Diagrammes et categories — Part 2

0:00 Now, I think that if Maclean had chosen a different category, I think that the relationship would have existed. Besides, it would have been a very good book, and it's not when we talk about categories that the others decide, there are a few that I agree with. So, I don't think it's a good book, but in any case, I think that it's a good book. It's the same thing, because what's aimed at mathematics, in terms of categories, is the same as what's aimed at physics. We have categories that we can work on, we have categories that are not an example of mathematics. But when we do that, we have to continue, because it makes sense. And for us, it's something else. Not necessarily. For a mathematician, I would say that I am very happy to see an example, an example of a category that I can give to my students, which is not vector space and linear application, which is something else. Here is a category of musical objects. And then, the morphisms. These are all the relations between the values ​​of the realizations, at Artis and at Cornell, etc. And now we're going to talk about the musicals. We have already done something rather post-harmonic.

2:30 The objects are quite general in this theory, but to simplify it, we will take small notes to expand it. This is a very good example that allows us to have a real approach to the category theory, on the other hand, it is a very good example that allows us to have a real approach to the category theory, on the other hand, it is a very good example that allows us to have a real approach to the category theory, on the other hand, it is a very good example that allows us to have a real approach to the category theory, The categories that are used are essentially the monoidal categories, that is to say that we are interested in the products in the field, we add the products in the field, we talk about that, and therefore the categories that come from the nodes, I do not think that it seems very difficult for me to use that. For the music, what I did in music was something very interesting because when you take serial music and you have the two sounds, the way to place the two sounds, it's a point in the set of permutations and then you can build. There is a node that has six double points, which is associated with the theory, and this node has a number of bodies that come into contact with each other, and we place the two sounds on the circles, and we have a line that goes on and on and on and on and on and on and on and on and on and on and on and on and on and on and on and on and on and on and on and on and on and on and on and on and on and on and on

5:00 Introduce a problem, I mean, if we have a physical approach to a game. No, I don't mean that. I'm sorry, I'm sorry. So for the moment, it's just analogies. There is no other way. Well, just one thing, musical theory is also a mathematical theory that has... We don't have to do aesthetics, for example, without being... Minimalism is used for the purpose of understanding the physical world and the place of objects. What I think is really important is to understand these concepts and to see that there are more and more relations between them, and that some parts of them are pleasant and some parts are unpleasant. Each concept is related to the other, and now the goal is simply a diagram, and the objective is precisely to understand what is the engine of what we can do.

7:30 I don't want to take up too much of my time to say that it's a pleasure for me to read this thesis, not because, as it has been said, it is very rich, very dense, too dense, in any case, and the pleasure is augmented by the fact that Franck belongs to CEVA, and I know that in this institution, the effort to try to think... Practicals are the others. Mathematics and physics are not particularly encouraged. And even if there is no relationship of cause and effect between the work of Ferrer and the work of Franck, I would like to conclude that, in any case, it is imminent, we are two. So, we may have... Simply... I'm going to talk about the thesis in three parts. The first part is about the diagrams, and I read it with a lot of attention because it enlightened me about the fact that we physicists, when we teach physics, or when we practice it, we put the diagram in general in the background of the theory, in terms of topology, and these are the arguments that are sometimes found in this part of the thesis. The diagram shows that the diagram actually has its place in the center, in the center of life, and that the fact of secondaryizing it permanently, either as a calculation, or as a metaphor, or as an analogy, makes it lose its essential quality, which is very well explained in these hundreds of balls. Well, we know that the diagram occupies a decisive place in the elaboration and completion of the theoretical theory. The question of the imagery that the formalism will then answer can outline the solution of a problem and the role of the interface between the virtual and the virtual. But there is also an aspect of the theorem that is not explained in this work and that I think we will discuss a little, which are the risks associated with the theorem.

10:00 That is to say, the fact of using the theorem, it can present risks. For example, if we take Feynman's theorem, the risk is to ontologize what is represented. However, Feynman's theorem only has the meaning of a term in a sum that is a quantum superposition. And by writing or drawing diagrams, we tend to consider that what happens physically Interaction is the exchange of a virtual particle, as represented by diagrams, by forgetting all the other diagrams that, when added, create the true amplitude of probability, which is the physical process, and which precisely is not represented by a diagram. And I wondered if speaking as you like to do was something that was expected elsewhere. Also, the fact of systematically agreeing to the diagram, the fact of being the sign of, I quote, a formula that ensures a pre-eminent ontology, does not lead to, for once, exaggerate the place that it plays in the theory. Well, we will perhaps also hear earlier about Maxwell's terms, the terms of the universe, so there is a little question here in the thesis. All of this to say that this sort of passage of time that is made around the theorems, the theorems of Horace, Witten, Huber, Feynman, Penrose, etc. shows that the way in which the pictorial is present in the scientific world is the sign of a non-territoriality of the theorems on the formal. In any case, it is to be seen as something in the test and perhaps at the time of the questions I will be able to come back to it. I will quickly move on to the end of the categories, but I found that the questions I asked were full of expertise in terms of concepts that are still very popular and I would like to thank Franck for being part of clarifying these very difficult notions. What caused me the most problems is the end of the thesis, that is to say the pages in which we try to cross ontology and topology.

