the science
Lex Fridman (39:27.800)
or do we use common sense?
Lex Fridman (39:30.360)
The UV thing is cool.
Stephen Wolfram (39:32.000)
Yeah, yeah, well, we'll see.
Lex Fridman (39:32.880)
This is a QA moment, as I say.
Lex Fridman (39:35.040)
It's, do we trust the product?
Lex Fridman (39:37.960)
Yes, we trust the product, so.
Lex Fridman (39:39.560)
And then there'll be a data point either way.
Lex Fridman (39:42.240)
If I'm desperately sunburned,
Stephen Wolfram (39:43.560)
I will send in an angry feedback.
Lex Fridman (39:46.840)
Because we mentioned the concept so much
Lex Fridman (39:50.760)
and a lot of people know it,
Lex Fridman (39:51.960)
but can you say what computational reducibility is?
Stephen Wolfram (39:54.480)
Yeah, right.
Lex Fridman (39:55.320)
The question is, if you think about things
Stephen Wolfram (39:58.760)
that happen as being computations,
Lex Fridman (3:00:01.400)
and formal abstract ideas, but are not specialists
Stephen Wolfram (3:00:04.960)
in physics or other kinds of things.
Lex Fridman (3:00:07.240)
I mean, the thing with the physics part of it is,
Stephen Wolfram (3:00:10.280)
you know, there's both a way of thinking
Lex Fridman (3:00:14.600)
and literally a mathematical formalism.
Stephen Wolfram (3:00:16.840)
I mean, it's like, you know,
Lex Fridman (3:00:18.040)
to know that we get the Einstein equations,
Stephen Wolfram (3:00:19.960)
to know we get the energy momentum tensor,
Lex Fridman (3:00:22.120)
you kind of have to know what the energy momentum tensor is.
Lex Fridman (3:00:24.800)
And that's physics.
Lex Fridman (3:00:25.880)
I mean, that's kind of graduate level physics basically.
Lex Fridman (3:00:29.240)
And so that, you know, making that final connection
Lex Fridman (3:00:33.360)
is requires some depth of physics knowledge.
Stephen Wolfram (3:00:37.440)
I mean, that's the unfortunate thing,
Lex Fridman (3:00:38.880)
the difference in machine learning and physics
Stephen Wolfram (3:00:40.600)
in the 21st century.
Lex Fridman (3:00:42.880)
Is it really out of reach of a year or two worth of study?
Stephen Wolfram (3:00:47.440)
No, you could get it in a year or two,
Lex Fridman (3:00:49.920)
but you can't get it in a month.
Stephen Wolfram (3:00:51.600)
Right.
Lex Fridman (3:00:52.440)
I mean.
Stephen Wolfram (3:00:53.280)
So, but it doesn't require necessarily like 15 years.
Lex Fridman (3:00:56.160)
No, it does not.
Lex Fridman (3:00:57.000)
And in fact, a lot of what has happened with this project
Lex Fridman (3:01:00.240)
makes a lot of this stuff much more accessible.
Stephen Wolfram (3:01:02.800)
There are things where it has been quite difficult
Lex Fridman (3:01:04.800)
to explain what's going on.
Lex Fridman (3:01:06.040)
And it requires much more, you know,
Lex Fridman (3:01:09.160)
having the concreteness of being able to do simulations,
Stephen Wolfram (3:01:11.840)
knowing that this thing that you might've thought
Lex Fridman (3:01:15.160)
was just an analogy is really actually what's going on,
Stephen Wolfram (3:01:19.000)
makes one feel much more secure
Lex Fridman (3:01:21.040)
about just sort of saying, this is how this works.
Lex Fridman (3:01:24.240)
And I think it will be, you know,
Lex Fridman (3:01:26.240)
the, I'm hoping the textbooks of the future,
Stephen Wolfram (3:01:28.520)
the physics textbooks of the future,
Lex Fridman (3:01:30.480)
there will be a certain compression.
Stephen Wolfram (3:01:32.120)
There will be things that used to be
Lex Fridman (3:01:33.360)
very much more elaborate because for example,
Stephen Wolfram (3:01:35.240)
even doing continuous mathematics
Lex Fridman (3:01:36.720)
versus this discrete mathematics,
Stephen Wolfram (3:01:38.880)
that, you know, to know how things work
Lex Fridman (3:01:40.680)
in continuous mathematics,
Stephen Wolfram (3:01:41.800)
you have to be talking about stuff
Lex Fridman (3:01:43.120)
and waving your hands about things.
Stephen Wolfram (3:01:44.760)
Whereas with discrete, the discrete version,
Lex Fridman (3:01:47.120)
it's just like, here is a picture.
Stephen Wolfram (3:01:49.280)
This is how it works.
Lex Fridman (3:01:50.920)
And there's no, oh, do we get the limit right?
Stephen Wolfram (3:01:53.240)
Did this, you know, did this thing that is of,
Lex Fridman (3:01:55.560)
you know, zero, you know, measure zero object,
Stephen Wolfram (3:01:59.440)
you know, interact with this thing in the right way.
Lex Fridman (3:02:01.960)
You don't have to have that whole discussion.
Stephen Wolfram (3:02:03.400)
It's just like, here's a picture, you know,
Lex Fridman (3:02:05.520)
this is what it does.
Stephen Wolfram (3:02:07.160)
And, you know, you can, then it takes more effort to say,
Lex Fridman (3:02:09.560)
what does it do in the limit when the picture gets very big?
Lex Fridman (3:02:12.040)
But you can do experiments
Lex Fridman (3:02:13.120)
to build up an intuition actually.
Stephen Wolfram (3:02:14.360)
Yes, right.
Lex Fridman (3:02:15.200)
And you can get sort of core intuition for what's going on.
Stephen Wolfram (3:02:17.480)
Now, in terms of contributing to this, the, you know,
Lex Fridman (3:02:20.160)
I would say that the study of the computational universe
Lex Fridman (3:02:23.240)
and how all these programs work
Lex Fridman (3:02:24.520)
in the computational universe,
Stephen Wolfram (3:02:26.000)
there's just an unbelievable amount to do there.
Lex Fridman (3:02:28.760)
And it is very close to the surface.
Stephen Wolfram (3:02:31.320)
That is, you know, high school kids,
Lex Fridman (3:02:34.400)
you can do experiments.
Stephen Wolfram (3:02:36.080)
It's not, you know, and you can discover things.
Lex Fridman (3:02:38.960)
I mean, you know, we, you can discover stuff about,
Stephen Wolfram (3:02:42.600)
I don't know, like this thing about expansion
Lex Fridman (3:02:44.320)
of branchial space.
Stephen Wolfram (3:02:45.160)
That's an absolutely accessible thing to look at.
Lex Fridman (3:02:47.760)
Now, you know, the main issue with doing these things
Stephen Wolfram (3:02:50.680)
is not, there isn't a lot of technical depth difficulty
Lex Fridman (3:02:55.200)
there.
Stephen Wolfram (3:02:56.040)
The actual doing of the experiments, you know,
Lex Fridman (3:02:58.040)
all the code is all on our website to do all these things.
Stephen Wolfram (3:03:01.360)
The real thing is sort of the judgment
Lex Fridman (3:03:03.880)
of what's the right experiment to do.
Lex Fridman (3:03:05.600)
How do you interpret what you see?
Lex Fridman (3:03:07.800)
That's the part that, you know,
Stephen Wolfram (3:03:09.920)
people will do amazing things with.
Lex Fridman (3:03:11.840)
And that's the part that, but,
Lex Fridman (3:03:13.520)
but it isn't like you have to have done 10 years of study
Lex Fridman (3:03:17.040)
to get to the point where you can do the experiments.
Stephen Wolfram (3:03:18.840)
You don't.
Lex Fridman (3:03:19.680)
That's a cool thing you can do experiments day one,
Stephen Wolfram (3:03:21.840)
basically.
Lex Fridman (3:03:22.680)
That's the amazing thing about,
Lex Fridman (3:03:25.040)
and you've actually put the tools out there.
Lex Fridman (3:03:27.240)
It's beautiful.
Stephen Wolfram (3:03:28.080)
It's mysterious.
Lex Fridman (3:03:29.640)
There's still, I would say, maybe you can correct me.
Stephen Wolfram (3:03:32.720)
It feels like there's a huge number of log hanging fruit
Lex Fridman (3:03:36.440)
on the mathematical side, at least not the physics side,
Stephen Wolfram (3:03:39.440)
perhaps.
Lex Fridman (3:03:40.280)
No, there's, look on the, on the, okay.
Stephen Wolfram (3:03:42.800)
On the physics side, we are,
Lex Fridman (3:03:45.160)
we're definitely in harvesting mode, you know.
Lex Fridman (3:03:48.440)
Of which, which fruit, the low hanging ones or?
Lex Fridman (3:03:50.960)
The low hanging ones, yeah, right.
Stephen Wolfram (3:03:52.560)
I mean, basically here's the thing.
Lex Fridman (3:03:54.200)
There's a certain list of, you know,
Stephen Wolfram (3:03:56.120)
here are the effects in quantum mechanics.
Lex Fridman (3:03:57.800)
Here are the effects in general activity.
Stephen Wolfram (3:03:59.760)
It's just like industrial harvesting.
Lex Fridman (3:04:02.240)
It's like, can we get this one, this one, this one,
Lex Fridman (3:04:04.480)
this one, this one?
Lex Fridman (3:04:05.560)
And the thing that's really, you know,
Stephen Wolfram (3:04:07.560)
interesting and satisfying, and it's like, you know,
Lex Fridman (3:04:10.120)
is one climbing the right mountain?
Lex Fridman (3:04:11.520)
Does one have the right model?
Lex Fridman (3:04:12.920)
The thing that's just amazing is, you know,
Lex Fridman (3:04:15.920)
we keep on like, are we going to get this one?
Lex Fridman (3:04:18.280)
How hard is this one?
Stephen Wolfram (3:04:19.920)
It's like, oh, you know, it looks really hard.
Lex Fridman (3:04:22.920)
It looks really hard.
Stephen Wolfram (3:04:23.800)
Oh, actually we can get it.
Lex Fridman (3:04:26.760)
And.
Lex Fridman (3:04:27.600)
And you're, you're continually surprised.
Lex Fridman (3:04:29.040)
I mean, it seems like I've been following your progress.
Stephen Wolfram (3:04:31.520)
It's kind of exciting.
Lex Fridman (3:04:32.520)
All the, in harvesting mode,
Stephen Wolfram (3:04:34.320)
all the things you're picking up along the way.
Lex Fridman (3:04:35.880)
Right, right.
Stephen Wolfram (3:04:36.720)
No, I mean, it's, it's the thing that is,
Lex Fridman (3:04:38.320)
I keep on thinking it's going to be more difficult
Stephen Wolfram (3:04:40.200)
than it is.
Lex Fridman (3:04:41.040)
Now that's a, you know, that's a, who knows what,
Stephen Wolfram (3:04:43.360)
I mean, the one thing, so the, the, the,
Lex Fridman (3:04:45.880)
the thing that's been a, was a big thing
Stephen Wolfram (3:04:48.640)
that I think we're, we're pretty close to.
Lex Fridman (3:04:50.900)
I mean, I can give you a little bit of the roadmap.
Stephen Wolfram (3:04:52.480)
It's sort of interesting to see, it's like,
Lex Fridman (3:04:54.640)
what are particles?
Lex Fridman (3:04:55.720)
What are things like electrons?
Lex Fridman (3:04:56.880)
How do they really work?
Stephen Wolfram (3:04:58.520)
Are you close to get like, what, what's a,
Lex Fridman (3:05:01.400)
are you close to trying to understand like the atom,
Lex Fridman (3:05:03.800)
the electrons, neutrons, protons?
Lex Fridman (3:05:06.480)
Okay, so this is, this is the stack.
Lex Fridman (3:05:08.080)
So the first thing we want to understand is
Lex Fridman (3:05:11.680)
the quantization of spin.
Lex Fridman (3:05:13.360)
So particles, they, they kind of spin,
Lex Fridman (3:05:15.960)
they have a certain angular momentum,
Stephen Wolfram (3:05:18.120)
that angular momentum,
Lex Fridman (3:05:19.400)
even though the masses of particles are all over the place,
Stephen Wolfram (3:05:22.280)
you know, the electron has a mass of 0.511 MeV,
Lex Fridman (3:05:25.920)
but you know, the proton is 938 MeV, et cetera, et cetera,
Stephen Wolfram (3:05:28.760)
et cetera, they're all kind of random numbers.
Lex Fridman (3:05:30.640)
The, the spins of all these particles
Stephen Wolfram (3:05:32.720)
are either integers or half integers.
Lex Fridman (3:05:34.880)
And that's a fact that was discovered in the 1920s, I guess.
Stephen Wolfram (3:05:38.440)
The, I think that we are close to understanding
Lex Fridman (3:05:44.120)
why spin is quantized.
Lex Fridman (3:05:45.800)
And that's a, and it, it appears to be
Lex Fridman (3:05:48.280)
a quite elaborate mathematical story
Stephen Wolfram (3:05:50.280)
about homotopic groups in twister space
Lex Fridman (3:05:53.040)
and all kinds of things.
Lex Fridman (3:05:54.400)
But bottom line is that seems within reach.
Lex Fridman (3:05:58.000)
And that's, that's a big deal
Stephen Wolfram (3:05:59.200)
because that's a very core feature of understanding
Lex Fridman (3:06:01.680)
how particles work in quantum mechanics.
Stephen Wolfram (3:06:04.160)
Another core feature is this difference between particles
Lex Fridman (3:06:07.280)
that obey the exclusion principle and sort of stay apart,
Stephen Wolfram (3:06:10.600)
that leads to the stability of matter and things like that,
Lex Fridman (3:06:13.680)
and particles that love to get together
Lex Fridman (3:06:15.360)
and be in the same state, things like photons,
Lex Fridman (3:06:18.120)
that, and that's what leads to phenomena like lasers,
Stephen Wolfram (3:06:22.160)
where you can get sort of coherently
Lex Fridman (3:06:23.800)
everything in the same state.
Stephen Wolfram (3:06:25.280)
That difference is the particles of integer spin
Lex Fridman (3:06:29.240)
are bosons like to get together in the same state,
Stephen Wolfram (3:06:31.760)
the particles of half integer spin are fermions,
Lex Fridman (3:06:34.440)
like electrons that they tend to stay apart.
Lex Fridman (3:06:37.520)
And so the question is, can we get that in our models?
Lex Fridman (3:06:41.800)
And, oh, just the last few days, I think we made,
Stephen Wolfram (3:06:45.400)
I mean, I think the story of,
Lex Fridman (3:06:47.920)
I mean, it's one of these things where we're really close.
Lex Fridman (3:06:51.400)
Is this connected fermions and bosons?
Lex Fridman (3:06:53.680)
Yeah, yeah.
Lex Fridman (3:06:54.520)
So this was what happens is what seems to happen, okay?
Lex Fridman (3:06:57.720)
It's, you know, subject to revision in the next few days.
Lex Fridman (3:07:01.440)
But what seems to be the case is that
Lex Fridman (3:07:04.200)
bosons are associated with essentially
Stephen Wolfram (3:07:06.360)
merging in multiway graphs,
Lex Fridman (3:07:08.400)
and fermions are associated with branching
Stephen Wolfram (3:07:10.440)
in multiway graphs.
Lex Fridman (3:07:11.920)
And that essentially the exclusion principle
Stephen Wolfram (3:07:15.120)
is the fact that in branchial space,
Lex Fridman (3:07:18.320)
things have a certain extent in branchial space
Stephen Wolfram (3:07:21.360)
that in which things are being sort of forced apart
Lex Fridman (3:07:24.000)
in branchial space, whereas the case of bosons,
Stephen Wolfram (3:07:26.280)
they get, they come together in branchial space.
Lex Fridman (3:07:29.400)
And the real question is, can we explain the relationship
Stephen Wolfram (3:07:32.360)
between that and these things called spinners,
Lex Fridman (3:07:34.520)
which are the representation of half integer spin particles
Stephen Wolfram (3:07:37.440)
that have this weird feature that usually when you go
Lex Fridman (3:07:39.320)
around 360 degree rotation,
Stephen Wolfram (3:07:41.520)
you get back to where you started from.
Lex Fridman (3:07:43.400)
But for a spinner, you don't get back
Stephen Wolfram (3:07:44.760)
to where you started from.
Lex Fridman (3:07:46.040)
It takes 720 degrees of rotation to get back
Stephen Wolfram (3:07:48.800)
to where you started from.
Lex Fridman (3:07:50.240)
And we are just, it feels like we are,
Stephen Wolfram (3:07:53.160)
we're just incredibly close to actually having that,
Lex Fridman (3:07:55.440)
understanding how that works.
Lex Fridman (3:07:57.160)
And it turns out, it looks like,
Lex Fridman (3:07:59.000)
my current speculation is that it's as simple
Stephen Wolfram (3:08:01.640)
as the directed hypergraphs versus undirected hypergraphs,
Lex Fridman (3:08:07.760)
the relationship between spinners and vectors.
Stephen Wolfram (3:08:10.240)
So, which is just interesting.
Lex Fridman (3:08:11.800)
Yeah, that would be interesting if these are all these kind
Stephen Wolfram (3:08:13.840)
of nice properties of this multi way graphs of branching
Lex Fridman (3:08:18.600)
and rejoining.
Stephen Wolfram (3:08:19.920)
Spinners have been very mysterious.
Lex Fridman (3:08:21.760)
And if that's what they turn out to be,
Stephen Wolfram (3:08:23.880)
there's going to be an easy explanation
Lex Fridman (3:08:25.240)
of what's going on.
Stephen Wolfram (3:08:26.080)
Directive versus undirective.
Lex Fridman (3:08:27.160)
It's just, and that's why there's only two different cases.
Lex Fridman (3:08:30.600)
It's why are spinners important in quantum mechanics?
Lex Fridman (3:08:34.160)
Can you just give a...
Stephen Wolfram (3:08:35.680)
Yeah, so spinners are important because they are,
Lex Fridman (3:08:39.040)
they're the representation of electrons
Stephen Wolfram (3:08:41.480)
which have half an inch of spin.
Lex Fridman (3:08:43.400)
They are, the wave functions of electrons are spinners.
Stephen Wolfram (3:08:48.320)
Just like the wave functions of photons are vectors,
Lex Fridman (3:08:51.280)
the wave functions of electrons are spinners.
Lex Fridman (3:08:54.280)
And they have this property that when you rotate
Lex Fridman (3:08:58.040)
by 360 degrees, they come back to minus one of themselves
Lex Fridman (3:09:02.880)
and take 720 degrees to get back to the original value.
Lex Fridman (3:09:06.760)
And they are a consequence of,
Stephen Wolfram (3:09:10.640)
we usually think of rotation in space as being,
Lex Fridman (3:09:15.160)
when you have this notion of rotational invariance
Lex Fridman (3:09:18.720)
and rotational invariance, as we ordinarily experience it,
Lex Fridman (3:09:22.160)
doesn't have the feature.
Stephen Wolfram (3:09:23.280)
If you go through 360 degrees,
Lex Fridman (3:09:24.760)
you go back to where you started from,
Lex Fridman (3:09:26.440)
but that's not true for electrons.
Lex Fridman (3:09:28.480)
And so that's why understanding how that works is important.
Stephen Wolfram (3:09:32.480)
Yeah, I've been playing with Mobius Strip
Lex Fridman (3:09:34.920)
quite a bit lately, just for fun.
Stephen Wolfram (3:09:37.000)
Yes, yes.
Lex Fridman (3:09:37.840)
It adds some funk, it has the same kind of funky properties.
Stephen Wolfram (3:09:41.000)
Yes, right, exactly.
Lex Fridman (3:09:41.840)
You can have this so called belt trick,
Stephen Wolfram (3:09:43.560)
which is this way of taking an extended object
Lex Fridman (3:09:45.960)
and you can see properties like spinners
Stephen Wolfram (3:09:47.600)
with that kind of extended object that...
Lex Fridman (3:09:50.200)
Yeah, it would be very cool if there's,
Stephen Wolfram (3:09:51.720)
it somehow connects the directive versus undirective.
Lex Fridman (3:09:53.840)
I think that's what it's gonna be.
Stephen Wolfram (3:09:54.680)
I think it's gonna be as simple as that, but we'll see.
Lex Fridman (3:09:57.480)
I mean, this is the thing that,
Stephen Wolfram (3:09:59.680)
this is the big sort of bizarre surprise is that,
Lex Fridman (3:10:03.200)
because I learned physics as probably, let's say,
Stephen Wolfram (3:10:07.720)
let's say a fifth generation in the sense that,
Lex Fridman (3:10:10.080)
if you go back to the 1920s and so on,
Stephen Wolfram (3:10:11.960)
there were the people who were originating
Lex Fridman (3:10:13.720)
quantum mechanics and so on.
Stephen Wolfram (3:10:15.400)
Maybe it's a little less than that.
Lex Fridman (3:10:16.280)
Maybe I was like a third generation or something.
Stephen Wolfram (3:10:19.760)
I don't know, but the people from whom I learned physics
Lex Fridman (3:10:23.560)
were the people who had been students of the students
Stephen Wolfram (3:10:26.760)
of the people who originated
Lex Fridman (3:10:28.920)
the current understanding of physics.
Lex Fridman (3:10:31.240)
And we're now at probably the seventh generation
Lex Fridman (3:10:33.920)
of physicists or something
Stephen Wolfram (3:10:35.080)
from the early days of 20th century physics.
Lex Fridman (3:10:38.320)
And whenever a field gets that many generations deep,
Stephen Wolfram (3:10:43.360)
it seems the foundations seem quite inaccessible.
Lex Fridman (3:10:46.640)
And they seem, it seems like
Stephen Wolfram (3:10:48.160)
you can't possibly understand that.
Lex Fridman (3:10:49.800)
We've gone through seven academic generations
Lex Fridman (3:10:52.720)
and that's been, you know, that's been this thing
Lex Fridman (3:10:55.320)
that's been difficult to understand for that long.
Stephen Wolfram (3:10:58.600)
It just can't be that simple.
Lex Fridman (3:11:01.240)
But in a sense, maybe that journey takes you
Stephen Wolfram (3:11:03.800)
to a simple explanation that was there all along.
Lex Fridman (3:11:07.640)
That's the whole. Right, right, right.
Stephen Wolfram (3:11:08.480)
I mean, you know, and the thing for me personally,
Lex Fridman (3:11:10.640)
the thing that's been quite interesting is, you know,
Stephen Wolfram (3:11:13.200)
I didn't expect this project to work in this way.
Lex Fridman (3:11:16.200)
And I, you know, but I had this sort of weird piece
Stephen Wolfram (3:11:19.080)
of personal history that I used to be a physicist
Lex Fridman (3:11:21.840)
and I used to do all this stuff.
Lex Fridman (3:11:23.040)
And I know, you know, the standard canon of physics,
Lex Fridman (3:11:26.880)
I knew it very well.
Stephen Wolfram (3:11:28.760)
And, you know, but then I'd been working
Lex Fridman (3:11:31.280)
on this kind of computational paradigm
Stephen Wolfram (3:11:33.000)
for basically 40 years.
Lex Fridman (3:11:35.120)
And the fact that, you know, I'm sort of now coming back
Stephen Wolfram (3:11:38.800)
to, you know, trying to apply that in physics,
Lex Fridman (3:11:42.240)
it kind of felt like that journey was necessary.
Lex Fridman (3:11:44.920)
Was this, when did you first try to play with a hypergraph?
