Stephane Dugowson / Charles Alunni Pensées des Sciences, ENS, Paris 2007
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Recorded at Pensées des Sciences, ENS, Paris (2007), featuring Stephane Dugowson, Charles Alunni. From the Michael Wright Collection, held by the Archive Trust for Research in Mathematical Sciences & Philosophy.

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Michael Wright Collection
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0:00 Speakers are essentially the same thing as domes, domes and domes, but when the domes, the domes and the domes, the domes and the domes, the domes and the domes and the domes and the domes and the domes and the domes and the domes and the domes and the domes and the domes and the domes and the domes and the domes and the domes and the domes and the domes and the domes and the domes and the domes and the domes and the domes and the domes and the domes and the domes and the domes and the domes and the domes and the domes and the domes and the domes and the domes and the domes and the domes and the domes and the domes and the domes and the domes and the domes and the domes and the domes and the domes and the domes and the domes and the domes and the domes and the domes and The idea is that one can know a space by studying the class of functions there. And Baidu makes reference to this principle in the Scrooge's book. The spaced spaces, which I will mention very briefly in this lecture, finally, the empiric ensembles of Benabou, they constitute an original formalization for the omega-6s, but with a part of the intuitive interpretation of the degrees of gravity as an ensemble of observers. In this case, the set of observers for which this x is related to this y, or the set of observers for which this x belongs to this part, at least at the first level, because then the empiric sets call the degrees of truth as sets of observers who see that, for example, in the set of causes in which the corolle is engendered by this y, Each observer sees exactly two elements in the corresponding empirical set, even if there is no element in the observation of which all the observers agree. The fact is that it is not possible to assemble, to make an assembly that includes all the elements. In other words, between the particularities of the empirical sets, of the elements, the matrix organization is the value of truth. They are based on a matrix calculation. The matrices are usually of an infinite dimension, and the coefficients are good. In fact, they are simple.

2:30 They are open to the field of view. This formalization allows to give direct demonstrations concerning the ESS without having to go through the tests. All these theories that take place are the result of the transformation of a puzzle into another puzzle Each transformation can perhaps be represented by a single piece, in some way a magic piece of the maximum size. This is a piece that has no particular aspect, but when you place it on top of a given piece of the same size, a piece of the same shape appears in its place, namely the one in which it is transformed by the transformation. So, a transformation or a morphism arrow in the pose continuum can be represented by a maximum-size object, which is an active object, not a logical object, but an object that acts on any-size objects on the surface of which we have crossed. I'm not going to go into details to see how it works, it's just that the structure of the post-transformation is linked to the impossibilities that may exist to prolong such and such a transformation beyond our understanding of the form. The way I just presented, quickly, too quickly, the transformation of a post-territorial post, a post is a post.

5:00 There is a whole of these components. A pose is only a part. There are other parts of a smaller size, there, in the general case of transformations, but the rest, the poses, the sub-poses of a pose are the same. It is interpreted as a pose of transformations, a pose of a particular sphere, a pose of a particular graph, which is called a monograph. In the same way, we can characterize the subconcepts of an ensemble by the characteristic subconcept that takes into account the value of the set of elements 0 and 1, where each element at the beginning is 0 or 1 depending on whether it belongs by the number to the final part. In the same way, the function of the subconcept of the subconcept identifies the subconcepts of the transformations of the subconcepts towards a classifying subconcept. In other words, we can form sentences that are analogous to those that we use in the concept, by replacing the concept with the present tense. You have an ensemble and a sub-ensemble, you have an ensemble, a set, a question mark. In the same way, you have a pose and a sub-pose, a pose and a transformation. The present tense is considered separately from each other.

