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Jonas I (Feb 06 2025 at 15:08):https://ncatlab.org/nlab/show/Science+of+Logic
Jonas I (Feb 06 2025 at 15:09):seems to me to explain how and why our universe started from nothing, and why string theory is right, whats your opinion
Morgan Rogers (he/him) (Feb 06 2025 at 16:49):I'm pretty sure you're going to have to be more specific. There are tens of thousands of words on that page...
Jonas I (Feb 06 2025 at 19:52):Morgan Rogers (he/him) said:
I'm pretty sure you're going to have to be more specific. There are tens of thousands of words on that page...
Does it explain how our universe started from nothing and the emergence of string theory as inevitable following. I think it does. But my real question is, what does it say about the nature of consciousness and the meaning of life? Hegel wrote alot about that if he is right about that also its interesting
Jonas I (Feb 06 2025 at 19:58):has anyone formalized hegels other theories in hott in a similar vein as scheriber
Jonas I (Feb 06 2025 at 19:58):about consciousness for instance
David Michael Roberts (Feb 07 2025 at 02:03):Jonas I said:
Morgan Rogers (he/him) said:
I'm pretty sure you're going to have to be more specific. There are tens of thousands of words on that page...
Does it explain how our universe started from nothing and the emergence of string theory as inevitable following. I think it does. But my real question is, what does it say about the nature of consciousness and the meaning of life? Hegel wrote alot about that if he is right about that also its interesting
No. Urs is making a rigorous mathematical model of Hegel's framework. It says nothing about actual reality, unless you take as hypothesis that string theory is a model of the real world. It says nothing at all about consciousness, let alone any putative meaning of life. No one that I know of has picked up what Urs has put down, though David Corfield was involved with the discussions somewhat—but I don't see him doing anything like taking the process further into Hegel's work.
David Corfield (Feb 07 2025 at 16:05):I don't think you should look for someone to supply definitive answers to such questions, but if you are looking for what is probably the gentlest way into the system, I'd start with Urs's Laws of Type.
Pablo Donato (Feb 07 2025 at 20:27):David Corfield said:
I don't think you should look for someone to supply definitive answers to such questions, but if you are looking for what is probably the gentlest way into the system, I'd start with Urs's Laws of Type.
That's a nice article, but the interpretation of the function type symbol as corresponding to the severing line in Laws of Form (LoF) feels a little bit forced. It turns out that LoF itself is just a spinoff of C. S. Peirce's existential graphs (see also #learning: questions > Peirce, logic and the categories), or rather of his entitative graphs, which Peirce deemed vastly inferior to the existential graphs.
In the existential graphs, the universe is denoted by empty space which Peirce calls the blank sheet of assertion, and is logically interpreted as trivial truth (the unit type ). Then the existence of something in the universe is denoted by drawing literally a single line (not an arbitrary arrow symbol), called a line of identity.
As for implications/function types, they are denoted by what Peirce calls the scroll, which is a self-intersecting closed continuous curve that looks like this for :
scroll.png
See how it is made of an outer close and an inner close , with two boundaries. Then LoF's "law of crossing" is captured by the law that the two boundaries can collapse when the outer close is empty, corresponding to the logical equivalence . Thus there only needs to be one line/scroll/implication (admittedly not a straight line as in the Kabbalah) to sever the space in two, rather than two implications as in Urs' analysis.
I really recommend reading this from the source, in Peirce's article Prolegomena to an Apology for Pragmaticism (you can read starting from page 533 if you're only interested in the scroll). Otherwise the only freely available source in english that I know of is my own work: there is a short introduction to EGs and the scroll in the first 4 sections of my article on the Flower Calculus, as well as more in-depth exegesis in chapters 9 and 10 of my PhD thesis (section 10.1.1 for the scroll).
Jonas I (Apr 13 2025 at 20:43):I have a question, if I understand correctly, Urs work is a proof that string theory emerges if one start with empty object in a particular kind of topos. But how can one justify philosophically or otherwise that nature preferred this topos over any other topos or logical system ?
John Baez (Apr 13 2025 at 21:13):It's a very appealing topos.
John Baez (Apr 13 2025 at 21:15):Urs is trying to get to M-theory by making mathematical constructions that seem very nice. But M-theory is still undefined, and there's no experimental evidence that's it's a correct description of our universe. So think of this as a work in progress.
Madeleine Birchfield (Apr 13 2025 at 21:33):Jonas I said:
I have a question, if I understand correctly, Urs work is a proof that string theory emerges if one start with empty object in a particular kind of topos. But how can one justify philosophically or otherwise that nature preferred this topos over any other topos or logical system ?
