Exploring Rulial Space: The Case of Turing Machines | Hacker News Reader

Exploring Rulial Space: The Case of Turing Machines

writings.stephenwolfram.com

20 pointsbobm_kite910 comments

I feel like this is the start of an interesting conversation, which gets distracted by a thousand aesthetically pleasing yet irrelevant graphs.

The interesting idea is, what if we modeled the physical world as operating by all rules at once, and the part that we are able to observe is only the part of it that operates according to our physics?

This makes me think of a model kind of like Borges's library, but with a datacenter. Let's say you had an infinite number of computers, running every possible computer program. Would this model contain our physical universe?

If the Turing hypothesis is correct, yes. That means there is some program whose results are equivalent to our physical universe, and so somewhere in this infinite datacenter exists a copy of our universe.

Is this a useful model? I don't think it is, no. The question of finding the rules of physics has just changed into an equally difficult question of finding out which computer in the infinite datacenter is running our universe.

But I think the "infinite datacenter" model is equivalent to Wolfram's "rulial space". You can make a thousand pretty charts of what the infinite datacenter looks like. CPU usage, network traffic, yeah all of those probably could be graphed. But that doesn't really make the model useful.

I confess that while I was very interested in Wolfram's project when it came out, I was unable to find any actual content in this extremely long article (despite reading the whole thing a couple of days ago). Would someone be able to summarise in a couple of lines what the article actually says? I know it's meant to be an "exploration" without necessarily having a goal, but even then I was hoping for more of a conclusion than the best I was able to derive, "if you consider an evolution graph obtained by applying all possible rules at every point, you get some pretty pictures, and you can think of that as a space all on its own, which might be interesting".

I think your summary is accurate. For reference, I'm willing to cut Wolfram more slack than some people are, I think his quest to discover the ultimate laws of physics from the other end is potentially interesting, but I don't think this particular article really has even any interesting conjectures.

I was thinking something like "Turing machines themselves can form various kinds of adjacency graphs", but I would also doubt how much we can learn from this: the behavior of adjacent Turing machines is often radically different and it's rapidly going to become undecidable to say how different, or even to confirm whether it's different or not.

If you think about software running on a CPU, you can get different behavior with a very small change. I gave a talk a couple of times about how real-world fencepost errors (like writing <= in a loop when you meant <) will compile to just a single-bit difference in the binary, yet in one case you have a correct program [at least in that regard!] and in the other you have a buggy and potentially exploitable one.

Or software crackers from different eras would sometimes try to remove copying restriction routines just by injecting NOPs over random conditional branches or function calls, in the hope of overwriting the relevant instruction and causing the program to entirely skip that logic.

These programs are adjacent in terms of their code, or are separated by a very short distance in the CPU version of Wolfram's rulial space, but their behavior completely diverges. And I think that's a common case. Or maybe some chaos theory ideas are apposite and we could say that there are a lot of attractors and so it's never unlikely that a small change to the code will produce a big change in its behavior.

Like you, I also don't mind that Wolfram is excited by this, and also am not sure that he's discovered anything here. :-)

It’s an interesting description of the space of computation and I quite enjoyed this article even though, as many, I have issues with the way wolfram participates in science. Certainly what he is describing can be a way to view the universe but that is somewhat trivial. It is not surprising that you get something like the universe when you start considering universal computation. The fact that we can write down e.g. equations of motion means there is a Turing machine that computes it. The real test is whether this perspective is useful in the sense that we can predict properties of the universe with it. That test is still out and until it’s addressed there is no way to evaluate or criticize this model. It’s too flexible to be useful at this point.

This is fab. It mirrors and takes far far further ideas I have been noodling around with for a while. I will be reading and rereading this for a while.

My genuine question from elsewhere in this thread: what ideas does it take, and where does it take them? I used to be something of a Wolfram fanboy (and certainly Mathematica is nothing less than miraculous), but I really can't see what content there is in this article.

Seconding Smaug123's question. I read the article through and can't understand what is meant to be insightful about it. Enlighten us?

I've been trying to grok where Wolfram is heading with this approach, and I just had a minor epiphany, probably brought on by binge-watching Devs: All of the rules he's constructing and using seem to be deterministic.

Interesting.

Not quite Crank Territory, but like most Wolfram's activities, it dances between possible brilliance and CT.

Note:

Crank Territory: That appellation does apply to his much laughed at previous effort "A New Kind of Science".

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