7:30 Each topological space that is formed is in the case of a corresponding one. In a sense, each component of this genre is a variation of the category, with an internal logic characterized by a balance of truth led by a rule. That is to say, in the case where we are placed, the balance of truth leads us to a new dimension of discrepancy. For discrepancy, we maintain that we are all one, no matter which category we are in. And the category of the set itself corresponds, in the case of a typological space, to a single point, that is to say, a miracle of its creator in terms of the set. On the other hand, inside each of these categories, The arrow in the middle is always a variant of what Badiou calls an identity in this case. Moreover, the brutal taking of consciousness by Badiou, there are two times when we get a message that the ensembles that represent Badiou do not contain at all this famous taking of consciousness. Here is an ensemble. There is nothing in it, it does not exist at all. If the consciousness by Badiou makes the ensembles naturally not contain the existence, it is not accompanied by the great anguish when it becomes an ensemble. The fact that I am not only referring to the popularity of the populace of materialism and feminism, but also to all the artificial instruments of the world that are present at this stage, must be referred to by going back to the last phase of the academic lecture, which is to say, to the non-arbitrary, the non-partisan remains the castle of the future. But what of it? Why so much amplitude? Because with the academic lecture, it is about a collapse in the level of linear transformation, except that there is a change of logic. Sorry, we may have to take into account the passage from one proposal to another, but for which Badiou, in the name of this conversion, which all the time, assuming, continues to be part of a quasi-mathematic approach, ceases in fact to establish itself. Indeed, to the symbol by which, as we will see just now, is used, Badiou decides to create a maximal existence, without telling us which mathematical structure a paradoxical designation corresponds to. And Lagunière is absolutely right, because we cannot see it anywhere. He arrives.

10:00 In any case, my work, as well as those of my family, simultaneously, in this context of the event, is the result of an auto-appartement to an object, which explains the formula that quanta belongs to quanta, the subject of which is precise. Of course, in order to stabilize this brusque occurrence, quanta in its own transcendental field is conceivable, and he adds, the laws of the being refer immediately to what makes it exceptional. The auto-appartement is annulled as soon as possible, as soon as possible. A site is an evolving term, it appears or disappears, the problem is in the projection. At the same time, when we speak of a band, the only perspective is a projection. Even if it is conscientious, the consequences appear.

12:30 So here, I separate myself from Mathieu on two aspects of his theoretical evolution. First, by asking that we continue to follow the mathematical theory itself, which concerns the passage of something. These structures do not allow us to define a maximum of existence and non-existence, but allow us to have a second one. And secondly, by taking into account the fact that the granda belongs to the grand pas, since we know that the theory of the classical ensembles, the so-called theory of the hyper-ensemble antisponsor ensembles, was developed by Axel in 1937, a theory in which the equation of the grand pas belongs to the grand pas, All in all, the five key terms are the key elements and the five key terms of the theory itself, which is an axiom, and therefore, it is at the heart of our work, of our work, and that is the documentator paradox. You will see the documentator paradox, the paradox that leads to this idea of an antifundal ensemble. I would suggest that you consider the sequence of the sequence of the sequence of the first phase of the matrix with very rapid directions. The first point is to say that there are two points to which we start from the beginning. The first point is to see what we can really follow, what the scriptures of mathematics say.

15:00 So the question is to see how, at the level of the books, a transformation takes place on the logics, on the characteristics. That is to say, a transformation, however, on the framework of our works, but also on the assemblies of our works. Here, particularly, there are two questions. First, what is a change in the state of the body? Secondly, how can such a change of case be translated into processes? By our notion that in a particular case, we can obtain a particular test, which we can obtain in the association of the natural and the physical. What does mathematical theory mean? For each of these two questions, the answer is double, in the sense that we have to repeat the demorphism in the two senses, from the chronological case of the start to the case of the beginning, as well as from the second to the first, The topic of today's lecture is the condition of the function of the function of the function of the function of the function of the function of the function I would just like to say that if the algebraic meters act in an inverse direction, but not as much because one is defined by the other, on the contrary, the term algebra is a new elaboration. Going from A to B, then from B to A, it does not necessarily mean that everything is the same. Diversion, dispersion, or again, I will come back to this example in my next session, the cost, the resolution, the magnitude. As announced, I would like to say that...

17:30 There is a particular, simple and important aspect of the insertion of a point in a private assembly, which I called the event of coming to the world. The first transformation is to associate the universe with the universe of the grand theme, either zero or one, depending on whether this universe contains or not the point of insertion. To summarize the situation by saying that coming to the world implies distinguishing the circles to which it belongs and those to which it does not belong. In this case, we have one of the elements, a discrete topology, the objects, whatever they are, are the ensembles. The insertion of a point in an assembly takes place at a certain level, We ask you which one will be associated with the value of the world, while which one will be associated with the expectations of the world. Explaining the first point of this first transformation in the opposite direction of the meaning of the insertion.

