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Aurelio Carlucci (Apr 14 2020 at 18:16):Has anyone properly read about the Wolfram Physics Project? It appears to me there is some homotopy theory machinery involved, although it is not formulated in this language.
John Baez (Apr 14 2020 at 18:22):Oh?
Fabrizio Genovese (Apr 14 2020 at 18:23):Aurelio Carlucci said:
Has anyone properly read about the Wolfram Physics Project? It appears to me there is some homotopy theory machinery involved, although it is not formulated in this language.
Lol, he just emailed me his blog posts about this today xD
Fabrizio Genovese (Apr 14 2020 at 18:24):I think some of the insights they have are interesting, but I didn't find the time to dive into details yet
Aurelio Carlucci (Apr 14 2020 at 18:25):Is is being presented in a live stream right now. I would describe as describing processes by adjoining cells.
Fabrizio Genovese (Apr 14 2020 at 18:25):The rough outline seems to be that they want to derive foundations of physics from some simple computational axioms. I don't think it's that crazy, especially considering how geometry, logic and computation are deeply intertwined. But yes, I agree: Many of the ideas he has would benefit a lot from a categorical presentation.
Aurelio Carlucci (Apr 14 2020 at 18:29):Thanks Fabrizio Genovese, I agree with your description.
The rough outline seems to be that they want to derive foundations of physics from some simple computational axioms. I don't think it's that crazy, especially considering how geometry, logic and computation are deeply intertwined. But yes, I agree: Many of the ideas he has would benefit a lot from a categorical presentation.
My point, on which I would welcome the opinion of people more expert than me, is that these simple computational axioms are (not necessarily invertible) cells in some homotopic setting.
Fabrizio Genovese (Apr 14 2020 at 18:31):I think they are just lambda terms in the lambda calculus corresponding to the internal logic of whatever topos you are working in
Fabrizio Genovese (Apr 14 2020 at 18:31):Me and @Matteo Capucci are actually pursuing exactly this idea for studying something else
Fabrizio Genovese (Apr 14 2020 at 18:32):I guess our intuitions actually coincide if you take such topos to be very high-dimensional :P
Fabrizio Genovese (Apr 14 2020 at 18:32):This is also related to a tweet by @Jules Hedges of few days ago, btw
John Baez (Apr 14 2020 at 18:37):Yeah, it could be connected to homotopy theory slightly somehow.... but not much more than everything else, unless someone develops the connection a lot more.
John Baez (Apr 14 2020 at 18:38):It looks like Wolfram is shooting in the dark and engaging in a publicity blitz to get the pop science media to give him some attention. He emailed me too - so don't think you're special, Fabrizio. :upside_down:
He probably emailed 1000 people.
Fabrizio Genovese (Apr 14 2020 at 18:41):John Baez said:
It looks like Wolfram is shooting in the dark and engaging in a publicity blitz to get the pop science media to give him some attention. He emailed me too - so don't think you're special, Fabrizio. :upside_down:
He probably emailed 1000 people.
It may well be, yes
John Baez (Apr 14 2020 at 18:43):I got emails yesterday both from him and his publicity agent, Justin Klug:
Dear John:
I hope this message finds you safe and well.
Stephen Wolfram will be announcing an ambitious physics project in the coming days. We’re just giving a few journalists an early heads-up, as this project may be something that you find interesting. A draft of the beginnings of the announcement publication is attached for background, but please keep it confidential for now.
Please let us know if you’d like additional information or the details for the livestreamed launch.
Best regards,
Justin
Ho hum. :zzz:
Aurelio Carlucci (Apr 14 2020 at 18:48):Thank you John Baez. Maybe the statement
We’re just giving a few journalists an early heads-up,
was rather sensationalist.
Daniel Geisler (Apr 14 2020 at 18:51):Wolfram's current work reminds me of what Smolin was doing with posets twenty years ago.
Joe Moeller (Apr 15 2020 at 16:08):It could be that @Fabrizio Genovese and @John Baez are both special. I didn't get an email :stuck_out_tongue_wink:
Fabrizio Genovese (Apr 15 2020 at 16:09):Well, I have to say the blogposts were way better than the talk. I saw a part of the streamed video on YT and it was...
