Introduction / Alain Connes / Michael Atiyah / Q&A (contd.)

0:00 I forgot to mention something extremely simple, but which reveals that the texture of space-time when we look at it on a very fine scale, not on a macro scale, when we look at it on a very fine scale, but not at the one we expect, that is to say the one we call space-time, R4, But it has a texture that is a little more subtle and that can be described as a fine structure, exactly like spectra. And when we look at them, first we see the spectra. And if we look closer, we notice that there are different layers, different rays, and so on. So, if you want, the equivalence that we have, well, on the space-time, if we want... If we try to evaluate them, if we try to calculate them, we simply have to go from the relative constraint which is given by the trigonometric matrix, which is equal to 1, which is given by this matrix, we go back to this matrix which is that of the flat space, a matrix which is variable, which is quite short, of course, and which gives the potential for the national, and this potential for the national, it follows a principle of action which is extremely simple, which is the principle of action of Richter and Huber. And they consist of integrating quantum mechanics. So, in fact, there is this. On the other hand, in physics, as we know it, there is not only a number of sources. There is a number of terms that are standard. And the second thing that happens, which is a bit of a difficulty, is that we have to let go of the classical logic that there is a new experimental recipe, which is called Heimann's graph, which consists of replacing probabilities by an amplitude given by the exponential imaginary of the action in the universe. When we do this, we come up with a number of problems, and the main problem is that the parameters are in action, and they have to depend on the energy level.

2:30 The problem is that when we look at things in a very concrete way, we get stuck in the standard model. That is to say, when you give me a formula, it's clear that I don't want to use thermodynamics anymore. There are people who are going to tell me that I'm completely stupid. But if you can do the calculations with the standard model, that's it, you can calculate. That's what we call the universe. And that's what makes the interaction with the universe that contains all the metaphysics that we have on the hypercharge of particles, on the mechanics of the universe, on the spontaneous pressure of signals, on the interactions of forces, etc. You could say that in a complicated way, it's not true, but I used Einstein's transformation, which could give an extra value and sacrifice things, in the sense that what I give is the large-scale standard model in flat space. That is to say, I normally do it in a short space. As we said, they were cut in a minimal way with the validation, and there would be other terms that would appear, in particular, the terms in the scalar block, for example. In the last ten years, with A. C. Zedin, we had already done a work on the problem. We had announced a principle, the principle of spectral analysis, and which is a principle that allowed us to understand the standard model as it was at that time, in those years. It was before the experiments of Samuel Kanté, and we had a geometric model of this. In this case, we realized that we had not even tried to see if the same spectral principle and the same speculative principle were the same. A few years later, we finally got together this summer with Alexandrie and the other participants. And finally, we realized that there were a lot of defects in the old model, in particular the problem of couplers that always disappear by miracle and that, in addition, simply do not work. The fact that we change the gradation on antiparticles, well, we automatically obtain the neutrino balance, as we have already said, and the mechanism, that is to say, the mechanism that allows us to have extremely low masses, so we do not know how to get rid of them.

5:00 All these defects disappear, it means that the improved model, in fact, which appears in an extremely natural way, what disappears is that in the modern model... At the end of the lecture, we were still talking about representations and so on, but at the same time, they have a map of the past that comes to mind. That's what I wanted to explain, that's what I wanted to explain. The first thing I wanted to explain to you is why the mutative world? So why the mutative world? Because you saw the graph that I gave you. Well, it comes from an extremely simple reason why the mutative world appears in a very natural way. It appears simply by looking at the symmetries on the graph. You can see that in the first year, there was the gravitation. The gravitation brought symmetry to the group of students. And there was the theory of George. The theory of George brought symmetry. Symmetry is very different. It is a group of applications of n at the value of g, where g is the small number, the small number, if you will, and for the standard model, it is the number of 1, 3, 2, 3, etc. So, there is a question that is extremely natural to ask, if you will, which is, now, what is the total symmetry group? Well, the total symmetry group is neither the differential group, nor the group of George's transformations of the second species, that is to say, the application of M. It's what we call a semi-direct product. It's not the product. Why don't you make a differential where you change the transformations of George? You sit on it. So, in fact, it's what we call a semi-direct product. And this semi-direct product is the natural symmetry group of the norm of Lagrangian. So, it is only natural to ask a conceptual question. The conceptual question is, could this latrine be a biomechanical latrine, i.e. a gravitational latrine? If it was the case, we must remember that this group there, the group that is in this solar system, simply becomes a form of differentism in space. So, if we are looking for, among the ordinary lakes, an X-space in the form of differentism, either in this form there, we will never get there. We will never stop because there are so many theories, so many advantages, right? And the truth is, in general, if you take quantum mechanics as an example, you have different varieties, whatever they are. You can do all the variety choices you want, you can do the quadratic ones, you can do whatever you want. If you look at quantum mechanics as an example, it's a simple formula. A simple formula means absolutely nothing compared to the structure of the human process.