20:00 One of the circles in which it is about to belong to those in which it is not about to belong. The point that is inserted in the name of M belongs to it but does not belong to it. Always at this first level of definition of the insertion as M. The second transformation adjoins the law of the one that has just been presented and is defined in the following way. There is a unity of power. Each of us has the same power. In other words, there are only two to consider. There are only two open spaces that are very important points. At the void will be associated all the space of the arrival except the point A, the place of the insertion itself. In this second transformation, what is the same for a singular being appears as the trace in this being of a truth shared by all. However, what does not appear appears to all the others. This is why I see in this transformation that expresses the direct aspect of insertion as the face of the being. We see that our face is at the place of the head that we have visually speaking.

22:30 Concerning the objects themselves, there are also two adjacent transformations. The direct insertion is expressed very easily in the terms of the vessels, thanks to a formula that is imposed on itself, in conjunction with the first transformation that I described. So, altogether, we have all the objects, and above this frame will be associated In terms of pieces, we will see that the pieces are arranged according to their form. Behind each form, u is a form of a piece, v is a form of a piece, we associate a set. The set u will be associated with the set u. We do not have this information, since for u we have here the full part, the set u will be the whole of the full part, that is to say the whole of the whole of u. And finally, the insertion frame, where the non-existent is defined as f of i.2, i.e. non-existent, i.e. non-existent. In the same way, each cover of a quantum will be a set of its objects.

25:00 At this level, we can see that the state-of-the-art of the objects of the first world serves as a kind of primary material to the constitution of the new world. The exterior of this passage corresponds to a logical and complete logic. The non-existent that we see here, as it can be perceived or as unknown, corresponds to a minimal projection. That the being is structurally bound to operate on the world, to see that the other is a living being. When Van Gogh politically elects the relic of the non-existent, identified as the proletariat, he says that the non-existent is the relic of the non-existent by the words of the international and the international community. On the one hand, they do not take into account the hole in the existence that appears there when an insertion is made. After all, we are not going to take care of everything on this side. On the one hand, they do not take into account the hole in the existence that appears when an insertion is made. On the other hand, they do not have a real impact on the existence itself. The operation consists in deciding that the unknown number will be red, but at the same time, neither more nor less legitimate than the choice of a number of colors. This operation will in any case be inscribed in the natural structures. It is an unknown, it is not an unknown in such a way that the transformation is less than the left of the previous one. This inverse transformation does not start from objects on the frame defined by the Grand Theme assembly towards those of the frame of the

27:30 All of these are associated with the theme of the set of micro-parts that have been cut down, and the rest of the technology is cut down well in terms of space. In a particular case, where the point of accession is at the border of a part by returning to x1 or x2, it happens that in terms of the this point does not see anything in the universe, but it knows that it is not a part of the universe. The border does not show why, being in the middle of its border, In the passage of the dinner, we will go back to the truth, which is to say the end of the lecture. At the end of the lecture, I have the impression that there are thousands of people who will compete with each other on the topic of mathematics this evening, with the exception of the five of us and also of the five of us who are here today.

30:00 We will talk about the question of certain components on the political positions of the world without necessarily following the problems of the world. So the two aspects should be well separated. It is clear that we can find ourselves in some aspects of the work of physics without the word of the world following it. But this is obvious because it is found that the work of physics of the Germans is quite legitimate. The increase of the colony that it has in particular due to the publication of its record in 1963, that is to say that the question of the nature of the articulation of humanities is equal to art. Certain physical works of physics are interesting, especially in these modern relations between mathematics and physics. Of course, we can't believe that a mathematical demonstration like this will ever be possible without the help of Charles, the professor of mathematics at Berlin and at Benin. And also at... I'm talking about Benin. Benin? Oh no, I... There is a game of words about the names Benin and Benin. Charles, go ahead. Benin. Benin, yes, it doesn't work. I see that I refuse all this impartial discussion, even inside this very small room with all these pieces. So these are not practical pieces.

32:30 We understand that. We want the study to be done. And that's why I don't want to talk about it. I have a feeling that you have equipped the future and oriented the future a little bit. I think we can talk about the lessons that come together. And in France, it is an idea of mathematics more than it is a theory. Mathematics is not yet a real problem because it is not related to real problems. I am not in a position to really demonstrate this feeling. For me, it is a certain science. In my personal perception, what are the mathematics?

