How to Think Computationally about AI, the Universe and Everything
writings.stephenwolfram.com
writings.stephenwolfram.com
We didn't know this is in the eighties, when the first cellular automata ideas were conceived. So it was a worthy thing to explore in earnest. But it did not work. There is nothing to show for it. It did not strike a vein. These things happen. All the time. You have a great startup idea but no market fit. In this case the market is the Universe. And you cant fake it till you make it with the Universe.
The universe most certainly has a mysterious affinity with mathematics. And computation is a mathematical concept. So its a decent hypothesis. But there are a lot of mathematical concepts that dont manifest in any shape or form in physical reality.
From the simple geometric thinking of ancient cultures to Newton's and Leibnitz's calculus and then all the subsequent glories of 19th and 20th century physical theory, when new mathematical concepts "fit" the way the universe works there is just an avalanche of prediction, verification, learning, refinement, further prediction etc.
Its wrong to think we have reached the end of "mathematical physics". So new ideas are needed, and computation is as good an inspiration as a falling apple. But prunning dead-end ideas is a faster way to get closer to the truth.
It’s bigger problem than just to this. It’s that we’ve based everything off the Club of Rome style mindset of society and it’s all failed. But we haven’t figured out another way. So climate change, politics, democracy and marketing all continue to try to figure out the computational stable state of society.
What is this supposed to be a reference to?
Hahahaha!! That's so "psychohistory" ... it suggests such, almost 'individual'-like intention.
Also, none of it has failed. That's an absurd interpretation of where we are. The real problem is that everything we do ... all the day-to-day problems we solve, all the systems we build that fit and do a 'good job' helping us, say, in some respect, ... set us up to need even more of the same basically. As you wrote elsewhere ... increasingly complex etc.
I'd flesh out more, but, must run now.
The reality is simply that we WON'T outrun reality. There is no failure, nor is there success ... that dualistic thinking really tends to obscure rather than clarify ... by anchoring some 'conclusion' based on some specific perspective and cutting off wider views. We will follow 'the laws' of other organisms ... our own specific path, but the same basic fundamental arc ... game theoretic and in less ... abstract framings.
It's extremely easy to come up with models that reproduce most of modern physics if you at all know what you're doing. String theory does it, loop quantum gravity does, and so on. There are deterministic models that avoid the "God playing dice" aspects of quantum mechanics yet still reproduce all the classic results. There are rods + gears models of electromagnetism that give the right numbers even though the mechanisms are ludicrous.
The fact that it is so easy to come up with models that match modern physics is in itself a meaningful and not at all obvious thing, but it ultimately derives from the fact that the real universe seems to operate on laws that spring directly from symmetry principles. It turns out that most of the physics that matters is extremely "natural" and can be derived as a consequence of much simpler assumptions than you'd expect, even if the math that gets you from those assumptions to the resulting mechanics can be intense. If you're unfamiliar with this concept but understand calculus, you owe yourself a very deep dive on Noether's theorem, the way that symmetry radiates into every aspect of physics is one of the most profound things to study in physics.
The upshot of Noether's theorem and the ubiquity of its applications in modern physics is that it's very easy to create a theory that matches the predictions of e.g. special relativity: you just need to sneak it in by, for instance, defining your "foliations" in such a way that you have Lorentz symmetry, then everything else comes for free. If you want general relativity, then you (mostly) just need invariance under diffeomorphisms, which is really frickin easy to build into the limit of any graph-based model since you're basically redefining space altogether. I still don't entirely understand how Wolfram gets quantum theory in there; I don't doubt that his model does actually do it at a mathematical level, I just can't stand the verbose writing style and have too little interest in his particular theory to work through it, but once you start talking about constantly branching and recombining state graphs and stuff like that it's not at all hard to imagine that you could pick your definitions in such a way that Hilbert spaces pop out and then you define observers/observations in a way that makes it cleanly match a many-worlds interpretation of quantum mechanics.
But the fact that you have a model that reproduces all of known physics doesn't mean anything. We already have several of those. And people rightly criticize even the top contenders on the basis that they all tend to suffer from the same defect, they're overparameterized and could predict a lot of universes that don't work the way ours does, and there are very few experiments that would rule the models out altogether (rather than merely constrain the parameters). To the extent that their predictions differ from what current theory would predict, their parameters could be easily tuned to match almost any result, which makes it tough to have any faith that the goalposts wouldn't be moved when results did come in that could test, say, the extreme conditions where quantum gravity would be relevant. Wolfram's is no different, except that as far as I can tell he hasn't gone anywhere near as far as e.g. the string theorists in working out what the different predictions would even be for his theory. He's just blindly declaring it correct.