7:30 When you take a linear process, the subgroup, which is the subgroup of applications, is a normal subgroup, a distinct subgroup. A subgroup is not a distinct subgroup. It's not possible in the real world. So why is it possible in the real world? I'll give you two examples to explain. We're going to look at a simple example. We're going to look at, we're going to take, if you will, as a gene, not the gene of functions, we're going to look at genes. We are going to take an algebra that is a little bit different, but very, very little, when we say that these algebras are equivalent in the sense of an orbital, and that is simply, if you want, the chain of matrixes that are there, that are there. That is to say, I look at the time of the functions of n with a complex value, I look at, for example, the matrices of 2 functions, and I multiply them by matrices of 2, and then I multiply them by matrices of 1, 2, etc., and I multiply them by matrices of 2. So, this can be seen either when we have applications of n with a complex value. All of these are related to the function of the function of the function of the function of the function of the function of the function of the function of In a commutative framework, the following happens, each time we take an algebra that is not commutative, there are automorphisms that are those of the form F, the element F gives UF, UFS. You see that UF and UFS, if the algebra is commutative, it will always be a grade F. If the algebra is not commutative, it will give a transformation that is not trivial, but which is a basic automorphism to construct, because it is necessary to have read to construct it. And these automorphisms, we call them interior automorphisms. Other manifolds are normal, such as the algebra group, but the quotient, which is very important, is called the quantum group, or the task group. So, it is a small exercise that I recommend you to do a calculation of this sequence in the case where algebra is not the function of the scale, but the function of the matrix.

10:00 If you look at the exact sequence of the world's internal automobiles, you will find exactly the same exact sequence as when we looked at the standards of the world's automobiles. This time, the object will be the special group SEL. There is something that is extremely satisfying, which is that mathematical terminology coincides with mathematical terminology. That is to say, in mathematics, we talk about the interior, and physicists talk about the interior. So it's one of these many coincidences that makes all the terminologies are the same. So what does that suggest? Well, it suggests that it's only a good idea to look at spaces, okay? So that we pay a little more attention to the moment of the activity of the coordinates than we usually do. Not by chance, because in fact, we looked at a matrix of functions. So it's not much of a nuance, but we have to pay attention to the following, it consists of asking the question, well, it's very similar, but the real question is not that, the real question is what will be, if you will, in this framework, so the general framework of mathematics, but not space and globalization, of coordinates, but what will be, if you will, in the notion of the future, what will we mean by the notion of the future? Geometric notions are relatively easy to understand. All those that come in, what we call the two-round chronology, all those that come in, the outside, in connection with the outside, it's not very easy. There is a notion that is much more difficult, it is the notion of geometric law. And in the notion of geometric law, there is the notion of distance. This is the central notion. So this central notion actually has a meaning when I put it in the putative. And what does it give? Well, it gives a notion, if you will, which is entirely impossible to explain. But to explain it, so that you don't forget it, I'm not going to start with today's formulas, I'm going to start by explaining an evolution that has already happened in physics, that I'm simply not going to follow at the mathematical level to define this whole notion. So, what you understand is that, if you want, in the Muslim paradigm, in the complete Muslim paradigm, we all have, if we write the S2, we have the X1, the X2, the X3. That's the Muslim paradigm.