35:00 There are a number of methods on the other side of the spectrum, concerning what we can and can't do, what we can and can't do. My feeling is that it's only interesting to try to get as close to it as possible, to try to listen to what it says mathematically. That's why the condition is strong enough, as we know it, and it deserves it. In practice, there are some pieces that we will say that this is a technical term, but the definition is a little different, even if it carries an infinity of possible meaning that articulates itself around denouncing in a very compact way that there is in general nothing to go against at this level, but obviously given the condition of having the right reason to do so. So it's a bit of a whole theory that no one has ever studied. Anyway, I'm going to ask you about the notion, for example, but I will finally answer that it does not fall into the heart.

37:30 The heart, for me, is also the world. Let's say that I believe, recognize, the difference between making women collect what they grow, philosophically speaking, from mathematics. We can't go looking for arguments on a bit of a rhetorical level to support and do things that would allow us to enter the realm of light, but there will be no objective criteria. We have a problem. We have a problem. We have a problem with the... The problem with the question is that the person is always... 10 days. Because the truth is that I don't understand anything. I still have the feeling of being in a... I have the feeling that I'm not here.

40:00 Indeed, there is a... For example, I would like to touch on the subject of the reflection of different entities. So, I don't understand. I really don't understand. Except maybe... Maybe it's time to read the description of Collage and Lucien in the book concerning the representations that are made, maybe, but at some point, if with a bad spirit, if we say that it is not true, sometimes it is true, sometimes it is not true, when in reality it is not true. In fact, there are entire passages of these clubes where I find it very interesting the passages where they stick the most to each other, to each other. There, in fact, something that is sometimes very interesting, remarkable, which makes us fixate on the portals of meaning and of the future, and other passages where it calms us down. Are there any mathematical passages, any mathematical experiences? In general? Mathematics. Ah yes, so the answer is clearly yes. I mean, the first, daily experience is first and foremost to be able to understand. In the case of mathematics, I know that, through my work, I will be able to understand. And that's always too much. But I was already talking about that.

42:30 Well, we've seen that... No, we're not talking about that. No, we're not talking about that. That's what I'm asking too. I don't think it's very clear. I don't think it's clear. But we can talk about it. I don't know. Maybe we should look at the impact, for example, of Macron on the issues in terms of what is understandable and what is not. In other words, when people listen to Macron, they have the feeling that somewhere, despite everything, they heard something. And it was true. So it still inserted something of a reality, in my opinion. There are certain tendencies to say that since we do not understand these conditions at the right time, which is not always convinced by me, it is largely... Thank you very much for your time.

45:00 The beginning was mathematics, mathematics, and then mathematical physics of the elements. Sorry? The elements. Of the elements. Of the elements. So, that's it. So, the fact that you want to define mathematics rather than all that, you have to learn more or less what you understand, you understand that. And for you? My mind is the question of differences. Why? Because these hyperconcepts, which belong to themselves, represent a possibility, I mean, a modelization, a representation of the contents of physics. This represents what we expect in terms of applications, quite simply, without even talking about hyperconcepts. This is a very professional idea and a very good one. Mathematical physics is related to psychosecurity, to stress, and it has to do with the fiber, because the fiber is the one that makes the mathematics of the elements.

47:30 It is closely related to physics and mathematics. The element that has created this object, this fiber, in a way, represents the transformation, an element between the opposites. And so, it is what happens when, in this particular case, we insert a point in a lower tone. This point is enriched by insertion. There are also other parameters such as quantum physics, space, astronomy, and quantum physics, quantum physics, quantum physics, quantum physics, quantum physics, quantum physics, quantum physics, quantum physics, quantum physics, quantum physics, quantum physics, quantum physics, quantum physics, quantum physics, quantum physics, quantum physics, quantum physics, quantum physics. But how to talk about what I just talked about, without starting by setting up the idea in a simple way, in a dialogue, I don't know. It's true that I said at the beginning that I would not speak at all of the two.

50:00 There is a path, a small path, to be drawn, to be drawn like this. I am very happy to be here today to talk with you about this topic, which I have been interested in for a long time, and which I have been interested in for a long time, and which I have been interested in for a long time, and which I have been interested in for a long time, With interpreters who are not mathematicians.