Not string theory. Supergeometry, which is also used for the mathematics of ordinary quantum field theory, is what emerges if one starts with the empty object in that -topos. String theory requires additional assumptions like super-Poincare symmetry, which not all such -toposes satisfy. See e.g.
Applications of graded differential cohesion to non-supersymmetric quantum field theories
Madeleine Birchfield (Apr 13 2025 at 21:36):I find the string theory arguments very unconvincing and I wish that Urs Schreiber would emphasise the connections of his -topos to quantum field theories which actually explain the real world (standard model of particle physics, etc).
John Baez (Apr 13 2025 at 21:56):I thought Jonas was referring to M-theory from the superpoint:
Starting from the simplest possible super-Minkowski spacetime, the superpoint, which has no Lorentz structure and no spinorial structure, we give a systematic process of repeated "maximal invariant central extensions", and show that it discovers the super-Minkowski spacetimes that contain superstrings, culminating in the 10- and 11-dimensional super-Minkowski spacetimes of string/M-theory and leading directly to the brane bouquet.
You may think of this as happening within a -topos, but it requires a lot more than just the "empty object".
Anyway, let's face it: there's no way to "derive" the laws of physics, especially given our current absymal ignorance of fundamental physics, but even in principle. If we knew the right laws we might be able to cook up arguments that make them seem inevitable, and I'm sure people would try that. We might even find arguments now that will help us find the right laws - I think that's what Urs is trying to do. But they involve a series of aesthetic choices, and they in no way prove, using reason alone, that any laws of physics are right.
Jonas I (Apr 13 2025 at 22:25):I was watching the new video by Urs https://www.youtube.com/watch?v=1KUhLHlgG2Q here he emphasises the word proof, anyways I guess he doesnt have the answer to my question either :)
John Baez (Apr 13 2025 at 22:30):Don't watch videos on Theories of Everything if you want precise statements - read Urs' papers.
David Michael Roberts (Apr 14 2025 at 00:39):It's certainly true that Urs proves what he claims, and delineates what is a proposal from what is established rigorously, which is good for string theorists who make simple toy models and then claim certain things they observe about them must be true in general in the string theory they are thinking about.
John Baez (Apr 14 2025 at 00:56):Urs proves a lot of what he claims in his mathematical papers, but Jonas is claiming "Urs work is a proof that string theory emerges if one start with empty object in a particular kind of topos", and that deserves to be questioned. I also was trying to point out that while we can prove mathematical statements, we can't prove by sheer reason that any physical theory is a correct description of our universe.
David Michael Roberts (Apr 14 2025 at 03:00):"Urs work is a proof that string theory emerges if one start with empty object in a particular kind of topos"
Does Urs claim this outright? He might say this in the video, which is non-technical and as you say, @John Baez not to be relied on over the actual papers. It's true that Urs talks up the 'emergence from nothing', but this is window-dressing. The actual technical statements shorn of philosophical sparkle are qualitatively different from things like eg Witten claiming D-brane charges live in K-theory, when it's more of a plausibility argument, rather than some kind of derivation using something like dimensional reduction from 11d.
I'm also on the quietly skeptical side of string theory, but if all this work makes M-theory an actual rigorous mathematical model, then it makes me happy, because then it can be treated seriously. The question of linking it to the real world is a separate step, one I don't expect to happen soon, even if it even is a model of our world.
Madeleine Birchfield (Apr 14 2025 at 12:53):David Michael Roberts said:
I'm also on the quietly skeptical side of string theory, but if all this work makes M-theory an actual rigorous mathematical model, then it makes me happy, because then it can be treated seriously. The question of linking it to the real world is a separate step, one I don't expect to happen soon, even if it even is a model of our world.
If M-theory is made rigourous, it can be treated seriously as a branch of mathematics and potentially applied to other parts of mathematics like Langlands etc... The lack of connection to experiment anytime in the near future makes me sceptical it can be treated seriously as a scientific theory of physics.
John Baez (Apr 14 2025 at 21:31):Before making M-theory rigorous, people need to figure out what it is. I've never seen anyone say what this theory is... well, except for some people who say things I don't believe.
In the various superstring theories we can write down a Lagrangian and a Hamiltonian, we can formulate the classical versions of these theories quite precisely, we can describe the quantum theories in a nonrigorous way, and we can start worrying about making these theories. But in M-theory, while people have a lot of clues about what the theory should be like, I wouldn't say the theory actually exists.
For example, an nLab page (surely written by Urs) says:
The open problem of formulating M-theory
The tight web of hints and plausiblity checks notwithstanding, an actual formulation of M-theory as an actual theory remains an open problem.
