Lecture 4 (first part only) (contd.)

0:00 All these groups are established between the two, and that's what we're looking for. So there are the groups that are hidden. Most of the time, we represent them as a group. That's interesting. So I think we're going to lose a lot of space. This is the first discovery of the system. From there, we had the idea to explain it in person. In a system of coordinates, the distance to the point of reference, we can use small rules to implement a domain that lives more or less within the space's rules in relation to the coordinate of reference, the Earth, as we call it.

2:30 All of these terms are used to describe the space of the Earth, the space of the Earth, and so it is obvious that there is a link between the two dreams, and it leads to the creation of the space of the Earth, and Helmholtz does not consider this to be a dream, he considers it to be a reality, it is just the beginning, the beginning of the end, the end of the world, the end of the world. I have a question about the position of the human being, once he goes out into space, what does the human being mean to you? Well, he considers that... Practically? Well, he doesn't really explain himself, that's the point. I think he had a pre-judgment on him, because he wanted to have a homogeneous universe and... He didn't really think about the possibility of the human being, which is not a problem in terms of quantum mechanics, but in the case of Penrose, he didn't see the possibility of the human being. All of these have to do with the possibility of an advantage with the rules of Schumann. So, does he not like it or does he exclude it because it violates another criterion that is a requirement that is given to his geometry? I don't know. It's hard to explain because it doesn't really explain that Schumann can't... Schumann can't explain it. Schumann can't explain it. Schumann can't explain it. Schumann can't explain it. Schumann can't explain it. Schumann can't explain it. Schumann can't explain it. Schumann can't explain it. Schumann can't explain it. Schumann can't explain it. Schumann can't explain it. Schumann can't explain it. Schumann can't explain it. Schumann can't explain it. Schumann can't explain it. He says, beware, there are addition of structures, he does not have the priority at all, much, much less than the power of Riemann in France. In fact, the idea of ​​a space, where we left, excuse me, it does not invite precisely this macroscopy and this universe of co-ordination, which have these relations between star and moon.

5:00 He has the idea for him that the body, the free will... Corrugation is a requirement for the bodies of the fugitives, and so the fact that we do not have corrigative units means that we could only have a nuclear space. And so, this is the one that is wrong, but obviously there is not this requirement in Riemann, and Riemann is more general. But what I say is that, fundamentally, it is, let's say, that Helmholtz could very well avoid this constraint of having corregative units. We don't need all that, but we can do these reasonings, and in addition, when we look at the structure of these reasonings, they are always infinitesimal reasonings, that is to say, they are placed in a binary, they are placed in a small domain, so we can immediately redo all these reasonings, there is nothing in the structure of these reasonings that allows us to take finite extension strings. On the contrary, he himself makes the reasoning, first at the beginning with Corny, and then he says that Riemann demonstrated that in order to clarify the level of mobility of the body, we can only have the geometric order constant. He refers to Riemann, by the way. So, there are many, among a few commentators, who say that it is a flaw, it is a deep flaw of the Morse approach. No, because the essence of Helmholtz's idea, for me, the essence of Helmholtz's approach has nothing to do with the homogeneity of space. What did you want Helmholtz's approach to be? What we wanted Helmholtz's approach to be was to demonstrate the necessity of the geometry of Cliquet, not only to exclude the geometry of the two. First of all, he had not seen the cohomological case of Provence. He had seen the case of spherical geometry, but he excluded the case of the case of infinite geometry.

7:30 So, in fact, his project at the beginning was a project at the level of Kantianism, where he was trying to justify a project that failed and that led to a plurality of geometry, but a plurality still quite limited, since it is the essential which is still the result of the movement. This is to demonstrate the necessity of... It's not Cartan who did it. I don't understand anything yet and I'm starting to work on it. It's been a month and a half. The idea of Cartan is that we take the long spaces as model spaces. We take, for example, space R2 as the quotient of the Euclidean group by... It's all the translations plus all the rotations, it's a 3-dimensional group. And the quotient by the thing of dimension 1, which is the metropolis of a point, which is the set of rotations around this point, which is a space of dimension 2, which is 2. There is a whole generalization of this homogeneous space, so, for example, in the case of Mania, there is RM, which is the quotient of the group of units in dimension 1,