52:30 I believe neither this nor that is true, because it is not that we can judge how the information we learn, etc., etc., can be related to this and that which we learn. It is not that we are destined to go back and forth between them. And so it is not that I say that there is a technical error or a technical error. This is a technical dialogue that says where such and such notation is lost, but here it is in the allocation of such and such. The feeling is the same, I am here as a reference to Badiou, but I see it not very clearly. I have the impression that if you want to model the buzz, you will have several... I have an idea for you, I don't want to tell you that you are trying to pass it on to mathematicians or mathematicians, because it's in this sense that you have the answer. So that's the first step, I've explained it, I find it a bit complicated, in the case of the world, it has a correlation as well as what you say about the imaginary quantities, maybe it will continue yesterday, I don't know, it's not very good. And so, the virtue of all of this, of all of them, is that it is done in the art of science. That's the first point. The second point, which I feel is quite interesting, is that we have an operator who can criticize values, who can criticize certain types of values, so I'm going to go back to this point.

55:00 And then the third point, which is ultimately something to be estimated in our own research, as well as in the scientific research. Let's move on from this imagination or this orientation of trying to find new possibilities. So, I look at the second one, since it's the point that I would like to make quite proudly in your presentation. I still have the impression, if you don't mind, at the end, when I refer to the text, that in reality, when you look at the third period of time, it is ultimately the algebra, because you did not devote yourself to it here, but that the... The philosophy of physics, which deserves to be considered, is, however, a bit mistreated, sometimes mistreated in its own way, in the sense that the report that I am making does not seem appropriate at all. That is to say that, well, we do physics, and the reference, it is not my request, it is not that I do not use it, it is simply that I know a little bit about any of the brands. So, for him, it is a question of focusing on such and such fragments of mathematics, of physics, of philosophical questions, to move things, in this case, to move the question of materialism, but also to move the question of philosophy. It is to this that he uses such and such fragments of the thing, so he follows it in part, and even when he follows it, it is not excessive, it is not excessive, it is not excessive, it is not excessive, it is not excessive, it is not excessive, it is not excessive, it is not excessive, it is not excessive, it is not excessive, it is not excessive, it is not excessive, it is not excessive, it is not excessive, it is not excessive, it is not excessive, it is not excessive, it is not excessive, it is not excessive.

57:30 Maybe it would be interesting for you to say, well, this philosophy, even if I sit here and do this, it's not that I'm projecting myself in the direction of the galaxy, but I'm going to predict it in the direction of the galaxy. Most of the time, we don't have to deal with the philosophy of mathematics, but we have to deal with the philosophy of mathematics. It's possible, but we can't help it. And that's where I think there's a kind of mistreatment, a mistreatment. It is a book of philosophy. I like to see a book of philosophy in the sense that I do not understand the subject of philosophy and that I do not understand much of it and I do not understand that the study must be on the other side. At this point, it turns out that you do not have precisely what you need in order to understand yours. I feel that, but at the same time, with commerce, we have a difference. There is another difference. It is bad to see distance. In this triple function, if I may say so, it is marked a little in the vocabulary that is used at the time. Of course, when we call it fusion, we call it fusion. It was not by chance that it was used. It is true that even in the 18th century, the fusion of values, the fusion of fields, etc. I don't know, I don't want to say too much. I'm talking about the 5th century, I'm talking about the 20th century. I don't know why mathematicians and physicists don't understand each other. I don't know why mathematicians and physicists don't understand each other. I don't know why mathematicians and physicists don't understand each other.

1:00:00 I don't know why mathematicians and physicists don't understand each other. I don't know why mathematicians and physicists don't understand each other. I don't know why mathematicians and physicists don't understand each other. I don't know why mathematicians and physicists don't understand each other. I don't know why mathematicians and physicists don't understand each other. I don't know why mathematicians and physicists don't understand each other. I don't know why mathematicians and physicists don't understand each other. I don't know why mathematicians and physicists don't understand each other. I don't know why mathematicians and physicists don't understand each other. I don't know why mathematicians and physicists don't understand each other. I would like to ask you, François-Alain Duclas, for the different policies of your library, but especially mine, apart from the one of the library, it does not make me happy to participate in your lectures. Besides, go and seek inspiration for your lectures, it is not really what you want.