12:30 And what do the paradigms correspond to? Well, they correspond, if you want, to the fact that we have a blogger's personality, and if we calculate the distance between two points A and B, We calculate this distance by the formula that says that the distance between m and m is the kinetic distance. It is the refinement of our integrals of a to b of t and c. So that's how, for the end of the 15th century, we defined the meter from the number of hours calculated from the 48th of the 10th century. So, what happened then? Two things. The first point, if you will, of the thematic. And so, in the meantime, in Dirac, we have a way to extract the equation given by Laplacian and call it the equation of physics. The equation of physics is that we are aware that the master Talon, who was somewhere there, is aware that in the 1927s, something like that, that is to say, in the region, there were religions, okay, in which he had taken as a competitor the master Talon, and they are aware that, in fact, if... The measurements, in a very fine way, with its length, are completely identical to the length of the triangle. And how did they perceive it? They perceived it by comparing the length of the triangle with the length of the triangle. For 33 years, we realized that this parameter changed the definition of the length of the triangle. The length of the triangle is the length of the triangle of a pure triangle. In this case, the length of the triangle is a krypton and the length of the triangle is a cisel. The change of formula in relation to this formula... In this example, you will obtain the same distance, but it will be multiplied by the following number, the distance between two points A and B.

15:00 It will no longer be given as a decimal, it will be given as a suffix. And it will be given by the suffix f of a times f of b for the absolute value. And there will be a condition on the function f, which is a kind of bound function, if you like. This condition on the function f is simply the function of the computer with operator t on the norm of the logarithm. What is the meaning of A? If you want to know what it means, it means that our algebra A, which is the algebra that we put on our space, we don't want to see it as an abstract, we want to see it as an operator algebra in this Witten space. That is to say that the elements of the algebra are not separate, they are concretely represented, what we call the representation of an algebra in this Witten space. So, if you look at it from the point of view of A and the representation of A in H, it's nothing, that's what we're going to do at the end. It gives you a particular balance. But if you want to measure distances, you need to measure them, and so you find operator D. Note that operator T here does not have the dimension of a length, but the dimension of the inverse of a length. Why? Because you find the result on the length. You see that there, perhaps, is the product of the debate. So what is it, in fact, that operator D, when we think about it a little bit, is the dictionary, if you will, between the calculation of the classical decimal and the calculation of the decimal that comes out. If we look at quantum mechanics, we see that the real variable is a notion that is a little more complex. Because the real variable shows that space is an application of the real variable. In quantum mechanics, it is much simpler. It is much simpler because it is simply an operator. If you want, it has a spectrum, it is the set of variables. We can see that in the dictionary. It is all in the dictionary, I could not do it. But what is remarkable is that in this dictionary, there is a place for the dictionary. And we will be able to read the physical magic of the compact operator, which was illustrated by Dirac in the patient's square root. There is a formula in quantum physics, and this formula is called T.S. T.S. is the operator T.

17:30 T.S. is the operator D. It has, indeed, the dimensions of the length. And how does it intervene in physics in a completely regular way? For example, everywhere. It intervenes in physics as the operator T.S. That is to say, the point we are making, please, we now have the point of interaction. The point we are making as a physical theory, one way or another, should be the same. On the math side, mathematicians have thought a lot about what a space is, which is not in a way, how to say, by giving a variety of components, a collage of pieces of space, which is a recipe, but they have understood, in terms of mathematics, what is an extremely important component of a variety, and this important component is not only the duality of squares. So this is the duality of Poincaré, but it's not the duality of Poincaré in your ordinary homology, that's far too weak, but it's the duality of Poincaré in a more fine theory called K-homology. If you want, I can tell you just one sentence, it's that if you take a space, and you only take this space with an ordinary Poincaré duality in your homology, you know very well the structure of the French variety, there are 36 different varieties. They all have the same structure in that sense, and the new structure, really important, is the case of the triad. And these classes come from the chain of what we call the fundamental class in the red square. What is it? It is given exactly by the same data as what defines the commutative space. So a non-computative geometry, a spectral geometry, not called a non-computative geometry, a spectral geometry is given by this. That is to say, it is given by an algebra, I'll show it to you later, it is concretely represented in this Hilbert's theorem, and we have the inverse of it. So this long-term inverse has two ingredients in it. It has the metric on one side, because it's a formula. This formula will have a sense of general meaning in stories that are more connexed by art, etc. We don't measure it in terms of geometry. We measure it by sending a number and by looking at the phases of the number. It's very different. Now, the ordinary geometry is an intermediary of this geometry. We feel that if we take a derivative invariant, we actually have a spectral geometry, which is given by Robert Atiyah.