Lex Fridman (3:11:49.040)
So what happened is,
Stephen Wolfram (3:11:50.520)
yeah, so what I had was, okay, so this is again,
Lex Fridman (3:11:53.320)
you know, one always feels dumb after the fact.
Stephen Wolfram (3:11:56.320)
It's obvious after the fact.
Lex Fridman (3:11:58.800)
But so back in the early 1990s,
Stephen Wolfram (3:12:02.240)
I realized that using graphs
Lex Fridman (3:12:05.240)
as a sort of underlying thing underneath space and time
Stephen Wolfram (3:12:07.760)
was going to be a useful thing to do.
Lex Fridman (3:12:09.720)
I figured out about multiway systems.
Stephen Wolfram (3:12:12.760)
I figured out the things about general relativity
Lex Fridman (3:12:14.960)
I'd figured out by the end of the 1990s.
Lex Fridman (3:12:17.400)
But I always felt there was a certain inelegance
Lex Fridman (3:12:20.040)
because I was using these graphs
Lex Fridman (3:12:21.880)
and there were certain constraints on these graphs
Lex Fridman (3:12:23.880)
that seemed like they were kind of awkward.
Stephen Wolfram (3:12:26.440)
It was kind of like, you can pick,
Lex Fridman (3:12:28.320)
it's like you couldn't pick any rule.
Stephen Wolfram (3:12:30.240)
It was like pick any number, but the number has to be prime.
Lex Fridman (3:12:33.360)
It was kind of like you couldn't,
Stephen Wolfram (3:12:34.600)
it was kind of an awkward special constraint.
Lex Fridman (3:12:36.920)
I had these trivalent graphs,
Stephen Wolfram (3:12:38.400)
graphs with just three connections from every node.
Lex Fridman (3:12:41.440)
Okay, so, but I discovered a bunch of stuff with that.
Lex Fridman (3:12:44.280)
And I thought it was kind of inelegant.
Lex Fridman (3:12:46.280)
And, you know, the other piece of sort of personal history
Stephen Wolfram (3:12:48.680)
is obviously I spent my life
Lex Fridman (3:12:50.160)
as a computational language designer.
Lex Fridman (3:12:52.960)
And so the story of computational language design
Lex Fridman (3:12:55.160)
is a story of how do you take all these random ideas
Stephen Wolfram (3:12:58.000)
in the world and kind of grind them down
Lex Fridman (3:13:00.720)
into something that is computationally
Stephen Wolfram (3:13:02.720)
as simple as possible.
Lex Fridman (3:13:04.760)
And so, you know, I've been very interested
Stephen Wolfram (3:13:06.680)
in kind of simple computational frameworks
Lex Fridman (3:13:09.280)
for representing things and have, you know,
Stephen Wolfram (3:13:12.600)
ridiculous amounts of experience in trying to do that.
Lex Fridman (3:13:15.800)
And actually all of those trajectories of your life
Stephen Wolfram (3:13:18.280)
kind of came together.
Lex Fridman (3:13:19.320)
So you make it sound like you could have come up
Stephen Wolfram (3:13:21.600)
with everything you're working on now decades ago,
Lex Fridman (3:13:24.640)
but in reality.
Stephen Wolfram (3:13:26.440)
Look, two things slowed me down.
Lex Fridman (3:13:28.080)
I mean, one thing that slowed me down was
Stephen Wolfram (3:13:30.280)
I couldn't figure out how to make it elegant.
Lex Fridman (3:13:32.840)
And that turns out hypergraphs were the key to that.
Lex Fridman (3:13:35.600)
And that I figured out about less than two years ago now.
Lex Fridman (3:13:40.160)
And the other, I mean, I think,
Lex Fridman (3:13:43.360)
so that was sort of a key thing.
Lex Fridman (3:13:46.160)
Well, okay, so the real embarrassment of this project, okay,
Stephen Wolfram (3:13:49.760)
is that the final structure that we have
Lex Fridman (3:13:52.680)
that is the foundation for this project
Stephen Wolfram (3:13:55.840)
is basically a kind of an idealized version,
Lex Fridman (3:14:00.000)
a formalized version of the exact same structure
Stephen Wolfram (3:14:03.560)
that I've used to build computational languages
Lex Fridman (3:14:05.640)
for more than 40 years.
Lex Fridman (3:14:07.160)
But it took me, but I didn't realize that.
Lex Fridman (3:14:09.840)
And, you know.
Lex Fridman (3:14:11.280)
And there yet may be others.
Lex Fridman (3:14:12.840)
So we're focused on physics now,
Lex Fridman (3:14:14.360)
but I mean, that's what the new kind of science was about.
Lex Fridman (3:14:17.720)
Same kind of stuff.
Lex Fridman (3:14:19.120)
And this, in terms of mathematically,
Lex Fridman (3:14:21.720)
well, the beauty of it.
Lex Fridman (3:14:22.960)
So there could be entire other kind of objects
Lex Fridman (3:14:26.160)
that are useful for,
Stephen Wolfram (3:14:27.600)
like we're not talking about, you know,
Lex Fridman (3:14:29.760)
machine learning, for example.
Stephen Wolfram (3:14:31.760)
Maybe there's other variants of the hypergraph
Lex Fridman (3:14:33.880)
that are very useful for reasoning.
Stephen Wolfram (3:14:35.720)
Well, we'll see whether the multiway graph
Lex Fridman (3:14:37.440)
or machine learning system is interesting.
Stephen Wolfram (3:14:40.320)
Okay.
Lex Fridman (3:14:41.480)
Let's leave it at that.
Stephen Wolfram (3:14:42.320)
That's conversation number three.
Lex Fridman (3:14:43.640)
That's, we're not gonna go there right now, but.
Stephen Wolfram (3:14:47.440)
One of the things you've mentioned
Lex Fridman (3:14:49.040)
is the space of all possible rules
Stephen Wolfram (3:14:52.640)
that we kind of discussed a little bit.
Lex Fridman (3:14:55.200)
That, you know, that could be, I guess,
Stephen Wolfram (3:14:58.000)
the set of possible rules is infinite.
Lex Fridman (3:15:00.800)
Right.
Stephen Wolfram (3:15:01.640)
Well, so here's the big sort of one of the conundrums
Lex Fridman (3:15:04.200)
that I'm kind of trying to deal with is,
Stephen Wolfram (3:15:07.840)
let's say we think we found the rule for the universe
Lex Fridman (3:15:11.720)
and we say, here it is.
Stephen Wolfram (3:15:13.160)
You know, write it down.
Lex Fridman (3:15:14.200)
It's a little tiny thing.
Lex Fridman (3:15:15.800)
And then we say, gosh, that's really weird.
Lex Fridman (3:15:18.000)
Why did we get that one?
Stephen Wolfram (3:15:20.640)
Right.
Lex Fridman (3:15:21.480)
And then we're in this whole situation
Stephen Wolfram (3:15:23.240)
because let's say it's fairly simple.
Lex Fridman (3:15:25.480)
How did we come up the winners
Lex Fridman (3:15:27.680)
getting one of the simple possible universe rules?
Lex Fridman (3:15:30.400)
Why didn't we get what some incredibly complicated rule?
Lex Fridman (3:15:33.600)
Why do we get one of the simpler ones?
Lex Fridman (3:15:34.880)
And that's a thing which, you know,
Stephen Wolfram (3:15:36.560)
in the history of science, you know,
Lex Fridman (3:15:38.800)
the whole sort of story of Copernicus and so on was,
Stephen Wolfram (3:15:42.680)
you know, we used to think the earth
Lex Fridman (3:15:43.920)
was the center of the universe,
Lex Fridman (3:15:44.960)
but now we find out it's not.
Lex Fridman (3:15:46.320)
And we're actually just in some, you know,
Stephen Wolfram (3:15:47.760)
random corner of some random galaxy
Lex Fridman (3:15:50.480)
out in this big universe, there's nothing special about us.
Lex Fridman (3:15:53.800)
So if we get, you know, universe number 317
Lex Fridman (3:15:58.120)
out of all the infinite number of possibilities,
Lex Fridman (3:16:00.400)
how do we get something that small and simple?
Lex Fridman (3:16:02.720)
Right, so I was very confused by this.
Lex Fridman (3:16:05.040)
And it's like, what are we going to say about this?
Lex Fridman (3:16:06.720)
How are we going to explain this?
Lex Fridman (3:16:08.560)
And I thought it was, might be one of these things
Lex Fridman (3:16:10.320)
where you just, you know, you can get it to the threshold,
Lex Fridman (3:16:13.320)
and then you find out its rule number, such and such,
Lex Fridman (3:16:15.480)
and you just have no idea why it's like that.
Stephen Wolfram (3:16:17.760)
Okay, so then I realized
Lex Fridman (3:16:20.040)
it's actually more bizarre than that, okay?
Lex Fridman (3:16:22.560)
So we talked about multiway graphs.
Lex Fridman (3:16:25.040)
We talked about this idea that
Stephen Wolfram (3:16:26.760)
you take these underlying transformation rules
Lex Fridman (3:16:29.040)
on these hypergraphs, and you apply them
Stephen Wolfram (3:16:31.840)
wherever the rule can apply, you apply it.
Lex Fridman (3:16:34.720)
And that makes this whole multiway graph of possibilities.
Stephen Wolfram (3:16:37.680)
Okay, so let's go a little bit weirder.
Lex Fridman (3:16:39.960)
Let's say that at every place,
Stephen Wolfram (3:16:42.800)
not only do you apply a particular rule
Lex Fridman (3:16:45.240)
in all possible ways it can apply,
Lex Fridman (3:16:47.160)
but you apply all possible rules
Lex Fridman (3:16:49.520)
in all possible ways they can apply.
Stephen Wolfram (3:16:51.920)
As you say, that's just crazy.
Lex Fridman (3:16:53.760)
That's way too complicated.
Stephen Wolfram (3:16:54.920)
You're never going to be able to conclude anything.
Lex Fridman (3:16:57.240)
Okay, however, turns out that...
Stephen Wolfram (3:17:00.800)
Don't tell me there's some kind of invariance.
Lex Fridman (3:17:02.880)
Yeah, yeah.
Lex Fridman (3:17:04.000)
So what happens is...
Lex Fridman (3:17:06.440)
And that would be amazing.
Stephen Wolfram (3:17:08.080)
Right, so this thing that you get
Lex Fridman (3:17:11.240)
is this kind of ruleal multiway graph,
Stephen Wolfram (3:17:13.360)
this multiway graph that is a branching of rules
Lex Fridman (3:17:15.880)
as well as a branching of possible applications of rules.
Stephen Wolfram (3:17:19.760)
This thing has causal invariance.
Lex Fridman (3:17:22.080)
It's an inevitable feature that it shows causal invariance.
Lex Fridman (3:17:25.320)
And that means that you can take different reference frames,
Lex Fridman (3:17:28.640)
different ways of slicing this thing,
Lex Fridman (3:17:30.920)
and they will all in some sense be equivalent.
Lex Fridman (3:17:33.920)
If you make the right translation, they will be equivalent.
Stephen Wolfram (3:17:37.360)
So, okay, so the basic point here is...
Lex Fridman (3:17:40.360)
If that's true, that would be beautiful.
Stephen Wolfram (3:17:43.040)
It is true, and it is beautiful.
Lex Fridman (3:17:45.640)
It's not just an intuition, there is some...
Stephen Wolfram (3:17:47.480)
No, no, no, there's real mathematics behind this,
Lex Fridman (3:17:50.120)
and it is...
Stephen Wolfram (3:17:53.360)
Okay, so here's where it comes in.
Lex Fridman (3:17:55.160)
Yeah, that's amazing.
Stephen Wolfram (3:17:57.360)
Right, so by the way, I mean,
Lex Fridman (3:17:58.800)
the mathematics it's connected to
Stephen Wolfram (3:18:00.240)
is the mathematics of higher category theory
Lex Fridman (3:18:02.360)
and group voids and things like this,
Stephen Wolfram (3:18:04.240)
which I've always been afraid of,
Lex Fridman (3:18:05.880)
but now I'm finally wrapping my arms around it.
Lex Fridman (3:18:09.960)
But it's also related to...
Lex Fridman (3:18:13.120)
It also relates to computational complexity theory.
Stephen Wolfram (3:18:16.160)
It's also deeply related to the P versus NP problem
Lex Fridman (3:18:19.200)
and other things like this.
Stephen Wolfram (3:18:20.440)
Again, it seems completely bizarre
Lex Fridman (3:18:21.880)
that these things are connected,
Lex Fridman (3:18:22.960)
but here's why it's connected.
Lex Fridman (3:18:25.160)
This space of all possible...
Stephen Wolfram (3:18:28.000)
Okay, so a Turing machine, very simple model of computation.
Lex Fridman (3:18:32.080)
You know, you just got this tape
Stephen Wolfram (3:18:34.280)
where you write down, you know, ones and zeros
Lex Fridman (3:18:36.480)
or something on the tape,
Lex Fridman (3:18:37.400)
and you have this rule that says, you know,
Lex Fridman (3:18:40.120)
you change the number,
Stephen Wolfram (3:18:41.520)
you move the head on the tape, et cetera.
Lex Fridman (3:18:44.320)
You have a definite rule for doing that.
Stephen Wolfram (3:18:46.040)
A deterministic Turing machine
Lex Fridman (3:18:47.880)
just does that deterministically.
Stephen Wolfram (3:18:50.000)
Given the configuration of the tape,
Lex Fridman (3:18:51.760)
it will always do the same thing.
Stephen Wolfram (3:18:53.600)
A non deterministic Turing machine
Lex Fridman (3:18:55.760)
can have different choices that it makes at every step.
Lex Fridman (3:18:58.960)
And so, you know, you know this stuff,
Lex Fridman (3:19:01.840)
you probably teach this stuff.
Stephen Wolfram (3:19:04.440)
It, you know, so a non deterministic Turing machine
Lex Fridman (3:19:09.200)
has the set of branching possibilities,
Stephen Wolfram (3:19:11.680)
which is in fact, one of these multiway graphs.
Lex Fridman (3:19:14.360)
And in fact, if you say,
Stephen Wolfram (3:19:16.240)
imagine the extremely non deterministic Turing machine,
Lex Fridman (3:19:19.520)
the Turing machine that can just do,
Stephen Wolfram (3:19:22.560)
that takes any possible rule at each step,
Lex Fridman (3:19:25.440)
that is this real multiway graph.
Stephen Wolfram (3:19:27.520)
The set of possible histories
Lex Fridman (3:19:31.280)
of that extreme non deterministic Turing machine
Stephen Wolfram (3:19:33.720)
is a Rulio multiway graph.
Lex Fridman (3:19:35.880)
And you're, what term are you using?
Lex Fridman (3:19:37.680)
Rulio?
Lex Fridman (3:19:38.520)
Rulio.
Stephen Wolfram (3:19:39.360)
Rulio, I like it.
Lex Fridman (3:19:40.200)
It's a weird word.
Lex Fridman (3:19:41.040)
Yeah, it's a weird word, right?
Lex Fridman (3:19:41.880)
Rulio multiway graph.
Stephen Wolfram (3:19:44.160)
Okay, so this, so that.
Lex Fridman (3:19:45.880)
I'm trying to think of,
Stephen Wolfram (3:19:48.880)
I'm trying to think of the space of rules.
Lex Fridman (3:19:51.800)
So these are basic transformations.
Lex Fridman (3:19:54.240)
So in a Turing machine,
Lex Fridman (3:19:55.760)
it's like it says, move left, move, you know,
Stephen Wolfram (3:19:58.280)
if it's a one, if it's a black square under the head,
Lex Fridman (3:20:02.320)
move left and right to green square.
Stephen Wolfram (3:20:04.840)
That's a rule.
Lex Fridman (3:20:05.720)
That's a very basic rule,
Lex Fridman (3:20:06.720)
but I'm trying to see the rules on the hypergraphs,
Lex Fridman (3:20:09.880)
how rich of the programs can they be?
Lex Fridman (3:20:12.200)
Or do they all ultimately just map into something simple?
Lex Fridman (3:20:15.520)
Yeah, they're all, I mean, hypergraphs,
Stephen Wolfram (3:20:18.000)
that's another layer of complexity on this whole thing.
Lex Fridman (3:20:20.200)
You can think about these in transformations of hypergraphs,
Lex Fridman (3:20:23.040)
but Turing machines are a little bit simpler.
Lex Fridman (3:20:24.360)
You just think of it Turing machines, okay.
Stephen Wolfram (3:20:25.600)
Right, they're a little bit simpler.
Lex Fridman (3:20:27.280)
So if you look at these extreme
Stephen Wolfram (3:20:29.120)
non deterministic Turing machines,
Lex Fridman (3:20:30.920)
you're mapping out all the possible non deterministic paths
Stephen Wolfram (3:20:35.120)
that the Turing machine can follow.
Lex Fridman (3:20:37.160)
And if you ask the question, can you reach, okay,
Lex Fridman (3:20:41.040)
so a deterministic Turing machine follows a single path.
Lex Fridman (3:20:44.800)
The non deterministic Turing machine fills out
Stephen Wolfram (3:20:46.960)
this whole sort of ball of possibilities.
Lex Fridman (3:20:50.680)
And so then the P versus MP problem
Stephen Wolfram (3:20:53.280)
ends up being questions about,
Lex Fridman (3:20:55.160)
and we haven't completely figured out
Stephen Wolfram (3:20:56.760)
all the details of this,
Lex Fridman (3:20:57.600)
but it's basically has to do with questions
Stephen Wolfram (3:20:59.920)
about the growth of that ball relative
Lex Fridman (3:21:03.320)
to what happens with individual paths and so on.
Lex Fridman (3:21:05.800)
So essentially there's a geometrization
Lex Fridman (3:21:07.800)
of the P versus MP problem that comes out of this.
Stephen Wolfram (3:21:10.120)
That's a sideshow, okay.
Lex Fridman (3:21:12.000)
The main event here is the statement
Stephen Wolfram (3:21:14.960)
that you can look at this multiway graph
Lex Fridman (3:21:19.960)
where the branches correspond
Stephen Wolfram (3:21:21.800)
not just to different applications of a single rule,
Lex Fridman (3:21:24.200)
but to different applications of different rules, okay.
Lex Fridman (3:21:28.200)
And that then that when you say,
Lex Fridman (3:21:31.960)
I'm going to be an observer embedded in that system
Lex Fridman (3:21:35.440)
and I'm going to try and make sense
Lex Fridman (3:21:36.960)
of what's going on in the system.
Lex Fridman (3:21:38.760)
And to do that, I essentially am picking a reference frame
Lex Fridman (3:21:43.040)
and that turns out to be, well, okay.
Lex Fridman (3:21:46.560)
So the way this comes out essentially
Lex Fridman (3:21:48.600)
is the reference frame you pick
Stephen Wolfram (3:21:50.720)
is the rule that you infer is what's going on
Lex Fridman (3:21:53.800)
in the universe, even though all possible rules
Stephen Wolfram (3:21:57.440)
are being run, although all those possible rules
Lex Fridman (3:22:01.240)
are in a sense giving the same answer
Stephen Wolfram (3:22:02.720)
because of causal invariance.
Lex Fridman (3:22:04.560)
But what you see could be completely different.
Stephen Wolfram (3:22:08.480)
If you pick different reference frames,
Lex Fridman (3:22:10.360)
you essentially have a different description language
Stephen Wolfram (3:22:12.920)
for describing the universe.
Lex Fridman (3:22:14.960)
Okay, so what does this really mean in practice?
Lex Fridman (3:22:17.320)
So imagine there's us.
Lex Fridman (3:22:19.640)
We think about the universe in terms of space and time
Lex Fridman (3:22:22.280)
and we have various kinds of description models and so on.
Lex Fridman (3:22:25.000)
Now let's imagine the friendly aliens, for example, right?
Lex Fridman (3:22:29.040)
How do they describe their universe?
Lex Fridman (3:22:31.320)
Well, you know, our description of the universe
Stephen Wolfram (3:22:33.440)
probably is affected by the fact that, you know,
Lex Fridman (3:22:36.160)
we are about the size we are, you know,
Stephen Wolfram (3:22:37.920)
a meter ish tall, so to speak.
Lex Fridman (3:22:40.240)
We have brain processing speeds,
Stephen Wolfram (3:22:41.840)
we're about the speeds we have.
Lex Fridman (3:22:43.680)
We're not the size of planets, for example,
Stephen Wolfram (3:22:46.320)
where the speed of light really would matter.
Lex Fridman (3:22:48.600)
You know, in our everyday life,
Stephen Wolfram (3:22:50.040)
the speed of light doesn't really matter.
Lex Fridman (3:22:51.800)
Everything can be, you know,
Stephen Wolfram (3:22:52.920)
the fact that the speed of light is finite is irrelevant.
Lex Fridman (3:22:55.200)
It could as well be infinite.
Stephen Wolfram (3:22:56.720)
We wouldn't make any difference.
Lex Fridman (3:22:58.480)
You know, it affects the ping times on the internet.
Stephen Wolfram (3:23:01.240)
That's about the level of how we notice the speed of light.
Lex Fridman (3:23:06.040)
In our sort of everyday existence,
Stephen Wolfram (3:23:07.400)
we don't really notice it.
Lex Fridman (3:23:09.360)
And so we have a way of describing the universe
Stephen Wolfram (3:23:12.240)
that's based on our sensory, you know, our senses,
Lex Fridman (3:23:17.240)
these days also on the mathematics we've constructed
Lex Fridman (3:23:19.760)
and so on, but the realization is
Lex Fridman (3:23:22.520)
it's not the only way to do it.
Stephen Wolfram (3:23:24.160)
There will be completely, utterly incoherent descriptions
Lex Fridman (3:23:28.200)
of the universe, which correspond
Stephen Wolfram (3:23:30.840)
to different reference frames in this sort of ruleal space.
Lex Fridman (3:23:34.240)
In the ruleal space, that's fascinating.
Lex Fridman (3:23:36.080)
So we have some kind of reference frame
Lex Fridman (3:23:38.200)
in this ruleal space, and from that.
Stephen Wolfram (3:23:41.680)
That's why we are attributing this rule to the universe.
Lex Fridman (3:23:45.600)
So in other words, when we say,
Lex Fridman (3:23:47.320)
why is it this rule and not another,
Lex Fridman (3:23:49.440)
the answer is just, you know,
Stephen Wolfram (3:23:52.280)
shine the light back on us, so to speak.
Lex Fridman (3:23:54.600)
It's because of the reference frame that we've picked
Stephen Wolfram (3:23:57.240)
in our way of understanding what's happening
Lex Fridman (3:23:58.960)
in this sort of space of all possible rules and so on.
Lex Fridman (3:24:02.320)
But also in the space from this reference frame,
Lex Fridman (3:24:06.120)
because of the ruleal, the invariance,
Stephen Wolfram (3:24:12.200)
that simple, that the rule on which the universe,
Lex Fridman (3:24:17.200)
with which you can run the universe,
Stephen Wolfram (3:24:19.840)
might as well be simple.
Lex Fridman (3:24:21.360)
Yes, yes, but okay, so here's another point.
Lex Fridman (3:24:23.720)
So this is, again, these are a little bit mind twisting
Lex Fridman (3:24:26.800)
in some ways, but the, okay, another thing that's sort of,
Stephen Wolfram (3:24:31.400)
we know from computation is this idea
Lex Fridman (3:24:34.640)
of computation universality.
Stephen Wolfram (3:24:36.480)
The fact that given that we have a program
Lex Fridman (3:24:38.880)
that runs on one kind of computer, we can as well,
Stephen Wolfram (3:24:42.320)
you know, we can convert it to run
Lex Fridman (3:24:44.280)
on any other kind of computer.