10:00 divided by the orthogonal group. It is a general fact that all quotients of the group of units, I have this or that, or I have a group of units of any kind, and there I have a group of units of any kind. There are infinite multiplications and we cannot understand all these spaces. And what Cartan does is that he says that we have spaces that generalize the equation of H. We will keep free mobility, but only in the infinitesimal, in the neighborhood. But we will not have global rigid free mobility for finite bodies. And that's exactly what we're trying to say here. It is clear. No, it is not. No, it is not. No, it is not. No, it is not. No, it is not. No, it is not. No, it is not. No, it is not. No, it is not. No, it is not. No, it is not. No, it is not. No, it is not. No, it is not. No, it is not. No, it is not. No, it is not. No, it is not. No, it is not. No, it is not. No, it is not. No, it is not. No, it is not. No, it is not. No, it is not. No, it is not. No, it is not. And so the question that arises is that if, indeed, we ask that we can make a monomyth of TEMER two days before a PISMAT, one, one, one, one, one, one, one, one, one, one, one, one, one, one, one, one, one, one, one, one, one, one, one, one, one, one, one, one, one, one, one, one, one, one, one, one, one, one, one, one, one, one, one, one, one, one, one, one, one, one, one, one, one, one, one, one, one, one, one, one, one, one, one, one, one, one, one, one, one, one, one, one, one, one. Yes, by being in a space-time machine. Yes, by being in a space-time machine, yes, it works. My question is, does this not imply the homogeneity of space in general? I don't know. I think we need to add the homogeneity of space. Obviously, I don't know. I think that the elements I am talking about are magnetic and non-linear, but it is clear that in the future we will have problems with this notion of the level. But in the end, I think that... We know that it works, but there must be a way to multi-directorize the practice of the art, of the advantage and of the non-advancement of the rules.

12:30 I just want to ask about the freedom of the rules, of the advantage. We need to know in what way the rules are being moved. Are they unidimensional rules that move? No, no, no, they are unidimensional rules. I don't have any kind of movement. I don't have to move, I can do whatever I want. Because a very straight rule... If I push it to the other side of the screen, it won't be able to move anymore. And if I push it to the other side of the screen, it won't be able to move anymore. If I push it to the other side of the screen, it won't be able to move anymore. If I push it to the other side of the screen, it won't be able to move anymore. If I push it to the other side of the screen, it won't be able to move anymore. If I push it to the other side of the screen, it won't be able to move anymore. If I push it to the other side of the screen, it won't be able to move anymore. If I push it to the other side of the screen, it won't be able to move anymore. If I push it to the other side of the screen, it won't be able to move anymore. Most of them are rigid. But even at the same level, we can't separate them. You have the rules. We are on the surface where you can. When you see the approximation, you can consider that they are small enough. So it's a matter of deformation along this surface. Then, is the way Brunei asks for this in mathematics, we don't know. But I don't know what the answer is. I repeat, what we are saying is that the free mobility of the rule, conceptually and basically, is that when we take two points at random, we take a small rule on the first point, we can transport it on our point, by conserving the length, it is very important, it implies that there is a group of transitive transformations in space that establishes the length.

15:00 I'll give you an example. Let's take a ruler on the right. It's on the table here, but on the right it's only placed on the two-dimensional space, because if I see it in the tridimensional space, I won't have the right intuition. But if suddenly a talus comes, I can't see it anymore. It's blocked because of its rigidity, even if it's infinitesimal. Most Gauss surfaces have no group of transformation. The group is better than the group. The general notion of space does not have any mobility. Generally, there will not be a small disturbance of a plane, but there will only be the transformation of reality, which will stabilize the universe. So there is no mobility. Maybe locally we have remained flat, yes, if we restrict the size of these planes, but it is very easy to construct functions in the middle of the field, which are quite wild, so that there is no more than identity, even if we restrict it to any other plane. I don't know if you can hear me, but I think it's a good idea to talk about this topic, because I think it's a good idea to talk about this topic, because I think it's a good idea to

17:30 The point of divergence with Griegman is that there is no consideration of cohomology. It is an apparent divergence. Griegman did not see it. So we can do the same thing as a concept of local time that I did for space, so we have a first time, an individual time, an individual time, we can, of course, organize, there is the consciousness that organizes the events, so there is the awareness that one perceives, that one gives a personal time to the original, after, using... Any kind of natural superconductive process can be done, for example, to create a terminal time, these waves, which are these waves of personnel, then we can operationalize it with the help of superconductive processes, such as space-time, space-time, etc. We can take any kind of process. There is a convention in Madrid, there is a myth on possible conventions, such as the one we have in Paris. And from there, we can build a continuous realization. So, we have a lot of things here, like space, space, time, so we're going to move on to space-time, and we're going to recover a local time, a poetic time, which is also possible if we have a distance synchronization method, then we can do it with the Naïve method, the transportation of clocks, synchronization through a clock chain.