20:00 You can see that the grader has two roles, he can calculate distances, and he also has a role on the road. And this role on the road is to fix the fundamental class. So to keep it in a positive way, please, it means that this fundamental class, you have several external means. As you can see, it is fixed by this structure. We know that we are going to have a space where we can have the notion of variance. You can see the physics itself, why it is important. It's important because, if you want, you have a meeting point between gravitation and field theory. What is this meeting point? In particular, we need what we call a real structure, which plays a very important role at the level of mathematics, where it is what we call the operator of charge conjugations, rather than mathematics. In mathematics, there is another very interesting coincidence. When we look at an algebraic diagram, What happens is that the gradient of the hierarchy that is going to be real, that is to say, it does not mean that the stars of the universe are going to be real, no, it means that it is endowed with an antilineal isometry. So the square can be more or less that, it depends on the dimension of the sphere. And you have here the rules of commutation in D and in relation to the Z over 2 of the radiation. The Z over 2 of the radiation is called the Hiram-Iterative. It only intervenes when it is in the structure. So that's the structure.

22:30 In fact, there are two different dimensions. There is the metric dimension, which is the dimension that comes from the presence of the proper values of O'Connor. You see that if you are in a dimension space, there is not the power of the operator, there is the power of an object, if you will, the volume of the space. There are these two different dimensions. And there was something that had blocked us, if you will, there was something that had really blocked us for a very long time, it is that space allows us to solve the problem, to transform it into something else, towards the adaptation that is very simple, well, it was that, in fact, because we had worked with Amiga a few years ago, We thought that the metric dimension was the same as the cohomology dimension. And at that time, there were no specific examples of spectral geometry in mathematics. And since then, there have been a lot of examples of spectral geometry in mathematics, which we have understood as quantum space. In which, precisely, these two dimensions are not the same. Why the n over 8? Because it has three signs. So, there are two answers. And there is a practical answer, which is the same as in the theory. If you want, exactly as we had the symmetries of quantum mechanics, the metrics that are linked in an integer way, because it is still very important, it is the prototype of things that have no sense in the computational and that acquire a sense in the computational.

25:00 So what is this notion? It is the notion of the equivalence of our methods. If both of them were computers, they would be the same. A projective module on the Maritimes would be the sections of phi. The example is the epsilon and the a. In this case, we would have the same matrix. It's very simple. These two elements are linked. They are not identical, but they are very similar. In this case, it's very natural. Suppose I have a matrix for a, that is to say, a spectrometer for a, a, h, b. Can I use a spectrometer for p? It's easy to put p here. It's easy to see how the space of a tree will change. You simply take epsilon. Tension is divided by h on a, you see, it acts on epsilon. Tension is divided by b on a, you see, it acts on epsilon. You are looking for operator b. And if you write, for example, operator 1 tension b, because it does not communicate with a in this space, and you must be able to communicate with a.

27:30 Do you know what it gives you? It gives you a notion that is absolutely fundamental and that is not found in a lot of equations in the standard model. It is what we call internal fluctuations in the matrix. And you do not have a choice. In fact, what happens is that you have to replace them. In other words, in relation to all the metrics, in order to understand whether the algebra of A is the same and where B is equal to A, you have a whole class of metrics that are naturally linked to the metrics of A and that are given by this formula. What I want to say here is that this is a very new fact that has no sense at all. It is a very new fact that has absolutely no sense at all. Do you understand what I mean? Mathematics automatically has linear equations, just as the autoconflicts have a class of autoconflicts that are decomposable to them. It's a little algebraic calculation, and the reason why the formula that appears here, the formula for the commensal, the formula for which it appears, is that the difficulty of defining a transcendent is precisely the difficulty that the commutator has with the algebra. So it's normal that the commutators don't do anything. I'm going to give you the theorem, and if there's time, I'm going to give you an idea of the theorem, applied to a small space that will give the structure. So, M, if you want, is a space in a linear way.

30:00 We're going to do that, okay? Dimension 4, okay? And F will be the structure. It's a very simple idea. You can tell me, but how do you make the product of these spaces? I'll tell you in a minute. There's nothing simple. You make the product of the two algebras, one of them in its two. And if one of the two is clear, in any case, you make the product of the space. At the level of operator T, we have two intents, plus the ray of gamma in this element. So it's very, very simple. It's extremely simple to take two mobility spaces. A very particular characteristic is that space F will be finite. This space will be finite. A finite space in a mobility space means that the algebra is two finite dimensions. So the algebra will be a finite dimension. It will be simply a matrix, an operator in an extremely simple space. In the last years, we took AF, HF space, etc. and we took the scales. So since then, and I hope I have explained it to you, the progress is substantial. It's that we can still see the HF space. And we classify the Dirac operators. And we classify the Dirac operators. And we obtain exactly the same number of parameters as here. Two spectra geometries are the same. I would say that, if you want, two spectra geometries, A, A, H, B, are the same because they are interchangeable, of course, they are interchangeable, they are all equivalent, and the operations are all interchangeable. There may be something that I should also say, which is that there is a very good characterization of the spinorian geometry in its case. All of these are formed by incredibly simple actions. So, I told you, you can't believe that we put all the gradients of geometry in it. No, we put the external characteristics in it.