Stephen Wolfram (3:24:45.380)
We can emulate one kind of computer with another.
Lex Fridman (3:24:47.880)
So that might lead you to say, well,
Stephen Wolfram (3:24:50.640)
you think you have the rule for the universe,
Lex Fridman (3:24:52.800)
but you might as well be running it on a Turing machine
Stephen Wolfram (3:24:54.840)
because we know we can emulate any computational rule
Lex Fridman (3:24:59.000)
on any kind of machine.
Lex Fridman (3:25:00.920)
And that's essentially the same thing
Lex Fridman (3:25:02.300)
that's being said here.
Stephen Wolfram (3:25:03.680)
That is that what we're doing is we're saying
Lex Fridman (3:25:07.320)
these different interpretations of physics correspond
Stephen Wolfram (3:25:11.280)
to essentially running physics
Lex Fridman (3:25:13.400)
on different underlying, you know,
Stephen Wolfram (3:25:16.040)
thinking about the physics as running in different
Lex Fridman (3:25:18.140)
with different underlying rules
Stephen Wolfram (3:25:19.540)
as if different underlying computers were running them.
Lex Fridman (3:25:22.980)
And, but because of computation universality
Stephen Wolfram (3:25:26.060)
or more accurately, because of this principle
Lex Fridman (3:25:27.720)
of computational equivalence thing of mine,
Stephen Wolfram (3:25:30.360)
there's that they are,
Lex Fridman (3:25:33.520)
these things are ultimately equivalent.
Lex Fridman (3:25:35.760)
So the only thing that is the ultimate fact
Lex Fridman (3:25:38.120)
about the universe, the ultimate fact that doesn't depend
Stephen Wolfram (3:25:40.920)
on any of these, you know, we don't have to talk
Lex Fridman (3:25:42.760)
about specific rules, et cetera, et cetera, et cetera.
Stephen Wolfram (3:25:44.640)
The ultimate fact is the universe is computational
Lex Fridman (3:25:48.360)
and it is the things that happen in the universe
Stephen Wolfram (3:25:52.640)
are the kinds of computations that the principle
Lex Fridman (3:25:54.920)
of computational equivalence says should happen.
Stephen Wolfram (3:25:57.560)
Now that might sound like you're not really saying
Lex Fridman (3:26:00.440)
anything there, but you are because you can,
Stephen Wolfram (3:26:03.920)
you could in principle have a hyper computer
Lex Fridman (3:26:06.640)
that things that take an ordinary computer
Stephen Wolfram (3:26:09.720)
an infinite time to do the hyper computer can just say,
Lex Fridman (3:26:12.000)
oh, I know the answer.
Stephen Wolfram (3:26:13.480)
It's this immediately.
Lex Fridman (3:26:15.720)
What this is saying is the universe is not a hyper computer.
Stephen Wolfram (3:26:19.600)
It's not simpler than a,
Lex Fridman (3:26:21.800)
an ordinary Turing machine type computer.
Stephen Wolfram (3:26:24.040)
It's exactly like an ordinary Turing machine type computer.
Lex Fridman (3:26:28.080)
And so that's the, that's in the end,
Stephen Wolfram (3:26:30.040)
the sort of net net conclusion is that's the thing
Lex Fridman (3:26:34.000)
that is the sort of the hard immovable fact
Stephen Wolfram (3:26:36.600)
about the universe.
Lex Fridman (3:26:38.000)
That's sort of the fundamental principle of the universe
Stephen Wolfram (3:26:41.600)
is that it is computational and not hyper computational
Lex Fridman (3:26:45.440)
and not sort of infra computational.
Stephen Wolfram (3:26:47.280)
It is this level of computational ability
Lex Fridman (3:26:50.360)
and it's, it kind of has,
Lex Fridman (3:26:53.080)
and that's sort of the, the, the core fact, but now,
Lex Fridman (3:26:57.080)
you know, this, this idea that you can have these different
Stephen Wolfram (3:26:59.800)
kind of a rule reference frames,
Lex Fridman (3:27:02.280)
these different description languages for the universe.
Stephen Wolfram (3:27:05.280)
It makes me, you know, I used to think, okay, you know,
Lex Fridman (3:27:08.840)
imagine the aliens,
Stephen Wolfram (3:27:09.840)
imagine the extraterrestrial intelligence thing, you know,
Lex Fridman (3:27:12.560)
at least they experienced the same physics.
Lex Fridman (3:27:15.560)
And now I've realized it isn't true.
Lex Fridman (3:27:17.440)
They could have a different rule frame.
Stephen Wolfram (3:27:19.240)
That's fascinating.
Lex Fridman (3:27:20.480)
That they can end up with a, a, a,
Stephen Wolfram (3:27:23.920)
a description of the universe that is utterly,
Lex Fridman (3:27:26.040)
utterly incoherent with ours.
Lex Fridman (3:27:28.040)
And that's also interesting in terms of how we think about,
Lex Fridman (3:27:31.320)
well, intelligence, the nature of intelligence and so on.
Stephen Wolfram (3:27:33.600)
You know, I'm, I'm fond of the quote, you know,
Lex Fridman (3:27:35.440)
the weather has a mind of its own because these are,
Stephen Wolfram (3:27:38.640)
you know, these are sort of computationally that,
Lex Fridman (3:27:41.040)
that system is computationally equivalent to the system
Stephen Wolfram (3:27:44.760)
that is our brains and so on.
Lex Fridman (3:27:46.560)
And what's different is we don't have a way to understand,
Stephen Wolfram (3:27:49.960)
you know, what the weather is trying to do, so to speak.
Lex Fridman (3:27:52.520)
We have a story about what's happening in our brains.
Stephen Wolfram (3:27:54.880)
We don't have a sort of connection
Lex Fridman (3:27:56.680)
to what's happening there.
Lex Fridman (3:27:57.800)
So we actually, it's funny,
Lex Fridman (3:27:59.680)
last time we talked maybe over a year ago,
Stephen Wolfram (3:28:04.160)
we talked about how it was more based on your work
Lex Fridman (3:28:08.080)
with Arrival.
Stephen Wolfram (3:28:09.920)
We talked about how would we communicate
Lex Fridman (3:28:11.600)
with alien intelligences.
Lex Fridman (3:28:14.160)
Can you maybe comment on how we might,
Lex Fridman (3:28:18.000)
how the Wolfram Physics Project changed your view,
Lex Fridman (3:28:20.720)
how we might be able to communicate
Lex Fridman (3:28:22.200)
with alien intelligence?
Stephen Wolfram (3:28:23.280)
Like if they showed up,
Lex Fridman (3:28:25.040)
is it possible that because of our comprehension
Stephen Wolfram (3:28:30.080)
of the physics of the world might be completely different,
Lex Fridman (3:28:33.640)
we would just not be able to communicate at all?
Stephen Wolfram (3:28:36.600)
Here's the thing, you know, intelligence is everywhere.
Lex Fridman (3:28:41.520)
The fact this idea that there's this notion of,
Stephen Wolfram (3:28:43.800)
oh, there's gonna be this amazing
Lex Fridman (3:28:45.080)
extraterrestrial intelligence
Lex Fridman (3:28:46.400)
and it's gonna be this unique thing.
Lex Fridman (3:28:48.760)
It's just not true.
Stephen Wolfram (3:28:50.080)
It's the same thing.
Lex Fridman (3:28:51.360)
You know, I think people will realize this
Stephen Wolfram (3:28:53.240)
about the time when people decide
Lex Fridman (3:28:54.840)
that artificial intelligences are kind of
Stephen Wolfram (3:28:57.280)
just natural things that are like human intelligences.
Lex Fridman (3:29:01.160)
They'll realize that extraterrestrial intelligences
Stephen Wolfram (3:29:04.520)
or intelligences associated with physical systems
Lex Fridman (3:29:07.720)
and so on, it's all the same kind of thing.
Stephen Wolfram (3:29:09.760)
It's ultimately computation.
Lex Fridman (3:29:11.160)
It's all the same.
Stephen Wolfram (3:29:12.080)
It's all just computation.
Lex Fridman (3:29:13.280)
And the issue is, can you, are you sort of inside it?
Lex Fridman (3:29:17.160)
Are you thinking about it?
Lex Fridman (3:29:19.200)
Do you have sort of a story you're telling yourself
Lex Fridman (3:29:22.200)
about it?
Lex Fridman (3:29:23.160)
And you know, the weather could have a story
Stephen Wolfram (3:29:25.200)
it's telling itself about what it's doing.
Lex Fridman (3:29:27.560)
We just, it's utterly incoherent with the stories
Stephen Wolfram (3:29:30.920)
that we tell ourselves based on how our brains work.
Lex Fridman (3:29:33.560)
I mean, ultimately it must be a question
Stephen Wolfram (3:29:37.080)
whether we can align.
Lex Fridman (3:29:39.280)
Exactly.
Stephen Wolfram (3:29:40.120)
Align with the kind of intelligence.
Lex Fridman (3:29:41.960)
Right, right, right.
Lex Fridman (3:29:42.800)
So there's a systematic way of doing it.
Lex Fridman (3:29:44.200)
Right, so the question is in the space
Stephen Wolfram (3:29:45.520)
of all possible intelligences,
Lex Fridman (3:29:47.240)
what's the, how do you think about the distance
Stephen Wolfram (3:29:50.440)
between description languages
Lex Fridman (3:29:52.400)
for one intelligence versus another?
Lex Fridman (3:29:54.680)
And needless to say, I have thought about this
Lex Fridman (3:29:57.120)
and you know, I don't have a great answer yet,
Lex Fridman (3:30:00.880)
but I think that's a thing
Lex Fridman (3:30:02.920)
where there will be things that can be said
Lex Fridman (3:30:04.440)
and there'll be things that where you can sort of
Lex Fridman (3:30:06.000)
start to characterize, you know,
Lex Fridman (3:30:08.400)
what is the translation distance between this,
Lex Fridman (3:30:12.880)
you know, version of the universe
Stephen Wolfram (3:30:15.120)
or this kind of set of computational rules
Lex Fridman (3:30:17.840)
and this other one.
Stephen Wolfram (3:30:18.800)
In fact, okay, so this is a, you know,
Lex Fridman (3:30:21.480)
there's this idea of algorithmic information theory.
Stephen Wolfram (3:30:23.560)
There's this question of sort of what is the,
Lex Fridman (3:30:25.800)
when you have something,
Lex Fridman (3:30:28.680)
what is the sort of shortest description you can make of it
Lex Fridman (3:30:31.520)
where that description could be saying,
Lex Fridman (3:30:33.320)
run this program to get the thing, right?
Lex Fridman (3:30:36.480)
So I'm pretty sure that there will be a physicalization
Stephen Wolfram (3:30:45.280)
of the idea of algorithmic information
Lex Fridman (3:30:47.720)
and that, okay, this is again, a little bit bizarre,
Lex Fridman (3:30:51.560)
but so I mentioned that there's the speed of light,
Lex Fridman (3:30:54.480)
maximum speed of information transmission in physical space.
Stephen Wolfram (3:30:57.560)
There's a maximum speed of information transmission
Lex Fridman (3:30:59.840)
in branchial space, which is a maximum entanglement speed.
Stephen Wolfram (3:31:02.920)
There's a maximum speed of information transmission
Lex Fridman (3:31:05.240)
in ruleal space, which is,
Stephen Wolfram (3:31:07.160)
has to do with a maximum speed of translation
Lex Fridman (3:31:10.600)
between different description languages.
Lex Fridman (3:31:14.480)
And again, I'm not fully wrapped my brain around this one.
Lex Fridman (3:31:17.440)
Yeah, that one just blows my mind to think about that,
Lex Fridman (3:31:20.080)
but that starts getting closer to the, yeah,
Lex Fridman (3:31:22.800)
the intelligence. It's kind of a physicalization.
Stephen Wolfram (3:31:25.280)
Right, and it's also a physicalization
Lex Fridman (3:31:27.840)
of algorithmic information.
Lex Fridman (3:31:29.920)
And I think there's probably a connection between,
Lex Fridman (3:31:32.320)
I mean, there's probably a connection
Stephen Wolfram (3:31:33.600)
between the notion of energy and some of these things,
Lex Fridman (3:31:36.600)
which again, I hadn't seen all this coming.
Stephen Wolfram (3:31:39.400)
I've always been a little bit resistant
Lex Fridman (3:31:41.120)
to the idea of connecting physical energy
Stephen Wolfram (3:31:43.480)
to things in computation theory,
Lex Fridman (3:31:45.640)
but I think that's probably coming.
Lex Fridman (3:31:47.200)
And that's what essentially at the core
Lex Fridman (3:31:48.560)
with the physics project is
Stephen Wolfram (3:31:50.680)
that you're connecting information theory with physics.
Lex Fridman (3:31:55.560)
Yeah, it's computation.
Stephen Wolfram (3:31:56.880)
Computation with our physical universe.
Lex Fridman (3:31:59.560)
Yeah, right.
Stephen Wolfram (3:32:00.400)
I mean, the fact that our physical universe is,
Lex Fridman (3:32:03.480)
right, that we can think of it as a computation
Lex Fridman (3:32:05.720)
and that we can have discussions like,
Lex Fridman (3:32:08.760)
the theory of the physical universe
Stephen Wolfram (3:32:11.000)
is the same kind of a theory as the P versus MP problem
Lex Fridman (3:32:14.520)
and so on is really, I think that's really interesting.
Lex Fridman (3:32:18.640)
And the fact that, well, okay,
Lex Fridman (3:32:21.520)
so this kind of brings me to one more thing
Stephen Wolfram (3:32:24.240)
that I have to in terms of this sort of unification
Lex Fridman (3:32:26.120)
of different ideas, which is metamathematics.
Stephen Wolfram (3:32:29.640)
Yeah, let's talk about that.
Lex Fridman (3:32:30.520)
You mentioned that earlier.
Lex Fridman (3:32:31.680)
What the heck is metamathematics and...
Lex Fridman (3:32:34.760)
Okay, so here's what, okay.
Lex Fridman (3:32:36.880)
So what is mathematics?
Lex Fridman (3:32:38.840)
Mathematics, sort of at a lowest level,
Stephen Wolfram (3:32:43.840)
one thinks of mathematics as you have certain axioms.
Lex Fridman (3:32:47.400)
You say things like X plus Y is the same as Y plus X.
Stephen Wolfram (3:32:51.840)
That's an axiom about addition.
Lex Fridman (3:32:55.360)
And then you say, we've got these axioms
Lex Fridman (3:32:57.360)
and from these axioms, we derive all these theorems
Lex Fridman (3:33:00.560)
that fill up the literature of mathematics.
Stephen Wolfram (3:33:02.880)
The activity of mathematicians
Lex Fridman (3:33:04.760)
is to derive all these theorems.
Stephen Wolfram (3:33:06.800)
Actually, the axioms of mathematics are very small.
Lex Fridman (3:33:10.360)
You can fit, when I did my new kind of science book,
Stephen Wolfram (3:33:13.520)
I fit all of the standard axioms of mathematics
Lex Fridman (3:33:16.000)
on basically a page and a half.
Stephen Wolfram (3:33:18.760)
Not much stuff.
Lex Fridman (3:33:19.640)
It's like a very simple rule
Stephen Wolfram (3:33:21.400)
from which all of mathematics arises.
Lex Fridman (3:33:24.000)
The way it works though is a little different
Stephen Wolfram (3:33:26.640)
from the way things work in sort of a computation
Lex Fridman (3:33:31.720)
because in mathematics, what you're interested in
Stephen Wolfram (3:33:33.440)
is a proof and the proof says,
Lex Fridman (3:33:36.160)
from here, you can use, from this expression, for example,
Stephen Wolfram (3:33:40.360)
you can use these axioms to get to this other expression.
Lex Fridman (3:33:43.040)
So that proves these two things are equal.
Stephen Wolfram (3:33:45.440)
Okay, so we can begin to see how this has been going to work.
Lex Fridman (3:33:49.040)
What's gonna happen is there are paths
Stephen Wolfram (3:33:51.360)
in metamathematical space.
Lex Fridman (3:33:53.400)
So what happens is each, two different ways to look at it.
Stephen Wolfram (3:33:57.640)
You can just look at it as mathematical expressions
Lex Fridman (3:33:59.880)
or you can look at it as mathematical statements,
Stephen Wolfram (3:34:02.640)
postulates or something.
Lex Fridman (3:34:04.120)
But either way, you think of these things
Lex Fridman (3:34:06.440)
and they are connected by these axioms.
Lex Fridman (3:34:11.480)
So in other words, you have some fact
Stephen Wolfram (3:34:14.760)
or you have some expression, you apply this axiom,
Lex Fridman (3:34:16.960)
you get some other expression.
Lex Fridman (3:34:18.840)
And in general, given some expression,
Lex Fridman (3:34:21.600)
there may be many possible different expressions
Stephen Wolfram (3:34:23.880)
you can get.
Lex Fridman (3:34:24.840)
You basically build up a multiway graph
Lex Fridman (3:34:27.320)
and a proof is a path through the multiway graph
Lex Fridman (3:34:31.120)
that goes from one thing to another thing.
Stephen Wolfram (3:34:34.200)
The path tells you how did you get from one thing
Lex Fridman (3:34:36.920)
to the other thing.
Stephen Wolfram (3:34:37.760)
It's the story of how you got from this to that.
Lex Fridman (3:34:40.680)
The theorem is the thing at one end
Stephen Wolfram (3:34:42.840)
is equal to the thing at the other end.
Lex Fridman (3:34:44.640)
The proof is the path you go down
Stephen Wolfram (3:34:46.880)
to get from one thing to the other.
Lex Fridman (3:34:48.600)
You mentioned that Gödel's incompleteness theorem
Stephen Wolfram (3:34:52.600)
fits naturally there.
Lex Fridman (3:34:53.560)
How does it fit?
Stephen Wolfram (3:34:54.400)
Yeah, so what happens there is that the Gödel's theorem
Lex Fridman (3:34:57.160)
is basically saying that there are paths of infinite length.
Stephen Wolfram (3:35:01.240)
That is that there's no upper bound.
Lex Fridman (3:35:03.120)
If you know these two things,
Stephen Wolfram (3:35:04.240)
you say, I'm trying to get from here to here,
Lex Fridman (3:35:06.200)
how long do I have to go?
Stephen Wolfram (3:35:07.920)
You say, well, I've looked at all the paths of length 10.
Lex Fridman (3:35:10.800)
Somebody says, that's not good enough.
Stephen Wolfram (3:35:12.600)
That path might be of length a billion.
Lex Fridman (3:35:14.720)
And there's no upper bound on how long that path is.
Lex Fridman (3:35:17.400)
And that's what leads to the incompleteness theorem.
Lex Fridman (3:35:19.760)
So I mean, the thing that is kind of an emerging idea
Stephen Wolfram (3:35:24.480)
is you can start asking,
Lex Fridman (3:35:26.160)
what's the analog of Einstein's equations
Lex Fridman (3:35:27.840)
in metamathematical space?
Lex Fridman (3:35:29.720)
What's the analog of a black hole
Lex Fridman (3:35:31.160)
in metamathematical space?
Lex Fridman (3:35:33.120)
What's the hope of this?
Lex Fridman (3:35:33.960)
So yeah, it's fascinating to model all the mathematics
Lex Fridman (3:35:36.840)
in this way.
Lex Fridman (3:35:37.680)
So here's what it is.
Lex Fridman (3:35:38.520)
This is mathematics in bulk.
Lex Fridman (3:35:40.320)
So human mathematicians have made a few million theorems.
Lex Fridman (3:35:44.000)
They've published a few million theorems.
Lex Fridman (3:35:45.800)
But imagine the infinite future of mathematics.
Lex Fridman (3:35:48.400)
Apply something to mathematics
Stephen Wolfram (3:35:50.440)
that mathematics likes to apply to other things.
Lex Fridman (3:35:52.360)
Take a limit.
Lex Fridman (3:35:53.520)
What is the limit of the infinite future of mathematics?
Lex Fridman (3:35:56.320)
What does it look like?
Lex Fridman (3:35:57.560)
What is the continuum limit of mathematics?
Lex Fridman (3:35:59.560)
What is the, as you just fill in
Stephen Wolfram (3:36:01.560)
more and more and more theorems,
Lex Fridman (3:36:03.120)
what does it look like?
Lex Fridman (3:36:04.040)
What does it do?
Lex Fridman (3:36:05.040)
How does, what kinds of conclusions can you make?
Lex Fridman (3:36:07.360)
So for example, one thing I've just been doing
Lex Fridman (3:36:09.800)
is taking Euclid.
Lex Fridman (3:36:10.960)
So Euclid, very impressive.
Lex Fridman (3:36:12.760)
He had 10 axioms, he derived 465 theorems, okay?
Stephen Wolfram (3:36:17.400)
His book, you know,
Lex Fridman (3:36:19.120)
that was the sort of defining book of mathematics
Stephen Wolfram (3:36:21.960)
for 2000 years.
Lex Fridman (3:36:24.120)
So you can actually map out,
Lex Fridman (3:36:25.640)
and I actually did this 20 years ago,
Lex Fridman (3:36:28.800)
but I've done it more seriously now.
Stephen Wolfram (3:36:30.720)
You can map out the theorem dependency
Lex Fridman (3:36:32.640)
of those 465 theorems.
Lex Fridman (3:36:34.760)
So from the axioms, you grow this graph,
Lex Fridman (3:36:37.520)
it's actually a multiway graph,
Stephen Wolfram (3:36:39.200)
of how all these theorems get proved from other theorems.
Lex Fridman (3:36:42.400)
And so you can ask questions about, you know,
Stephen Wolfram (3:36:45.240)
well, you can ask things like,
Lex Fridman (3:36:46.080)
what's the hardest theorem in Euclid?
Stephen Wolfram (3:36:47.520)
The answer is, the hardest theorem
Lex Fridman (3:36:48.840)
is that there are five platonic solids.
Stephen Wolfram (3:36:50.960)
That turns out to be the hardest theorem in Euclid.
Lex Fridman (3:36:52.800)
That's actually his last theorem in all his books.
Stephen Wolfram (3:36:55.320)
That's the final.
Lex Fridman (3:36:56.160)
What's the hardness, the distance you have to travel?
Stephen Wolfram (3:36:58.440)
Yeah, let's say it's 33 steps from the,
Lex Fridman (3:37:01.080)
the longest path in the graph is 33 steps.
Lex Fridman (3:37:03.720)
So that's the, there's a 33 step path you have to follow
Lex Fridman (3:37:07.400)
to go from the axioms, according to Euclid's proofs,
Stephen Wolfram (3:37:10.920)
to the statement there are five platonic solids.
Lex Fridman (3:37:13.560)
So, okay, so then the question is,
Lex Fridman (3:37:17.480)
in, what does it mean if you have this map?
Lex Fridman (3:37:22.360)
Okay, so in a sense, this metamathematical space
Stephen Wolfram (3:37:26.400)
is the infrastructural space of all possible theorems
Lex Fridman (3:37:29.200)
that you could prove in mathematics.
Stephen Wolfram (3:37:31.560)
That's the geometry of metamathematics.
Lex Fridman (3:37:34.360)
There's also the geography of mathematics.
Lex Fridman (3:37:37.120)
That is, where did people choose to live in space?
Lex Fridman (3:37:40.760)
And that's what, for example,
Stephen Wolfram (3:37:42.240)
exploring the sort of empirical metamathematics
Lex Fridman (3:37:44.320)
that Euclid is doing.