12:30 It has been said with other words, but do not consider that you are a delineator. There are a number of notions that are not defined, there are quite a few citations in the end. The reader I am, who has been assigned several times to these pages, sometimes seems to be embarked on a series of propositions which he does not perceive as successive. And suddenly, this series of statements, without the deduction being very present, without the questioning being explicit, I think I can say that there is not a single question on the subject. And some of the questions I've seen are part of quotes from Kant and others, but the question is sometimes used in an argument to allow us to spot the place where we are going to see how the ideas that we put in front of us are going to continue in a problematic way that we claim to be very large. So I won't ask any questions on this part because... The lecture I followed lacked a speculative core that was explicitly clear. There were some phrases that seemed to me to be insufficiently argued, and it prevented me from seeing the tipping points that allowed me to get to the philosophical thesis that you are developing at the end. Moreover, before the presentation of the thesis, there is a presupposition The question that deserves to be re-questioned is the one according to which, and I quote a sentence from page 8, there is such a reciprocity between physical sciences and mathematical sciences that one cannot underestimate their proximity. So, when I read this sentence, I think of the problem that is part of what is now the retornal, which is that of the efficiency of physical mathematics. This is the subject of a lot of work at the moment, and it is to be affirmed as a kind of proof that we know the proximity between mathematics and physics.

15:00 Of course, physics uses a mathematical language, but we must also ask ourselves the question of why all mathematical mathematics do not have a physical application? Why do there exist mathematical systems? Why do we talk about quantum physics? Can we characterize the most frequently used system? It seems to me that what is affirmed here is rather a problem that we can not afford to discuss. And it seems to me that we must doubt the existence of the isomorphism between the mathematical language and nature. And mathematics, which is seen, I quote, always in page 8, with a particular evidence in the theory of supercordes, where the two fields succeed specifically, precisely, it becomes a problem. That is to say, we talked earlier about the book by Lewis Moulin, there are still more and more physicists who ask the question of whether the theory of supercordes is a theory of physics or not. And the argument is that we have not yet succeeded in making this theory predictive. In any case, to the energies, for example, of the LHC, which started in daily life, so that we are obliged to see today that it has produced no verifiable effect, despite the innumerable work we have done with objects, so that it has not yet been confronted with the experience. So, is it right to say that it has enriched physics? Because there is a growing discomfort. Produced by the observation of a more and more perceptive deletion between the hopes, especially measured, that it has aroused in its first successes on the mathematical plane and their real physical range. So that may be it for the first question. Are mathematics ontological? Do mathematics have as a program to cover ontology in the long run? It's a sentence that you put in the summary of the thesis, so I think it's the sign that has a certain importance in your eyes. You wrote that the virtual is necessary because a table does not exist in the same way as the blue of the sky, which, in itself, does not have a material reality.

17:30 So, is what is material not real? Because the blue of the sky does not have a material reality, but we explain the fact that it is blue by the properties of the matter that, in this way, makes this blue emergent. So the question is, is what is real only material? You will see, there are a number of questions that revolve around this question. There is a virtuality issue that seems to take a different meaning from the text, which is not the same everywhere. Yoneda's letter, which seems, as you have noticed, to be of great importance, actually expresses that an object is determined by the set of points of view that we have on this object, with this equivalence that you have just recalled between the object objectified and the object subjectified. So, what you have said is that an object is determined by all the points of view that we have on this object. And I wondered if this sentence was equivalent to a sentence that Dominique Lambert, who was precisely interested in the question of the efficiency of metaphysical mathematics, says about what he calls the elements of reality. He says that an element of reality is characterized by the fact that it resists. The question is whether these two sentences, yours and hers, are compatible or whether they differ on what we call an element of reality. The argument of Nick Lambert is that the mathematical theories that are most used by physicists are theories that mobilize formalisms that offer an abundance in invariance. It is therefore no coincidence that it is these formalisms that can grasp elements of reality defined as being able to... I have other questions about virtuality, but I want to be certain of them.