Models are great, and I think there is something useful in Wolfram going down the rabbit hole in terms of showing what a model that reproduces quantum effects looks like, I feel like that is underexplored (the rules of quantum mechanics are usually taken as a given, even in theories of "everything"). But his breathless declarations of having solved physics are ludicrous, and I feel like his ideas might actually be taken much more seriously if he had a more realistic understanding of what he was working with.
The idea that the universe is discrete/computational is a fine idea, but underspecified and useless on its own. There's an infinite array of computable rules to choose from. But the fact that with a few assumptions on the rules you can then limit to both GR and QM is very non-trivial and, in my opinion, pretty surprising.
To your point, does it prove that this is _the_ correct theory? Definitely not, and metering language around the claims is important. Still, the result feels novel, surprising, and worthy of further investigation, alongside the other popular models being explored. I think it's a shame that Wolfram's demeanor turns people off from the work.
Perhaps you're not familiar with the literature here, but GP isn't exaggerating, using e.g. Noether's Theorem you can derive the expected laws of physics from very simple symmetry principles. This means that any model with these symmetries will produce these behaviours.
If you make up a new model of Newtonian mechanics that doesn't depend explicitly on time, so that your laws are the same tomorrow as today, then it's proven that such a model will conserve "energy". You could point at this as an indication of the correctness of your theory, but it's really unavoidable. You can play a similar trick for the fundamental forces if you have the patience to work through the derivation.
A better test is these models is if they're predictive, and I haven't seen a such a result about this CA-physics outside of Wolfram's blog.
But it's also slightly different; in Tegmark's description of the MUH there's not a meaningful connection between the universe that realizes (let's say) Euclid's axioms and our universe. They're just separate places in the Platonic realm; they way we learn about Euclidean geometry is by computing, using some little Turing-complete region to simulate geometry. If I understand correctly, the ruliad says no, it is possible, in principle, to navigate through the hell of a mess and actually find the place in the hypergraph, not disconnected from the place that describes our lived experience, that is Euclidean geometry. It's sort of the ultimate reading of the Copernican principle: the laws we see around us are not particularly special and aren't privileged over other laws.
I find that to be a pretty beautiful philosophical idea while also thinking it's not a very practical one for doing actual science. If it contains representations all possible consistent axioms, well, how would you ever make a prediction about an actual experiment nearby? In the framework of relativistic QFTs we can make a bunch of different models and test them, settle on one, and use it to make predictions. Or find that actually it was just a low-energy EFT all along, falsifying our model. But the ruliad can never be falsified; the claim is that every possible universe is in there. How do I use it to make predictions about physics beyond the standard model? Or even just SM physics? Unclear.
Is that really true?
Could it be more fair to say that mathematics has a (not so) mysterious affinity with the universe?
Specifically, where do our 'axioms' come from? Why did people spend centuries trying to prove the parallel postulate?
Partly, I'm being rhetorical, but, also, partly I'm really not. I would certainly not categorically dispute what you wrote, but I'd also not embrace it 'out-of-hand'.
... So, 'the floor is open', so-to-speak... if any have other perspectives on math-universe connection, rebuttals, etc. :)
(I don't think the universe is a simulation, to be clear.)
If you think about quantum mechanics, it's something that could sure look like a bug. Systems that you expect to be deterministic are stochastic if you look closely enough? If it were a program I was writing, I'd start wondering if there were rounding errors and/or concurrency issues. But we've come up with math to understand it.
Math is very general, I'm not sure there's a process that you couldn't describe with a complex enough mathematical system, and thereby conclude it had it's origins outside of our universe.
Let's say you throw a baseball into orbit. That's very strange, a profound mystery. You tell me that we must live in a simulation. I contend something strange happened which we don't understand, because we only have one datapoint, but that a satisfactory explanation does exist. How do you know I'm wrong?
If you have even a faint interest in philisophy and have taken algorithms 101 you will find something mind-blowing in this paper. My favorite part is about how the “Chinese room” problem takes on totally different character depending on your assumptions about the type of machinery behind the black box.
The whole thing basically boils down to "there's this room that can speak perfect Chinese, and we don't know how it works, or how your brain works, but somehow we can say with absolute certainly that they couldn't possibly be the same."
