
Exploring Rulial Space: The Case of Turing Machines - bobm_kite9
https://writings.stephenwolfram.com/2020/06/exploring-rulial-space-the-case-of-turing-machines/
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lacker
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.

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Smaug123
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".

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rwallace
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.

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schoen
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. :-)

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nil-sec
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.

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plutonorm
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.

~~~
Smaug123
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.

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webmaven
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.

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Ice_cream_suit
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".