20:00 I come back to the question I asked earlier about the aether. I explained to you that Maxwell designed the aether to represent it in the form of a mechanism. It allows us to realize how an electric current, which is a longitudinal movement, can convert an magnetic field into a circular one. And the land that it has built, that it has drawn, represented by a kind of diagram, allows this kind of shift in space. And if we have to agree to the diagram, in this case, the ontological point that we could claim, So what to say about the event of the astral reality that said there is no aether? In other words, did the aether designed by Maxwell not have a purely heuristic role without any ontological counterpart? Since the equations remained the same, with Einstein, without relying on the aether. So the ontological point of the aether, in this case, turned out to be null. Well, I don't want to multiply the questions, but about Popper, to quote page 41, I don't know what it is about Popper, but I'm not sure that the Popperians would accept the sentence you wrote, the Popperian theory that wants progress and knowledge to be described only in terms of truth, And that the only possible description of the core consists in the elimination of an infinite number of errors is based on a postulatively proven one, that the error is the only absolute that the scholar knows. Does Hopper really say that proof and knowledge cannot be written when they are the truth? Including the notion of falsifying the truth. That's true. Well, the truth is not the same as verisimilitude. So now I come back to a point that is perhaps less anecdotal, by reading the part devoted to diagrams and especially to Feynman's diagram, I wondered if, sometimes, you do not make the confusion between virtual particle and antiparticle.

22:30 So it's something that got me a little bit, as if antiparticles were virtual particles of a certain type. But I said to myself, after all, maybe this is how Dirac reasoned when he studied the existence of antiparticles. And then I came across page 85 on a sentence that, for once, made me jump over. And that made me hear that you were indeed making this confusion, or at least that you were making this assimilation, which may be relevant. In any case, if you consider it relevant, you have to explain it. You write... It is the principle of Heisenberg's uncertainty that allows an element of matter to go back in time. That's why I think it's weird that what we call a virtual particle in the form of particles is a particle that is outside of its mass layer, that is to say that it has an energy such that it is not equal to A2 equals T2C2 times N2C4. That means that it is not on what we call its mass layer. It absolutely does not say that it is not a mass layer. It simply says that, thanks to Heisenberg, in principle, she has been able to borrow energy, which she will reimburse by disintegrating, before the principle of collision will last. And so, I wonder if there is no counter-sense between antiparticle and antivirtual, knowing that an antiparticle is not, by the fact that it is an antiparticle... In addition to his mask layer, there are two things that are completely different from each other. I would like to end with two questions that may be anecdotal. The chapter that caused me the most difficulty in understanding is chapter 6, which is called Differences and Dualities. And maybe by asking you the following question, I will better understand what you are trying to say. Well, the duality is important for you because it is part of the quadrilateral, it is a fundamental notion in this destiny of the scientific disciplines that you mention, but let's take the fact that the fundamental equations of physics are reversible in time, that is to say that when we change t to minus t in the equation, we reverse over time, it does not change the equation, it is therefore reversible by the conversion of time. Is this reversibility for you?

25:00 Are they related to what you call duality? Or are they related to ambiguity, that is, the course of time is arbitrary, it could flow in both directions without changing the physical law? Or is it something else? And since you talked about the article by Gareth Leasy, who wrote the book recently, he uses the group of eight, the group of exceptional links. When we read this article, which is 20 pages long, there is almost no calculation. Few sentences. Few sentences for the issue of the article, which is still not interesting at all. The only keyword he puts is T.O.E. T.O.E. is nothing else. He speaks of nothing else at all. And in this article, there are only a few sentences and a lot of dialogue. And I would like to know what you think of it. For us, it is an indication that it fits into the mental disposition of yours. Do you think it is a theory capable of rivaling the nature of the body? And does the fact that it contains 20 additional particles mean that it has the largest number of groups in the world? So there is so much space in this group that we obviously need the space to put the groups of scales of the four interactions in the world. So it is so big that we can put all the interactions and it leaves so much space that we can predict the existence of many more particles. Without specifying their masses, since the group numbers are not specified, so are we there in the physical theory or is it a kind of program like the natural economy?