Between this and the recent "techno-optimist" rant, I get the sense that maybe we shouldn't give popular voices platforms for things outside the scope that made them famous in the first place, and if they really have something interesting to say, it should be determined as such by the content of its argument and not the pseudo-authority of its author.
Michael Jordon didn't have a stellar baseball record and likely wouldn't have made the cut for a team if he wasn't Michael Jordon. And what I see a lot of these days are people that made a name for themselves metaphorically playing basketball suddenly blogging about baseball and getting way too much attention for what are fundamentally 0.202 batting average ideas.
Looking at Physics historically there are multiple examples of scientists who did productive and fully credible work in their prime and later ended up stuck on crank theories.
You'll have a much better time telling people how and why those "billionaire crankers" are not making sound arguments than trying to gatekeep what they say. Even then, that's no guarantee.
all in all, the idea that people "speaking up" in this way does anything at all is fairly wishful thinking.
Does it maybe read a bit different from the post above?
Roger Penrose has a Nobel Prize in physics. But his consciousness collapse interpretation and "consciousness arises from microtubules" interpretations aren't taken very seriously, nor is his fecund universes cosmology.
And his work on those things is arguably much more rigorous relative to what Wolfram is doing here - but still falls short of what serious theories by serious theoretical physicists involve.
A dissertation extending views of particle physics under the supervision of Feynman is a very different story from reinventing physics 40 years later with the 'superpowers' of your own mathematical language as best expressed by what happens to generative AI rendering a cat in a party hat.
He didn't play in the major leagues of physics over the past 40 years, and quite a lot has happened since 1980 in that field.
So for him to go from the field where he had meaningful success and spent almost the entirety of his career and adult life to one he'd not been a part of for four decades is very much like Jordan going from basketball to baseball.
It wouldn't really have mattered if Jordan had played baseball in college. It's not where he made a name for himself and the quality of his play when he switched to it after his basketball career was subpar. Just as most physicists find Wolfram's current work: https://www.scientificamerican.com/article/physicists-critic...
Sorry you don't find it a good analogy, but I'm pretty happy with it.
"And that the structure of space and everything in it is just defined by the network of relations between these elements—that we might call atoms of space. It’s very elegant—but deeply abstract."
How about this one, shortly after describing "in the history of science there's four models":
"But now there’s something even more: in our Physics Project things become multicomputational, with many threads of time, that can only be knitted together by an observer." Wow, one of the four models in the history of science is the thing you just came up with?
Or this one: "But how is that rule picked? Well, actually, it isn’t. Because all possible rules are used. And we’re building up what I call the ruliad: the deeply abstract but unique object that is the entangled limit of all possible computational processes."
Dude overfitted basic physics with a model and thinks he discovered a theory of everything.
"OK, so the ruliad is everything." Pythagoras move over, there's a new mathematician's Monad in town.
"And there are two crucial facts about us. First, we’re computationally bounded—our minds are limited. And second, we believe we’re persistent in time—even though we’re made of different atoms of space at every moment.
So then here’s the big result. What observers with those characteristics perceive in the ruliad necessarily follows certain laws. And those laws turn out to be precisely the three key theories of 20th-century physics: general relativity, quantum mechanics, and statistical mechanics and the Second Law."
How convenient.
"We can think of this as a place in the ruliad described using the concept of a cat in a party hat:" Wait, what now?
"Maybe we need a promptocracy where people write prompts instead of just voting." This is still on the rails for you?
"Before our Physics Project we didn’t know if our universe really was computational. But now it’s pretty clear that it is. And from that we’re inexorably led to the ruliad—with all its vastness, so hugely greater than all the physical space in our universe." Oh great, it's pretty clear.
I can't imagine that he hasn't convinced respected physicists of his claims.
Did he show them the video of the cat in the party hat becoming a "cat island" and then turning into abstract concept spaces mirroring the development of actual spacetime from the big bang? He should definitely lead with that next time.
It's scary because I was never as smart as he used to be. I could be even more off base with even less to back it up, and equally unable to see that.
- Contact with reality (feedback). Predict, try, did it work?
- Having a good reasoning framework. For some it's 1. Religious text, 2. what others they respect think, 3. reasoning for understanding. This is not the worst but not the best. Perhaps a better one would be 1. Science/rationality, 2. religious/philosophical/spiritual texts, 3. first principles thinking
- Humility, you don't know anything unless you have great reasoning and empirical evidence to back up what you're saying. Even then, when faced with complexity (i.e. unless you are dealing with the most atomic/simple concept), you're still almost certainly wrong.
The whole thing reminds me of a book written by one of the researchers who was first reviewing the Dead Sea Scrolls.
