There is an excellent interview by Lex Fridman with Wolfram on this topic. It's just them talking about this concept and the related concepts and their relationships to both the universe as a whole and to various scientific fields.
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.
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.
Specifically in relation to this theory of ruliads and Hossenfelder's take, one "pop" mathematical concept that comes to mind is Godel's incompleteness theorem. It may indeed be mathematically feasible that some holy grail equation exists within the ruliad given that Godel et al have shown that it is possible to just keep recursively describing internally consistent algebraic systems and meta algebraic systems ad infinitum, and that in an infinitely arbitrary meta mathematical system you could describe anything that is "true".
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.
I'll wait for this to be formalized with precise technical language before really giving it weight. Until then, to me it sounds a lot like the kind of "profound" philosophical stuff I would come up with while high in grad school ha. And once I was out of the hazy stupor, there was nothing concrete and precise I could build out of the ideas.
Probably wise. Also relatable, I have tons of old notes of ideas at some point I thought were potentially profound, only to realize they were half-baked and/or already explored.
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.
The recent 3Blue1Brown video on "How a Mandelbrot set arises from Newton’s work" (https://www.youtube.com/watch?v=LqbZpur38nw) made me think how, similarly to how different areas of the Mandelbrot set represent some halting property of the given complex number and the iteration z_n+1 = z_n²+c, programming languages could be visualized.
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.
> In many ways, the ruliad is a strange and profoundly abstract thing. But it’s something very universal—a kind of ultimate limit of all abstraction and generalization. And it encapsulates not only all formal possibilities but also everything about our physical universe—and everything we experience can be thought of as sampling that part of the ruliad that corresponds to our particular way of perceiving and interpreting the universe.
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?
Simple rules can lead to complex results. Given almost infinitely powerful computing and a lifetime of hacking, you might figure out the secrets of the universe, or not.
It's a very interesting rabbit hole that Stephen has dug. I'm not sure I want to get stuck down there. ;-)
What makes you think that the idea of "the collection of all possible computations can be seen as a single object, instead of multiple processes" can be used as a tool to figure out the secrets of the universe? ;-)
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.
Reminds me of the various versions of a paper published by Alexandre Harvey-Tremblay, including the most recent: https://www.academia.edu/33079029/The_Design_of_a_Formal_Sys... - A previous version even had the public praise of Gregory Chaitin, himself, though it appears to have been removed/superseded.
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[ 3.5 ms ] story [ 62.2 ms ] threadIt'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.
The issue being that Wolfram is presenting himself as some sort of serious scientist, not as the lyricist of a 70s prog band
https://news.ycombinator.com/newsguidelines.html
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.
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.
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.
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?
Uncomputable function only "exist" in our imagination as an implicaton of imagined axioms. There is no physical evidence for them.
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.