20:00 We don't want to do this because we don't have enough time to transport it, or because we don't know how long it will take to solve it, or because we don't know how long it will take to solve it, or because we don't know how long it will take to solve it, or because we don't know how long it will take to solve it, or because we don't know how long it will take to solve it, or because we don't know how long it will take to solve it. But if there is a maximum speed of multiplication, the synchronization is still possible by crossing the signals in the form of Kuhn-Einstein and Poseret-Rousseau. So, it is obvious from this method and from this point of view that if the clocks are linked to a cable, their distance is well determined because the distance remains constant. We consider two cases. Of course, since synchronization is linked to one case of logic, we can take the cases of logic in the other and compare them to each other. At this point, you will have to compare the terms that are used, and we can do it in the same way as in the case of algebra. I made a hypothesis, a linear hypothesis, because at this point, the relativistic movement causes the distortion, and the transformation of the corollary is not the same.

22:30 When you have the freedom to rotate the two frames, you can orient them in such a way that the coordinates of the coordinates of the transformations take form there. Then you will find the basis for local relativity. In this combination, you do not see anything but the square. There is not an aether, for example, which means that when the square is turned into an aether, it will affect the process. This means that we can be more liberal in terms of the transformation of the universe, and so you have the expression, the expression, by the way, you explain the fact that the maximal equation, the maxima equation, the maximal test C, must be the same in both cases, and by multiplying this relation between this equation and this expression, this expression, this expression, this expression, this expression, this expression, this expression, this expression, this expression, this expression, this expression, this expression, this expression, this expression, this expression, this expression, So, you have used these two relations to re-encrypt the karma of the plant in a way that shows that all this remains in the same spirit, that is to say that it is more and more in an old-fashioned spirit, like the one we have seen in the past, in a way that is no longer Christian, but still sufficient, because the linear transformations that exist in the world of physics include the form of a parameter. We know that the version is written, which implies that the elements of the generator are null. There is the first case, which is the case of the generator, that's it, by differentiation.

25:00 In the case of the length of the generator, you have the unit of the trace, the unit of the determinant, it is a very real thing. And the character of the information is pure, so you can see that the generator is a lower generator, by differentiation, you can see that it is a prince, and a lot of other things. And you have a function that leaves a barrier, as you can see, it's quite simple. So I don't know if it's a miracle or if it was intended to debunk the method of Newton, but it's interesting to see the parallelism. So what we see here, in fact, is that the precedents do not move locally, After that, we imagine that in many cases, we can find in the paralogies of space that we arrive at the notion of space, time, the human being, so with as many paralogies as possible of the idea that space is there, it leaves us completely in the back of the idea of generalizing, if you will, this idea that we can criticize, this idea that we can lose the advantage in the case of space, which was there and which is still there.

27:30 There are a lot of examples, even if we don't know them all. Is there something analogous in the case of the space-time? Well, it's hard to say because the general notion of the space-time is a subject. We are trying to solve the problems with the complexity of the space-time. In any case, if we wanted to understand the relationship of these waves with concrete waves that would come from distant places, And so, the attempts to justify or rationalize the idealization of mathematics are not based on a little bit of passive movements, nor on the movements traced by the parts of the text. Yes, it's quite subtle, of course, but it's the least, the least in the analogy, the most personal aspect of things, that's it. The difference is the distance between the points, that's what we're talking about, that's what we're talking about, that's what we're talking about, that's what we're talking about, that's what we're talking about, that's what we're talking about, that's what we're talking about, that's what we're talking about, that's what we're talking about, that's what we're talking about, that's what we're talking about, that's what we're talking about,

