You're reading the public-facing archive of the Category Theory Zulip server.
To join the server you need an invite. Anybody can get an invite by contacting Matteo Capucci at name dot surname at gmail dot com.
For all things related to this archive refer to the same person.
Ben Sprott (Oct 25 2024 at 14:15):I have a new paper I have put together. It essentially outlines a proof that is a no-go theorem for classical spacetimes (causal structures) of quantum systems. You can find it here. It would be great to hear any discussion about it. I will try to answer any questions, but like always, fatherhood and running my startup make it so, so difficult to keep up with the really technical points that get raised. I want to thank the community for being understanding of my, at times, unprofessional posting.
Jean-Baptiste Vienney (Oct 25 2024 at 15:39):I think it would be good for you that you understand why your paper is not something that will be considered by a mathematician as a serious math paper that is as something which could be published in a math journal. In fact unfortunately we are very far from that! Even as part of an undergrad/master/phd thesis, it would be very problematic!
Maybe there are interesting ideas, but a few things will make any mathematician (and also PhD students apparently!) trying to read it crazy. Two big points are:
(1) It is absolutely not rigorous!
(2) It is written in a (very) pretentious way!
Jean-Baptiste Vienney (Oct 25 2024 at 15:40):But I want to say that maybe there are interesting ideas. I can't really say because it is very difficult for me to read it because of the above points.
Jean-Baptiste Vienney (Oct 25 2024 at 15:59):Maybe you could try to address the two above points and then it will be easier to discuss about the new version.
Jean-Baptiste Vienney (Oct 25 2024 at 16:02):It would be good if you used numbered definitions-propositons-proof-examples etc… as in any math paper.
Jean-Baptiste Vienney (Oct 25 2024 at 16:05):Here we only have one numbered definition and not any numbered propostions, proofs, examples!
As such it looks more like a blog post than a math paper.
Ben Sprott (Oct 25 2024 at 16:25):@Jean-Baptiste Vienney Thank you for your critique. This will help me to improve the paper greatly. My worry, as an armchair applied mathematician, is that there are bigger problems that need to be addressed.
Jean-Baptiste Vienney (Oct 25 2024 at 16:42):These are already big problems! When I read the sentence
"This paper is going to use one of the most advanced mathematical results of 2024 to prove something surprising.", I immediately enter into "reject mode" and don't want to read what's after.
Jean-Baptiste Vienney (Oct 25 2024 at 16:45):The issue is that when I read this I a doubt a lot that
(1) you're going to use one of the most advanced mathematical results of 2024 in a correct way,
(2) you will prove something surprising in this way.
The reason is probably that we would never find in a paper which use one of the most advanced results of 2024 in a correct way to prove something surprising a sentence like this. Because such a person would be a well-established mathematician and it is not in the customs to write like this in the academic community. The paper will just prove the surprising thing in an humble way.
And how could you use a very advanced mathematical result in such a short paper? And without any proof, let alone any proposition written in the conventional way?
Jean-Baptiste Vienney (Oct 25 2024 at 16:53):Do you really think that your paper use one of the most advanced mathematical results of 2024 to prove something surprising?
Kevin Carlson (Oct 25 2024 at 18:19):It's particularly annoying that you claim you're going to prove the past doesn't exist, which would indeed be surprising, but in the body of the paper you describe this result as "facetious", i.e. you don't really mean it. So what do you mean? What, if anything, do you think you've proved?
Ben Sprott (Oct 25 2024 at 19:46):@Kevin Carlson @Jean-Baptiste Vienney Hi, yes, sorry about this. I am not sure what mood I was in when I wrote this. I see the proof as very simple. It's all that I am capable of right now. I think John Baez has said that CT proofs can come out very simple after a bunch of definitions. Perhaps that applies. I believe that the outline in the paper is enough for good researchers to begin drawing their own conclusions based on some good facts and the application I give.
Jean-Baptiste Vienney (Oct 26 2024 at 12:45):@Ben Sprott What is the partial monoidal product on the category of monads on ? If you’re talking about the composition of monads, when you have a distributive law, it would be better:
Jean-Baptiste Vienney (Oct 26 2024 at 12:47):Moreover, you should delete everything which says that monad are a highly advanced concept etc… Monads are one of the basic concepts of category theory.
Ben Sprott (Oct 26 2024 at 13:29):@Jean-Baptiste Vienney yes, this has to go. Thank you!
Ben Sprott (Nov 13 2024 at 03:40):I cleaned up the paper and put it on researchgate here.
David Michael Roberts (Nov 13 2024 at 08:24):In future work we need to define a distributive law that provides for the composition of the two mentioned monads, pointed cyclic list and multiset.
This should be proved before you go any further, since everything that follows that relies on could be vacuous. Stating almost immediately afterwards
This is modeled by the fact that, since is a monad, then...
You literally cannot claim this as a (justification for a) fact, since you have deferred the proof. At best one would flag this as entirely conjectural. And that really undermines the confident statements about proving things about reality (which, incidentally, mathematics alone has a hard time doing, to say the least)
We have a monad structure,
what monad structure? Write it down, or it didn't happen. The ingredients are so concrete one should be able to do this.
We have it that our monad composition is thus:
Really? This is still conjectural, and you haven't said anything yet.
Let us assume that you could have a “Domain Comonad”, DOM, that gives subdomains as histories.
but what is this? What properties do you think it has? What is the category it is an endofunctor on?
If we take our simple model of quantum systems, we should be able to imagine a spacetime which is a domain of quantum systems “residing” at each point in spacetime. The model is simple: at every point in spacetime, there is sitting some quantum system
what does this even mean? I'm not sure this is consistent with quantum theory, in particular with things like the uncertainty principle (talking vaguely here, because I'm responding to things that aren't precise enough to rigorously unpack). What do you mean by a quantum system here? Your definition had better encompass what physics thinks is a quantum system in all possible variants, or your result would only apply to your own definition.
By the way, how is the pointed cyclic list monad different from the list monad? It seems to me like they might be isomorphic, but I'm not claiming this is true, because I have things I need to do for my day job, but it should be something one can write down if true.
This paper is not a philosophy paper.
I'm afraid it is. Or at least, it's closer to a philosophy paper rather than a maths paper, and I know that there are branches of philosophy that are more pedantic than mathematicians.
Jean-Baptiste Vienney (Nov 13 2024 at 12:15):Ben Sprott said:
I cleaned up the paper and put it on researchgate here.
I must say I think this is strictly better than the first version. Now, I also agree with all the suggestions given by David for further improvement.
Jean-Baptiste Vienney (Nov 13 2024 at 12:19):(Clearly, they should be adressed if you want it to be closer from what is usually considered “a math paper”.)