Introductory remarks / Charles Alunni: Pensée, diagramme, categories

0:00 I don't know if I can't respond to your questions, but in one minute. Simplement commenter deux points dont je voudrais que vous rappeliez le rapport que vous placez avec l'orientation de la pensée. Le premier concerne Eddington et le second concerne Leibniz. Alors pour Eddington, j'ai été tout à fait intéressé par la conceptualisation des cerveaux tournants qu'il donne, which recours, in my sense, the status of the letter in the mathematical writing. Or, it's the point of view of a physicist, although this controversy had already made the object at Fréguet and Ressal of a popular discussion. And we have here, the question of the letter, it's that it represents both an individual and a class, and that this, rhetorically explained, is a contradiction. And so, we have here the point of view of a physicist the moment, in introducing the time, can arrive at dissoudre, or at least at intégring this contradiction. So I would like to place this polimic, this controversy, in the case of the orientation of the pensée. The second concern the AENIS, it's rather a remark than a question. To say that the analysis situs of the AENIS is built on the of the metric. To say that the form and the situs they come from, for example, in another vocabulary, of the metric. This is not, in my opinion, any by Brouhacky, nor by Serre. The example that we give frequently is that Leunit considers that two figures semblables can be distinguished only by compresence. It is to say that two individuals who are in a separate room with two figures semblables cannot say that they are distinct. It is necessary that there is a co-presence, that they are all together. At this moment-là, they can say that they are distinct. They are obviously, by abstraction, the concept of form and of situs. I would also like to remind you, because maybe I haven't understood it at this moment-là,

2:30 how do you relate that to the orientation of the pensée? Alors, sur la première question, donc le rapport de cette description par Eddington du cerveau tournant, par rapport à la représentation dans la pensée, But what I was interested in, when I tried to circuit this description eddingtonian with the question that Berthos can ask, is that the brain, in terms of functioning physiologically, etc., pourrait être décrit dans les questions de son orientation par des tenseurs. Moi, ce qui m'intéresse, c'est cette espèce d'entrelacement, d'entrecroisement entre, d'une part, un dispositif matériel et un dispositif symbolique. And how, in a certain way, how to say... Well, I would like to say that it would be a bit of an electromagnetic wave, of the electromagnetic wave. we have two phenomena, electric and magnetic, and what the relativity has shown is that it is the same thing due to a different point of view, or in any case, which are in a form of invagination, that is to say of a rapport invaginant between the one and the other. It's not really a question of controversy, it's a question of trying to in the orientation of the pensée and of the pensée, this kind of relationship dialectic permanent between, at the limit, what is the first thing about the poulet and the oeuf? It's a bit the question that I was asked about the current of Dorham. is that in the orientation of the theory of Durham,

5:00 at the same time, he had certainly co-present in his mind the electromagnetic model, and at the same time, he developed a mathematical theory very abstract that he made a sense of this phenomenon. So it's a bit of the intrication material and symbolical that, in the imagination, in the sense of the French, that I'm worried about. In terms of the language, of course, I think that it's very clear what you have mentioned, to know that we all do the economy of the metric. This is absolutely certain. It's a philosophy of co-presence, as you say. But what I interested in was the link between Kant's question, and the apparition of the question of the site tel que l'a évoqué la guise, et sur le fait aussi que ça aura une généalogie, une descendance vers la topologie. Voilà, je ne sais pas si je réponds à votre question. J'ai en fait une question qui va dans la même direction. Je veux rappeler comment une petite anecdote sur une discussion d'un étudiant d'Heisenberg et Heisenberg lui-même. I think it is cited in a little book of Longchak, the geometry of physics. And it goes on the following. The student asks to Heisenberg, and if after all, the space is nothing that the application of the operators. And Heisenberg responds, it's absurd to the space. It's a blue, there's a vase that goes on. And it's very important, because I'm not going to put it on the same terms that Mr. Lama, l'individuation concrète dans la discussion physique, mathématique, l'utilisation de diagrammes, l'utilisation de la géométrie. Et c'est pour ça que je veux vous poser si vous voyez un parallèle dans ce panthéismus strait que vous avez cité,