Fabrizio Genovese (Apr 15 2020 at 16:10):Well let's just say that in the beginning I really put a lot of effort to understand if some of the things he was presenting could be rephrased categorically. After a bit tho it was just sad, honestly
Reid Barton (Apr 15 2020 at 16:21):There's supposed to be a more technical session today, I think.
Fabrizio Genovese (Apr 15 2020 at 16:23):I think I'll skip (there's also Jules talk in like 40 mins, right?)
John Baez (Apr 15 2020 at 18:37):Joe Moeller said:
It could be that Fabrizio Genovese and John Baez are both special. I didn't get an email :stuck_out_tongue_wink:
Wolfram had talked to both of us about Petri nets, it turns out... so he probably sent out emails to everyone he talks to.
Amar Hadzihasanovic (Apr 16 2020 at 10:31):So according to Wolfram's hypothesis the fundamental structure of the universe is a hypergraph rewrite system.
I hope this gains traction so I can apply for theoretical physics grants to work on higher-dimensional rewriting.
Jules Hedges (Apr 16 2020 at 10:34):Since rewriting is kinda like homotopy, makes me wonder if he's secretly trying to reinvent higher homotopy theory.....
Amar Hadzihasanovic (Apr 16 2020 at 10:35):And not only that, there are also modern mathematical ideas—geometric group theory, higher-order category theory, non-commutative geometry, geometric complexity theory, etc.—that seem so well aligned that one might almost think they must have been built to inform the analysis of our models.
<< oh he even mentions higher categories
Jules Hedges (Apr 16 2020 at 10:38):Does Wolfram-the-company or Wolfram-the-person fund external researchers? Several people around here are working on higher dimensional rewriting, might be eligible for funding if so
Morgan Rogers (he/him) (Apr 16 2020 at 10:38):Amar Hadzihasanovic said:
So according to Wolfram's hypothesis the fundamental structure of the universe is a hypergraph rewrite system.
I hope this gains traction so I can apply for theoretical physics grants to work on higher-dimensional rewriting.
What are people's thoughts on this? Has anyone here subscribed to his project? Does it hold water or has Wolfram gone mad with (computational) power?
Amar Hadzihasanovic (Apr 16 2020 at 10:45):Based on what I understand about the guy and the company, my guess is: “you may try to pitch an idea to him, and he may give you some money to work on it, there isn't any kind of formal request and/or evaluation”
Amar Hadzihasanovic (Apr 16 2020 at 10:49):https://www.wolframphysics.org/help/
<< this seems to confirm -- a list of “research directions” and then just some email addresses :)
Jules Hedges (Apr 16 2020 at 10:50):"Higher-order category theory, topos theory and geometric group theory are examples of relevant areas" ...... doesn't seem to be any mention of them giving out money though, more like the opposite
Jules Hedges (Apr 16 2020 at 10:51):Ah, at the bottom, I see
Fabrizio Genovese (Apr 16 2020 at 10:52):Jules Hedges said:
Does Wolfram-the-company or Wolfram-the-person fund external researchers? Several people around here are working on higher dimensional rewriting, might be eligible for funding if so
I'd be careful with taking money from Wolfram. There are multiple sources pointing out how they can be _very_ aggressive wrt the intellectual property of your research
Fabrizio Genovese (Apr 16 2020 at 10:53):There's a big controversy around a new kind of science, for instance, where a guy figured out some of the mathematical results in there, and couldn't even claim to have done so
Fabrizio Genovese (Apr 16 2020 at 10:53):Like, the story seems to be that Wolfram jumped in and claimed the results as his.
Amar Hadzihasanovic (Apr 16 2020 at 10:55):Sounds like the old Disney comic books being all credited to Walt Disney himself
Amar Hadzihasanovic (Apr 16 2020 at 10:56):“Stephen Wolfram: the Walt Disney of mathematics”...
Fabrizio Genovese (Apr 16 2020 at 10:56):Yes, so i mean, if they provide some form of funding/grant it's worth to look into them. But I'd be very careful with reading all the fineprint conditions
Morgan Rogers (he/him) (Apr 16 2020 at 10:57):Amar Hadzihasanovic said:
“Stephen Wolfram: the Walt Disney of mathematics”...
He certainly animates things...
Fabrizio Genovese (Apr 16 2020 at 10:57):"Being dragged in court by a multi-billion enterprise" is very low on my current list of priorities :P
Daniel Geisler (Apr 16 2020 at 10:58):Yeah, Mathew Cook proved rule 110 was universal but he had signed a non-disclosure agreement. So Cook goes to a conference and is told he can't present his research.