Stephen Wolfram (3:37:45.160)
You could put each individual, like, human mathematician,
Lex Fridman (3:37:48.360)
you can embed them into that space.
Stephen Wolfram (3:37:49.840)
I mean, they kind of live.
Lex Fridman (3:37:51.000)
They represent a path in the space.
Stephen Wolfram (3:37:52.320)
The little path.
Lex Fridman (3:37:53.160)
The things they do.
Stephen Wolfram (3:37:54.000)
Maybe a set of paths.
Lex Fridman (3:37:54.820)
Right.
Lex Fridman (3:37:55.660)
So like a set of axioms that are chosen.
Lex Fridman (3:37:58.480)
Right, so for example,
Stephen Wolfram (3:37:59.400)
here's an example of a thing that I realized.
Lex Fridman (3:38:01.960)
So one of the surprising things about,
Stephen Wolfram (3:38:03.920)
well, there are two surprising facts about math.
Lex Fridman (3:38:06.040)
One is that it's hard,
Lex Fridman (3:38:07.520)
and the other is that it's doable, okay?
Lex Fridman (3:38:10.200)
So first question is, why is math hard?
Stephen Wolfram (3:38:12.640)
You know, you've got these axioms.
Lex Fridman (3:38:13.800)
They're very small.
Lex Fridman (3:38:14.980)
Why can't you just solve every problem in math easily?
Lex Fridman (3:38:17.640)
Yeah, it's just logic.
Stephen Wolfram (3:38:19.120)
Right, yeah.
Lex Fridman (3:38:19.960)
Well, logic happens to be a particular special case
Stephen Wolfram (3:38:22.560)
that does have certain simplicity to it.
Lex Fridman (3:38:25.280)
But general mathematics, even arithmetic,
Stephen Wolfram (3:38:27.580)
already doesn't have the simplicity that logic has.
Lex Fridman (3:38:30.360)
So why is it hard?
Stephen Wolfram (3:38:31.720)
Because of computational irreducibility.
Lex Fridman (3:38:33.840)
Right.
Stephen Wolfram (3:38:35.560)
Because what happens is, to know what's true,
Lex Fridman (3:38:38.900)
and this is this whole story about the path
Stephen Wolfram (3:38:40.720)
you have to follow and how long is the path,
Lex Fridman (3:38:43.000)
and Gödel's theorem is the statement
Stephen Wolfram (3:38:44.520)
that the path is not a bounded length,
Lex Fridman (3:38:47.680)
but the fact that the path is not always compressible
Stephen Wolfram (3:38:50.440)
to something tiny is a story of computational irreducibility.
Lex Fridman (3:38:54.480)
So that's why math is hard.
Lex Fridman (3:38:56.800)
Now, the next question is, why is math doable?
Lex Fridman (3:38:59.520)
Because it might be the case that most things you care about
Stephen Wolfram (3:39:02.260)
don't have finite length paths.
Lex Fridman (3:39:04.200)
Most things you care about might be things
Stephen Wolfram (3:39:06.720)
where you get lost in the sea of computational irreducibility
Lex Fridman (3:39:10.160)
and worse, undecidability.
Stephen Wolfram (3:39:12.520)
That is, there's just no finite length path
Lex Fridman (3:39:14.760)
that gets you there.
Lex Fridman (3:39:17.000)
Why is mathematics doable?
Lex Fridman (3:39:19.040)
Gödel proved his incompleteness theorem in 1931.
Stephen Wolfram (3:39:22.200)
Most working mathematicians don't really care about it.
Lex Fridman (3:39:25.240)
They just go ahead and do mathematics,
Stephen Wolfram (3:39:27.240)
even though it could be that the questions they're asking
Lex Fridman (3:39:29.720)
are undecidable.
Stephen Wolfram (3:39:31.040)
It could have been that Fermat's last theorem
Lex Fridman (3:39:32.880)
is undecidable.
Stephen Wolfram (3:39:33.720)
It turned out it had a proof.
Lex Fridman (3:39:35.120)
It's a long, complicated proof.
Stephen Wolfram (3:39:36.960)
The twin prime conjecture might be undecidable.
Lex Fridman (3:39:40.200)
The Riemann hypothesis might be undecidable.
Stephen Wolfram (3:39:43.020)
These things might be, the axioms of mathematics
Lex Fridman (3:39:45.920)
might not be strong enough to reach those statements.
Stephen Wolfram (3:39:49.020)
It might be the case that depending on what axioms
Lex Fridman (3:39:51.400)
you choose, you can either say that's true
Stephen Wolfram (3:39:53.440)
or that's not true.
Lex Fridman (3:39:54.760)
So...
Lex Fridman (3:39:55.600)
And by the way, from Fermat's last theorem,
Lex Fridman (3:39:57.640)
there could be a shorter path.
Stephen Wolfram (3:39:59.420)
Absolutely.
Lex Fridman (3:40:00.360)
Yeah, so the notion of geodesics in metamathematical space
Stephen Wolfram (3:40:03.720)
is the notion of shortest proofs in metamathematical space.
Lex Fridman (3:40:07.260)
And that's a, you know, human mathematicians
Stephen Wolfram (3:40:09.400)
do not find shortest paths,
Lex Fridman (3:40:11.400)
nor do automated theorem provers.
Lex Fridman (3:40:13.940)
But the fact, and by the way, the, I mean,
Lex Fridman (3:40:16.840)
this stuff is so bizarrely connected.
Stephen Wolfram (3:40:18.760)
I mean, if you're into automated theorem proving,
Lex Fridman (3:40:21.640)
there are these so called critical pair lemmas
Lex Fridman (3:40:23.500)
and automated theorem proving.
Lex Fridman (3:40:24.900)
Those are precisely the branch pairs in our,
Stephen Wolfram (3:40:28.600)
that in multiway graphs.
Lex Fridman (3:40:30.600)
Let me just finish on the why mathematics is doable.
Stephen Wolfram (3:40:32.920)
Oh yes, the second part.
Lex Fridman (3:40:34.120)
So you know why it's hard, why is it doable?
Stephen Wolfram (3:40:36.680)
Right, why do we not just get lost
Lex Fridman (3:40:38.120)
in undecidability all the time?
Stephen Wolfram (3:40:39.520)
Yeah.
Lex Fridman (3:40:40.560)
So, and here's another fact,
Stephen Wolfram (3:40:43.160)
is in doing computer experiments
Lex Fridman (3:40:45.400)
and doing experimental mathematics,
Stephen Wolfram (3:40:47.020)
you do get lost in that way.
Lex Fridman (3:40:49.020)
When you just say, I'm picking a random integer equation.
Lex Fridman (3:40:53.860)
How do I, does it have a solution or not?
Lex Fridman (3:40:56.200)
And you just pick it at random
Stephen Wolfram (3:40:57.400)
without any human sort of path getting there.
Lex Fridman (3:41:00.900)
Often, it's really, really hard.
Stephen Wolfram (3:41:03.280)
It's really hard to answer those questions.
Lex Fridman (3:41:04.760)
We just pick them at random from the space of possibilities.
Lex Fridman (3:41:07.840)
But what I think is happening is,
Lex Fridman (3:41:10.720)
and that's a case where you just fell off
Stephen Wolfram (3:41:12.460)
into this ocean of sort of irreducibility and so on.
Lex Fridman (3:41:15.560)
What's happening is human mathematics
Stephen Wolfram (3:41:18.220)
is a story of building a path.
Lex Fridman (3:41:19.920)
You started off, you're always building out
Stephen Wolfram (3:41:23.220)
on this path where you are proving things.
Lex Fridman (3:41:25.720)
You've got this proof trajectory
Lex Fridman (3:41:28.120)
and you're basically, the human mathematics
Lex Fridman (3:41:30.320)
is the sort of the exploration of the world
Stephen Wolfram (3:41:34.160)
along this proof trajectory, so to speak.
Lex Fridman (3:41:36.760)
You're not just parachuting in from anywhere.
Stephen Wolfram (3:41:42.840)
You're following Lewis and Clark or whatever.
Lex Fridman (3:41:44.840)
You're actually going, doing the path.
Lex Fridman (3:41:48.160)
And the fact that you are constrained to go along that path
Lex Fridman (3:41:52.080)
is the reason you don't end up with,
Stephen Wolfram (3:41:53.760)
every so often you'll see a little piece of undecidability
Lex Fridman (3:41:55.840)
and you'll avoid that part of the path.
Lex Fridman (3:41:57.980)
But that's basically the story of why human mathematics
Lex Fridman (3:42:00.960)
has seemed to be doable.
Stephen Wolfram (3:42:02.640)
It's a story of exploring these paths
Lex Fridman (3:42:05.200)
that are by their nature,
Stephen Wolfram (3:42:07.240)
they have been constructed to be paths that can be followed.
Lex Fridman (3:42:10.480)
And so you can follow them further.
Lex Fridman (3:42:12.260)
Now, why is this relevant to anything?
Lex Fridman (3:42:14.920)
So, okay, so here's my belief.
Stephen Wolfram (3:42:19.480)
The fact that human mathematics works that way
Lex Fridman (3:42:22.640)
is I think there's some sort of connections
Stephen Wolfram (3:42:26.080)
between the way that observers work in physics
Lex Fridman (3:42:29.720)
and the way that the axiom systems of mathematics are set up
Stephen Wolfram (3:42:32.980)
to make mathematics be doable in that kind of way.
Lex Fridman (3:42:36.360)
And so, in other words, in particular,
Stephen Wolfram (3:42:38.880)
I think there is an analog of causal invariance,
Lex Fridman (3:42:41.720)
which I think is, and this is again,
Stephen Wolfram (3:42:44.800)
it's sort of the upper reaches of mathematics
Lex Fridman (3:42:46.620)
and stuff that it's a thing,
Stephen Wolfram (3:42:50.680)
there's this thing called homotopy type theory,
Lex Fridman (3:42:52.900)
which is an abstract, it's came out of category theory,
Lex Fridman (3:42:56.120)
and it's sort of an abstraction of mathematics.
Lex Fridman (3:42:58.380)
Mathematics itself is an abstraction,
Lex Fridman (3:43:00.360)
but it's an abstraction of the abstraction of mathematics.
Lex Fridman (3:43:03.980)
And there is the thing called the univalence axiom,
Stephen Wolfram (3:43:06.620)
which is a sort of a key axiom in that set of ideas.
Lex Fridman (3:43:12.220)
And I'm pretty sure the univalence axiom
Stephen Wolfram (3:43:14.200)
is equivalent to causal invariance.
Lex Fridman (3:43:16.220)
What was the term you used again?
Stephen Wolfram (3:43:18.120)
Univalence.
Lex Fridman (3:43:19.000)
Is that something for somebody like me accessible?
Lex Fridman (3:43:21.560)
Or is this?
Lex Fridman (3:43:23.200)
There's a statement of it that's fairly accessible.
Stephen Wolfram (3:43:25.560)
I mean, the statement of it is,
Lex Fridman (3:43:29.680)
basically it says things which are equivalent
Stephen Wolfram (3:43:32.760)
can be considered to be identical.
Lex Fridman (3:43:35.520)
In which space?
Stephen Wolfram (3:43:38.160)
Yeah, it's in higher category.
Lex Fridman (3:43:40.720)
In category.
Stephen Wolfram (3:43:41.720)
Okay, so it's a, but I mean,
Lex Fridman (3:43:43.880)
the thing just to give a sketch of how that works.
Lex Fridman (3:43:46.160)
So category theory is an attempt to idealize,
Lex Fridman (3:43:49.680)
it's an attempt to sort of have a formal theory
Stephen Wolfram (3:43:52.060)
of mathematics that is at a sort of higher level
Lex Fridman (3:43:54.400)
than mathematics.
Stephen Wolfram (3:43:55.600)
It's where you just think about these mathematical objects
Lex Fridman (3:43:59.560)
and these categories of objects and these morphisms,
Stephen Wolfram (3:44:03.720)
these connections between categories.
Lex Fridman (3:44:05.600)
Okay, so it turns out the morphisms and categories,
Stephen Wolfram (3:44:08.640)
at least weak categories,
Lex Fridman (3:44:10.840)
are very much like the paths in our hypergraphs and things.
Lex Fridman (3:44:14.820)
And it turns out, again, this is where it all gets crazy.
Lex Fridman (3:44:18.480)
I mean, the fact that these things are connected
Stephen Wolfram (3:44:20.800)
is just bizarre.
Lex Fridman (3:44:22.000)
So category theory, our causal graphs
Stephen Wolfram (3:44:27.080)
are like second order category theory.
Lex Fridman (3:44:29.940)
And it turns out you can take the limits
Stephen Wolfram (3:44:32.640)
of infinite order category theory.
Lex Fridman (3:44:34.160)
So just give roughly the idea.
Stephen Wolfram (3:44:36.480)
This is a roughly explainable idea.
Lex Fridman (3:44:39.120)
So a mathematical proof will be a path
Stephen Wolfram (3:44:43.400)
that says you can get from this thing to this other thing.
Lex Fridman (3:44:45.920)
And here's the path that you get from this thing
Stephen Wolfram (3:44:47.480)
to this other thing.
Lex Fridman (3:44:48.720)
But in general, there may be many paths,
Stephen Wolfram (3:44:51.160)
many proofs that get you many different paths
Lex Fridman (3:44:53.960)
that all successfully go from this thing
Lex Fridman (3:44:55.800)
to this other thing, okay?
Lex Fridman (3:44:57.700)
Now you can define a higher order proof,
Stephen Wolfram (3:45:00.400)
which is a proof of the equivalence of those proofs.
Lex Fridman (3:45:03.840)
Okay, so you're saying there's a...
Stephen Wolfram (3:45:05.440)
A path between those proofs essentially.
Lex Fridman (3:45:07.120)
Yes, a path between the paths, okay?
Lex Fridman (3:45:09.800)
And so you do that.
Lex Fridman (3:45:10.960)
That's the sort of second order thing.
Stephen Wolfram (3:45:12.300)
That path between the paths is essentially related
Lex Fridman (3:45:16.120)
to our causal graphs.
Stephen Wolfram (3:45:18.240)
Then you can take the limit.
Lex Fridman (3:45:19.560)
Wow, okay.
Stephen Wolfram (3:45:20.400)
The path between path, between path, between path.
Lex Fridman (3:45:23.040)
The infinite limit.
Stephen Wolfram (3:45:24.640)
That infinite limit turns out to be
Lex Fridman (3:45:26.340)
our Rulial Multiway System.
Stephen Wolfram (3:45:28.800)
Yeah, the Rulial Multiway System,
Lex Fridman (3:45:31.600)
that's a fascinating, both in the physics world
Lex Fridman (3:45:33.860)
and as you're saying now, that's fast.
Lex Fridman (3:45:36.920)
I'm not sure I've loaded it in completely, but...
Stephen Wolfram (3:45:39.120)
Well, I'm not sure I have either.
Lex Fridman (3:45:40.320)
And it may be one of these things where,
Stephen Wolfram (3:45:42.560)
in another five years or something, it's like,
Lex Fridman (3:45:45.160)
it was obvious, but I didn't see it.
Stephen Wolfram (3:45:47.120)
No, but the thing which is sort of interesting to me
Lex Fridman (3:45:49.360)
is that there's sort of an upper reach of mathematics,
Stephen Wolfram (3:45:53.080)
of the abstraction of mathematics.
Lex Fridman (3:45:55.880)
This thing, there's this mathematician called Grothendieck
Stephen Wolfram (3:45:59.000)
who's generally viewed as being sort of one
Lex Fridman (3:46:00.680)
of the most abstract,
Stephen Wolfram (3:46:02.320)
sort of creator of the most abstract mathematics
Lex Fridman (3:46:04.800)
of 1970s ish timeframe.
Lex Fridman (3:46:09.360)
And one of the things that he constructed was this thing
Lex Fridman (3:46:11.560)
he called the Infinity Grupoid.
Lex Fridman (3:46:13.280)
And he has this sort of hypothesis
Lex Fridman (3:46:15.820)
about the inevitable appearance of geometry
Stephen Wolfram (3:46:18.380)
from essentially logic in the structure of this thing.
Lex Fridman (3:46:22.420)
Well, it turns out this Rulial Multiway System
Stephen Wolfram (3:46:24.660)
is the Infinity Grupoid.
Lex Fridman (3:46:26.620)
So it's this limiting object.
Lex Fridman (3:46:29.700)
And this is an instance of that limiting object.
Lex Fridman (3:46:33.560)
So what to me is, I mean, again,
Stephen Wolfram (3:46:35.460)
I've been always afraid of this kind of mathematics
Lex Fridman (3:46:37.980)
because it seemed incomprehensibly abstract to me.
Lex Fridman (3:46:42.260)
But what I'm sort of excited about with this
Lex Fridman (3:46:45.620)
is that we've sort of concretified the way
Stephen Wolfram (3:46:49.540)
that you can reach this kind of mathematics,
Lex Fridman (3:46:51.860)
which makes it, well, both seem more relevant
Lex Fridman (3:46:55.260)
and also the fact that I don't yet know exactly
Lex Fridman (3:46:58.820)
what mileage we're gonna get from using
Stephen Wolfram (3:47:01.120)
the sort of the apparatus that's been built
Lex Fridman (3:47:03.340)
in those areas of mathematics to analyze what we're doing.
Lex Fridman (3:47:06.500)
But the thing that's.
Lex Fridman (3:47:07.340)
So both ways.
Lex Fridman (3:47:08.180)
So using mathematics to understand what you're doing
Lex Fridman (3:47:10.020)
and using what you're doing computationally
Stephen Wolfram (3:47:12.340)
to understand that.
Lex Fridman (3:47:13.180)
Right, so for example,
Stephen Wolfram (3:47:14.020)
the understanding of metamathematical space,
Lex Fridman (3:47:17.860)
one of the reasons I really want to do that
Stephen Wolfram (3:47:19.860)
is because I want to understand quantum mechanics better.
Lex Fridman (3:47:22.620)
And that, what you see,
Stephen Wolfram (3:47:25.980)
we live that kind of the multiway graph of mathematics
Lex Fridman (3:47:30.260)
because we actually know this is a theorem we've heard of.
Stephen Wolfram (3:47:32.540)
This is another one we've heard of.
Lex Fridman (3:47:34.020)
We can actually say these are actual things in the world
Stephen Wolfram (3:47:36.900)
that we relate to,
Lex Fridman (3:47:38.480)
which we can't really do as readily for the physics case.
Lex Fridman (3:47:43.100)
And so it's kind of a way to help my intuition.
Lex Fridman (3:47:45.180)
It's also, there are bizarre things
Stephen Wolfram (3:47:47.820)
like what's the analog of Einstein's equations
Lex Fridman (3:47:50.020)
in metamathematical space?
Lex Fridman (3:47:51.880)
What's the analog of a black hole?
Lex Fridman (3:47:53.980)
It turns out it looks like not completely sure yet,
Lex Fridman (3:47:57.660)
but there's this notion of nonconstructive proofs
Lex Fridman (3:48:00.180)
in mathematics.
Lex Fridman (3:48:01.500)
And I think those relate to,
Lex Fridman (3:48:03.540)
well, actually they relate to things
Stephen Wolfram (3:48:07.780)
related to event horizons.
Lex Fridman (3:48:10.420)
So the fact that you can take ideas from physics
Stephen Wolfram (3:48:13.500)
like event horizons.
Lex Fridman (3:48:14.460)
And map them into the same kind of space, metamath.
Stephen Wolfram (3:48:17.100)
It's really.
Lex Fridman (3:48:17.940)
So do you think there'll be,
Lex Fridman (3:48:19.460)
do you think you might stumble upon
Lex Fridman (3:48:22.140)
some breakthrough ideas in theorem proving?
Lex Fridman (3:48:25.860)
Like for, from the other direction?
Lex Fridman (3:48:28.700)
Yeah, yeah, yeah.
Stephen Wolfram (3:48:29.540)
No, I mean, what's really nice is that we are using,
Lex Fridman (3:48:32.180)
so this absolutely directly maps to theorem proving.
Lex Fridman (3:48:35.640)
So pods and multiway graphs,
Lex Fridman (3:48:37.240)
that's what a theorem prover is trying to do.
Lex Fridman (3:48:38.540)
But I also mean like automated theorem.
Lex Fridman (3:48:40.780)
Yeah, yeah, yeah.
Stephen Wolfram (3:48:41.620)
That's what, right.
Lex Fridman (3:48:42.440)
So the finding of pods, the finding of shortest pods
Stephen Wolfram (3:48:45.180)
or finding of pods at all
Lex Fridman (3:48:46.840)
is what automated theorem provers do.
Lex Fridman (3:48:48.780)
And actually what we've been doing.
Lex Fridman (3:48:51.020)
So we've actually been using automated theorem proving
Stephen Wolfram (3:48:53.760)
both in the physics project to prove things
Lex Fridman (3:48:56.340)
and using that as a way to understand multiway graphs.
Lex Fridman (3:49:00.540)
And because what an automated theorem prover is doing
Lex Fridman (3:49:04.080)
is it's trying to find a path through a multiway graph
Lex Fridman (3:49:07.380)
and its critical pair lemmas
Lex Fridman (3:49:09.300)
are precisely little stubs of branch pairs
Stephen Wolfram (3:49:12.960)
going off into branchial space.
Lex Fridman (3:49:15.080)
And that's, I mean, it's really weird.
Stephen Wolfram (3:49:16.860)
You know, we have these visualizations in Wolfram language
Lex Fridman (3:49:19.100)
of proof graphs from our automated theorem proving system.
Lex Fridman (3:49:24.180)
And they look reminiscent of.
Lex Fridman (3:49:25.660)
Well, it's just bizarre
Stephen Wolfram (3:49:26.860)
because we made these up a few years ago
Lex Fridman (3:49:28.820)
and they have these little triangle things
Lex Fridman (3:49:30.740)
and they are, we didn't quite get it right.
Lex Fridman (3:49:33.020)
We didn't quite get the analogy perfectly right,
Lex Fridman (3:49:35.100)
but it's very close.
Lex Fridman (3:49:36.220)
You know, just to say,
Stephen Wolfram (3:49:37.460)
in terms of how these things are connected.
Lex Fridman (3:49:39.940)
So there's another bizarre connection
Stephen Wolfram (3:49:41.520)
that I have to mention because which is,
Lex Fridman (3:49:46.160)
which again, we don't fully know,
Lex Fridman (3:49:47.940)
but it's a connection to something else
Lex Fridman (3:49:51.140)
you might not have thought was in the slightest
Lex Fridman (3:49:52.660)
but connected, which is distributed blockchain like things.
Lex Fridman (3:49:56.840)
Now you might figure out that that's,
Stephen Wolfram (3:49:58.140)
you would figure out that that's connected
Lex Fridman (3:49:59.900)
because it's a story of distributed computing.
Lex Fridman (3:50:02.860)
And the issue, you know, with the blockchain,
Lex Fridman (3:50:04.860)
you're saying there's going to be this one ledger
Stephen Wolfram (3:50:07.580)
that globally says, this is what happened in the world.
Lex Fridman (3:50:11.700)
But that's a bad deal.
Stephen Wolfram (3:50:14.000)
If you've got all these different transactions
Lex Fridman (3:50:15.640)
that are happening and you know,
Stephen Wolfram (3:50:17.300)
this transaction in country A
Lex Fridman (3:50:20.660)
doesn't have to be reconciled with the transaction
Stephen Wolfram (3:50:23.380)
in country B, at least not for a while.
Lex Fridman (3:50:26.220)
And that story is just like what happens
Stephen Wolfram (3:50:29.380)
with our causal graphs.