An expert on his field, he eventually writes a book about how everything was actually connected to magic mushrooms. But the key is - it's all using abstract references and coded language.
So much like how online "pedophile investigators" suddenly saw flying in Chicago deep dish pizza as code for child trafficking because triangles are coded symbolism - it becomes a self fulfilling abstraction.
Redefine first principles off a presumed conclusion with enough abstraction and you can magically arrive at that conclusion from those first principles in ways no one can understand unless they embrace your abstractions! Crazy, right?
If QM and GR turned out to be required by the anthropic principle it would be a pretty big deal.
But those two theories are known to be incomplete and incompatible, so I would really like to think that this is incorrect.
It's a serious question rather than snark as I am only moderately familiar with his work. I appreciate some of his thoughts (ex: computational irreducibility), but I feel like I've got at least 20 years of asking "So what?" when he publishes. And yet here we are, discussing him, again.
Perhaps it would help if he had clarified what he meant by:
`So then here’s the big result. What observers with those characteristics perceive in the ruliad necessarily follows certain laws. And those laws turn out to be precisely the three key theories of 20th-century physics: general relativity, quantum mechanics, and statistical mechanics and the Second Law. `
So it sounds like he's saying that if you take an arbitrary system of generating infinite rules and apply it to itself, you'll make a system that shares traits of our universe, which if true is actually fascinating in itself. Curious if any advocates can speak to evidence of this claim.
"Ruliad" represents the abstract and unique object that arises from the application of all possible computational processes or rules; the totality of all potential computational processes, an infinite, complex network of all possibilities that can ever exist. Wolfram explains that our perceptions of the universe, and our understanding of the laws of physics themselves, are influenced by our specific sampling or experience of the ruliad.
https://en.m.wikipedia.org/wiki/Von_Neumann%E2%80%93Wigner_i...
I like to think it's literally an observation that creates the universe, otherwise the entire universe is just one giant superposition.
An interesting thing is also the Quantum Zeno paradox, in that a consistently observed thing is less likely to do the unlikely (by collapsing the wave function according to the Copenhagen interpretation, many worlds by another).
So: - observers contain the possible states of the universe but only with those which they are consistently interacting with - observers interact and enter superposition with the thing they observe to an outside observer (shrodingers cat) - an observer can only be defined by another observer through observation (when we open the box)
Which leads to: The universe was not created until it was observed to have been created, which is the observer-created universe.
What troubles me is that the more we take away any determining factors for free will the more it sounds like randomness.
Whether there is any meaningful notion of free will here is another matter. IMO the term free will is a red-herring. We obviously make choices and those choices are attributable to us. The only relevant question is whether we have a sufficient kind of authorship over our choices such that we can/should be rendered accountable for their outcomes. But this is mostly tangential to the kinds of disputes people have about free will.
- the theory is not mainstream, guess it is not attractive enough to study it right now
- the theory is not able to make any new predictions (yet). This has to change I think to get traction.
On the personal level, maybe you are right - but it doesn't matter, if he is right...
AFAIK, the theory is not able to make _any_ predictions yet.
It purports to be one of those "theories of everything" in the form of a kind of "universe building kit".
But all it produces are a bunch of pretty "hypergraphs" that have some loose analogies with some physical theories.
If, at the end of the day, one's "theory of everything" can't replicate classical mechanics, the spectra of Hydrogen atoms, and the laws of thermodynamics, then it probably doesn't warrant bloviating on the big bang, black holes and information theory as Mr Wolfram is apt to do.
Sean Carroll is more of a "just let the guest say what they want to" interviewer, so he doesn't grill him very hard. Despite that, I think it comes across pretty clearly in the interview that Wolfram doesn't actually have any compelling reason to think that this is the way the universe actually is.
Wolfram is a very smart fellow and deserves much credit for Mathematica. But these little side projects are very much outsider physics. No one is actually interested in pursuing his ideas because they're not particularly compelling. He has a couple of folks on his payroll doing work on it, and he'll show up on Lex Fridman or other internet talking head shows but that's pretty much the extent of it.
There's no harm in it, I guess. He's not a crank... though maybe somewhat crank-adjacent.
“…theoretical physicist Wolfgang Pauli, was known for his colorful objections to incorrect or careless thinking.
Rudolf Peierls documents an instance in which "a friend showed Pauli the paper of a young physicist which he suspected was not of great value but on which he wanted Pauli's views.
Pauli remarked sadly, 'It is not even wrong'."”