30:00 Because if we try to transpose the naïve elements with the correct ones, we will not have any problems. The Bible is totally a sign of the earth, but I don't know if you understand it. Yes, so... Ah well, it's a sign of the earth. So, there is a natural, emotional way to arrive at a certain necessity of the structure. Locally, there is space, there is the structure. Locally, there is what is space. I think we can ask ourselves what is the consequence of this law. We are waiting for something on a more classic question, this is a classic question and obviously this is the problem. I don't think we have anything original to say on this question, but what we can see is that the question is asked in a particularly very obvious way, especially when we have this initial approach, which is clear for a concrete realization given by the class of mathematics, What is space-time? Space-time can be defined by the number of objects, by the number of objects, by the number of objects, by the number of objects, by the number of objects, by the number of objects, by the number of objects, by the number of objects, by the number of objects, by the number of objects, by the number of objects, by the number of objects, by the number of objects, by the number of objects, by the number of objects, by the number of objects. The concrete realization of space is something that is largely conventional, very conventional, because my deductions on the two points of gravity and multiplicity, they give a huge freedom in the choice of possible realizations of space.

32:30 For example, this is the case when we come to a rule that says that its displacement, for example, depends on the length of the sky, it is displaced on the 14th. It should give you an idea of what the sphere is, and it is compatible with mathematics. So, there is this complexity, there is the idea of causality, etc. and it would remain important. So, in the extreme, we have to add physical factors, for example, in general, we have to do it in a simple way, in the sense that the realisation, by demanding that the realisation is concrete, is the rule of the collection on the 4th of January. And so on and so on, and so on, and so on, and so on, and so on, and so on, There is a clear argument that the approach of Levy is based on structural analogies between the two.

35:00 I have already told you that I am an elementary teacher, apart from the other two. But Levy believes that in mathematics, it is directly useful to discuss the problem. Only the global theory can say that the processes pass under a non-classical framework. You may want to know if space is a substance or not. So, if you take the case of a simple space, spatial variations in relation to the space of a given object may be considered to be the properties of a substance. In the case of the Earth, the surface of the Earth is very small. As for space-time, the local events in space-time are very important. Classes such as the U.S.A. tend to be affected by such phenomena, such as violence, violence, violence, violence, violence, violence, violence, violence, violence, violence, violence, violence, violence, violence, violence, violence, violence, violence, violence, violence. In the case of Spasta, he was often criticized in the last few years, and a good part of it is due to the fact that he is a scientist, not a scientist by name, by name, by name, by name, by name, by name, by name, by name, by name, by name, by name, by name, by name, by name, According to the equations of general relativity, the evolution of time and other varieties is determined by the moment.

37:30 So that's the point. That is, as soon as you have shared your space with time, by location, space, you have shared your past with your past, you can always imagine, a little bit more, the quantities in the past, in the time that you arrange. You know, with this new morphism, from a solution of Einstein, we will be able to build another one, which will be the same as in the past, but which will be different in the future. And so, the theory seems to be deterministic, and what is excluded is this. There are a lot of functions that allow you to do a lot of things in order to regulate and apply them in order to react on different fields in a very complex way. It's not that you have to be in the field, but you have to be able to solve them. The equations are very important. The basic equations are the general equations. So we're going to take the equation that is equal to f of x. We're going to take the equation that is equal to f of x. Y' is the integral of f, and what you are trying to say is that if at the origin we change f, we change the solution, which is the integral of f, that's for sure.

40:00 If we change the function f, we change the integral of f. There is no doubt about that. But when we say that things are defined in different ways, it's not like that. You are changing the equation and changing the problem. As well as those of the Humanities, as well as those of the Humanities in general, have to deal with a lot of different things. We give ourselves a differential equation and we can achieve a global change of coordinates in the space in which we are and it gives the same thing, but in a different system. We don't have the right to judge. That's what I was going to say. I didn't mean it that way. No, no, it's precisely that. There is the argument of the hole. It's an argument that is not valid. It's an argument that is not valid or not. It's an argument that is not valid or not. I agree. I'm going to refute it. But it was Chelle too. Thank you for watching this video, see you in the next one! Because what is not clearly stated is that there is a grasping of an algebraic, mathematical or physical material and that we must un-grab, we must have the thought of the un-grabbing of a first grasping. And where the un-grabbing of a first grasping takes place, it is to grasp the object as it is. Thank you very much for your attention. It's a lot of different things. Cross-referencing, changing labels, etc. It's an exegesis. But we haven't changed anything. I mean, we're still here, but I was leaving to try to see this trap. I think we can't stop if we don't construct things in an administrative way. We don't have, at this point, any idea what the people are doing.