Lex Fridman (3:50:31.000)
That whole reconciliation thing is just like
Lex Fridman (3:50:33.220)
what happens with light cones and all this kind of thing.
Lex Fridman (3:50:35.740)
That's where the causal awareness comes into play.
Stephen Wolfram (3:50:37.420)
I mean, that's, you know,
Lex Fridman (3:50:39.180)
most of your conversations are about physics,
Lex Fridman (3:50:41.380)
but it's kind of funny that this probably
Lex Fridman (3:50:46.000)
and possibly might have even bigger impact
Lex Fridman (3:50:49.340)
and revolutionary ideas and totally other disciplines.
Lex Fridman (3:50:53.980)
Right, well, you see, yeah, right.
Lex Fridman (3:50:55.400)
So the question is, why is that happening, right?
Lex Fridman (3:50:57.640)
And the reason it's happening,
Stephen Wolfram (3:50:59.140)
I've thought about this obviously,
Lex Fridman (3:51:00.700)
because I like to think about these meta questions of,
Stephen Wolfram (3:51:03.300)
you know, what's happening is this model that we have
Lex Fridman (3:51:06.380)
is an incredibly minimal model.
Lex Fridman (3:51:08.740)
And once you have an incredibly minimal model,
Lex Fridman (3:51:11.360)
and this happened with cellular automata as well,
Stephen Wolfram (3:51:13.620)
cellular automata are an incredibly minimal model.
Lex Fridman (3:51:16.040)
And so it's inevitable that it gets you,
Stephen Wolfram (3:51:19.100)
it's sort of an upstream thing
Lex Fridman (3:51:20.600)
that gets used in lots of different places.
Lex Fridman (3:51:22.720)
And it's like, you know, the fact that it gets used,
Lex Fridman (3:51:25.280)
you know, cellular automata is sort of a minimal model
Stephen Wolfram (3:51:27.380)
of let's say road traffic flow or something.
Lex Fridman (3:51:29.140)
And they're also a minimal model of something in,
Stephen Wolfram (3:51:31.340)
you know, chemistry,
Lex Fridman (3:51:32.180)
and they're also a minimal model of something
Lex Fridman (3:51:33.560)
in epidemiology, right?
Lex Fridman (3:51:35.860)
It's because they're such a simple model that they can,
Stephen Wolfram (3:51:38.140)
that they apply to all these different things.
Lex Fridman (3:51:40.300)
Similarly, this model that we have with the physics project
Stephen Wolfram (3:51:43.060)
is another, cellular automata are a minimal model
Lex Fridman (3:51:47.300)
of parallel, of basically of parallel computation
Stephen Wolfram (3:51:50.580)
where you've defined space and time.
Lex Fridman (3:51:52.840)
These models are minimal models
Stephen Wolfram (3:51:54.820)
where you have not defined space and time.
Lex Fridman (3:51:57.180)
And they have been very hard to understand in the past,
Lex Fridman (3:52:00.340)
but the, I think the,
Lex Fridman (3:52:01.980)
perhaps the most important breakthrough there
Stephen Wolfram (3:52:04.500)
is the realization that these are models of physics.
Lex Fridman (3:52:07.440)
And therefore that you can use everything
Stephen Wolfram (3:52:09.180)
that's been developed in physics
Lex Fridman (3:52:11.140)
to get intuition about how things like that work.
Lex Fridman (3:52:13.880)
And that's why you can potentially use ideas from physics
Lex Fridman (3:52:17.500)
to get intuition about how to do parallel computing.
Lex Fridman (3:52:20.140)
And because the underlying model is the same.
Lex Fridman (3:52:24.940)
But we have all of this achievement in physics.
Stephen Wolfram (3:52:27.060)
I mean, you know, you might say,
Lex Fridman (3:52:28.500)
oh, you've come up with the fundamental theory of physics
Stephen Wolfram (3:52:30.160)
that throws out what people have done in physics before.
Lex Fridman (3:52:32.500)
Well, it doesn't, but also the real power
Stephen Wolfram (3:52:35.540)
is to use what's been done before in physics
Lex Fridman (3:52:37.940)
to apply it in these other places.
Stephen Wolfram (3:52:39.620)
Yes, absolutely.
Lex Fridman (3:52:41.500)
This kind of brings up,
Stephen Wolfram (3:52:43.020)
I know you probably don't particularly love commenting
Lex Fridman (3:52:47.900)
on the work of others,
Lex Fridman (3:52:48.820)
but let me bring up a couple of personalities
Lex Fridman (3:52:51.260)
just because it's fun and people are curious about it.
Lex Fridman (3:52:53.660)
So there's Sabine Hassenfelder.
Lex Fridman (3:52:58.700)
I don't know if you're familiar with her.
Stephen Wolfram (3:53:00.460)
She wrote this book that I need to read,
Lex Fridman (3:53:04.920)
but I forget what the title is,
Lex Fridman (3:53:06.980)
but it's Beauty Leads Us Astray in Physics
Lex Fridman (3:53:10.480)
is a subtitle or something like that.
Stephen Wolfram (3:53:12.420)
Which so much about what we're talking about now,
Lex Fridman (3:53:15.100)
like this simplification,
Stephen Wolfram (3:53:17.860)
to us humans seems to be beautiful.
Lex Fridman (3:53:20.440)
Like there's a certain intuition with physicists,
Stephen Wolfram (3:53:23.540)
with people that a simple theory,
Lex Fridman (3:53:26.700)
like this reducibility,
Stephen Wolfram (3:53:28.060)
pockets of reducibility is the ultimate goal.
Lex Fridman (3:53:30.580)
And I think what she tries to argue is no,
Stephen Wolfram (3:53:34.780)
we just need to come up with theories
Lex Fridman (3:53:37.740)
that are just really good at predicting physical phenomena.
Stephen Wolfram (3:53:40.620)
It's okay to have a bunch of disparate theories
Lex Fridman (3:53:44.360)
as opposed to trying to chase this beautiful theory
Stephen Wolfram (3:53:48.580)
of everything is the ultimate beautiful theory,
Lex Fridman (3:53:51.140)
a simple one.
Lex Fridman (3:53:52.140)
What's your response to that?
Lex Fridman (3:53:54.620)
Well, so what you're quoting,
Stephen Wolfram (3:53:56.340)
I don't know the Sabine Hassenfelder's,
Lex Fridman (3:53:59.820)
exactly what she said,
Lex Fridman (3:54:00.660)
but I mean that you're quoting the title of her book.
Lex Fridman (3:54:03.780)
Okay.
Stephen Wolfram (3:54:04.620)
Let me respond to what you were describing,
Lex Fridman (3:54:07.780)
which may or may not have nothing to do with
Lex Fridman (3:54:09.620)
what Sabine Hassenfelder says or thinks.
Lex Fridman (3:54:14.660)
Sorry, Sabine.
Stephen Wolfram (3:54:16.460)
Right.
Lex Fridman (3:54:17.300)
Sorry for misquoting.
Lex Fridman (3:54:18.420)
But I mean, the question is,
Lex Fridman (3:54:23.300)
is beauty a guide to whether something is correct?
Stephen Wolfram (3:54:26.540)
Which is kind of also the story of Occam's razor.
Lex Fridman (3:54:29.180)
If you've got a bunch of different explanations of things,
Stephen Wolfram (3:54:32.140)
is the thing that is the simplest explanation
Lex Fridman (3:54:34.500)
likely to be the correct explanation?
Lex Fridman (3:54:36.580)
And there are situations where that's true
Lex Fridman (3:54:38.100)
and there are situations where it isn't true.
Stephen Wolfram (3:54:39.940)
Sometimes in human systems, it is true
Lex Fridman (3:54:41.900)
because people have kind of,
Stephen Wolfram (3:54:43.140)
in evolutionary systems, sometimes it's true
Lex Fridman (3:54:45.220)
because it's sort of been kicked
Stephen Wolfram (3:54:46.780)
to the point where it's minimized.
Lex Fridman (3:54:49.340)
But in physics, does Occam's razor work?
Stephen Wolfram (3:54:53.580)
Is there a simple, quotes, beautiful explanation for things
Lex Fridman (3:54:57.420)
or is it a big mess?
Stephen Wolfram (3:54:59.780)
We don't intrinsically know.
Lex Fridman (3:55:01.940)
I think that the, I wouldn't,
Stephen Wolfram (3:55:03.660)
before I worked on the project in recent times,
Lex Fridman (3:55:07.180)
I would have said,
Stephen Wolfram (3:55:08.220)
we do not know how complicated
Lex Fridman (3:55:09.900)
the rule for the universe will be.
Lex Fridman (3:55:12.100)
And I would have said, the one thing we know,
Lex Fridman (3:55:15.940)
which is a fundamental fact about science,
Stephen Wolfram (3:55:17.780)
that's the thing that makes science possible,
Lex Fridman (3:55:19.740)
is that there is order in the universe.
Stephen Wolfram (3:55:21.860)
I mean, early theologians would have used that
Lex Fridman (3:55:24.860)
as an argument for the existence of God
Lex Fridman (3:55:27.140)
because it's like, why is there order in the universe?
Lex Fridman (3:55:29.420)
Why doesn't every single particle in the universe
Lex Fridman (3:55:31.500)
just do its own thing?
Lex Fridman (3:55:33.980)
Something must be making there be order in the universe.
Stephen Wolfram (3:55:37.180)
We, in the sort of early theology point of view,
Lex Fridman (3:55:41.820)
that's the role of God is to do that, so to speak.
Stephen Wolfram (3:55:45.180)
In our, we might say,
Lex Fridman (3:55:47.580)
it's the role of a formal theory to do that.
Lex Fridman (3:55:50.140)
And then the question is,
Lex Fridman (3:55:51.060)
but how simple should that theory be?
Lex Fridman (3:55:53.260)
And should that theory be one that,
Lex Fridman (3:55:57.060)
where I think the point is, if it's simple,
Stephen Wolfram (3:56:00.620)
it's almost inevitably somewhat beautiful
Lex Fridman (3:56:03.180)
in the sense that, because all the stuff that we see
Stephen Wolfram (3:56:06.460)
has to fit into this little tiny theory.
Lex Fridman (3:56:08.740)
And the way it does that has to be,
Stephen Wolfram (3:56:11.380)
it depends on your notion of beauty,
Lex Fridman (3:56:13.300)
but I mean, for me, the sort of the surprising
Stephen Wolfram (3:56:17.940)
connectivity of it is, at least in my aesthetic,
Lex Fridman (3:56:21.980)
that's something that responds to my aesthetic.
Lex Fridman (3:56:25.100)
But the question is, I mean,
Lex Fridman (3:56:27.780)
you're a fascinating person in the sense that
Stephen Wolfram (3:56:31.060)
you're at once talking about computational,
Lex Fridman (3:56:34.460)
the fundamental computational reducibility of the universe,
Lex Fridman (3:56:37.940)
and on the other hand,
Lex Fridman (3:56:40.380)
trying to come up with a theory of everything,
Stephen Wolfram (3:56:42.540)
which simply describes the,
Lex Fridman (3:56:47.740)
the simple origins of that computational reducibility.
Stephen Wolfram (3:56:51.460)
I mean, both of those things are kind of,
Lex Fridman (3:56:53.820)
it's paralyzing to think that we can't make any sense
Stephen Wolfram (3:56:56.340)
of the universe in the general case,
Lex Fridman (3:56:58.580)
but it's hopeful to think like,
Stephen Wolfram (3:57:01.060)
one, we can think of a rule
Lex Fridman (3:57:03.060)
and that generates this whole complexity,
Lex Fridman (3:57:05.980)
and two, we can find pockets of reducibility
Lex Fridman (3:57:10.980)
that are powerful for everyday life
Stephen Wolfram (3:57:13.420)
to do different kinds of predictions.
Lex Fridman (3:57:15.540)
I suppose Sabine wants to find,
Stephen Wolfram (3:57:19.060)
focus on the finding of small pockets of reducibility
Lex Fridman (3:57:22.940)
versus the theory of everything.
Stephen Wolfram (3:57:26.780)
You know, it's a funny thing because,
Lex Fridman (3:57:29.300)
you know, a bunch of people have started working
Stephen Wolfram (3:57:30.780)
on this physics project,
Lex Fridman (3:57:32.980)
people who are physicists, basically,
Lex Fridman (3:57:36.780)
and it is really a fascinating sociological phenomenon
Lex Fridman (3:57:39.820)
because what, you know,
Stephen Wolfram (3:57:41.780)
when I was working on this before in the 1990s,
Lex Fridman (3:57:45.300)
you know, wrote it up, put it,
Stephen Wolfram (3:57:47.900)
it's 100 pages of this 1200 page book
Lex Fridman (3:57:50.060)
that I wrote, New Kind of Science,
Stephen Wolfram (3:57:51.300)
is, you know, 100 pages of that is about physics,
Lex Fridman (3:57:54.140)
but I saw it at that time,
Stephen Wolfram (3:57:57.380)
not as a pinnacle achievement,
Lex Fridman (3:57:59.620)
but rather as a use case, so to speak.
Stephen Wolfram (3:58:01.820)
I mean, my main point was this new kind of science,
Lex Fridman (3:58:04.100)
and it's like, you can apply it to biology,
Stephen Wolfram (3:58:05.940)
you can apply it to, you know, other kinds of physics,
Lex Fridman (3:58:08.420)
you can apply it to fundamental physics,
Stephen Wolfram (3:58:09.900)
it's just an application, so to speak,
Lex Fridman (3:58:12.420)
it's not the core thing.
Lex Fridman (3:58:14.740)
But then, you know, one of the things that was interesting
Lex Fridman (3:58:18.100)
with that book was, you know,
Stephen Wolfram (3:58:21.180)
book comes out, lots of people think it's pretty interesting
Lex Fridman (3:58:24.580)
and lots of people start using what it has
Stephen Wolfram (3:58:26.460)
in different kinds of fields.
Lex Fridman (3:58:28.100)
The one field where there was sort of a heavy pitchforking
Stephen Wolfram (3:58:32.500)
was from my friends, the fundamental physics people,
Lex Fridman (3:58:35.940)
which was, it's like, no,
Stephen Wolfram (3:58:37.460)
this can't possibly be right.
Lex Fridman (3:58:38.700)
And, you know, it's like, you know,
Stephen Wolfram (3:58:40.180)
if what you're doing is right,
Lex Fridman (3:58:41.540)
it'll overturn 50 years of what we've been doing.
Lex Fridman (3:58:44.220)
And it's like, no, it won't, was what I was saying.
Lex Fridman (3:58:46.980)
And it's like, but, you know, for a while,
Stephen Wolfram (3:58:50.820)
when I started, you know, I was going to go on back in 2002,
Lex Fridman (3:58:54.380)
well, 2004, actually, I was going to go on
Stephen Wolfram (3:58:57.060)
working on this project.
Lex Fridman (3:58:58.500)
And I actually stopped,
Stephen Wolfram (3:58:59.820)
partly because it's like, why am I, you know,
Lex Fridman (3:59:03.100)
this is like, I've been in business a long time, right?
Stephen Wolfram (3:59:05.380)
I'm building a product for a target market
Lex Fridman (3:59:08.100)
that doesn't want the product.
Lex Fridman (3:59:09.700)
And it's like.
Lex Fridman (3:59:10.700)
Why work, yeah, yeah, why work against the,
Stephen Wolfram (3:59:13.260)
swim against the current or whatever.
Lex Fridman (3:59:14.620)
Right, but you see what's happened,
Stephen Wolfram (3:59:16.100)
which is sort of interesting is that,
Lex Fridman (3:59:18.060)
so a couple of things happened and it was like,
Stephen Wolfram (3:59:22.580)
you know, it was like, I don't want to do this project
Lex Fridman (3:59:25.700)
because I can do so many other things,
Stephen Wolfram (3:59:28.540)
which I'm really interested in where, you know,
Lex Fridman (3:59:31.820)
people say, great, thanks for those tools.
Stephen Wolfram (3:59:34.100)
Thanks for those ideas, et cetera.
Lex Fridman (3:59:36.380)
Whereas, you know, if you're dealing with kind of a,
Stephen Wolfram (3:59:40.020)
you know, a sort of a structure where people are saying,
Lex Fridman (3:59:42.820)
no, no, we don't want this new stuff.
Stephen Wolfram (3:59:44.220)
We don't need any new stuff.
Lex Fridman (3:59:45.300)
We're really fine with what we're doing.
Stephen Wolfram (3:59:46.660)
Yeah, there's like literally like, I don't know,
Lex Fridman (3:59:48.300)
millions of people who are thankful for Wolfram Alpha.
Stephen Wolfram (3:59:51.140)
A bunch of people wrote to me, how thankful,
Lex Fridman (3:59:53.260)
they are a different crowd
Stephen Wolfram (3:59:55.460)
than the theoretical physics community, perhaps.
Lex Fridman (3:59:57.820)
Yeah, well, but you know,
Stephen Wolfram (3:59:58.900)
the theoretical physics community
Lex Fridman (40:01.160)
you think about some process in physics,
Stephen Wolfram (40:06.080)
something that you compute in mathematics, whatever else,
Lex Fridman (40:09.120)
it's a computation in the sense it has definite rules.
Stephen Wolfram (40:11.920)
You follow those rules.
Lex Fridman (40:13.640)
You follow them many steps and you get some result.
Lex Fridman (40:18.360)
So then the issue is,
Lex Fridman (40:20.080)
if you look at all these different kinds of computations
Stephen Wolfram (40:21.960)
that can happen,
Lex Fridman (40:22.800)
whether they're computations
Stephen Wolfram (40:23.760)
that are happening in the natural world,
Lex Fridman (40:24.880)
whether they're happening in our brains,
Stephen Wolfram (40:26.560)
whether they're happening in our mathematics,
Lex Fridman (40:28.080)
whatever else,
Lex Fridman (40:29.040)
the big question is, how do these computations compare?
Lex Fridman (40:32.120)
Is, are there dumb computations and smart computations
Lex Fridman (40:35.560)
or are they somehow all equivalent?
Lex Fridman (40:37.520)
And the thing that I kind of was sort of surprised to realize
Stephen Wolfram (40:41.720)
from a bunch of experiments that I did in the early nineties
Lex Fridman (40:43.960)
and now we have tons more evidence for it,
Stephen Wolfram (40:46.080)
this thing I call the principle of computational equivalence,
Lex Fridman (40:48.880)
which basically says, when one of these computations,
Stephen Wolfram (40:51.920)
one of these processes that follows rules,
Lex Fridman (40:54.280)
doesn't seem like it's doing something obviously simple,
Stephen Wolfram (40:57.640)
then it has reached the sort of equivalent level
Lex Fridman (41:00.120)
of computational sophistication of everything.
Lex Fridman (41:03.720)
So what does that mean?
Lex Fridman (41:04.560)
That means that, you might say, gosh,
Stephen Wolfram (41:07.560)
I'm studying this little tiny program on my computer.
Lex Fridman (41:11.600)
I'm studying this little thing in nature,
Lex Fridman (41:14.280)
but I have my brain
Lex Fridman (41:15.360)
and my brain is surely much smarter than that thing.
Stephen Wolfram (41:18.440)
I'm gonna be able to systematically outrun
Lex Fridman (41:20.520)
the computation that it does
Stephen Wolfram (41:22.120)
because I have a more sophisticated computation
Lex Fridman (41:24.000)
that I can do.
Lex Fridman (41:25.160)
But what the principle of computational equivalence says
Lex Fridman (41:27.400)
is that doesn't work.
Stephen Wolfram (41:29.000)
Our brains are doing computations
Lex Fridman (41:31.800)
that are exactly equivalent to the kinds of computations
Stephen Wolfram (41:34.600)
that are being done in all these other sorts of systems.
Lex Fridman (41:36.920)
And so what consequences does that have?
Stephen Wolfram (41:38.320)
Well, it means that we can't systematically
Lex Fridman (41:40.640)
outrun these systems.
Stephen Wolfram (41:42.240)
These systems are computationally irreducible
Lex Fridman (41:45.840)
in the sense that there's no sort of shortcut
Stephen Wolfram (41:47.800)
that we can make that jumps to the answer.
Lex Fridman (41:50.440)
Now the general case.
Stephen Wolfram (41:51.880)
Right, right.
Lex Fridman (41:52.920)
But the, so what has happened,
Lex Fridman (41:55.280)
what science has become used to doing
Lex Fridman (41:58.760)
is using the little sort of pockets
Stephen Wolfram (42:00.720)
of computational reducibility,
Lex Fridman (42:02.840)
which by the way are an inevitable consequence
Stephen Wolfram (42:04.800)
of computational irreducibility,
Lex Fridman (42:06.680)
that there have to be these pockets
Stephen Wolfram (42:08.640)
scattered around of computational reducibility
Lex Fridman (42:11.480)
to be able to find those particular cases
Stephen Wolfram (42:14.440)
where you can jump ahead.
Lex Fridman (42:15.280)
I mean, one thing sort of a little bit
Stephen Wolfram (42:17.320)
of a parable type thing that I think is fun to tell.
Lex Fridman (42:20.440)
If you look at ancient Babylon,
Stephen Wolfram (42:22.440)
they were trying to predict three kinds of things.
Lex Fridman (42:25.120)
They tried to predict where the planets would be,
Lex Fridman (42:27.960)
what the weather would be like,
Lex Fridman (42:29.440)
and who would win or lose a certain battle.
Lex Fridman (42:32.160)
And they had no idea which of these things
Lex Fridman (42:34.560)
would be more predictable than the other.
Stephen Wolfram (42:36.480)
That's funny.
Lex Fridman (42:37.320)
And it turns out where the planets are
Stephen Wolfram (42:40.920)
is a piece of computational reducibility
Lex Fridman (42:43.600)
that 300 years ago or so we pretty much cracked.
Stephen Wolfram (42:46.680)
I mean, it's been technically difficult
Lex Fridman (42:48.000)
to get all the details right,
Lex Fridman (42:49.040)
but it's basically, we got that.
Lex Fridman (42:52.160)
Who's gonna win or lose the battle?
Stephen Wolfram (42:54.160)
No, we didn't crack that one.
Lex Fridman (42:55.400)
That one, that one, right.
Stephen Wolfram (42:57.600)
Game theorists are trying.
Lex Fridman (42:58.920)
Yes. And then the weather.
Stephen Wolfram (43:00.800)
It's kind of halfway on that one.
Lex Fridman (43:02.480)
Halfway?
Stephen Wolfram (43:03.320)
Yeah, I think we're doing okay on that one.
Lex Fridman (43:05.520)
Long term climate, different story.
Lex Fridman (43:07.360)
But the weather, we're much closer on that.
Lex Fridman (43:10.040)
But do you think eventually we'll figure out the weather?
Lex Fridman (43:11.920)
So do you think eventually most think
Lex Fridman (43:15.120)
we'll figure out the local pockets in everything,
Lex Fridman (43:17.600)
essentially the local pockets of reducibility?
Lex Fridman (43:19.800)
No, I think that it's an interesting question,
Lex Fridman (43:22.720)
but I think that there is an infinite collection
Lex Fridman (43:25.560)
of these local pockets.
Stephen Wolfram (43:26.720)
We'll never run out of local pockets.
Lex Fridman (43:28.560)
And by the way, those local pockets
Stephen Wolfram (43:30.600)
are where we build engineering, for example.
Lex Fridman (43:33.120)
That's how we, if we want to have a predictable life,
Lex Fridman (43:36.880)
so to speak, then we have to build
Lex Fridman (43:40.520)
in these sort of pockets of reducibility.