32:30 So, that being said, now, let me think about the theoretical part. So, yes, the geometry ends as I read it. So, here, it's not the same, okay? The operations are linear, the operators are linear. And then, something very strange happens. Something very strange happens. And that's what we've been talking about for a very long time, is that, if you will, when we calculate the dimension, the dimension of this finite space, it goes to zero, in metric, since the space is finite, right, and it will not stop, it will not end. On the other hand, if we look at the table that I showed you earlier, for the dimension in which it is, we can see that the dimension is here, in this case, at the top, etc. And we're going to see, well, in fact, if you want to, the rules for the next lesson, you have put a link with the link below. So, it is simply given by the following chance, you take the metric in the complex space, the internal situation, so it tells you that D is now going to be decoded by A, that's what we called A, okay, this is the internal situation. And so now you want, you have the fields, because the fields are simply, if you want the D, you eliminate the internal situations, that's what corresponds to the internal field, that's what you need. What is really surprising is that what is the action itself? Now you can ask yourself the question. The function of the action, we wish it to be simple, as simple as possible. What is this function of science? And it is simply to count the number of observables that are in front of us. It's not very difficult, so I'm going to ask you a question and explain the difficulty. What is the difficulty? Well, the difficulty is that if you do gravitation, the first question we should ask is what are the observables?

35:00 And if you think a little bit, you will realize that the distance between the points is not the observable. Why is it not the observable? Because it is not the observable. What does that mean? It means that you can't compare points A and B. The only thing that is invariant in France is, for example, the channel. So you can, afterwards, have invariants in the field of physics, etc. But what we don't understand is that there are only a few invariants like that. First, they are additive in the space of the player. In fact, we can make them integral to the function of the momentum of the magnet. For example, in the case of Decatrix, we can make them integral like that. But it's extremely difficult to calculate these functions. That means that you have to go all over the universe, you need to compute and integrate these functions, which is extremely difficult to calculate. However, among these variables, among these functions, there is a set of them that appear in the spectrum. And they appear for a long time. They appear from the possible coefficients of B, from the value of the trace of the function of the operator B. So now what happens is that these functions are obviously generated by a physical phenomenon. Because the operator of the Dirac, as I said, is not a single object. So these are the spectral functions. So the principle we learned with Anne Chartigny, a few years ago, is what we call the spectral principle. And it's the principle that the function of the interaction itself must be spectral. The problem must be admissible when you take space applications. It's not possible for everyone. Theoretically, when we calculate this beast, which is a little tricky, we will find the norms of the equation, and in addition, we will see that we will have a set of predictions. I will explain how. So the first thing that appears in the calculation is a dictionary. That is, there is a dictionary that contains the terms of the standard model, as we know them, with the geometric terms that appear in the sciences. So, the terms of the standard model, if you will, are, so, you see, for example, you have the boson of Lewis in the standard model, well, how does it appear? It appears as an inner part of the metric, but the metric, when you are in a product space, in a space M by another space F, well, it has the components of type 0, 1 and type 1, 0, so the logarithm says that it has the components of type 0, 1 and 0, so how do we look at the components of type 0, 1 in the boson of Lewis?