Jules Hedges (Apr 16 2020 at 10:59):Amar Hadzihasanovic said:
And not only that, there are also modern mathematical ideas—geometric group theory, higher-order category theory, non-commutative geometry, geometric complexity theory, etc.—that seem so well aligned that one might almost think they must have been built to inform the analysis of our models.
<< oh he even mentions higher categories
What the heck does he think geometric complexity theory have to do with physics? :thinking:
Jules Hedges (Apr 16 2020 at 11:00):The other things sound like physics adjacent, but that one seems to be thrown in just for hype
Amar Hadzihasanovic (Apr 16 2020 at 11:01):Well, a part of it seems to be just “this is so fundamental that it must connect to all the deep unsolved problems”
Amar Hadzihasanovic (Apr 16 2020 at 11:02):But trying to take it seriously, I think it connects to a bit in the end of his blogpost
Fabrizio Genovese (Apr 16 2020 at 11:03):Well you know how these things work. You give a ton of money to everyone researching into things that are even tangentially connected with the goal he has in mind, and hopefully among all these people there will be a few that will actually obtain a breakthrough
Amar Hadzihasanovic (Apr 16 2020 at 11:03):The essential idea seems to be: this model of physics has the Church-Turing thesis in-built, because the universe “is” a computer, modelled as a rewrite system
Amar Hadzihasanovic (Apr 16 2020 at 11:03):So then he asks, how do we find out which rewrite system
Amar Hadzihasanovic (Apr 16 2020 at 11:04):And he says: well, most of them are going to be universal computers, hence they are all computationally equivalent
Amar Hadzihasanovic (Apr 16 2020 at 11:05):So maybe we can avoid choosing, and say all (universal?) rewrite systems can apply
Fabrizio Genovese (Apr 16 2020 at 11:05):Yes, but aside of this, can we talk about the fact that the last YT video was really well beyond borderline crackpot science? :confused: I always found the idea of explaining physics from a computational point of view very intriguing and fascinating.Still, many of the things presented were a stretch to say the least.
Amar Hadzihasanovic (Apr 16 2020 at 11:06):And that this generates a kind of additional dimension of “computational space” corresponding to the different “computational gauges”
Amar Hadzihasanovic (Apr 16 2020 at 11:06):Bla bla maybe this space has some interesting geometry that connects to complexity theory (this sounds like wishful thinking of course)
Amar Hadzihasanovic (Apr 16 2020 at 11:08):Fabrizio Genovese said:
Yes, but aside of this, can we talk about the fact that the last YT video was really well beyond borderline crackpot science? :/ I always found the idea of explaining physics from a computational point of view very intriguing and fascinating.Still, many of the things presented were a stretch to say the least.
I haven't watched the videos! I guess the blogpost must have been edited to remove most of the crackpottery. ;)
Amar Hadzihasanovic (Apr 16 2020 at 11:09):It's waffly and has an enormous amount of handwaving and wishful thinking, but doesn't go into crackpot territory, I'd say.
Fabrizio Genovese (Apr 16 2020 at 11:12):The blogposts are more refined, the YT video was really something tho
Fabrizio Genovese (Apr 16 2020 at 11:13):In any case, I'd wait for some experienced physicist to chime in, review the general idea, and give me an informed opinion. I don't know enough about modern physics to come up with an informed judgement :slight_smile:
Amar Hadzihasanovic (Apr 16 2020 at 12:47):Why isn't Stefano Gogioso here? He must have an opinion.
Fabrizio Genovese (Apr 16 2020 at 13:18):I told him at least a couple of times to join, but he didn't!
Philip Zucker (Apr 16 2020 at 13:48):My immediate impulse was an uncharitable one, but the website is fun. The connection to actual physics seems very sketchy. Maybe we are in a time ripe for a mathematical leap, although I'm rather doubtful this is it. There are a couple of concepts out there that people are somewhat sure are right in some conceptual sense. Optimistically, we could be compared to the old quantum period, with piles of basically the right idea, waiting for whatever screw went loose in Heisenberg to make the leap he did.