Stephen Wolfram (43:43.000)
Otherwise, if we were sort of existing
Lex Fridman (43:46.520)
in this kind of irreducible world,
Stephen Wolfram (43:48.720)
we'd never be able to have definite things
Lex Fridman (43:51.800)
to know what's gonna happen.
Stephen Wolfram (43:53.240)
I have to say, I think one of the features,
Lex Fridman (43:55.400)
when we look at sort of today from the future, so to speak,
Stephen Wolfram (43:59.920)
I suspect one of the things where people will say
Lex Fridman (44:02.120)
I can't believe they didn't see that
Stephen Wolfram (44:04.440)
is stuff to do with the following kind of thing.
Lex Fridman (44:07.000)
So if we describe, oh, I don't know,
Stephen Wolfram (44:10.160)
something like heat, for instance,
Lex Fridman (44:12.880)
we say, oh, the air in here, it's this temperature,
Stephen Wolfram (44:17.880)
this pressure, that's as much as we can say.
Lex Fridman (44:20.320)
Otherwise, just a bunch of random molecules bouncing around.
Stephen Wolfram (44:23.240)
People will say, I just can't believe they didn't realize
Lex Fridman (44:26.080)
that there was all this detail
Lex Fridman (44:27.240)
and how all these molecules were bouncing around
Lex Fridman (44:29.320)
and they could make use of that.
Lex Fridman (44:31.800)
And actually, I realized there's a thing
Lex Fridman (44:32.920)
I realized last week, actually,
Stephen Wolfram (44:34.720)
was a thing that people say, one of the scenarios
Lex Fridman (44:37.680)
for the very long term history of our universe
Stephen Wolfram (44:40.040)
is a so called heat death of the universe,
Lex Fridman (44:42.560)
where basically everything just becomes
Stephen Wolfram (44:44.840)
thermodynamically boring.
Lex Fridman (44:47.160)
Everything's just this big kind of gas
Lex Fridman (44:48.840)
and thermal equilibrium.
Lex Fridman (44:50.080)
People say, that's a really bad outcome.
Lex Fridman (44:52.640)
But actually, it's not a really bad outcome.
Lex Fridman (44:54.960)
It's an outcome where there's all this computation going on
Lex Fridman (44:57.360)
and all those individual gas molecules
Lex Fridman (44:58.920)
are all bouncing around in very complicated ways
Stephen Wolfram (45:01.440)
doing this very elaborate computation.
Lex Fridman (45:03.520)
It just happens to be a computation that right now,
Stephen Wolfram (45:06.360)
we haven't found ways to understand.
Lex Fridman (45:09.560)
We haven't found ways, our brains haven't,
Lex Fridman (45:12.560)
and our mathematics and our science and so on,
Lex Fridman (45:14.960)
haven't found ways to tell an interesting story about that.
Stephen Wolfram (45:17.960)
It just looks boring to us.
Lex Fridman (45:19.560)
So you're saying there's a hopeful view
Stephen Wolfram (45:23.080)
of the heat death, quote unquote, of the universe
Lex Fridman (45:26.320)
where there's actual beautiful complexity going on.
Stephen Wolfram (45:30.400)
Similar to the kind of complexity we think of
Lex Fridman (45:34.440)
that creates rich experience in human life and life on Earth.
Lex Fridman (45:38.120)
So those little molecules interacting complex ways,
Lex Fridman (45:40.720)
that could be intelligence in that, there could be.
Stephen Wolfram (45:43.320)
Absolutely.
Lex Fridman (45:44.160)
I mean, this is what you learn from this principle.
Stephen Wolfram (45:46.120)
Wow, that's a hopeful message.
Lex Fridman (45:48.000)
Right.
Stephen Wolfram (45:48.840)
I mean, this is what you kind of learn
Lex Fridman (45:49.680)
from this principle of computational equivalence.
Stephen Wolfram (45:51.720)
You learn it's both a message of sort of hope
Lex Fridman (45:56.200)
and a message of kind of, you know,
Stephen Wolfram (45:59.040)
you're not as special as you think you are, so to speak.
Lex Fridman (46:01.120)
I mean, because, you know, we imagine that
Stephen Wolfram (46:03.520)
with sort of all the things we do with human intelligence
Lex Fridman (46:06.360)
and all that kind of thing,
Lex Fridman (46:07.640)
and all of the stuff we've constructed in science,
Lex Fridman (46:09.880)
it's like, we're very special.
Lex Fridman (46:12.000)
But actually it turns out, well, no, we're not.
Lex Fridman (46:15.200)
We're just doing computations
Stephen Wolfram (46:17.000)
like things in nature do computations,
Lex Fridman (46:19.480)
like those gas molecules do computations,
Stephen Wolfram (46:21.280)
like the weather does computations.
Lex Fridman (46:23.280)
The only thing about the computations that we do
Stephen Wolfram (46:26.120)
that's really special is that we understand
Lex Fridman (46:30.000)
what they are, so to speak.
Stephen Wolfram (46:31.160)
In other words, we have a, you know,
Lex Fridman (46:33.120)
to us they're special because kind of,
Stephen Wolfram (46:35.320)
they're connected to our purposes,
Lex Fridman (46:37.040)
our ways of thinking about things and so on.
Lex Fridman (46:39.160)
And that's some, but so.
Lex Fridman (46:41.000)
That's very human centric.
Stephen Wolfram (46:42.560)
That's, we're just attached to this kind of thing.
Lex Fridman (46:45.520)
So let's talk a little bit of physics.
Stephen Wolfram (46:48.280)
Maybe let's ask the biggest question.
Lex Fridman (46:50.960)
What is a theory of everything in general?
Lex Fridman (46:55.320)
What does that mean?
Lex Fridman (46:56.160)
Yeah, so I mean, the question is,
Stephen Wolfram (46:58.000)
can we kind of reduce what has been physics
Lex Fridman (47:01.720)
as a something where we have to sort of pick away and say,
Stephen Wolfram (47:05.680)
do we roughly know how the world works
Lex Fridman (47:08.280)
to something where we have a complete formal theory
Stephen Wolfram (47:11.040)
where we say, if we were to run this program
Lex Fridman (47:14.240)
for long enough, we would reproduce everything,
Stephen Wolfram (47:17.680)
you know, down to the fact that we're having
Lex Fridman (47:19.600)
this conversation at this moment,
Stephen Wolfram (47:21.160)
et cetera, et cetera, et cetera.
Lex Fridman (47:22.800)
Any physical phenomena, any phenomena in this world?
Stephen Wolfram (47:25.480)
Any phenomenon in the universe.
Lex Fridman (47:27.040)
But the, you know, because of computational irreducibility,
Stephen Wolfram (47:30.320)
it's not, you know, that's not something where you say,
Lex Fridman (47:33.720)
okay, you've got the fundamental theory of everything.
Stephen Wolfram (47:36.160)
Then, you know, tell me whether, you know,
Lex Fridman (47:39.920)
lions are gonna eat tigers or something.
Stephen Wolfram (47:42.480)
You know, that's a, no, you have to run this thing
Lex Fridman (47:45.440)
for, you know, 10 to the 500 steps or something
Lex Fridman (47:48.560)
to know something like that, okay?
Lex Fridman (47:50.800)
So at some moment, potentially, you say,
Stephen Wolfram (47:54.200)
this is a rule and run this rule enough times
Lex Fridman (47:57.560)
and you will get the whole universe, right?
Stephen Wolfram (47:59.760)
That's what it means to kind of have
Lex Fridman (48:02.400)
a fundamental theory of physics as far as I'm concerned
Stephen Wolfram (48:04.720)
is you've got this rule.
Lex Fridman (48:06.600)
It's potentially quite simple.
Stephen Wolfram (48:07.720)
We don't know for sure it's simple,
Lex Fridman (48:09.360)
but we have various reasons to believe it might be simple.
Lex Fridman (48:12.560)
And then you say, okay, I'm showing you this rule.
Lex Fridman (48:15.800)
You just run it only 10 to the 500 times
Lex Fridman (48:18.720)
and you'll get everything.
Lex Fridman (48:20.080)
In other words, you've kind of reduced the problem
Stephen Wolfram (48:22.800)
of physics to a problem of mathematics, so to speak.
Lex Fridman (48:25.600)
It's like, it's as if, you know, you'd like,
Stephen Wolfram (48:27.760)
you generate the digits of pi.
Lex Fridman (48:29.760)
There's a definite procedure.
Stephen Wolfram (48:30.920)
You just generate them and it'd be the same thing
Lex Fridman (48:33.720)
if you have a fundamental theory of physics
Stephen Wolfram (48:35.600)
of the kind that I'm imagining, you know,
Lex Fridman (48:38.640)
you get this rule and you just run it out
Lex Fridman (48:42.760)
and you get everything that happens in the universe.
Lex Fridman (48:45.880)
So a theory of everything is a mathematical framework
Stephen Wolfram (48:52.160)
within which you can explain everything that happens
Lex Fridman (48:55.360)
in the universe, it's kind of in a unified way.
Stephen Wolfram (48:58.640)
It's not, there's a bunch of disparate modules of,
Lex Fridman (49:01.600)
does it feel like if you create a rule
Lex Fridman (49:07.120)
and we'll talk about the Wolfram physics model,
Lex Fridman (49:11.200)
which is fascinating, but if you have a simple set
Stephen Wolfram (49:16.280)
of rules with a data structure, like a hypergraph,
Lex Fridman (49:21.840)
does that feel like a satisfying theory of everything?
Stephen Wolfram (49:25.120)
Because then you really run up against the irreducibility,
Lex Fridman (49:29.320)
computational irreducibility.
Stephen Wolfram (49:32.360)
Right, so that's a really interesting question.
Lex Fridman (49:34.240)
So I, you know, what I thought was gonna happen
Stephen Wolfram (49:38.200)
is I thought we, you know, I thought we had a pretty good,
Lex Fridman (49:42.280)
I had a pretty good idea for what the structure
Stephen Wolfram (49:45.480)
of this sort of theory that sort of underneath space
Lex Fridman (49:47.960)
and time and so on might be like.
Lex Fridman (49:50.200)
And I thought, gosh, you know, in my lifetime,
Lex Fridman (49:52.920)
so to speak, we might be able to figure out what happens
Stephen Wolfram (49:55.040)
in the first 10 to the minus 100 seconds of the universe.
Lex Fridman (49:58.160)
And that would be cool, but it's pretty far away
Stephen Wolfram (4:00:00.260)
pretty much uniformly uses Wolfram language
Lex Fridman (4:00:03.180)
and Mathematica, right?
Lex Fridman (4:00:04.380)
And so it's kind of like, you know, and that's,
Lex Fridman (4:00:08.340)
but the thing is what happens, you know,
Stephen Wolfram (4:00:11.180)
this is what happens, mature fields do not, you know,
Lex Fridman (4:00:14.980)
it's like, we're doing what we're doing.
Stephen Wolfram (4:00:16.420)
We have the methods that we have
Lex Fridman (4:00:18.220)
and we're just fine here.
Stephen Wolfram (4:00:20.220)
Now what's happened in the last 18 years or so,
Lex Fridman (4:00:23.380)
I think there's a couple of things have happened.
Stephen Wolfram (4:00:25.460)
First of all, the hope that, you know,
Lex Fridman (4:00:29.260)
string theory or whatever would deliver
Stephen Wolfram (4:00:31.300)
the fundamental theory of physics,
Lex Fridman (4:00:32.460)
that hope has disappeared.
Stephen Wolfram (4:00:34.540)
That the, another thing that's happened
Lex Fridman (4:00:36.820)
is the sort of the interest in computation around physics
Stephen Wolfram (4:00:41.020)
has been greatly enhanced
Lex Fridman (4:00:42.460)
by the whole quantum information,
Stephen Wolfram (4:00:44.020)
quantum computing story.
Lex Fridman (4:00:46.020)
People, you know, the idea there might be something
Stephen Wolfram (4:00:47.940)
sort of computational related to physics
Lex Fridman (4:00:51.100)
has somehow grown.
Lex Fridman (4:00:53.060)
And I think, you know, it's sort of interesting.
Lex Fridman (4:00:55.820)
I mean, right now, if we say, you know,
Stephen Wolfram (4:00:58.060)
it's like, if you're like,
Lex Fridman (4:00:59.700)
who else is trying to come up
Lex Fridman (4:01:00.820)
with the fundamental theory of physics?
Lex Fridman (4:01:02.420)
It's like, there aren't professional,
Stephen Wolfram (4:01:04.460)
no professional physicists, no professional physicists.
Lex Fridman (4:01:07.220)
What are your, I mean, you've talked with him,
Lex Fridman (4:01:10.820)
but just as a matter of personalities,
Lex Fridman (4:01:12.820)
cause it's a beautiful story.
Lex Fridman (4:01:13.820)
What are your thoughts about Eric Weinstein's work?
Lex Fridman (4:01:17.100)
You know, I think his, I mean,
Stephen Wolfram (4:01:20.580)
he did a PhD thesis in mathematical physics at Harvard.
Lex Fridman (4:01:23.420)
He's a mathematical physicist.
Stephen Wolfram (4:01:24.580)
And, you know, it seems like it's kind of,
Lex Fridman (4:01:28.900)
you know, it's in that framework.
Lex Fridman (4:01:30.940)
And it's kind of like,
Lex Fridman (4:01:32.820)
I'm not sure how much further it's got than his PhD thesis,
Stephen Wolfram (4:01:35.940)
which was 20 years ago or something.
Lex Fridman (4:01:37.580)
And I think that, you know, the, you know,
Stephen Wolfram (4:01:40.740)
it's a fairly specific piece of mathematical physics.
Lex Fridman (4:01:43.780)
That's quite nice.
Stephen Wolfram (4:01:44.940)
And...
Lex Fridman (4:01:45.780)
What trajectory do you hope it takes?
Stephen Wolfram (4:01:47.540)
I mean...
Lex Fridman (4:01:48.620)
Well, I think in his particular case,
Stephen Wolfram (4:01:50.100)
I mean, from what I understand,
Lex Fridman (4:01:51.380)
which is not everything at all,
Stephen Wolfram (4:01:52.940)
but, you know, I think I know the rough tradition,
Lex Fridman (4:01:54.820)
at least what he's operating in is sort of theory of gauge theories.
Stephen Wolfram (4:01:58.980)
Gauge theories, yeah.
Lex Fridman (4:01:59.740)
Local gauge invariants and so on.
Stephen Wolfram (4:02:01.100)
Okay, we are very close to understanding
Lex Fridman (4:02:04.180)
how local gauge invariants works in our models.
Lex Fridman (4:02:06.220)
And it's very beautiful.
Lex Fridman (4:02:07.620)
And it's very...
Stephen Wolfram (4:02:09.420)
And, you know, does some of the mathematical structure
Lex Fridman (4:02:12.260)
that he's enthusiastic about fit?
Stephen Wolfram (4:02:14.340)
Quite possibly, yes.
Lex Fridman (4:02:15.820)
So there might be a possibility of trying to understand
Lex Fridman (4:02:17.740)
how those things fit, how gauge theory fits.
Lex Fridman (4:02:19.780)
Yeah, very well.
Stephen Wolfram (4:02:20.620)
I mean, the question is, you know,
Lex Fridman (4:02:21.980)
so there are a couple of things
Stephen Wolfram (4:02:22.820)
one might try to get in the world.
Lex Fridman (4:02:24.100)
So for example, it's like,
Lex Fridman (4:02:25.660)
can we get three dimensions of space?
Lex Fridman (4:02:27.100)
We haven't managed to get that yet.
Stephen Wolfram (4:02:28.860)
Gauge theory, the standard model of particle physics says,
Lex Fridman (4:02:32.380)
but it's SU3 cross SU2 cross U1.
Stephen Wolfram (4:02:35.620)
Those are the designations of these Lie groups.
Lex Fridman (4:02:39.980)
It doesn't, but anyway,
Lex Fridman (4:02:41.340)
so those are sort of representations
Lex Fridman (4:02:43.700)
of symmetries of the theory.
Lex Fridman (4:02:46.460)
And so, you know, it is conceivable
Lex Fridman (4:02:50.060)
that it is generically true.
Stephen Wolfram (4:02:52.660)
Okay, so all those are subgroups of a group called E8,
Lex Fridman (4:02:55.340)
which is a weird, exceptional Lie group, okay?
Stephen Wolfram (4:02:59.620)
It is conceivable, I don't know whether it's the case,
Lex Fridman (4:03:02.100)
that that will be generic in these models,
Stephen Wolfram (4:03:05.100)
that it will be generic,
Lex Fridman (4:03:06.780)
that the gauge invariance of the model has this property,
Stephen Wolfram (4:03:12.020)
just as things like general relativity,
Lex Fridman (4:03:15.100)
which corresponds to the thing called general covariance,
Stephen Wolfram (4:03:20.100)
which is another gauge like invariance.
Lex Fridman (4:03:23.100)
It could conceivably be the case
Stephen Wolfram (4:03:25.340)
that the kind of local gauge invariance
Lex Fridman (4:03:27.460)
that we see in particle physics is somehow generic.
Lex Fridman (4:03:30.580)
And that would be a, you know,
Lex Fridman (4:03:32.300)
the thing that's really cool, I think, you know,
Stephen Wolfram (4:03:35.380)
sociologically, although this hasn't really hit yet,
Lex Fridman (4:03:38.100)
is that all of these different things,
Stephen Wolfram (4:03:40.020)
all these different things people have been working on
Lex Fridman (4:03:41.660)
in these, in some cases,
Stephen Wolfram (4:03:43.260)
quite abstruse areas of mathematical physics,
Lex Fridman (4:03:46.500)
an awful lot of them seem to tie into what we're doing.
Stephen Wolfram (4:03:49.420)
And, you know, it might not be that way.
Lex Fridman (4:03:51.460)
Yeah, absolutely.
Stephen Wolfram (4:03:52.300)
That's a beautiful thing, I think.
Lex Fridman (4:03:53.740)
I mean, but the reason Eric Weinstein is important
Stephen Wolfram (4:03:58.100)
is to the point that you mentioned before,
Lex Fridman (4:04:00.180)
which is, it's strange that the theory of everything
Stephen Wolfram (4:04:04.380)
is not at the core of the passion, the dream,
Lex Fridman (4:04:09.780)
the focus, the funding of the physics community.
Stephen Wolfram (4:04:14.140)
It's too hard.
Lex Fridman (4:04:16.420)
It's too hard and people gave up.
Stephen Wolfram (4:04:17.980)
I mean, basically what happened is ancient Greece,
Lex Fridman (4:04:21.420)
people thought we're nearly there.
Stephen Wolfram (4:04:23.060)
You know, the world is made of platonic solids.
Lex Fridman (4:04:25.100)
It's, you know, water is a tetrahedron or something.
Lex Fridman (4:04:27.700)
We're almost there, okay?
Lex Fridman (4:04:29.700)
Long period of time where people were like,
Stephen Wolfram (4:04:32.180)
no, we don't know how it works.
Lex Fridman (4:04:34.020)
You know, time of Newton, you know, we're almost there.
Stephen Wolfram (4:04:36.980)
Everything is gravitation.
Lex Fridman (4:04:38.740)
You know, time of Faraday and Maxwell, we're almost there.
Lex Fridman (4:04:42.380)
Everything is fields, everything is the ether, you know?
Lex Fridman (4:04:45.500)
Then...
Lex Fridman (4:04:46.340)
And the whole time we're making big progress though.
Lex Fridman (4:04:48.940)
Oh yes, absolutely.
Lex Fridman (4:04:50.140)
But the fundamental theory of physics is almost a footnote
Lex Fridman (4:04:53.860)
because it's like, it's the machine code.
Stephen Wolfram (4:04:56.900)
It's like we're operating in the high level languages.
Lex Fridman (4:04:59.340)
Yeah.
Stephen Wolfram (4:05:00.180)
You know, that's what we really care about.
Lex Fridman (4:05:01.700)
That's what's relevant for our everyday physics.
Stephen Wolfram (4:05:03.660)
You talked about different centuries
Lex Fridman (4:05:05.020)
and the 21st century will be everything is computation.
Stephen Wolfram (4:05:08.820)
Yes.
Lex Fridman (4:05:09.660)
If that takes us all the way, we don't know,
Lex Fridman (4:05:11.500)
but it might take us pretty far.
Lex Fridman (4:05:13.260)
Yes, right, that's right.
Lex Fridman (4:05:14.580)
And I, but I think the point is that it's like, you know,
Lex Fridman (4:05:17.060)
if you're doing biology, you might say,
Lex Fridman (4:05:18.700)
how can you not be really interested in the origin of life
Lex Fridman (4:05:21.140)
and the definition of life?
Stephen Wolfram (4:05:22.700)
Well, it's irrelevant.
Lex Fridman (4:05:23.540)
You know, you're studying the properties of some virus.
Stephen Wolfram (4:05:26.020)
It doesn't matter, you know, where, you know,
Lex Fridman (4:05:28.020)
you're operating at some much higher level.
Lex Fridman (4:05:30.620)
And it's the same, what's happening with physics is,
Lex Fridman (4:05:34.180)
I was sort of surprised actually.
Stephen Wolfram (4:05:35.420)
I was sort of mapping out this history of people's efforts
Lex Fridman (4:05:38.780)
to understand the fundamental theory of physics.
Lex Fridman (4:05:41.180)
And it's remarkable how little has been done on this question.
Lex Fridman (4:05:45.220)
And it's, you know, because, you know,
Stephen Wolfram (4:05:47.100)
there've been times when there's been bursts of enthusiasm.
Lex Fridman (4:05:49.340)
Oh, we're almost there.
Lex Fridman (4:05:50.940)
And then it decays and people just say,
Lex Fridman (4:05:54.940)
oh, it's too hard, but it's not relevant anyway.
Lex Fridman (4:05:57.260)
And I think that the thing that, you know,
Lex Fridman (4:06:01.140)
so the question of, you know, one question is,
Lex Fridman (4:06:04.860)
why does anybody, why should anybody care, right?
Lex Fridman (4:06:07.420)
Why should anybody care
Lex Fridman (4:06:08.500)
what the fundamental theory of physics is?
Lex Fridman (4:06:10.420)
I think it's intellectually interesting,
Lex Fridman (4:06:13.140)
but what will be the sort of,
Lex Fridman (4:06:14.820)
what will be the impact of this?
Stephen Wolfram (4:06:16.460)
What, I mean, this is the key question.
Lex Fridman (4:06:18.900)
What do you think will happen
Lex Fridman (4:06:20.660)
if we figure out the fundamental theory of physics?
Lex Fridman (4:06:25.260)
Right.
Stephen Wolfram (4:06:26.100)
Outside of the intellectual curiosity of us.
Lex Fridman (4:06:28.140)
Okay, so here's my best guess, okay?
Lex Fridman (4:06:31.340)
So if you look at the history of science,
Lex Fridman (4:06:33.540)
I think a very interesting analogy is Copernicus.
Lex Fridman (4:06:37.420)
Okay, so what did Copernicus do?
Lex Fridman (4:06:39.740)
There'd been this Ptolemaic system
Stephen Wolfram (4:06:41.340)
for working out the motion of planets.
Lex Fridman (4:06:43.260)
It did pretty well.
Stephen Wolfram (4:06:44.740)
It used epicycles, et cetera, et cetera, et cetera.
Lex Fridman (4:06:47.100)
It had all this computational ways
Stephen Wolfram (4:06:49.340)
of working out where planets will be.
Lex Fridman (4:06:51.180)
When we work out where planets are today,
Stephen Wolfram (4:06:52.740)
we're basically using epicycles.