This is not outrageous in itself: In [[mathematics]] there are good examples of cases where a collection of situations was or is suspected to be limiting cases of a single unified theory, without that theory itself having been or being known.
One example of this is the putative theory "absolute geometry over the [[field with one element]]". In this [[analogy]], the various [[perturbative string theories]] ([[heterotic string theory|HET]], [[type I string theory|I]], [[type IIA string theory|IIA]], [[type IIB string theory|IIB]] and their [[KK-compactifications]]) correspond to [[arithmetic geometry|arithmetic geometries]] over [[ground field|base]] [[prime field]] for , and the would-be M-theory corresponds to a theory of a "[[field with one element]]" that unifies all this, by describing it at a deeper level (literally: a deeper base).
On the other hand, parts of the physics-minded literature tends to forget or downplay the conjectural nature of many assumptions or leaps of faiths that are being made when it comes to discussion of [[D-brane]]/M-brane dynamics and generally of [[non-perturbative effects]] in string theory.
The following is a collection of quotes from authors that highlight the open problem:
David Corfield (Apr 15 2025 at 06:27):Their work on general principles of mathematical physics is worth noting. Take their position on flux quantization, for instance.
John Baez said:
In the various superstring theories we can write down a Lagrangian and a Hamiltonian, we can formulate the classical versions of these theories quite precisely, we can describe the quantum theories in a nonrigorous way, and we can start worrying about making these theories. But in M-theory, while people have a lot of clues about what the theory should be like, I wouldn't say the theory actually exists. (My emphasis)
Right, so maybe that needs to change:
Traditionally, flux quantization laws have been postulated sporadically and in ad-hoc fashion, in order to patch up “anomalous” theories: Since the ancient past it has been common to define physical theories by stationary action principles embodied by Lagrangian densities, from which perturbative BRST complexes are extracted, whose quantization (e.g. [Henneaux et al. 1992]) is generally afflicted with problems (“anomalies”) some of which are dealt with by ad-hoc flux quantization ...
More systematically, the available choices of flux-quantization laws are algebro-topologically determined by the form of the higher Gauss law on any Cauchy surface, and any such choice, given by a compatible non-abelian cohomology theory, determines the non-perturbative phase space stack of flux-quantized gauge fields. This process makes no reference to Lagrangian densities and applies seamlessly to field theories that do not even have a natural Lagrangian description, such as self-dual higher gauge theories.
Right now they're applying this approach to the fractional quantum Hall effect, see here. Good old down-to-earth physics.
John Baez (Apr 15 2025 at 06:55):I'm not wedded to Lagrangians, but phase space is a classical concept, so "describing the nonperturbative phase space stack" means either describing the kinematics of a classical theory (if the phase space is described in terms of initial data) or possibly the dynamics of a classical theory (if it's described in terms of data given at all times, e.g. solutions of the equations of motion). This is not yet describing the dynamics of a quantum theory, which is what we need in quantum physics.
(The term "flux quantization" just means that for topological reasons certain integrals take discrete values; this happens already in classical physics.)
John Baez (Apr 15 2025 at 07:00):So, while this was perhaps not your intent, what you write does not budge me from my conviction that M-theory is not yet a full-fledged physical theory, just a collection of nice ideas that might someday lead to such a theory. The fact that Urs agrees with this in an article on the nLab (which I quoted earlier) increases my confidence.
The reason I'm so insistent on this is that so many people seem to think there's a theory called "M-theory".
David Corfield (Apr 15 2025 at 07:56):John Baez said:
The fact that Urs agrees with this in an article on the nLab (which I quoted earlier) increases my confidence.
We should probably ask him, but worth noting the formation of that page. It's only right at the very end that 'Hypothesis H' is even mentioned, and that was a late revision. To know what he claims about his own theory, we'd have to look at his own patch of the nlab. So there's a page [[Schreiber: Hypothesis H]] which links, among many other things, to an [[Introduction to Hypothesis H]].
Hypothesis H is described as
a hypothesis on the precise mathematical nature of at least a core part of the theory
It would be interesting to hear his views on what else needs to be there.
I wonder how one would characterize a physical theory as "full-fledged". At what point did GR or QM make the grade? But then maybe a century later we have a better sense of what there needs to be, and can more clearly point out the kind of theoretical thing that's missing, let alone the empirical support part.
David Corfield (Apr 15 2025 at 10:54):I've posed some relevant questions to Urs over here.
Madeleine Birchfield (Apr 15 2025 at 12:33):David Corfield said:
Right now they're applying this approach to the fractional quantum Hall effect, see here. Good old down-to-earth physics.