Fabrizio Genovese (Apr 16 2020 at 13:56):I think the "future" will be something toposy. That's because toposes provide an unified environment for geometry, logic and computation. So if all these different ways to interpret physics can be combined, a topos of some sort is the most obvious environment to do so.
Philip Zucker (Apr 16 2020 at 14:46):I see the appeal, but I think I would be rather disappointed if that were the case. That sounds like a mathematician's dream for physics. Would some topos thing enable a new prediction or calculate some new number? It seems like you'd have to shred off all that machinery to get down to the concrete level. I could be wrong of course.
sarahzrf (Apr 16 2020 at 14:47):Would some topos thing enable a new prediction or calculate some new number?
yes!
sarahzrf (Apr 16 2020 at 14:48):there are topoi where everything is computable, for one
sarahzrf (Apr 16 2020 at 14:48):working in a topos could mean that everything is more computable
Philip Zucker (Apr 16 2020 at 14:51):What does computability mean in regards to physics? I feel like the issue in many physics problems is not computability but rather complexity/intractability.
Morgan Rogers (he/him) (Apr 16 2020 at 14:55):Toposes seem big, overly abstract and scary to anyone who hasn't been gently introduced to them, but the major advantage of them (imo) is that many constructions that have classically been obtained in an ad hoc way in maths find themselves realised "concretely" (as far as that adjective can be applied to topos theory :joy:) or have natural expressions in terms of toposes.
Philip Zucker (Apr 16 2020 at 14:58):Is it a sensible question to ask what electromagnetism is from a topos perspective? This sounds like a non sequiter. If topos theory is a foundation for mathematics, then there must be PDEs bumping around somewhere in there, but I don't really see how it could inform physical questions
Philip Zucker (Apr 16 2020 at 15:00):I would love to be enlightened, btw. New ways to think about old things is quite nice.
Morgan Rogers (he/him) (Apr 16 2020 at 15:02):I'm yet to be shown a convincing attempt, or even a convincing roadmap, to the application of topos theory in theoretical physics, but it's certainly something that my colleagues in Como are thinking about. One reason for thinking it could or should be a good approach is the success of abstract geometry in physics, and the success of topos theory in geometry (in the context of algebraic geometry and cohomology theories).
Philip Zucker (Apr 16 2020 at 15:09):Ok. That sounds reasonable
Dan Doel (Apr 16 2020 at 15:09):So, for instance, this paper suggests that synthetic differential geometry avoids some issues that occur with singularities.
Dan Doel (Apr 16 2020 at 15:15):Being computable might not be a match for physics, but there are mathematical settings (which can be viewed as other toposes or what have you) that are a better match for computable mathematics than classical set theory. So it doesn't seem like a huge stretch that there would also be better settings for physical mathematics. And working in a better setting might make it easier to figure things out, or ask good questions.
Gershom (Apr 16 2020 at 16:19):When people talk about topos theory, we need to distinguish between "the theory of elementary toposes" and "the theory of grothendieck toposes". For the latter, since they are simply categories of sheaves, then topos-theoretic technology arises pervasively in the underlying machinery of modern approaches to theoretical physics, no? As soon as you're working with vector bundles there's some stuff you can think of from a topos perspective lying around (whether or not doing so buys you much immediately is a different question).
This paper from Urs also sets out how some modern physics machinery might look in an infinity-topos: https://arxiv.org/abs/1310.7930
Philip Zucker (Apr 16 2020 at 16:32):oh my. That's 800 pages long.
Dan Doel (Apr 16 2020 at 16:55):Perhaps a simpler example, which doesn't necessarily get you anything new, but may be illustrative...
There are lots of tricks physicists do with differential and integral stuff that you hear some mathematicians complaining about, because they're not 'technically correct' or something, even though they work in physical scenarios. My vague understanding is that most/all of these actually are justified in SDG, and it might even justify similar but fancier tricks that physicists haven't thought of. So one might instead say that the complaints of correctness are unjustified, because they are based on studying the wrong foundational system for physics.
Morgan Rogers (he/him) (Apr 16 2020 at 16:57):Gershom said:
When people talk about topos theory, we need to distinguish between "the theory of elementary toposes" and "the theory of grothendieck toposes".