Lex Fridman (4:06:54.860)
But Copernicus had this different way of formulating things
Stephen Wolfram (4:06:58.060)
in which he said, you know,
Lex Fridman (4:07:00.260)
and the earth is going around the sun,
Lex Fridman (4:07:02.980)
and that had a consequence.
Lex Fridman (4:07:04.180)
The consequence was you can use this mathematical theory
Stephen Wolfram (4:07:07.900)
to conclude something which is absolutely not
Lex Fridman (4:07:10.740)
what we can tell from common sense, right?
Lex Fridman (4:07:14.180)
So it's like, trust the mathematics, trust the science, okay?
Lex Fridman (4:07:18.420)
Now fast forward 400 years,
Lex Fridman (4:07:21.060)
and now we're in this pandemic,
Lex Fridman (4:07:23.900)
and it's kind of like everybody thinks the science
Stephen Wolfram (4:07:26.500)
will figure out everything.
Lex Fridman (4:07:28.260)
It's like from the science,
Stephen Wolfram (4:07:30.020)
we can just figure out what to do.
Lex Fridman (4:07:31.380)
We can figure out everything.
Stephen Wolfram (4:07:32.940)
That was before Copernicus.
Lex Fridman (4:07:34.820)
Nobody would have thought if the science says something
Stephen Wolfram (4:07:37.700)
that doesn't agree with our everyday experience,
Lex Fridman (4:07:40.780)
where we just have to compute the science
Lex Fridman (4:07:43.180)
and then figure out what to do,
Lex Fridman (4:07:44.420)
people would say that's completely crazy.
Lex Fridman (4:07:46.380)
And so your sense is,
Lex Fridman (4:07:47.580)
once we figure out the framework of computation
Stephen Wolfram (4:07:49.820)
that can basically do any,
Lex Fridman (4:07:51.780)
understand the fabric of reality,
Stephen Wolfram (4:07:53.780)
we'll be able to derive totally counterintuitive things.
Lex Fridman (4:07:58.900)
No, the point I think is the following.
Stephen Wolfram (4:08:01.580)
That right now, you know,
Lex Fridman (4:08:03.020)
I talk about computational irreducibility.
Stephen Wolfram (4:08:05.740)
People, you know, I was very proud
Lex Fridman (4:08:07.820)
that I managed to get the term computational irreducibility
Stephen Wolfram (4:08:10.140)
into the congressional record last year.
Lex Fridman (4:08:13.020)
That's right, by the way,
Stephen Wolfram (4:08:13.860)
that's a whole nother topic we could talk about.
Lex Fridman (4:08:15.460)
Fascinating. Different topic.
Stephen Wolfram (4:08:17.140)
Different topic.
Lex Fridman (4:08:18.180)
But Tim, in any case, you know,
Lex Fridman (4:08:20.420)
but so computational irreducibility
Lex Fridman (4:08:22.140)
is one of these sort of concepts
Stephen Wolfram (4:08:23.900)
that I think is important in understanding
Lex Fridman (4:08:25.420)
lots of things in the world.
Lex Fridman (4:08:26.980)
But the question is, it's only important
Lex Fridman (4:08:29.180)
if you believe the world is fundamentally computational.
Lex Fridman (4:08:32.100)
Right?
Lex Fridman (4:08:33.140)
But if you know the fundamental theory of physics
Lex Fridman (4:08:35.940)
and it's fundamentally computational,
Lex Fridman (4:08:38.260)
then you've rooted the whole thing.
Stephen Wolfram (4:08:40.180)
That is, you know the world is computational.
Lex Fridman (4:08:43.140)
And while you can discuss whether, you know,
Stephen Wolfram (4:08:47.260)
it's not the case that people would say,
Lex Fridman (4:08:48.820)
well, you have this whole computational irreducibility,
Stephen Wolfram (4:08:50.940)
all these features of computation.
Lex Fridman (4:08:52.580)
We don't care about those
Stephen Wolfram (4:08:54.100)
because after all the world isn't computational,
Lex Fridman (4:08:56.180)
you might say.
Lex Fridman (4:08:57.300)
But if you know, you know, base, base, base thing,
Lex Fridman (4:09:01.260)
physics is computational,
Stephen Wolfram (4:09:03.220)
then you know that that stuff is, you know,
Lex Fridman (4:09:05.540)
that that's kind of the grounding for that stuff.
Stephen Wolfram (4:09:07.700)
Just as in a sense Copernicus was the grounding
Lex Fridman (4:09:10.540)
for the idea that you could figure out something
Stephen Wolfram (4:09:12.900)
with math and science
Lex Fridman (4:09:14.620)
that was not what you would intuitively think
Stephen Wolfram (4:09:18.820)
from your senses.
Lex Fridman (4:09:20.100)
So now we've got to this point where, for example,
Stephen Wolfram (4:09:22.780)
we say, you know, once we have the idea
Lex Fridman (4:09:25.220)
that computation is the foundational thing
Stephen Wolfram (4:09:27.940)
that explains our whole universe,
Lex Fridman (4:09:30.100)
then we have to say, well, what does it mean
Lex Fridman (4:09:32.020)
for other things?
Lex Fridman (4:09:32.860)
Like it means there's computational irreducibility.
Stephen Wolfram (4:09:35.220)
That means science is limited in certain ways.
Lex Fridman (4:09:37.860)
That means this, that means that.
Lex Fridman (4:09:39.740)
But the fact that we have that grounding means that,
Lex Fridman (4:09:43.260)
you know, and I think, for example, for Copernicus,
Stephen Wolfram (4:09:45.660)
for instance, the implications of his work
Lex Fridman (4:09:49.140)
on the set of mathematics of astronomy were cool,
Lex Fridman (4:09:52.340)
but they involved a very small number of people.
Lex Fridman (4:09:54.540)
The implications of his work for sort of the philosophy
Stephen Wolfram (4:09:56.900)
of how you think about things were vast
Lex Fridman (4:09:59.820)
and involved, you know, everybody more or less.
Lex Fridman (4:10:02.820)
But do you think, so that's actually the way scientists
Lex Fridman (4:10:05.740)
and people see the world around us.
Lex Fridman (4:10:08.540)
So it has a huge impact in that sense.
Lex Fridman (4:10:10.580)
Do you think it might have an impact more directly
Stephen Wolfram (4:10:14.220)
to engineering derivations from physics,
Lex Fridman (4:10:18.100)
like propulsion systems, our ability to colonize the world?
Stephen Wolfram (4:10:21.980)
Like, for example, okay, this is like sci fi,
Lex Fridman (4:10:24.580)
but if you understand the computational nature, say,
Stephen Wolfram (4:10:30.420)
of the different forces of physics, you know,
Lex Fridman (4:10:34.300)
there's a notion of being able to warp gravity,
Stephen Wolfram (4:10:38.420)
things like this.
Lex Fridman (4:10:39.260)
Yeah, can we make warp drive?
Stephen Wolfram (4:10:40.500)
Warp drive, yeah.
Lex Fridman (4:10:41.700)
So like, would we be able to, will, you know,
Lex Fridman (4:10:45.660)
will like Elon Musk start paying attention?
Lex Fridman (4:10:47.580)
Like it's awfully costly to launch these rockets.
Lex Fridman (4:10:50.460)
Do you think we'll be able to, yeah, create warp drive?
Lex Fridman (4:10:52.820)
And, you know, I set myself some homework.
Stephen Wolfram (4:10:55.340)
I agreed to give a talk at some NASA workshop
Lex Fridman (4:10:57.580)
in a few weeks about faster than light travel.
Lex Fridman (4:10:59.860)
So I haven't figured it out yet, but no, but.
Lex Fridman (4:11:02.700)
You got two weeks.
Stephen Wolfram (4:11:03.540)
Yeah, right.
Lex Fridman (4:11:04.380)
But do you think that kind of understanding
Stephen Wolfram (4:11:06.260)
of fundamental theory of physics can lead
Lex Fridman (4:11:07.980)
to those engineering breakthroughs?
Stephen Wolfram (4:11:09.540)
Okay, I think it's far away, but I'm not certain.
Lex Fridman (4:11:12.020)
I mean, you know, this is the thing that,
Stephen Wolfram (4:11:14.660)
I set myself an exercise when gravity waves,
Lex Fridman (4:11:16.940)
gravitational waves were discovered, right?
Stephen Wolfram (4:11:19.220)
I set myself the exercise of what would black hole
Lex Fridman (4:11:22.020)
technology look like?
Stephen Wolfram (4:11:23.780)
In other words, right now, you know,
Lex Fridman (4:11:25.260)
black holes are far away.
Lex Fridman (4:11:26.420)
They're, you know, how on earth can we do things with them?
Lex Fridman (4:11:28.100)
But just imagine that we could get, you know,
Stephen Wolfram (4:11:30.060)
pet black holes right in our backyard.
Lex Fridman (4:11:32.460)
You know, what kind of technology could we build with them?
Stephen Wolfram (4:11:34.500)
I got a certain distance, not that far,
Lex Fridman (4:11:36.700)
but I think in, you know, so there are ideas, you know,
Stephen Wolfram (4:11:40.020)
I have this, one of the weirder ideas is things
Lex Fridman (4:11:42.340)
I'm calling space tunnels,
Stephen Wolfram (4:11:44.140)
which are higher dimensional pieces of space time,
Lex Fridman (4:11:47.820)
where basically you can, you know,
Stephen Wolfram (4:11:50.020)
in our three dimensional space,
Lex Fridman (4:11:51.980)
there might be a five dimensional, you know,
Stephen Wolfram (4:11:54.620)
region, which actually will appear as a white hole
Lex Fridman (4:11:57.020)
at one end and a black hole at the other end,
Stephen Wolfram (4:11:59.300)
you know, who knows whether they exist.
Lex Fridman (4:12:01.060)
And then the questions, another one,
Stephen Wolfram (4:12:02.700)
okay, this is another crazy one,
Lex Fridman (4:12:04.420)
is the thing that I'm calling a vacuum cleaner, okay?
Stephen Wolfram (4:12:07.620)
So, I mentioned that, you know,
Lex Fridman (4:12:10.620)
there's all this activity in the universe,
Stephen Wolfram (4:12:12.580)
which is maintaining the structure of space.
Lex Fridman (4:12:14.980)
And that leads to a certain energy density
Stephen Wolfram (4:12:18.260)
effectively in space.
Lex Fridman (4:12:20.100)
And so the question, in fact, dark energy
Stephen Wolfram (4:12:23.620)
is a story of essentially negative mass
Lex Fridman (4:12:26.820)
produced by the absence of energy
Stephen Wolfram (4:12:30.900)
you thought would be there, so to speak.
Lex Fridman (4:12:33.180)
And we don't know exactly how it works
Stephen Wolfram (4:12:34.820)
in either our model or the physical universe,
Lex Fridman (4:12:37.700)
but this notion of a vacuum cleaner is a thing where,
Stephen Wolfram (4:12:41.860)
you know, you have all these things
Lex Fridman (4:12:43.060)
that are maintaining the structure of space,
Lex Fridman (4:12:44.500)
but what if you could clean out some of that stuff
Lex Fridman (4:12:47.580)
that's maintaining the structure of space
Lex Fridman (4:12:49.460)
and make a simpler vacuum somewhere?
Lex Fridman (4:12:51.860)
You know, what would that do?
Stephen Wolfram (4:12:52.700)
A totally different kind of vacuum.
Lex Fridman (4:12:54.220)
Right, and that would lead to negative energy density,
Stephen Wolfram (4:12:57.180)
which would need to, so gravity is usually
Lex Fridman (4:12:59.420)
a purely attractive force, but negative mass
Stephen Wolfram (4:13:02.420)
would lead to repulsive gravity
Lex Fridman (4:13:06.180)
and lead to all kinds of weird things.
Lex Fridman (4:13:08.540)
Now, can it be done in our universe?
Lex Fridman (4:13:11.220)
You know, my immediate thought is no,
Lex Fridman (4:13:14.820)
but you know, the fact is that, okay, so here's the thing.
Lex Fridman (4:13:18.420)
Well, once you understand the fact,
Stephen Wolfram (4:13:19.620)
because you're saying like, at this level of abstraction,
Lex Fridman (4:13:21.580)
can we reach to the lower levels and mess with it?
Stephen Wolfram (4:13:25.420)
Yes.
Lex Fridman (4:13:26.260)
Once you understand the levels, I think you can start to.
Stephen Wolfram (4:13:27.940)
I know, and I'm, you know, I have to say
Lex Fridman (4:13:30.700)
that this reminds me of people telling one years ago
Stephen Wolfram (4:13:34.660)
that, you know, you'll never transmit data
Lex Fridman (4:13:36.300)
over a copper wire at more than 1,000,
Lex Fridman (4:13:38.740)
you know, 1,000 board or something, right?
Lex Fridman (4:13:41.460)
And this is, why did that not happen?
Stephen Wolfram (4:13:43.940)
You know, why do we have this much,
Lex Fridman (4:13:45.580)
much faster data transmission?
Stephen Wolfram (4:13:46.940)
Because we've understood many more of the details
Lex Fridman (4:13:48.820)
of what's actually going on.
Lex Fridman (4:13:50.380)
And it's the same exact story here.
Lex Fridman (4:13:52.540)
And it's the same, you know, I think that this,
Stephen Wolfram (4:13:54.740)
as I say, I think one of the features of sort of,
Lex Fridman (4:13:58.580)
one of the things about our time
Stephen Wolfram (4:14:00.540)
that will seem incredibly naive in the future
Lex Fridman (4:14:03.020)
is the belief that, you know, things like heat
Stephen Wolfram (4:14:06.220)
is just random motion of molecules,
Lex Fridman (4:14:08.380)
that it's just throw up your hands, it's just random.
Stephen Wolfram (4:14:12.460)
We can't say anything about it.
Lex Fridman (4:14:14.060)
That will seem naive.
Stephen Wolfram (4:14:15.660)
Yeah, at the heat death of the universe,
Lex Fridman (4:14:18.100)
those particles would be laughing at us humans thinking.
Stephen Wolfram (4:14:20.980)
Yes, right.
Lex Fridman (4:14:22.380)
That life is not beautiful.
Stephen Wolfram (4:14:23.220)
I'll have a whole civilization, you know.
Lex Fridman (4:14:25.900)
Humans used to think they're special
Stephen Wolfram (4:14:27.580)
with their little brains.
Lex Fridman (4:14:28.980)
Well, right, but also, and they used to think
Stephen Wolfram (4:14:31.260)
that this would just be random and uninteresting.
Lex Fridman (4:14:33.940)
But that's, but so this question about whether you can,
Stephen Wolfram (4:14:37.620)
you know, mess with the underlying structure
Lex Fridman (4:14:39.980)
and how you find a way to mess with the underlying structure,
Stephen Wolfram (4:14:42.860)
that's a, you know, I have to say, you know,
Lex Fridman (4:14:45.660)
my immediate thing is, boy, that seems really hard,
Lex Fridman (4:14:48.820)
but then, and you know,
Lex Fridman (4:14:50.980)
possibly computational irreducibility will bite you,
Lex Fridman (4:14:54.020)
but then there's always some path
Lex Fridman (4:14:55.540)
of computational reducibility.
Lex Fridman (4:14:57.380)
And that path of computational reducibility
Lex Fridman (4:14:59.740)
is the engineering invention that has to be made.
Stephen Wolfram (4:15:02.540)
Those little pockets can have huge engineering impact.
Lex Fridman (4:15:05.980)
Right, and I think that that's right.
Lex Fridman (4:15:07.780)
And I mean, we live in, you know, we make use of so many
Lex Fridman (4:15:10.380)
of those pockets.
Lex Fridman (4:15:11.420)
And the fact is, you know, I, you know, this is, yes,
Lex Fridman (4:15:16.980)
it's a, you know, it's one of these things where,
Stephen Wolfram (4:15:20.380)
where, you know, I'm a person who likes to figure out ideas
Lex Fridman (4:15:24.740)
and so on, and the sort of tests of my level of imagination,
Lex Fridman (4:15:28.060)
so to speak.
Lex Fridman (4:15:29.180)
And so a couple of places where there's sort of serious
Stephen Wolfram (4:15:32.700)
humility in terms of my level of imagination,
Lex Fridman (4:15:35.460)
one is this thing about different reference frames
Stephen Wolfram (4:15:38.220)
for understanding the universe,
Lex Fridman (4:15:39.860)
where like, imagine the physics of the aliens,
Lex Fridman (4:15:42.260)
what will it be like?
Lex Fridman (4:15:43.660)
And I'm like, that's really hard.
Lex Fridman (4:15:45.780)
I don't know, you know?
Lex Fridman (4:15:47.500)
And I mean, I think that...
Lex Fridman (4:15:48.340)
But once you have the framework in place,
Lex Fridman (4:15:49.980)
you can at least reason about the things you don't know,
Stephen Wolfram (4:15:53.940)
maybe can't know, or like, it's too hard for you to know,
Lex Fridman (4:15:57.620)
but then the mathematics can, that's exactly it,
Stephen Wolfram (4:16:01.620)
allow you to reach beyond where you can reason about.
Lex Fridman (4:16:05.900)
So I'm, you know, I'm trying to not have, you know,
Stephen Wolfram (4:16:09.340)
if you think back to Alan Turing, for example,
Lex Fridman (4:16:11.660)
and, you know, when he invented Turing machines, you know,
Lex Fridman (4:16:14.260)
and imagining what computers would end up doing,
Lex Fridman (4:16:16.980)
so to speak.
Stephen Wolfram (4:16:17.820)
Yeah.
Lex Fridman (4:16:18.660)
You know, and it's...
Stephen Wolfram (4:16:19.500)
It's very difficult.
Lex Fridman (4:16:20.340)
It's difficult, right.
Lex Fridman (4:16:21.180)
And it's, and I mean, this thing...
Lex Fridman (4:16:22.020)
Made a few reasonable predictions,
Lex Fridman (4:16:23.460)
but most of it, he couldn't predict, possibly.
Lex Fridman (4:16:25.500)
By the time, by 1950, he was making reasonable predictions
Stephen Wolfram (4:16:28.300)
about some things.
Lex Fridman (4:16:29.140)
But not the 30s, yeah.
Stephen Wolfram (4:16:30.140)
Right, not when he first, you know, conceptualized,
Lex Fridman (4:16:34.660)
you know, and he conceptualized universal computing
Stephen Wolfram (4:16:37.380)
for a very specific mathematical reason
Lex Fridman (4:16:39.180)
that wasn't as general.
Lex Fridman (4:16:41.340)
But yes, it's a good sort of exercise in humility
Lex Fridman (4:16:44.220)
to realize that it's kind of like,
Stephen Wolfram (4:16:46.860)
it's really hard to figure these things out.
Lex Fridman (4:16:49.580)
The engineering of the universe,
Lex Fridman (4:16:52.260)
if we know how the universe works, how can we engineer it?
Lex Fridman (4:16:55.860)
That's such a beautiful vision.
Stephen Wolfram (4:16:57.580)
That's such a beautiful vision.
Lex Fridman (4:16:58.420)
By the way, I have to mention one more thing,
Stephen Wolfram (4:16:59.740)
which is the ultimate question from physics is,
Lex Fridman (4:17:04.300)
okay, so we have this abstract model of the universe.
Lex Fridman (4:17:07.380)
Why does the universe exist at all, right?
Lex Fridman (4:17:11.260)
So, you know, we might say there is a formal model
Stephen Wolfram (4:17:15.220)
that if you run this model, you get the universe,
Lex Fridman (4:17:18.100)
or the model gives you, you know, a model of the universe,
Stephen Wolfram (4:17:21.900)
right, you run this mathematical thing
Lex Fridman (4:17:25.300)
and the mathematics unfolds in the way
Stephen Wolfram (4:17:27.820)
that corresponds to the universe.
Lex Fridman (4:17:29.420)
But the question is, why was that actualized?
Lex Fridman (4:17:32.460)
Why does the actual universe actually exist?
Lex Fridman (4:17:35.980)
And so this is another one of these humility
Lex Fridman (4:17:39.220)
and it's like, can you figure this out?
Lex Fridman (4:17:41.700)
I have a guess, okay, about the answer to that.
Lex Fridman (4:17:44.780)
And my guess is somewhat unsatisfying,
Lex Fridman (4:17:47.820)
but my guess is that it's a little bit similar
Stephen Wolfram (4:17:50.380)
to Gödel's second incompleteness theorem,
Lex Fridman (4:17:52.740)
which is the statement that from within,
Stephen Wolfram (4:17:55.180)
as an axiomatic theory like piano arithmetic,
Lex Fridman (4:17:58.060)
you cannot from within that theory
Stephen Wolfram (4:17:59.780)
prove the consistency of the theory.
Lex Fridman (4:18:02.420)
So my guess is that for entities within the universe,
Stephen Wolfram (4:18:08.140)
there is no finite determination that can be made
Lex Fridman (4:18:11.540)
of the statement the universe exists
Stephen Wolfram (4:18:15.260)
is essentially undecidable to any entity
Lex Fridman (4:18:18.580)
that is embedded in the universe.
Lex Fridman (4:18:19.900)
Within that universe, how does that make you feel?
Lex Fridman (4:18:22.780)
Does that put you at peace that it's impossible,
Lex Fridman (4:18:27.980)
or is it really ultimately frustrating?
Lex Fridman (4:18:30.940)
Well, I think it just says that it's not a kind of question
Stephen Wolfram (4:18:35.460)
that, you know, there are things that it is reasonable.
Lex Fridman (4:18:40.140)
I mean, there's kinds of, you know,
Stephen Wolfram (4:18:42.780)
you can talk about hyper computation as well.
Lex Fridman (4:18:44.580)
You can say, imagine there was a hyper computer,
Stephen Wolfram (4:18:46.500)
here's what it would do.
Lex Fridman (4:18:47.700)
So okay, great, it would be lovely to have a hyper computer,
Lex Fridman (4:18:49.940)
but unfortunately we can't make it in the universe.
Lex Fridman (4:18:52.300)
Like it would be lovely to answer this,
Lex Fridman (4:18:53.540)
but unfortunately we can't do it in the universe.
Lex Fridman (4:18:56.300)
And you know, this is all we have, so to speak.
Lex Fridman (4:18:59.100)
And I think it's really just a statement.
Lex Fridman (4:19:02.340)
It's sort of, in the end, it'll be a kind of a logical,
Stephen Wolfram (4:19:06.180)
logically inevitable statement, I think.
Lex Fridman (4:19:08.380)
I think it will be something where it is,
Stephen Wolfram (4:19:10.700)
as you understand what it means to have,
Lex Fridman (4:19:13.260)
what it means to have a sort of predicate of existence
Lex Fridman (4:19:16.220)
and what it means to have these kinds of things,
Lex Fridman (4:19:17.780)
it will sort of be inevitable that this has to be the case,
Stephen Wolfram (4:19:20.460)
that from within that universe, you can't establish
Lex Fridman (4:19:23.460)
the reason for its existence, so to speak.
Stephen Wolfram (4:19:25.060)
You can't prove that it exists and so on.
Lex Fridman (4:19:26.900)
And nevertheless, because of computational reducibility,
Stephen Wolfram (4:19:29.940)
the future is ultimately not predictable, full of mystery,
Lex Fridman (4:19:34.140)
and that's what makes life worth living.
Stephen Wolfram (4:19:36.860)
Right, I mean, right.
Lex Fridman (4:19:37.780)
And you know, it's funny for me,
Stephen Wolfram (4:19:39.340)
because as a pure sort of human being doing what I do,
Lex Fridman (4:19:43.100)
it's, you know, like I'm interested in people,
Stephen Wolfram (4:19:46.780)
I like sort of the whole human experience, so to speak.