What they are doing in that approach is applying the mathematics that is being developed in this M-theory research programme to creating new 2+1D quantum field theories which can then be used in physics in the real world.
This I find to be a much better motivation for working on the mathematics of M-theory than anything related to quantum gravity / force unification.
Madeleine Birchfield (Apr 15 2025 at 12:42):John Baez said:
Before making M-theory rigorous, people need to figure out what it is. I've never seen anyone say what this theory is... well, except for some people who say things I don't believe.
From my perspective, M-theory / string theory is a currently underdeveloped subfield of mathematics similar to noncommutative geometry etc. I don't think we are ever going to get experimental confirmation in favour or against M-theory / string theory so we can forget about M-theory as a scientific theory.
Madeleine Birchfield (Apr 15 2025 at 12:48):Urs Schreiber is working in condensed matter / quantum information / quantum computing these days, but most of the other pure string theorists (e.g. Vafa Cumrun, Andy Strominger, Thomas van Riet, etc.) should move over to the mathematics department in my opinion.
Jonas I (Apr 15 2025 at 17:10):Empiricial evidence isnt a 100% proof either, so cant a proof of M-theory using mild assumptions be even better?
Hegel did it by pure reason so maybe we dont need assumptions either.
John Baez (Apr 15 2025 at 17:27):David Corfield said:
I wonder how one would characterize a physical theory as "full-fledged".
I simply meant that it needs to have a kinematics - a description of what can happen - and a dynamics - a description of what does happen. As far as I can tell, M-theory is lacking a dynamics, and Urs is trying to figure out the kinematics.
It's funny how people lose sight of this amid the piles of impressive math, Hegelian philosophy, etc. But it's obvious if you observe what string theorists are doing. If they actually had a candidate for what M-theory is - as a theory with dynamics - everyone would be trying to explain this theory to each other in simpler and simpler terms, and doing lots of calculations with it. But in fact what we have are just some clues, which is a discouraging situation. So there just a few people trying to work with those clues.
If you look at Hypothesis H, it's just a guess about what sort of thing one of the fields in M-theory should be. That's a hypothesis about the kinematics, not the dynamics: i.e., it doesn't say what this field does, just what type of thing it is, and thus what sort of things could happen. It's like Einstein saying gravity should involve the metric on spacetime (which he did, long before formulating general relativity) or Schrodinger saying quantum mechanics should involve a complex-valued wavefunction (but not saying what equation this should obey).
At what point did GR or QM make the grade?
GR made the grade as soon as Einstein presented what we call Einstein's equations to the Prussian Academy of Physics on November 25, 1915. If you've got some equation saying what matter does (and he did), that specifies the dynamics of GR.
QM made the grade as soon as Schrodinger wrote down the time-dependent Schrodinger's equation. I think he first did this publicly in the fourth of his famous papers, received by the Annalen der Physik on June 23, 1926. I could be a bit wrong here, but I believe earlier papers only considered the time-independent equation, and only in this paper did he realize that the wavefunction must be complex! I believe this version only applied to a single particle in a potential, but that's fine: it specifies the dynamics of this situation. (It was soon generalized.)
John Baez (Apr 15 2025 at 17:40):Jonas I said:
Empirical evidence isn't a 100% proof either, so can't a proof of M-theory using mild assumptions be even better?
As I've tried to explain in my series of comments here, M-theory does not exist yet so there's no way to prove it.
John Baez (Apr 15 2025 at 17:43):Remember, Urs wrote this:
The open problem of formulating M-theory
The tight web of hints and plausibility checks notwithstanding, an actual formulation of M-theory as an actual theory remains an open problem.
John Baez (Apr 15 2025 at 17:43):It's not an actual theory yet.
John Baez (Apr 15 2025 at 17:46):I just explained to David more precisely what I mean by that.
Madeleine Birchfield (Apr 15 2025 at 17:53):Jonas I said:
Empiricial evidence isnt a 100% proof either, so cant a proof of M-theory using mild assumptions be even better?
In that case, you are just left with a mathematical proof with no connections to experiment, so the theories belong to mathematics and philosophy rather than to science.
Madeleine Birchfield (Apr 15 2025 at 18:00):Anyways, after some discussion with Urs Schreiber and Alonso Perez-Lona on the nForum, I think that the supersymmetric M-theory conjectured in the 1980s is dead in the water, and the string theory community as a whole is moving away from supersymmetry towards other symmetry principles such as those based on the or Kac-Moody algebras.