This distinction is important historically but just a matter of perspective today, since Grothendieck toposes are just those elementary toposes bounded over . And given that quantum logic isn't classical, it might be sensible to expect that a judicious choice of base topos other than classical sets could provide a better foundation. Another great thing about topos theory is that as long as we work constructively, any argument that works for a topos of -valued sheaves on a space will carry across verbatim for a topos of -valued sheaves; and identifying the arguments that aren't valid constructively and the extent to which they fail in the context of would highlight how geometry behaves differently from our classical expectations.
John Baez (Apr 16 2020 at 17:08):Jules Hedges said:
Does Wolfram-the-company or Wolfram-the-person fund external researchers? Several people around here are working on higher dimensional rewriting, might be eligible for funding if so
Yes, he funds researchers and makes them sign nondisclosure agreements so their research is kept secret until it's deployed. Wolfram sued Matt Cook for breaking one of these nondisclosure agreements. So, your friends should read that story before trying to get a job with Wolfram.
John Baez (Apr 16 2020 at 17:17):Here's a quote. All this stuff is true to the best of my knowledge (I'm good friends with a good friend of Matt Cook). Matt Cook proved, while employed by Wolfram, that cellular automaton rule 110 is computationally universal:
basically, apparently wolfram SUED his own employee, matthew
cook, over the CA 110 proof. from what I can piece together
(some of this may not be exact) cook formulated and wrote up the proof
completely in a paper that was also available on his web site,
maybe around 1995, and apparently even presented it at a CA
conference. the paper was submitted for publication in
the book New Constructions in Cellular Automata coedited by
chris moore, who reviewed the proof & accepted it.http://www.amazon.com/exec/obidos/ASIN/0195137175/
however apparently wolfram obtained a COURT ORDER against cook to stop
publication of the paper (or something like that),
at which point the CA book was delayed
and eventually released without cook's proof,
"one of the most interesting results presented at the conference" acc.
to SFI web site.the paper was yanked from the web site also. apparently wolfram claims
it was a "trade secret". I actually tracked down the case number
on the LA civil complaint via the web (see below), maybe someone can get
more info on it, I assume it is part of the public record.
John Baez (Apr 16 2020 at 17:18):One moral: don't sign contracts you don't intend to obey.
Jules Hedges (Apr 16 2020 at 17:20):Ah, I was getting mixed up with Stephen Cook, who (arguably) invented complexity theory
Nathaniel Virgo (Apr 16 2020 at 17:35):They also used threats of legal action to prevent third parties from citing his proof, according to the story as told by Cosma Shalizi here.
Philip Zucker (Apr 16 2020 at 18:01):Hmm. I suppose this https://ncatlab.org/schreiber/show/Synthetic+variational+calculus might have some bearing on one of my objections, not that I understand it.
Morgan Rogers (he/him) (Apr 16 2020 at 18:18):Nathaniel Virgo said:
They also used threats of legal action to prevent third parties from citing his proof, according to the story as told by Cosma Shalizi here.
I enjoyed reading this very much, thanks for sharing.
John Baez (Apr 16 2020 at 18:22):Nathaniel Virgo said:
They also used threats of legal action to prevent third parties from citing his proof, according to the story as told by Cosma Shalizi here.
Ah, that's the account I was actually looking for.
Wolfram also threatened to sue Lee Smolin when the latter began exploring models of spacetime based on graph rewriting. Nothing ever came of that, though.
Amar Hadzihasanovic (Apr 16 2020 at 18:34):Sounds like the average “visionary tech entrepreneur” except he tried to patent mathematical ideas instead of design ideas.
Amar Hadzihasanovic (Apr 16 2020 at 18:35):(Including the fact that they were not originally his)
Amar Hadzihasanovic (Apr 16 2020 at 18:37):I wonder if the model of quantum systems in the “new” theory of physics is still a local hidden variable model, like Shalizi mentions the “old” one is? That would be quite damning.
Ben MacAdam (Apr 21 2020 at 18:35):Dan Doel said:
So, for instance, this paper suggests that synthetic differential geometry avoids some issues that occur with singularities.
I would probably look at Dominic Joyce's work on schemes if you want a framework for doing actual calculations in a model of synthetic differential geometry, he has developed many of the tools that algebraic geometers work with. I think he's using this stuff in his current work on actual differential/symplectic geometry, which is pretty exciting.
https://arxiv.org/pdf/1001.0023.pdf
https://people.maths.ox.ac.uk/joyce/Kuranishi.html