42:30 All of this leads us to a space-sufficiency notion that is non-metric. And in fact, the part of this physical application, in this sense, we don't know how to give a given number, a given curve, a given physical value, without giving the interpretation of the metric that it is a curve. In the approach that I gave, we start with the choice of a curve, a distance and a reference point. It's not the same as mathematics, because at least you have a certificate of physics, but which is constrained by integral relations, which tells us that the integral of the U.S. associated with the object is a point of reference, a common point, and you can find the value of the coordinate. So you have what we see in the dual expression of the Euclidean equation, which is completely clear. This interpretation, in fact, of the coordinates, it is not given at all, it is deducted from the human transformatory. That is to say, you will have, like once you have read the unit, you will be able to calculate the ds of a point of reference, but it is not given at all. And this is where the errors of the two transformatory systems correspond in fact to different institutions. And when the change in the etiquette is made, the measurements are the same, and our insects are not the same. I think it's a very interesting topic for you, because you have a mathematical point of view, so I'm going to go back to your point of view, because there are quite a lot of ideas, but in fact, it started with John Norton, who came up with Einstein's argument, which was blocked by the discovery of Einstein, and after that he really understood what was happening, but in the population of Naïve. It's quite difficult to explain this problem and when John Norton and Victor started to talk about it, they saw a real problem.

45:00 I think there is a real problem. What do we count as the same event? And that's the real problem. It's the possibility that there is a map that you put in your head if there are no more... But even in terms of events, for me, it's something... it's something to listen to, you know. It's something to listen to, that's for sure. But I take a good starting point, even if it's an event, it's a positive event. And there are a lot of things that we don't understand. In fact, I went to another... The system of cohesion is not the... I have another question, rather physical, let's say... Is it true, I don't know, but it seems to me that this idea of rigid rules, let's say, from the point of view of contemporary physics may not be of great importance. And on the other hand, if it is really this idea that is in front of the... the idea of rigid rules that move... And if it is true that the construction of Riemannian varieties, where each neighborhood is infinitesimal and Euclidean, if it is true that this construction still depends, according to Engholtz, on this idea, how can we look at it from the point of view of contemporary physics, of general relativity? Can we perhaps criticize this approach on the basis that something like a rigid movement is in fact a naive idea that is in the physical sense? That's what I was saying. We can certainly do that. It's probably not advantageous to start there.

47:30 What I can only say is that the actualization of the laws of general relativity, which are based on ideal operations, well, there are two. I would say that it is the theory of law that is relativistic. And there are others that I forgot to mention, there are three others that we discussed earlier, on the movements of particle tests. And that was apparently constructed with the idea that we could start with complex systems. It seems to me that it's not... I don't know, maybe we can do it again. But anyway, what we can say is that physically, it's not that complicated, because there is a limit, Concretely, in general, these are the effects. So, it means that if you have a chamber at the same time, the length of your progress is the same as the length of the chamber you have placed, then you can co-opt this part of the process. Obviously, when you have a correction, when there are temperatures, for example, for the progress, you can tell yourself that this is an analog situation, that anyway, the notion of cohomology is an operationally complex. Geometrics is an object notion, like the problem of metrology, of French decorations. But can we do it systematically and in the case of the general? I don't know, for me it's an open question. My question is perhaps a little bit the opposite. Can we save the idea of Riemannian variety without this idea of co-regime which is... Which obviously do not have much relevance in contemporary physics, or we can say that all these mathematical frames, we can demodel, we can change something else, but yes, we can always do that, it's clear. Of course, after we ask ourselves the question, if we ask ourselves the question today, you will have a certain number of questions, even if you see that the interpretation is a little more radical, in the case of an academic lecture, but to be able to understand, in fact, the spatio-temporal, geometric relationships in space-time, in what sense, in what form they exist, in terms of information, in terms of aspects that I have studied in general, I mean, I have a lot of trouble understanding, in the end, what the signification is.

50:00 We are used to space-time in modern biology, and in any case, we assign space-time on large scales, not only locally, and how do we do it in a coherent way, satisfactorily, etc.? There is a distinction between the field of science and the field of history, and there is a difference between the field of science and the field of history, and there is a difference between the field of science and the field of history, and there is a difference between the field of science and the field of history, and there is a difference between In the process, in the process of the process of the process of the process of the process of the process of the process of the Did he have in mind something like this genetic approach? But, fortunately, the people who took up the topic of mathematics did not quite understand what we mean by a static universe. Fortunately, the German government did not think about it. But it seems to me that it is a trap of mathematics, that is to say that people tend to think in a humanistic way.