37:30 There is a double of complex terms, there is a way to change the variable of the word, which is completely canonical. Then, if we look at the inner part of the matrix, which is of type A0, of type E0, we get exactly the terms we call BWB, which exactly correspond to the terms that are the photon, the Z-magnet, the complex intermediate bosons, W, and then the electrons, the electrons of the periodic table. All of these appear in the operator of Dirac in the small space, in the H-space. That is to say that the mass appears in the operator of Dirac by calculating the square of the module. In the operator of Dirac, there is more. There is more data than the square of the module. And when you look at the component of Dirac's operator of Dirac, They depend on a certain number of parameters, which are based on the carton we have here. So, you have the matrix of the mixture of electrons. It appears from this region here, in this sector here. There is a matrix of couplers that Majorana has, which is a great feature of his mathematics and physics. It is that we have realized that there is a mass term here, and that this mass term, in Majorana, allows us to do the calculations of the system. So, when we do the calculations, we find that we have exactly the same number of terms, which allows us to do the calculations of the system. So now, what's interesting is that when we look at the translation, we realize that the couplings of the theory of physics have the same meaning as in all the theories of physics. It depends on the theory of physics. If you look at the details of the theory of physics... So, of course, there is a difference between the two, but the equalities and the simplifications are always the same.

40:00 And it always implies this 5th constant that appears in the calculus. It implies that the square of a strong constant is equal to the square of a weak constant. So you have this relationship between the three doubling constants. It is exactly the same as the one we have here. But the good news is that we have not only unified the doubling constants for the two fields. But we also have to define the percentage of couplages for the x-axis. That is to say, Nelson talked about it in detail, and it's called the log of the x-axis. The x-axis plays the role in the log of the x-axis, and in the log of the x-axis, there is a value. That's why it's very important, Nelson, that in our modern model, we can calculate the value of this percentage of couplages. Alignification is very fast. It is very fast, and I'm going to show you the value of the parameter b, a, b, etc. It is very fast in terms of the masses and the places to have the numbers. So there is a prediction. And so it is fixed to amplification. There is another term that is related to the problem of naturalness, or the problem of hierarchies, and which is related this time to the square term in the standard, that is, in the ancient term. And in fact, what I want to say about Newton's constant is that the constant of Newton is also predictive. That is to say, it is very important to show a little more detail on what is happening. Yes, yes, yes, yes, yes, yes, yes, yes, yes, yes, yes, yes, yes, yes, yes, yes, yes, yes, yes, yes, yes, yes, These constants are specified in front of the term Watt, in front of the term Hilbert, in front of the term Watt, in front of the term Watt, in front of the term Watt, in front of the term Watt, in front of the term Watt, in front of the term Watt, in front of the term Watt, in front of the term Watt, in front of the term Watt, in front of the term Watt,

42:30 The philosophy is a little bit French. My philosophy is that when we use the same thing as in the theory of quantification, we will learn the point of view of Wilson, and we will say that when we use a mass parameter in the theory, since we have taken the mass, but we have used it somewhere else, we have a level of energy, and then we will consider that the theory is a theory that manipulates this energy. It's a hypothesis. And then we use the formulation of the mathematician. To go back, what we see in our chain is nothing more than the integrated part of this theory. And what we want to know is if it is compatible with Einstein. But it does not stop us from considering, in a functional way, a given energy. And we can integrate the modes of vibration here. The one with action. The one over there. The one over there. You mean the one with the engineer? Ah yes, the one over there. Well, this one we're going to see, we're not going to wait for it, but there's a video that we're going to see. We're not going to wait for it, we're going to discuss each one of these things. So, supposing that this structure, M3, is essentially an elliptic triangle, you wouldn't say that it's an elliptic triangle? That's right, that's right, which is definitely wrong. That's right, you're absolutely right. So, here, we're doing a hypothesis that's well written, but we don't know what's going to happen afterwards, because we don't have energy. So, we're doing the hypothesis of the Great Desert, okay? We've done it, we've taken it down, and we're going down, and we're going to see what happens. What we hope for is not that... If predictions are more than 1,000, it's not possible. What we hope, if you will, is that it is not very distant from reality. And that afterwards, when we show in energy, we will see that things will probably become deeper. And that, in fact, if you will, things will become deeper.

