It's been waiting for a genius, a visionary, a maverick, ...
Wolfram's narcissism is so extreme it's just comical. When I was really into complexity science and stuff everyone in the field would joke about it, suggesting a drinking game where you take a shot every time Wolfram refers to how he was a gifted child or started studying math in his teens or single-handedly accomplished some amazing feat. The guy toots his own horn like a circus clown.
It's too bad because he actually does have some very interesting ideas and a good skill at explaining things. His narcissism is self-defeating. He needs to just chill out, write like a normal human being, and publish. Maybe he should take up amateur astronomy. Nothing gives perspective more than carefully observing photons older than the human species with your own eyes.
I sometimes recommend A New Kind of Science with a huge caveat. It's a decent compendium of fascinating cellular automata, complexity, and theoretical CS research with some interesting speculation attached, but (1) Wolfram did not invent all this or do all this work himself, and (2) he takes his speculation too far to the point of flirting with crackpottery. If you can read NKS with those caveats in mind, it's worth at least skimming and taking in the interesting bits.
In university a professor was explaining how Wolfram formulated Physics in the 80s through finite automata instead of Mathematics, that must be the NKS. Is it actually (at least theoretically ;)) possible to calculate something with it, so that results match for instance Newtonian Physics?
It's "just" a different way of formulating mathematics, but sometimes formulating things differently can yield insights. At least attempting physics from this angle is a project with merit, especially since it seems as if conventional mathematical theoretical physics is a little stuck lately.
The problem with the CA-based physics approaches are that while you can create CA models that work and are predictive in ways that mimic conventional mathematical models, so far the approach has failed to produce a compelling model with testable predictions that is unique to the approach.
In other words there's no evidence (yet?) that this approach is better than conventional math, and a strong contrary argument in favor of math can be made from the angle that math maps more clearly to the conceptual space. It's possible to read an equation in terms of the concepts it models, assign units to variables that refer to specific forces or properties, etc. I'm not aware of a way to do that with CA. What you get there are weird rules that manifest something that seems to fit existing mathematical models or concrete observations, but those weird rules are "opaque." It's a relative to the opaqueness problem in AI / machine learning.
Lastly though I would add that the fact that you can create compelling CA models of physics at all does perhaps suggest something about reality. Maybe it suggests that reality is or is similar to a CA system under the hood. The fact that quantum comes from "quanta" and "quantized" suggests that things are in fact discrete at some level.
There is an argument, and I think Wolfram has made it, that one would expect the systems and the math to become simpler the deeper and more fundamental the models became, and the opposite seems to be true with modern physics.
When you say conventional math, you’re referring to math that would be quite difficult let’s say for even a dedicated undergraduate math, physics or electrical engineering major. The CA, on the other hand described a process an interested child can comprehend.
> one would expect the systems and the math to become simpler the deeper and more fundamental the models became
The notion that there exists a single expression, CA rule, or other fundamental truth at the root of the physical universe is an arbitrary assumption. It may or may not be true. We should go where the evidence leads us.
In the end we should have a model that is no more and no less complex than what is needed to model observed reality.
But it's only easier to comprehend because it's vaguer. If you wanted to express specific, nontrivial mathematical statements in CA language, it would immediately get more complicated. Certainly, a paragraph about Euclid's Elements would be easier to comprehend than a paragraph from the Elements, but that's not a fair comparison...
But my point is if the CA and the mathematical expression show the same things, then you could say the mathematics are simply a roundabout and confusing way to characterize the CA.
As a thought experiment (and a timely tribute) how would you (mathematically) characterize and/or describe an ongoing evolution of an instances of Conway's Game of Life if you didn't have a grid. Or even better, if you didn't have the grid and you could only see things a resolution of neighborhoods of 10-20 cell resolutions? You might be able to come up with some crazy complex math which does it. But if you knew about the grid and the underlying rules it would explain all of the observations perfectly AND more simply.
Don't get me wrong -- I don't think Wolfram has done that, nor do I really hold out hope that it could be true. But it's a real compelling, if only it were.
Admittedly, I only skimmed NKS. That said, I don't understand how the approach is different than anything else abusing the incidental fact that something is Turing complete to re-prove existing results.
The problem with these approaches, like trying to write a neural network in MS Excel, is that it's going to be cumbersome, slow, and provide little advantage over more straightforward calculation methods.
Wolfram's narcissism is so extreme it's just comical. When I was really into complexity science and stuff everyone in the field would joke about it, suggesting a drinking game where you take a shot every time Wolfram refers to how he was a gifted child or started studying math in his teens or single-handedly accomplished some amazing feat. The guy toots his own horn like a circus clown.
It's too bad because he actually does have some very interesting ideas and a good skill at explaining things. His narcissism is self-defeating. He needs to just chill out, write like a normal human being, and publish. Maybe he should take up amateur astronomy. Nothing gives perspective more than carefully observing photons older than the human species with your own eyes.
I sometimes recommend A New Kind of Science with a huge caveat. It's a decent compendium of fascinating cellular automata, complexity, and theoretical CS research with some interesting speculation attached, but (1) Wolfram did not invent all this or do all this work himself, and (2) he takes his speculation too far to the point of flirting with crackpottery. If you can read NKS with those caveats in mind, it's worth at least skimming and taking in the interesting bits.