27:30 I don't have to take the question. I see on the question that we are very close to the question. I'm going to go back to the question of not supposing reciprocity between mathematics and physics, but it's something that delimits my field of investigation. Mathematics and physics, I have all the examples around that, are mathematics and physics, and mathematics is a real osmosis. In all the examples that I take, between mathematics and physics, and I also believe that there is a very close relationship between mathematics and physics, and it has already been highlighted by Jean-Jacques Leclerc. I will not go into all the details, but it is obvious that if I want to experiment the law of the fall of bodies, what does the physicist do? He starts by writing. Thank you for your attention. This is the general approach of everything that is done in this institution. If we build an advanced university, we could have advanced mathematics theory, and that of Garek is part of advanced mathematics theory, which are perhaps more. We build the instrument for the real, the extra-adaptation, the parallel, in addition to the theory of physics. So, physics and physics, as well as mathematics.

30:00 So, then, on the question of mathematics, are they ontological? So, I think I've lost my answer, or is that it? It's a bit like that. Yes, but as you are opposed to the other way around. So, I say no to mathematics, but it's not ontological. I'm not sure if it's ontological. It is obvious that mathematics is not a subject of theology because the questions that are finally addressed are the vocation of our faculty, since it is one of the components of mathematics. On the question of materiality, I suppose that it is clear, but the number of questions ... Thank you for your attention. No, that's not natural. Mr. Ricard Mouchet, in the quotes, it's not the name of the sentence, it's the information of the name of the sentence. More seriously, there are questions that are implicit, there is no need to repeat them. As I place myself on the term of ontology, that is to say, what are you? All the questions are asked and in the end, it's almost all the same questions. What are the modalities? And that's the only question. So at the end... It's a big question. It's a big question. I would like you to say it again in other words.

32:30 So, the dream of the material women, I think that in the test... I think it's not explicitly said. On the question of the diagram, which I could eventually put in place, I don't know, because at some point it's a question of the diagram. In the diagram, as well as a calculator and a calculator, we have several elements of mathematics. And I think I'm talking about that too, and I'll give you an example of the 23rd chapter. There are all the possibilities of transitions, of relations between an element... Creation and ideation of a pair, in which page, in which percentage, etc. So we are on all these elements and we also have topological developments that do the same thing. We are also on all these elements of mathematics, for example, in the theory of mathematical physics. I even think at some point it's a sum of virtual components as a result of everything. I don't think the diagram is correlated with the fact that there is a calculation of a sum on several elements, on several elements. Whether it is the distinction between virtual particles and virtual antiparticles. First of all, I think I don't want to talk too much about a particle and an antiparticle, that's clear enough. In Feynman's diagram, let's be clear, we have to justify the fact that Feynman describes an antiparticle that returns time.

35:00 So what does it mean physically, concretely, that an antiparticle returns time? And what can justify the fact that we have this representation? In the end, the only justification is the relationship between the particles that are there. It's not that it's good, it's the causality, it's an equation of Gerard. Either we say that there are particles that rise over time, that's what Feynman said about Gerard, or we want to escape the idea that there are particles that rise over time. In the name of causality, we say that the particle that goes back to the conductor is the equivalent of the antiparticle that goes back to the conductor. So there are two ways of speaking. Either we take causality and we have particles that go back to the conductor, and they are just as real as the ones that follow them, they are just as real as the ones that follow them. Either we refuse that, we say that causality prevents it. Particularity, time, time, time, time, time, time, time, time, time, time, time, time, time, time, time, time, time, time, time, time, time, time, time, time, time, time, time, time, time, time, time, time, time, time, No, but on this matter, I'm... I'm sitting on the wall. Besides, we have to see what was the reaction of Eisenberg when he saw that Dirac predicted the properties that were going to exist. So at least this sentence, I think that Nathan left it. I think that, for example, the relationship of Eisenberg can derive from the way I see it. So, the time it takes is the time of the people in the world, and we can't go back to that time. And on the question of reversibility, is reversibility the fear of the world?

37:30 Is reversibility the fear of the world? I think so. I admit I haven't thought about the question, so in fact, throughout the session, I haven't thought about it. Because it's not a question that I address. When we talk about verifying events, I don't have time. Please, it can't last. We don't have time for events. In any case, what we can control... Thank you very much. It's a difficult situation because I can't say anything else. So I'm going to read a bit of what has been said and try to say something else which may take longer. It's an absolutely impractical situation. So, I would say that, like all jury members, your work is truly a source of hope. You have managed to compare them on a problematic level. I would still say questioning. Theories, methods, disciplines, very heterogeneous.

40:00 And you have managed to put together theories where the difficulties are extremely strong. Thank you very much. All of these are difficult to understand, but the theory allows us to understand them in a clear way. You have given us your attention, and I hope that your work will be accessible to the non-specialists.