Glen,

Thank you for looking into it. Yes, that is the publication. Also, thank
you for posting "The post-truth prophets"[0]. Sean Illing manages to get at
the heart of what I find myself defending regarding postmodernism[1]. You
may remember that some months ago, I was on a "Bergson through the eyes of
Deleuze"-kick. Bergson, a prominent philosopher of mind, space, and time
(in his time) was driven completely underground by Einstein, Russell, and
other promoters of relativity theory. By many historical accounts, the work
of Bergson could have been all but forgotten had Deleuze not resurrected
his ideas, and especially their applications to film. Crucial to Bergson's
conception was to recognize time and space as explicitly different kinds of
things, and via his admiration of Riemann, sought out but never found a
mathematical treatment for his ideas. Listening to Wolfram's interview on
Sean Carroll's podcast[2], I cannot help but wonder if this recent work is
a step toward Bergson's dream. Around 42 minutes into the interview, SeanC
and SteveW record:

"""
0:41:26.7 SW: That is, you might have thought to get something as
computationally sophisticated as us humans with our brains and all this
kind of thing you need the whole process that’s led to us humans. But what
the principle of computational equivalence says is that’s not true. Even
these very simple systems with very simple rules can do it, and that has…
Well, it has lots of consequences. If you’re worrying about
extraterrestrial intelligence, for example, that tells you it’s everywhere.
It’s a question of whether we are sufficiently aligned with that
intelligence to be able to recognize it as something that, for example, has
purposes that we can understand as sort of human-like purposes. And I think
this idea intelligence requires liquid water is almost laughable.

0:42:10.2 SC: Right. [laughter] I’m on your side when it comes to that, but
intelligence might require spacetime in some sense, so let’s at least try
to get that. Is this naïve picture that I have in mind, where you have the
hypergraph, you update, it’s a discrete updating… Can I think of the graph
at any one update as space and the update itself as time, or is that too
simple-minded?

0:42:35.3 SW: Okay, so it gets a little complicated. And in fact, the
complexity that arises is quantum mechanics, I think. And so it’s, in a
sense, you try and make it that simple and you… Okay, so the basic point
is, the rule says if you have a lump of atoms of space that are connected
in this way, transform it into a lump that’s connected in this other way,
and it… Basically the rule just says that’s what you do. It doesn’t say
where you do it, it doesn’t say when you do it, it’s just any time there’s
a lump that looks like this, you can transform it into a lump that looks
like that.

0:43:11.0 SW: And so those transformations can be happening all over this
hypergraph. And so it is not at all obvious that… That is, the only thing
that’s defined is these can happen. The question of when they happen, what
counts as the sort of simultaneity surface, what counts is that moment in
time, is something that’s really in the eye of the observer.

0:43:31.7 SC: Okay. But the updated graph is supposed to represent
spacetime and the things within it, or is it a more subtle map there?

0:43:37.9 SW: No, no. So at any given… What’s happening is this graph is
getting updated, and there are lots of little places where it can get
updated. And you can say, okay, I’m going to consider the graph with this
collection of updates having been done. I’m going to consider that as time
T equals 0, let’s say. And then another situation you’re going to say, now,
I’m going to say this collection of updates is time T equals 1, for
example. And at each one of those time slices, at each one of those sort
of… Well, in the language of physics, spacelike hypersurfaces, that
represents an instantaneous structure of space. But it is somewhat
arbitrary what you consider to be this instantaneous structure of space,
just as it is in general relativity.

0:44:26.9 SC: Well, sure, right. I mean, that’s very familiar from general
relativity, but I’m just saying is the collection of the whole shebang
spacetime, and the things within it?

0:44:35.0 SW: No. It’s just space. A single hypergraph, a single…

0:44:37.6 SC: No, the collection of all the updated hypergraphs, that’s
what I’m asking.

0:44:40.2 SW: Oh, yeah, yeah. Right. The sequence of updates, the
hypergraph together with all its updates is supposed to be spacetime. And
one of the things that is interesting and non-trivial here is most
traditional views of physics have thought of space and time as being the
same kind of thing. In this model they’re really not.

0:45:00.0 SC: Sure.

0:45:00.0 SW: Space is the extent of the spatial hypergraph. Time is the
computational process of updating this hypergraph. So time is the
progression of a computation. Space is just, oh, you follow these
connections in the hypergraph. And so that makes it not at all obvious that
you’re going to get things like relativity out of the model, because one is
breaking apart the traditional connection between space and time.
"""

Anyway, I hope including the transcript here was not too boring.

Cheers,
Jon

[0]
https://www.vox.com/features/2019/11/11/18273141/postmodernism-donald-trump-lyotard-baudrillard

[1] The other part is that this considerable body of work was the
result of serious thought by powerful thinkers. Discounting the whole
body of literature out of hand produces red flags for me.

[2]
https://www.preposterousuniverse.com/podcast/2021/07/12/155-stephen-wolfram-on-computation-hypergraphs-and-fundamental-physics
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