52:30 Without mathematics, it is already a spatial. This is a space in the sense that it has no spatial meaning, or anything that allows us to see objects. That's why we prefer relativity. Because there are two spaces, there are two spaces of dimensions. Because there is a tradition of parametric approaches. What do you think about Helmholtz's text? The idea of associating objectivity is one of the most important aspects of the question of objectivity, very succinctly, but it is also part of the idea of associating objectivity.

55:00 In the philosophical debate between relationalism, substantialism, and conventionalism, the position that Moll occupies is a mixed one, don't you think? Yes, there is a debate on conventionalism, but the problem is that there is a psychosociological context that makes the debate... So we have to make a difference between the logic of these elements and this decimus. All of this has been highlighted, on the contrary, to put it a little on the table, because, in addition to closing the table, we start with the string theory, for example, we never test that the formula is the same, and the idea of the algebra, etc., etc., we always think that it starts with a square, but in fact it is false, because there is an article in the Mons where, in fact, it is the same. But it is in passing, and then with in fact in the same way an exhibition of a practical benefit, it is not very important, but it comes from the fact that we can choose a mathematical theory, if you will, and this conventional freedom, it will not be put into practice. It is not very important. And so, as Karine says, we are going to do that in the future. I think he understood the logic of the thing, that there are passages in the book that depend on the question we are looking at. Two things, for information, I think that... At the end you were talking about the problem of dictation, Hammond-Weill called it the magic of the name, the people who fall into the error of believing that the name is something that is substantially attached to the thing.

57:30 This is a thing that was discussed by Marx to be a problem. Ok, but we're not done yet, it's in chapter 27, so it's about general relativity. It's probably about the hole problem or something like that. Otherwise, what's interesting is that on the vocabulary of... Maybe because you are a physicist, or maybe because you are involved in what you comment, but you use the vocabulary a bit like in the 19th century, that is to say, by distinguishing not systematically, by distinguishing not systematically. In other words, by not systematically distinguishing the local and infinitesimal. For example, it is locally Euclidean for infinitesimally Euclidean. And so, for us, it creates misunderstandings, I think, because... Small rules and infinitely small rules, for us, but it's because we come after the 1920s, 1930s, and it was not yet obvious at Einstein's level, because the mathematics of his time did not distinguish visually, we could still consider that the small rules were infinitely small, although for us it is relatively to see, either we place ourselves in the tangent plane and we are elsewhere than the variable. No, no, no, I agree, I agree, I agree that we have both at the same time. Ah, but it's obvious, and besides, it's the view of the human being, it's not the view of the human being, it's not the view of the human being, it's the intuitions... Well, after that, your view on what works best is... In every word of gender-difference that you say, you have something that lives in your mind at the same time. Yes, there is the symbolic mechanism in this term, but it's not... I agree, you distinguish the symbolic mechanics of how it works. I understand. At the level of activity, we walk, those who see it, walk both ways. I agree, but historically it turns out that there is a period where we found it interesting to distinguish, compared to the period that retrospectively appeared as a period of indistinction. I can't say that we should forget what was done in the past or that this indistinction was not rich and not important, so people before were doing anything.

1:00:00 It's not a question of saying that before 1930 we were doing anything, of saying that Élie Cartan in the 1920s was doing anything because when he says neighbor, in fact they hear infinitely neighbor. When I'm saying that they don't do anything. I agree that I'm not sharing the right intuitions with the wrong intuitions. No, I'm saying that there is something important to be played out in this book, namely how to build the architecture of intuition in your progression and in your understanding of everything. Of course, the work of Descartes is essentially to understand the architecture between these two levels of intuition, between infinitely small rules and small rules. I'm talking about connections, you could say it like that. Anyway, a neighborhood can be very big. That's what I'm talking about. You're talking about after 1920-1930. You're talking because... As an intuitionist, I think that saying something like that is not very... It's like there are people who think that the universe doesn't exist. There are structures that are made up of... I don't know if you take indistinction or rejection of indistinction, but...