7:30 je n'avais jamais pensé à ça, mais entre la raison et le génie, si vous voulez, and at the beginning of the 20th century, the discussion on the foundation of mathematics between Poincaré and Brewer, opposed to, for example, Russell, where Poincaré and Brewer were the intuitionists and represented what Poincaré called the spirit geometry. When we talk about diagramming, what does it mean? l'esprit géométrique, c'est-à-dire l'esprit de l'intuition dans la mathématiques, opposé au logisticien ou l'esprit algébique. Il y a quand même un petit problème là-dedans. Non, mais c'est exact. Je pense que c'est le fond du problème, effectivement. C'est simplement... Moi, ce qui m'intéresse, c'est la réintroduction, c'est le statut de l'intuition. Et de l'intuition, non pas comme un donné. On a eu une discussion d'ailleurs dans le colloque avec les quantistes et les physiciens de la quantique sur le fait que l'intuition n'est pas une donnée, contrairement à ce qui est souvent développé, qui peut être développé par les analytiques, etc. It's a construction, and so it lies the question of intuitionism, of constructivism, and the question that I'm interested in what is orienting to the French, it's also what is construing an intuition, and what to make that intuition is a complex device, built, and not done. And in what it is related to what we call in physics the experience of thought, for example? In what the integration, the orientation of the thought and of certain experiences of thought they create a revolution in the way to be able to think about the world, as well as the theoretical objects and the material objects. So the centrality of the thought at this level seems to be decisive.

10:00 Je voudrais essayer d'expliquer comment je comprends une partie de l'exposé, c'est-à-dire le fait que de parler des choses de Kant, de réflexion de Kant sur l'espace et sur les figures en entiomorphes, en fait, ça se passe déjà dans le plan, n'est-ce pas, puisque les figures dans le plan ne sont pas superposables par translation, mais aussi par retournement dans l'espace et dans l'espace de trois dimensions. on pourrait les superposer par rotation à quatre dimensions. Alors, ces exemples, et puis les observations par rapport à la question de la bascule chez Gilles Châtelet, ou même ce que tu dis près d'Einstein avec une théorie des points de vue, pour moi j'ai compris ça dans cet exposé comme, disons, une insistance sur la question d'un travail de la pensée dans un certain recul, dans un certain recul de l'objet. Deuxièmement, en quelque sorte, ce recul serait quelque chose qui va pouvoir être inscrit comme tel dans le diagrammatique. C'est-à-dire que le diagrammatique, il va être effectivement une entrée en scène de l'inscription du recul. Par exemple, le rôle de la flèche, tel que tu l'as souligné par la très intéressante citation de McLean, and the rapport with Beckett that you gave, it's not at all at the point of the formalization in the sense of the past, it's very exactly, I believe, at least from the point of view of the categorical work, it's at the possibility of writing a gesture of recul in relation to what we work. And then, if I understand what is said in the exposé here, The most interesting thing about the advancement of the pensée is that from the moment where we can do this inscription of the distance, so to take charge of the character entirely indirect of the math activity, which was not envisageable, for example, in the 18th century. I don't know, I don't know, it would be a question of history to know when is it that this indirect indirect becomes really admissible to the past of the mathematician.

12:30 In any case, with the emergence of the work with the flash, we can effectively start to inscribe the gesture of the indirect work and take it in charge of the calculation. Well, the second moment, it's perhaps also what will be mentioned about Gordon Dick, but the second moment is that it is the liberation that provoked this moment. by McLean, the Flèche becomes a concept, it's a lot to say, it becomes a mark of an act. And the fact that there are many who will be able to do that, to be able to do it and to be completely free, is obviously going to be a second moment. Grotendig, effectivement, ce qui peut être, à plus, si je puis dire, ou avec l'extraordinaire quantité de mathématiques qu'il a inventé, il a aussi inventé et proposé ce geste de faire des mathématiques en quelque sorte, pas en roue libre, mais en prenant en charge en permanence le travail même qu'on est en train de faire. In Recolter Sommage, you cite the difference between the mathematician who works with a marteau and the one who lets things be diluted. There's a dilution in the indirect which is indicated. Is it okay with what you say? Well, it's an excellent summary that I would not have to do as well as you did that. because, precisely, what is essential is that there is a link in which the theory of catégories is profoundly philosophical. It is this dimension of reflexivity, this gesture of recul, which is a gesture fundamentally philosophical, which inhabits the theory of catégories. And simply, one last word, I just want to cite Bill Lewis. He said, and I think it's one of the things that I like to say, and hence a particular being is known, at least partly by what it can do. And I think that's one of the things that I like to say, and on which there is a lot to say about mathematics, what is a theory of the act, what is an act of mathematics, what is a gesture, what is an experience of pensée, etc.