Madeleine Birchfield (Apr 15 2025 at 18:02):Whatever the conjectured M-theory ends up being will likely end up looking very different from the string theory of today. I also doubt it would still be called "M-theory" if it ends up being too different from string theory.
John Baez (Apr 15 2025 at 20:12):You're reminding me of a joke.
"I don't know what the Theory of Everything will be like, but I know what it will be called: string theory."
That's because as long as string theorists are around, whatever works they'll want to call string theory. For example now AdS/CFT is often considered "string theory".
David Michael Roberts (Apr 16 2025 at 08:17):*Quantum computation in solid state physics looking at quasiparticles under hypothesis H will be called M-theory
Madeleine Birchfield (Apr 16 2025 at 12:26):At least for the and programs, it is still string theory - the fundamental objects of the theory are still strings and higher membranes. The thing is that for these new conjectured theories, if I understand correctly, apart from the lack of super-Poincare symmetry, gravity and supergravity are no longer fundamental, but rather emergent from the degrees of freedom that actually exist inside of the theories.
Madeleine Birchfield (Apr 16 2025 at 12:27):I finally understand why there's been so much hype in the popular science media recently about how we need to replace spacetime with something more fundamental.
John Baez (Apr 16 2025 at 18:08):Who is working on those and programs besides Hermann Nikolai and his collaborators like Thibault Damour, Sophie de Buyl, Marc Henneaux and Christiane Schomblond? I wrote about their work here in 2013:
John Baez (Apr 16 2025 at 18:13):That was a long time ago. They showed that in 11d supergravity, if you run time back toward the big bang in certain cosmologies, the shape of space would change chaotically in a way that gets closer and closer to the motion of a billiard ball on a 9-dimensional billiard table shaped like one fundamental domain for the action of the Coxeter group on 9d hyperbolic space. Later Nicolai has claimed that this is evidence for some role of in the super-early universe, "before spacetime".
The mathematical result is beautiful, but since I don't believe in 11d supergravity I don't consider it very significant for physics, and I don't believe Nicolai's claim since it's mainly based on mathematical elegance: it would be beautiful if something like this were true.
Madeleine Birchfield (Apr 17 2025 at 00:48):John Baez said:
Who is working on those and programs besides Hermann Nikolai and his collaborators like Thibault Damour, Sophie de Buyl, Marc Henneaux and Christiane Schomblond?
I'm not sure who else is working on and but Urs Schreiber said on the nForum that and are the most likely routes to connecting his work on Hypothesis H etc with the matrix models and quantising gravity in string theory.
John Baez said:
They showed that in 11d supergravity, if you run time back toward the big bang in certain cosmologies, the shape of space would change chaotically in a way that gets closer and closer to the motion of a billiard ball on a 9-dimensional billiard table shaped like one fundamental domain for the action of the Coxeter group on 9d hyperbolic space. Later Nicolai has claimed that this is evidence for some role of in the super-early universe, "before spacetime".
Today Nicolai is claiming that going beyond spacetime with is a result of his trying to modify Gell-Mann's 1983 failed attempt to get the standard model to embed into supergravity:
John Baez said:
The mathematical result is beautiful, but since I don't believe in 11d supergravity I don't consider it very significant for physics, and I don't believe Nicolai's claim since it's mainly based on mathematical elegance: it would be beautiful if something like this were true.
I also don't really care about supergravity as a theory for physics, mostly because it can't be experimentally tested today and I'm really sceptical these days of theories that predict new particles that we haven't detected / can't detect yet.
Alex Kreitzberg (Apr 30 2025 at 22:13):The linked articles gave me some thoughts.
To indicate the absence of something, we usually specify a set without symbols , or set with "nothing" in it.
So if we hold we can have a box with nothing in it, then we can have a box holding a box with nothing in it: . So now that's at least something.
So from nothing we get something.
With certain rules about how we're allowed to build containers of stuff, we then "get everything".
And of course this isn't a theory of physics. Because of Baez's clarifying comment, we need to specify a kinematics and a dynamics. This is just a math foundation, the physical theory is as underdetermined as possible.
It is kinda fun that at least for algebraic stuff the line between nothing, something and everything is razor thin, with roads going both ways.
I'm sure the empty set being dual to the singleton set, plays some role here.
Jonas I (May 01 2025 at 20:50):I think mathematical reasoning will become more accepted as a science. Popper definition of science is getting outdated. Mathematics and physics will merge. There are other ways then experiment to assess truth about the real world.
Kevin Carlson (May 01 2025 at 21:26):This reminds me a bit of a post I saw sometime that theorized that the viola is soon going to be obsoleted from the symphony orchestra in favor of first and second cellos...