The Concept of the Ruliad
writings.stephenwolfram.com
writings.stephenwolfram.com
I'm still waiting on my "new kind of science." Wolfram makes all sorts of interesting claims, maybe he should focus more on interesting results.
Bear in mind this is merely a postulate, it isn't at all proven. It's our ability to make concrete predictions that's limited by what's computational, not necessarily the behavior of the universe itself. On a more pragmatic level however we don't really have any good ways to theorize about behaviors of creation that are uncomputable. Nonetheless, we know uncomputable functions exist so it's absurd to axiomatically rule out the possibility that there might be physical behaviors described by them. Perhaps all physical behaviors are and we're forever stuck with more or less congruent computable approximations?
It's a very interesting rabbit hole that Stephen has dug. I'm not sure I want to get stuck down there. ;-)
It's a mere change of perspective, but everything that you needed to find out about possible computations, you will need to find out about an infinite object containing them, in the same exact way.
Chris Barker's Zot http://web.archive.org/web/20200414141014/http://www.nyu.edu... is a turing complete system in which every binary string is a valid program. Input data is just appended as binary string to it. So the two dimensional "program+input => number of steps before halting" space can be visualized similarly without having blanks for syntax errors: https://i.imgur.com/ZGeZBBa.png
So not just mathematical computable spaces can be visualized this way, but also programming ones - another part of the Ruliad.
It's all very theoretical, but at the same time very stimulating, I found myself working out machine learning topics I had been thinking about while listening to them talk.
Just turn your critical mind off and let Wolfram's genius and wonderful mind expand your own, it's really quite a trip.
A good discussion that touches on these ideas in a fairly accessible way: https://www.youtube.com/watch?v=4-SGpEInX_c (Lex Friedman interviews Wolfram for the 3rd time)
I enjoyed Sabine Hossenfelder's thoughts on this and other 'Theory of everything' projects (Do we need a Theory of Everything? https://www.youtube.com/watch?v=mdu9KvLxHFg). A little bit of a reality-check for those who get really invested in these ideas, but I, like her, think it's really cool that there are people like Wolfram et al thinking these interesting thoughts and trying to push Physics in new directions.
It does not, however, follow that such an all-encompassing system physically exists, or that it is finite in some observably interesting way. I.e. the universe could just be infinite in every one of infinite aspects, in a monkeys-and-typewriters sort of way, and that would mean our existence would just necessarily be real, which is just not a very interesting conclusion. Or it could be that the universe is finite/limited in some way that the meta mathematical framework does not predict.
And that's where Hossenfelder's take comes in: we don't know that physics is as infinitely big as mathematics, and for the purposes of advancing the field of physics, one needs to work on increasing the confidence of what we do know, rather than saying that what we might eventually know happens to exist within some theoretically infinite set.