Lex Fridman (4:19:51.020)
And yet, it's a little bit weird when I'm thinking,
Stephen Wolfram (4:19:53.980)
you know, it's all hypergraphs down there,
Lex Fridman (4:19:56.460)
and it's all just.
Stephen Wolfram (4:19:57.780)
Hypergraphs all the way down.
Lex Fridman (4:19:59.580)
Right.
Stephen Wolfram (4:20:00.420)
It's like turtles all the way down.
Lex Fridman (4:20:01.380)
Yeah, yeah, right.
Lex Fridman (4:20:02.540)
And it's kind of, you know, to me, it is a funny thing,
Lex Fridman (4:20:06.580)
because every so often I get this, you know,
Stephen Wolfram (4:20:08.220)
as I'm thinking about, I think we've really gotten,
Lex Fridman (4:20:10.620)
you know, we've really figured out kind of the essence
Stephen Wolfram (4:20:12.500)
of how physics works, and I'm like thinking to myself,
Lex Fridman (4:20:14.780)
you know, here's this physical thing,
Lex Fridman (4:20:16.420)
and I'm like, you know,
Lex Fridman (4:20:17.780)
this feels like a very definite thing.
Lex Fridman (4:20:19.900)
How can it be the case that this is just
Lex Fridman (4:20:21.460)
some rule or reference frame of, you know,
Lex Fridman (4:20:23.980)
this infinite creature that is so abstract and so on?
Lex Fridman (4:20:28.420)
And I kind of, it is a, it's a funny sort of feeling
Stephen Wolfram (4:20:32.980)
that, you know, we are, we're sort of, it's like,
Lex Fridman (4:20:37.620)
in the end, it's just sort of,
Stephen Wolfram (4:20:39.580)
we're just happy we're just humans type thing.
Lex Fridman (4:20:42.220)
And it's kind of like, but we're making,
Stephen Wolfram (4:20:44.980)
we make things as, it's not like we're just a tiny speck.
Lex Fridman (4:20:50.020)
We are, in a sense, the, we are more important
Stephen Wolfram (4:20:54.500)
by virtue of the fact that, in a sense,
Lex Fridman (4:20:58.340)
it's not like there's, there is no ultimate, you know,
Stephen Wolfram (4:21:02.780)
it's like, we're important because,
Lex Fridman (4:21:06.540)
because, you know, we're here, so to speak,
Lex Fridman (4:21:08.900)
and we're not, it's not like there's a thing
Lex Fridman (4:21:10.900)
where we're saying, you know, we are just but one
Stephen Wolfram (4:21:15.780)
sort of intelligence out of all these other intelligences.
Lex Fridman (4:21:18.380)
And so, you know, ultimately there'll be
Stephen Wolfram (4:21:20.860)
the super intelligence, which is all of these put together
Lex Fridman (4:21:23.980)
and they'll be very different from us.
Stephen Wolfram (4:21:25.260)
No, it's actually going to be equivalent to us.
Lex Fridman (4:21:27.540)
And the thing that makes us a sort of special
Stephen Wolfram (4:21:31.380)
is just the details of us, so to speak.
Lex Fridman (4:21:34.740)
It's not something where we can say,
Stephen Wolfram (4:21:36.700)
oh, there's this other thing, you know,
Lex Fridman (4:21:38.980)
just, you think humans are cool,
Stephen Wolfram (4:21:40.900)
just wait until you've seen this.
Lex Fridman (4:21:43.260)
You know, it's going to be much more impressive.
Stephen Wolfram (4:21:45.100)
Well, no, it's all going to be
Lex Fridman (4:21:47.020)
kind of computationally equivalent.
Lex Fridman (4:21:48.900)
And the thing that, you know, it's not going to be,
Lex Fridman (4:21:51.380)
oh, this thing is amazingly much more impressive
Lex Fridman (4:21:53.980)
and amazingly much more meaningful, let's say.
Lex Fridman (4:21:56.860)
No, we're it.
Stephen Wolfram (4:21:58.980)
I mean, that's the...
Lex Fridman (4:22:01.460)
And the symbolism of this particular moment.
Lex Fridman (4:22:04.380)
So this has been one of the,
Lex Fridman (4:22:07.020)
one of the favorite conversations I've ever had, Stephen.
Stephen Wolfram (4:22:10.860)
It's a huge honor to talk to you,
Lex Fridman (4:22:12.700)
to talk about a topic like this for four plus hours
Stephen Wolfram (4:22:16.660)
on the fundamental theory of physics.
Lex Fridman (4:22:18.620)
And yet we're just two finite descendants of apes
Stephen Wolfram (4:22:22.900)
that have to end this conversation
Lex Fridman (4:22:24.940)
because darkness have come upon us.
Stephen Wolfram (4:22:28.020)
Right, and we're going to get bitten by mosquitoes
Lex Fridman (4:22:29.980)
and all kinds of terrible things.
Stephen Wolfram (4:22:30.820)
The symbolism of that,
Lex Fridman (4:22:32.540)
we're talking about the most basic fabric of reality
Lex Fridman (4:22:36.220)
and having to end because of the fact that things end.
Lex Fridman (4:22:40.900)
It's tragic and beautiful, Stephen.
Stephen Wolfram (4:22:42.580)
Thank you so much.
Lex Fridman (4:22:43.420)
Huge honor.
Stephen Wolfram (4:22:44.380)
I can't wait to see what you do in the next couple of days
Lex Fridman (4:22:47.100)
and next week, a month.
Stephen Wolfram (4:22:48.580)
We're all watching with excitement.
Lex Fridman (4:22:50.700)
Thank you so much.
Stephen Wolfram (4:22:51.540)
Thanks.
Lex Fridman (4:22:53.020)
Thanks for listening to this conversation
Stephen Wolfram (4:22:54.500)
with Stephen Wolfram.
Lex Fridman (4:22:55.660)
And thank you to our sponsors,
Stephen Wolfram (4:22:57.540)
SimplySafe, Sun Basket, and Masterclass.
Lex Fridman (4:23:00.940)
Please check out our sponsors in the description
Stephen Wolfram (4:23:03.220)
to get a discount and to support this podcast.
Lex Fridman (4:23:06.020)
If you enjoy this thing, subscribe on YouTube,
Stephen Wolfram (4:23:08.220)
review it with five stars on Apple Podcasts,
Lex Fridman (4:23:10.420)
follow on Spotify, support on Patreon,
Stephen Wolfram (4:23:12.980)
or connect with me on Twitter at Lex Friedman.
Lex Fridman (4:23:16.580)
And now let me leave you with some words
Stephen Wolfram (4:23:19.100)
from Richard Feynman.
Lex Fridman (4:23:21.220)
Physics isn't the most important thing, love is.
Stephen Wolfram (4:23:25.340)
Thank you for listening and hope to see you next time.
Lex Fridman (50:01.480)
from anything that we can see today.
Lex Fridman (50:03.840)
And it will be hard to test whether that's right
Lex Fridman (50:05.760)
and so on and so on and so on.
Stephen Wolfram (50:07.520)
To my huge surprise, although it should have been obvious
Lex Fridman (50:10.480)
and it's embarrassing that it wasn't obvious to me,
Lex Fridman (50:12.600)
but to my huge surprise,
Lex Fridman (50:15.600)
we managed to get unbelievably much further than that.
Lex Fridman (50:18.400)
And basically what happened is that it turns out
Lex Fridman (50:21.520)
that even though there's this kind of bed
Stephen Wolfram (50:23.160)
of computational irreducibility,
Lex Fridman (50:25.280)
that sort of these, all these simple rules run into,
Stephen Wolfram (50:30.040)
there are certain pieces of computational reducibility
Lex Fridman (50:34.240)
that quite generically occur
Stephen Wolfram (50:36.200)
for large classes of these rules.
Lex Fridman (50:38.400)
And, and this is the really exciting thing
Stephen Wolfram (50:40.960)
as far as I'm concerned,
Lex Fridman (50:42.400)
the big pieces of computational reducibility
Stephen Wolfram (50:46.000)
are basically the pillars of 20th century physics.
Lex Fridman (50:49.320)
That's the amazing thing,
Stephen Wolfram (50:50.280)
that general relativity and quantum field theory
Lex Fridman (50:52.680)
is sort of the pillars of 20th century physics
Stephen Wolfram (50:55.480)
turn out to be precisely the stuff you can say.
Lex Fridman (50:59.720)
There's a lot you can't say,
Stephen Wolfram (51:00.840)
there's a lot that's kind of at this irreducible level
Lex Fridman (51:03.360)
where you kind of don't know what's going to happen,
Stephen Wolfram (51:05.120)
you have to run it, you know,
Lex Fridman (51:06.400)
you can't run it within our universe,
Stephen Wolfram (51:07.840)
et cetera, et cetera, et cetera, et cetera.
Lex Fridman (51:10.240)
But the thing is there are things you can say
Lex Fridman (51:13.560)
and the things you can say turn out to be very beautifully
Lex Fridman (51:17.840)
exactly the structure that was found
Stephen Wolfram (51:19.760)
in 20th century physics,
Lex Fridman (51:21.520)
namely general relativity and quantum mechanics.
Lex Fridman (51:24.040)
And general relativity and quantum mechanics
Lex Fridman (51:26.960)
are these pockets of reducibility that we think of as,
Stephen Wolfram (51:32.000)
that 20th century physics
Lex Fridman (51:34.120)
is essentially pockets of reducibility.
Lex Fridman (51:36.880)
And then it is incredibly surprising
Lex Fridman (51:39.400)
that any kind of model that's generative
Stephen Wolfram (51:43.440)
from simple rules would have such pockets.
Lex Fridman (51:47.960)
Yeah, well, I think what's surprising
Stephen Wolfram (51:49.920)
is we didn't know where those things came from.
Lex Fridman (51:52.680)
It's like general relativity,
Stephen Wolfram (51:53.920)
it's a very nice mathematically elegant theory.
Lex Fridman (51:56.840)
Why is it true?
Lex Fridman (51:58.400)
You know, quantum mechanics, why is it true?
Lex Fridman (52:00.960)
What we realized is that from this,
Stephen Wolfram (52:04.160)
that these theories are generic
Lex Fridman (52:07.080)
to a huge class of systems
Stephen Wolfram (52:09.280)
that have these particular
Lex Fridman (52:10.440)
very unstructured underlying rules.
Lex Fridman (52:13.480)
And that's the thing that is sort of remarkable
Lex Fridman (52:16.920)
and that's the thing to me
Stephen Wolfram (52:18.280)
that's just, it's really beautiful.
Lex Fridman (52:20.320)
I mean, it's, and the thing that's even more beautiful
Stephen Wolfram (52:22.800)
is that it turns out that, you know,
Lex Fridman (52:24.400)
people have been struggling for a long time.
Stephen Wolfram (52:26.120)
You know, how does general relativity theory of gravity
Lex Fridman (52:29.000)
relate to quantum mechanics?
Stephen Wolfram (52:30.080)
They seem to have all kinds of incompatibilities.
Lex Fridman (52:32.400)
It turns out what we realized is
Stephen Wolfram (52:34.400)
at some level they are the same theory.
Lex Fridman (52:37.040)
And that's just, it's just great as far as I'm concerned.
Lex Fridman (52:40.840)
So maybe like taking a little step back
Lex Fridman (52:43.160)
from your perspective, not from the low,
Stephen Wolfram (52:47.120)
not from the beautiful hypergraph,
Lex Fridman (52:50.680)
well, from physics model perspective,
Lex Fridman (52:52.480)
but from the perspective of 20th century physics,
Lex Fridman (52:55.440)
what is general relativity?
Lex Fridman (52:57.240)
What is quantum mechanics?
Lex Fridman (52:58.320)
How do you think about these two theories
Lex Fridman (53:00.880)
from the context of the theory of everything?
Lex Fridman (53:04.000)
Like just even definition.
Stephen Wolfram (53:05.720)
Yeah, yeah, yeah, right.
Lex Fridman (53:06.560)
So I mean, you know, a little bit of history of physics,
Lex Fridman (53:08.800)
right?
Lex Fridman (53:09.640)
So, I mean the, you know, okay,
Lex Fridman (53:12.040)
very, very quick history of this, right?
Lex Fridman (53:14.200)
So, I mean, you know, physics, you know,
Stephen Wolfram (53:16.240)
in ancient Greek times, people basically said,
Lex Fridman (53:19.000)
we can just figure out how the world works.
Stephen Wolfram (53:21.200)
As you know, we're philosophers,
Lex Fridman (53:22.560)
we're gonna figure out how the world works.
Stephen Wolfram (53:24.560)
You know, some philosophers thought there were atoms.
Lex Fridman (53:26.600)
Some philosophers thought there were,
Stephen Wolfram (53:28.600)
you know, continuous flows of things.
Lex Fridman (53:30.600)
People had different ideas about how the world works.
Lex Fridman (53:33.000)
And they tried to just say,
Lex Fridman (53:33.840)
we're gonna construct this idea of how the world works.
Stephen Wolfram (53:36.840)
They didn't really have sort of notions
Lex Fridman (53:38.200)
of doing experiments and so on quite the same way
Stephen Wolfram (53:40.640)
as developed later.
Lex Fridman (53:41.480)
So that was sort of an early tradition
Stephen Wolfram (53:43.320)
for thinking about sort of models of the world.
Lex Fridman (53:46.600)
Then by the time of 1600s, time of Galileo and then Newton,
Stephen Wolfram (53:51.200)
sort of the big idea there was, you know,
Lex Fridman (53:55.280)
title of Newton's book, you know, Principia Mathematica,
Stephen Wolfram (53:57.640)
mathematical principles of natural philosophy.
Lex Fridman (54:00.440)
We can use mathematics to understand natural philosophy,
Stephen Wolfram (54:04.240)
to understand things about the way the world works.
Lex Fridman (54:07.080)
And so that then led to this kind of idea that, you know,
Stephen Wolfram (54:10.480)
we can write down a mathematical equation
Lex Fridman (54:12.760)
and have that represent how the world works.
Lex Fridman (54:14.960)
So Newton's one of his most famous ones
Lex Fridman (54:16.800)
is his universal law of gravity,
Stephen Wolfram (54:19.240)
inverse square law of gravity
Lex Fridman (54:21.160)
that allowed him to compute all sorts of features
Stephen Wolfram (54:23.360)
of the planets and so on.
Lex Fridman (54:24.920)
Although some of them he got wrong
Lex Fridman (54:26.240)
and it took another hundred years
Lex Fridman (54:28.000)
for people to actually be able to do the math
Stephen Wolfram (54:30.200)
to the level that was needed.
Lex Fridman (54:31.240)
But so that had been this sort of tradition
Stephen Wolfram (54:34.560)
was we write down these mathematical equations.
Lex Fridman (54:36.280)
We don't really know where these equations come from.
Stephen Wolfram (54:38.640)
We write them down.
Lex Fridman (54:39.960)
Then we figure out, we work out the consequences
Lex Fridman (54:42.480)
and we say, yes, that agrees with what we actually observe
Lex Fridman (54:45.320)
in astronomy or something like this.
Lex Fridman (54:47.320)
So that tradition continued.
Lex Fridman (54:49.480)
And then the first of these two
Stephen Wolfram (54:51.440)
sort of great 20th century innovations was,
Lex Fridman (54:55.480)
well, the history is actually a little bit more complicated,
Lex Fridman (54:57.320)
but let's say that there were two,
Lex Fridman (55:01.600)
quantum mechanics and general relativity.
Stephen Wolfram (55:03.440)
Quantum mechanics kind of 1900
Lex Fridman (55:05.400)
was kind of the very early stuff done by Planck
Stephen Wolfram (55:08.400)
that led to the idea of photons, particles of light.
Lex Fridman (55:12.320)
But let's take general relativity first.
Stephen Wolfram (55:14.880)
One feature of the story is that special relativity
Lex Fridman (55:19.240)
thing Einstein invented in 1905
Stephen Wolfram (55:21.800)
was something which surprisingly
Lex Fridman (55:24.240)
was a kind of logically invented theory.
Stephen Wolfram (55:27.040)
It was not a theory where it was something where
Lex Fridman (55:29.880)
given these ideas that were sort of axiomatically
Stephen Wolfram (55:32.960)
thought to be true about the world,
Lex Fridman (55:34.760)
it followed that such and such a thing would be the case.
Stephen Wolfram (55:38.360)
It was a little bit different
Lex Fridman (55:39.400)
from the kind of methodological structure
Stephen Wolfram (55:42.000)
of some existing theories in the more recent times,
Lex Fridman (55:45.920)
where it's just been, we write down an equation
Lex Fridman (55:47.640)
and we find out that it works.
Lex Fridman (55:49.960)
So what happened there.
Lex Fridman (55:51.560)
So there's some reasoning about the light.
Lex Fridman (55:53.680)
The basic idea was the speed of light
Stephen Wolfram (55:57.720)
appears to be constant.
Lex Fridman (55:59.960)
Even if you're traveling very fast,
Stephen Wolfram (56:01.920)
you shine a flashlight, the light will come out.
Lex Fridman (56:05.080)
Even if you're going at half the speed of light,
Stephen Wolfram (56:07.120)
the light doesn't come out of your flashlight
Lex Fridman (56:08.920)
at one and a half times the speed of light.
Stephen Wolfram (56:11.160)
It's still just the speed of light.
Lex Fridman (56:13.080)
And to make that work,
Stephen Wolfram (56:14.680)
you have to change your view of how space and time work
Lex Fridman (56:18.040)
to be able to account for the fact
Stephen Wolfram (56:20.200)
that when you're going faster,
Lex Fridman (56:21.480)
it appears that length is foreshortened
Lex Fridman (56:24.440)
and time is dilated and things like this.
Lex Fridman (56:26.240)
And that's special relativity.
Stephen Wolfram (56:27.200)
That's special relativity.
Lex Fridman (56:28.560)
So then Einstein went on with sort of
Stephen Wolfram (56:33.160)
vaguely similar kinds of thinking.
Lex Fridman (56:34.800)
In 1915, invented general relativity,
Stephen Wolfram (56:37.960)
which is the theory of gravity.
Lex Fridman (56:39.920)
And the basic point of general relativity
Stephen Wolfram (56:42.480)
is it's a theory that says,
Lex Fridman (56:44.840)
when there is mass in space, space is curved.
Lex Fridman (56:49.680)
And what does that mean?
Lex Fridman (56:52.320)
Usually you think of what's the shortest distance
Stephen Wolfram (56:55.160)
between two points.
Lex Fridman (56:56.000)
Like ordinarily on a plane in space, it's a straight line.
Stephen Wolfram (57:00.840)
Photons, light goes in straight lines.
Lex Fridman (57:04.640)
Well, then the question is,
Stephen Wolfram (57:06.440)
is if you have a curved surface,
Lex Fridman (57:10.280)
a straight line is no longer straight.
Stephen Wolfram (57:12.160)
On the surface of the earth,
Lex Fridman (57:13.560)
the shortest distance between two points is a great circle.
Stephen Wolfram (57:16.200)
It's a circle.
Lex Fridman (57:18.600)
So, you know, Einstein's observation was
Stephen Wolfram (57:21.040)
maybe the physical structure of space
Lex Fridman (57:24.520)
is such that space is curved.
Lex Fridman (57:26.800)
So the shortest distance between two points,
Lex Fridman (57:29.640)
the path, the straight line in quotes,
Stephen Wolfram (57:32.880)
won't be straight anymore.
Lex Fridman (57:34.160)
And in particular, if a photon is, you know,
Stephen Wolfram (57:37.160)
traveling near the sun or something,
Lex Fridman (57:39.320)
or if a particle is going,
Stephen Wolfram (57:40.600)
something is traveling near the sun,
Lex Fridman (57:42.400)
maybe the shortest path will be one
Stephen Wolfram (57:45.320)
that is something which looks curved to us
Lex Fridman (57:48.840)
because it seems curved to us
Stephen Wolfram (57:50.160)
because space has been deformed by the presence of mass
Lex Fridman (57:53.240)
associated with that massive object.
Lex Fridman (57:55.480)
So the kind of the idea there is,
Lex Fridman (57:59.240)
think of the structure of space
Stephen Wolfram (58:01.000)
as being a dynamical changing kind of thing.
Lex Fridman (58:03.680)
But then what Einstein did
Stephen Wolfram (58:04.840)
was he wrote down these differential equations
Lex Fridman (58:07.120)
that basically represented the curvature of space
Lex Fridman (58:10.240)
and its response to the presence of mass and energy.
Lex Fridman (58:13.040)
And that ultimately is connected to the force of gravity,
Stephen Wolfram (58:18.280)
which is one of the forces that seems to,
Lex Fridman (58:20.600)
based on its strength,
Stephen Wolfram (58:21.480)
operate on a different scale than some of the other forces.
Lex Fridman (58:24.800)
So it operates in a scale that's very large.
Lex Fridman (58:27.760)
What happens there is just this curvature of space,
Lex Fridman (58:32.160)
which causes, you know, the paths of objects to be deflected.
Stephen Wolfram (58:35.960)
That's what gravity does.
Lex Fridman (58:37.200)
It causes the paths of objects to be deflected.
Lex Fridman (58:39.720)
And this is an explanation for gravity, so to speak.
Lex Fridman (58:43.160)
And the surprise is that from 1915 until today,
Stephen Wolfram (58:47.280)
everything that we've measured about gravity
Lex Fridman (58:49.680)
precisely agrees with general relativity.
Lex Fridman (58:52.160)
And that, you know, it wasn't clear black holes
Lex Fridman (58:55.720)
were sort of a predict,
Stephen Wolfram (58:56.560)
well, actually the expansion of the universe
Lex Fridman (58:57.720)
was an early potential prediction,
Stephen Wolfram (58:59.560)
although Einstein tried to sort of patch up his equations
Lex Fridman (59:02.720)
to make it not cause the universe to expand,
Stephen Wolfram (59:05.080)
because it was kind of so obvious
Lex Fridman (59:06.320)
the universe wasn't expanding.
Stephen Wolfram (59:08.160)
And, you know, it turns out it was expanding
Lex Fridman (59:10.480)
and he should have just trusted the equations.
Lex Fridman (59:11.960)
And that's a lesson for those of us
Lex Fridman (59:14.480)
interested in making fundamental theories of physics
Stephen Wolfram (59:16.680)
is you should trust your theory and not try and patch it
Lex Fridman (59:19.840)
because of something that you think might be the case
Stephen Wolfram (59:22.000)
that might turn out not to be the case.
Lex Fridman (59:25.280)
Even if the theory says something crazy is happening.
Stephen Wolfram (59:28.360)
Yeah, right.
Lex Fridman (59:29.200)
Like the universe is expanding.
Stephen Wolfram (59:30.040)
Like the universe is expanding, right, which is,
Lex Fridman (59:31.880)
but, you know, then it took until the 1940s,
Stephen Wolfram (59:35.160)
probably even really until the 1960s,
Lex Fridman (59:36.840)
until people understood that black holes
Stephen Wolfram (59:38.600)
were a consequence of general relativity and so on.
Lex Fridman (59:42.200)
But that's, you know, the big surprise has been
Stephen Wolfram (59:45.640)
that so far this theory of gravity has perfectly agreed
Lex Fridman (59:50.000)
with, you know, these collisions of black holes
Stephen Wolfram (59:51.880)
seen by their gravitational waves, you know,
Lex Fridman (59:54.480)
it all just works.
Lex Fridman (59:55.880)
So that's been kind of one pillar of the story of physics
Lex Fridman (59:59.160)
it's mathematically complicated to work out
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