1:02:30 But I continue my remark on the fact that at some point the possibility of saying, but no, you can not say local at that time, because the fact is infinitesimal. This possibility of saying it emerges historically, which does not mean that it is the only way to do it and so on. And it emerges well after Helmholtz and even after Einstein. For Einstein it is a bit complicated. And this same distinction also poses a problem with the meaning of what we call a metric, since between a DS2 and a metric on variety, a lot of people don't care that it's the same thing. Is the metric on variety measured by the geodesic distance? Is that the question with Helmholtz? There are two meanings of the word metric, depending on whether we look at the infinitely small or the infinite size. But above all, he goes from the infinitesimal to the local without complexity. Well, the global, apparently, he does not even ask himself the question. Ah, the global. So he goes from the fact that for him there is not in the mathematical language a clear distinction for which we must systematically specify at what level we place ourselves, makes certain questions that we ask ourselves ... You can't put your finger on it at home, but that's a matter of history. It's the use of categories that are not the ones in which it is written. Maybe you can, if you're an academic. But it's true that it may also create misunderstandings with people who have learned mathematics in other fields. In any case, I think it's remarkable that there is a great deal of creativity. We can see that there is a lot of creativity. I remember Mordicus saying that this is the only thing that we can... Moving a ruler is a different thing. I think it's the only thing we can achieve. We have to move a lot of space around the ruler. All there is in the thinking of the group A and B is already local mobility.

1:05:00 It's locally. The structure is what we call the structure of the group A and B, which is in all modern references, because we have never globalized it with other things. We could have done something or other things that are non-servable. The local case has been a little under the surface, but it is played out, it is the different local systems, we can of course claim that if you have your ruler here, 200 meters, there is no need to move all the space with you, but Kelly will answer yes, because in fact it is played out locally, you do not need to move a lot of your ruler, so you have to send a small piece of space on a small piece of space, so you have a different type of space that will stabilize the distances, because it will not only stabilize your ruler, your little ruler, but it will do more than that. It all happens in a generic way. At this point, it is the whole of the isometric transformations of quantum mechanics. And here, we are looking at the model of homogeneity, that is to say, the group of local varieties of mathematics. Maybe even one point. Well, it can send any point on any point. Even though we know that the number is just a little bit. And I think what I'm saying is that, just imagine that space is a little flat here and very low there, the rule is two-dimensional, it is, how to say, forced to be two-dimensional, as it is rigid, even infinitesimal, it is difficult to consider an intuition that is in relation to what is precisely the theory of the universe, it is that we have the impression that if it is infinitesimal, if it bends a little bit, it will be able to follow, but no! Whatever its length, small or small, there will be anyway six or six... If space begins to move, it will be forced to go outside of space, in a three-dimensional space, in order to be able to move. This is a term, so it must remain in a three-dimensional space. Yet, in physics, it is clear that we can do everything we can, and if we go to the surface, there is a rule. I told you, it will tolerate a small rule of small deformations. You can do it with a given decision. Because you have the dimension. You can do it with an advantage. The third dimension. But if you were with something that is curved in the three-dimensional space, We don't see them because we have a new location, but it wouldn't be possible, we would have an efficiency, we would be like families, they would be able to walk around in certain places and suddenly they would see the clouds that are there. It may not be too open-ended, because it's a differential system.

1:07:30 It's just the metric, everything is differential. I didn't say very perverse, it's a small piece of furniture, a small piece of furniture with collars around Marseille. But it's an object, a piece of furniture. It's an object that falls on the surface. There is no other way. It must be able to move. It must be able to move. It must be able to stay on the surface. Thank you for watching this video. You don't have an idealization of precision level. Precision level is something that is different from idealization. If you count it, it's not the same thing. You can make it, I would say, small enough, but not as much as you want. Ideally, they are not of the same nature as the infinitesimal. One last question, more general. Helmholtz, when he begins his text, presents this in opposition to Riemann. From the philosophical point of view, that is to say, Riemann left a priori, and I am going to reconstruct, I am going to deduce what Riemann's starting point was. And in fact, we cannot say that he succeeded. There is an empiric will, I would say, which is a slight regression, even if elsewhere, it does not prevent anyone.

1:10:00 But it's true that for me, we learn as two, that is to say, we don't have to focus on one or the other but on the whole of the intellectual property. There are three. There are three. There are three. There are three. There are three. There are three. There are three. There are three. There are three. There are three.