45:00 In fact, the calculation from ten years ago with Hager was complete. We can't do anything else because, with the whole mass, they interact in a projective way. It must be true. It gives us a relation between the masses of Ferdinand and Ferdinand Poisson. And we can recapitulate it by saying that a quantity that is well known in the organization, which is the vector of S, which assembles squares, squares of a square, we put a 3 when we have the color, this quantity is the vector of S, and it takes the multiplication, it is called Cartesian. So this is a prediction, and I will show you on the graph that when we use this prediction, we find the mass of the top, because when we go back down in the equation, we find a post-section of the mass of the top, which gives 1 for the evocations of the mass of the top, like that. So you're talking about Goethe in mathematics, does that mean that we can calculate corrections at any point on this? Well, what we do, what we want, is that we say the theory, and I will explain in a more conceptual way afterwards what the thing is. Theoretically, there is a highly written theory that is valid for unification, and this theory is then re-designed using the group of re-enactments. And now we can calculate with a loop? Yes, of course, but it doesn't make a difference. In fact, it's really the calculation with a loop. If you calculate even with two loops, you will see that there is a very small difference in the flow. Okay, I'll show you the numbers. Good. So, let's continue. The following prediction is that we give the value of the strong coupling to unification, and when we give the value of the strong coupling to unification, what does that mean? It means that if we increase the FK model that you were talking about a moment ago, the constant of couplings is very precise.

47:30 We have calculated, I will show you the graphs, and it gives us what is at the rate of 166. The prediction is that, we will see, it is theoretical. To articulate the concept of the top, what are the parameters that we have compared to the concept of the top? Well, it is that the function f, we take the symbols, okay? There is a universality, and it only belongs to its values. So it only belongs to its value at zero, or its integral, or the integral of x, okay? And so we have simply scales. These scanners here, among them, if you will, we have a zero which is the value of zero at the first moment, so we come up with an x squared. So, in fact, what we come up with is that it is enough to think that this one is connected to that one by that, it is not... Okay, we have to have the right balance. So what happens to the x-parameter? To have the x-parameter, we have the value of the multiplication. We take the equations of the number of denominations to make the equations. Because we make the hypothesis of the number of zeros. If we didn't know the hypothesis of the number of zeros, of course we would have known the equations. So these equations are differential equations that we can solve with mathematics, etc. And so when we calculate them, what does it give? All of these terms are used, they start at the same level, we make them run on the rotation rotor, which adds value to our scales, and then, of course, we use them to calculate our mass, which of course is taken too seriously because we don't know what happens next.

50:00 But that's all we know, so that's it for now. So the relation of mass comes in a rather specific way, that is, when we do the radial change, well, look, there's a lot of... These variables are the standard parameters. The standard equation is the mass of the cube, the g is the constant of the cube, this is the mass of the cube, etc. And from the other side, we have the matrix. When we talk about variables, we realize that we have to do a parallel transformation. There is one thing that is quite important, and it is very useful. Usually, when people make masses in a cube, they add 10 times something that is not the same. By using this parallel transformation, we get back to the quantum operator. So, we don't make a lot of calculations. And what do we do? We use the way in which... We simply use the relation of traces, which is what gives us the relation. And then, we use, if you will, the... So, it gives this relation. Then, we use the group of interpretations. So, we use the way in which... the plot, the time of the law, and finally, we obtain the graph. And we obtain, in both cases, the relation between... There is an extremely important part of the project which is the gravitational terms. The gravitational terms, in general, can be written. This is what we obtain. When we obtain a term of Newton, we obtain a term of Weiss. When we obtain a term of... We obtain a term that had been predicted by, for example, the selection of a number.

52:30 The comparison, when we compare it to the standard equation, All of these conditions have been given to unification. One of the things we were afraid of at the beginning was that the term of Paris could have had experimental consequences at all levels, even for a non-essential term, to know how these terms moved with the course of the realization, The normality of the idea of renormalization is to use square terms, or terms like that. What happens is that it has what is called a point of action to the mass of the clock. We can perfectly consider it as an energy that is right below the mass of the clock, and then it goes down, and then it goes up. What we don't know how to do is to renormalize the constant of the equation. But we know how to renormalize the terms alpha 0, the terms rho 0, the terms xi 0, etc. We know how to do it, that's what we're going to do. The problem with the constant of the equation is that it's not what we're going to do. We don't know how to do that yet. So we did the calculations. We did the calculations. The equations in the equation are known. They are due to a probability of 1 in 100. So they were calculated. And so we have the equation of eta for these terms here. So we did the calculation with the initial data that we have. And what did we get? For the term eta, which was the term I had, and for the coefficient of the same, And so, as we have seen, if you want, the position of the terms of Baye, when we are in the descent of our energies, the rest is of the order of 1 to maybe 10. The higher limit given by the experience, so that it does not disturb the experience, is 10 to the power of 70. That's for the term of Baye. Then there is the same thing for the term of Hegel, I think that was the term of Hegel. No, that was the term of Hegel. We have a very special element in our theory which is that it can only be accessed by conformal terms, i.e. a kind of fundamental conformal analysis which means that the term in the square has a value of 0 at one point. So when we go down, we find a value. And the same thing for the term of possible value.

55:00 So there is something very amusing about these three terms. It's that when we calculate the direction in which they move, we are all at a speed of about 1000 times the speed of light. So they are all related to the data of our time. But in the red line, they converge with the points that we find in our computation. And you already know these points. There is a very particular value of these constants. And it is there that they converge in the red line. So now, if you will, we come to the following situation. We come to the situation where the geometries of this form of norms, this theory, at a certain scale. And what we observe is the effective theory at another scale. Now, what we have to try to understand is, I don't know if you can hear me, So, if you will, now we are trying to go there, of course, and we are trying to first understand what is the range. This is the space that, in the end, we put on the operator, let's say, an interval. That is to say, we put it in the vertical. It is not possible that the height there is very particular. No one knows. But it would be problematic if we managed to divide what is this space in the vertical. It would not be possible to define all the parameters of the equation of the trigonometric theorem, and then we would have to go back down. What is the... we should not have any theory. There is a possibility that the 6, the dimension 6, we have found in cohomology.

57:30 What people do in the theory of Korn, the dimension 6 is the same as in Karnivya. Because, in the end, the people of the theory of Korn say, well, it is not a fluid space, a cross, a triangle, it is a theory of Katsura Klein in the same space as the dimension 6. So, one of the flaws of the Kalashnikov Theorem is that the Kalashnikov Theorem has continuous modalities with no stability, etc., and that, in the end, we can't get to the landscape, that is to say, we can't get at all to see what's happening there. Here, we do things that we can't really understand. We talk about the standards, it's extremely difficult, okay, to find the space-time, but at least it is certain, as given by the humanities. What we can say is that the space-time as it is, there is this texture on the scales that we can look at, okay? So, now, obviously, we all think that theory will become more and more non-computative as we go up in scale, and the most important thing would be to be able to guess what, gradually, how non-computability will more and more mix with the coordinates of space, etc., etc. This is a work with the technology. We observe the paradoxes with the terms we use in the theory of the world. And so we are interested in the following thing, because there is something that is very important, that is very hard to explain. This really very important thing that people explain very rarely, is that in fact, the theory of gravity, of gravity in particular, is a theory of the solution of cycles. And so, what is the idea? The idea is the following. The idea is that, in fact, we have what we call spectral action. Spectral action has a group of invariants. What is the group of invariants? It is the symplectic unit of a fixed dimension. Why is it the symplectic unit of a fixed dimension? Well, because we don't have the Hilbert space, but we have this real structure, Xi. And in the dimension that we look at from the orbit, we will see that... And G is antilinear, so G with G equals minus G. So G with I is equal to Y. And all the operators you are going to look at have communicated with this.

1:00:00 So in the end, you had a strategic communication. Now, when you look at the data, this data geometry is called symmetry, only one of the most common things in the image operators. So when you have an image that you want to see, it is exactly the same as the image of the spontaneous pressure of symmetry for... And so, what is wonderful about this development is that the weak model is only a small part of the gravitational model. That is to say that the weak model is simply the geometry of space, F, okay? But in that, there is a little bit of the same pressure. So what it suggests, from the same system that we use to find the pressure of the weak symmetry, that is extremely useful in a physics report in which the calculation of the past is effective. And so what we are doing, particularly with Richard Sedina now, is to generalize this share calculation for the pressure of spontaneous symmetry that says that if the temperature is too high, there is no spontaneous symmetry measurement, there is no mass for the particles, and it is only through a function of phase when the temperature goes down that we obtain that. Well, even then, it suggests a change. It suggests that geometry has no meaning in the universe. What it suggests is that there is a system. We are beginning to understand. It is a system of quantum statistical mechanics, and it is a system that is based on all geometries, and all geometries are seen as random matrices, which is operator D. Operator D is seen as a random matrix. And this system is the following. Beyond the white mass, that is, beyond the white apparatus, the largest apparatus, there is in fact an extremely chaotic state that has absolutely no extension. And it is only through phase transitions that there is a spontaneous collision of symmetries and that the geometry as we know it appears. So, the reason for this, I can tell you, is that there is a dictionary that we are carrying out between a complicated triangle which is a theoretical one and the physical plane. And there is a lot of...