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0:00 Each particle has a certain propriety, and this space is a two-dimensional space. The state of each particle is something that is written on it, you see this movement, this band. We have two objects, two objects like this, at least, and an object like this, which will tell us what to do and what not to do. There are two objects, and to say that these two objects are the basis of a vector choice is to say that your space is represented by two numbers and that all spaces are represented by two numbers. So, what happens? So, what will happen to the state of space? That is to say that the first step consists of an before and an after, before you have this, and after you have a vector of a type that is either beta or zero, or alpha or zero, and the either refers to something that is completely random, that is to say that at the moment you pass it through a particle, reduce, it becomes totally random.

2:30 For stage 2, I will do exactly the same, since it is the same faculty, I will do the same treatment. So, at this point, the 1, first of all, it has gone into the basket, and the 1, which is the same as the 1, is corresponding to a deviation from this one. So, the zero now disappears, and we have stage 2. And, of course, we can do the same treatment with the t, 1 over 0, since it has no component. So, to imagine this, we just have to construct small problems. But the fact that I get a zero with a probability of 1,000,000 squared, I get a 1 with a probability of 0,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000, For now, that's all. At the end of the day. So, you have a lot of things to learn. So, at the end of the third stage, what happens? At the end of the third stage, you know how to change the quality. Basically, what do you do? You have a magnetic chamber. And then, now you change, turn, and you change again. But you don't know how smart you are, you're going to change everything. So, what happens when you have a magnetic chamber? Well, you know that... If you have a base, you have to make a base change, that is to say a vector that I have written like this, I would have preferred to write it like this, a vector that I have noted in a completely different way, for example, 8, which is not more than that, to have two representations of the same vector, which is 2. These things will become mathematically impossible to do in mathematics.

5:00 The trick is equal to 0, plus 1, and we put in 2, 3, root of 2, and that's the multiplication. The thing is equal to 0, minus 1, and that's the multiplication. So suppose that we have an anchor, and that the thing plays the same role for the prime quality as playing the same role for the emission quality. Turn your instrument of measurement, because here we are going to make a measurement. So I have a new base, two new bases. At this point, you have to write it in the form of A. You can do that all year round. Basically, A is the number of steps, the number of steps. You are going to write the number of steps. It is always the number of steps. So at this point, what happens in the prime equation? The same thing happens here. That is to say that now, what happens here? I'm going to go with the same three. Either... In fact, what we have discovered in this lecture is that, if we want to know more, we have to find two features, we send them to mathematics and mathematics, and then we continue. So here appears the miracle of the fourth case, which is that now, if I put these things back in the first case I did here, what I have to do, which is very important, is to objectify the thing in the form of an infinite number, of zero and one, the thing. There is neither zero nor one, so it decomposes again, it is uniform. Gamma is theta, and so now when it comes to k, we have these properties over zero. If we had thought of the properties that we measured as intrinsic properties of the squared particle, we would have only blue and black particles.

7:30 So no matter how much we measure the squared particle, we will have two zeros. So it's a little complicated, you see. This is a major part of the algebraic structure. That is to say, this column is a radical change of point of view. In France, we would expect to carry out measurements without doing statistics on the sets. Some are blue, others are not blue, and the blues, I did not write them right, the non-blues, I did not write them right. But something completely different in the fact of writing an algebraic one particle that forms this algebraic structure. And to decide for each particle that at the moment I take the measure, it becomes blue or it becomes yellow. There is only one particle and it chooses to do something different. And that, this change, is a really basic change that we are going to see. And all this is really a matter of evidence. And in some cases, there is no proof. We can say that it is indeed shocking. Except that the idea of this group is to show that we will have the means. All these phenomena, and to see that we are always in a situation where we are always in a situation where we are always in a situation where we are always in a situation where we are always in a situation where we are always in a situation She is going to describe two small remarks. First, we have a brutal change of speech because we have represented things in a vectorial form, with, essentially, what we call a plus sign.

10:00 You can also see that, in the end, the fact that it does not appear is credible. It is not complicated. Thirdly, something that is quite obvious, is the idea that when we go to the university, we have a class, we have a class, we have this thing here, we feel good here. So what happens at the level of the university? The idea of hidden barriers... I'm going to say three very complicated things. It's a bit like what happens when you take a liter of gas. You take a liter of gas, it's very complicated. Anyway, I have no experience of knowing precisely what it is. But I have a statistical theory that will allow us to realize exactly how much gas, how much liter of gas there is in the human body without having any idea of what's going on. The idea of a hidden variable, as soon as it is destroyed, is to say, as Einstein said, it is only random, which means that we do not understand this moment in time, but if we open the black door and look inside, we will find out that the effect is not very good. All this is completely false. All this is a state of the outside, You do the math, bang! You go there, you go there. No one knows how or why, but you will simply have, if you repeat the experiments, you will have the correct answer. So that's the deepening change, and it's a change, obviously, that I tell you that, again, I come back to this idea earlier, the idea that we had, when in fact we created the blue particles and the blue particles, it was the idea that the experiment...

12:30 We can go through all the parts of the system. So, we attribute, in an essentialist way, a property to each part of the system. Here, it's not a part of the system. Blue light, blue light. It's in a superposition. Each one of them is a part of the system. And it quickly chooses what can be revealed to the world around it. So, it's a bit like the last question. It's a bit like what happens in polls. Look, in the universe, people bomb the polls. When we talk about mathematics, when we look at the right side and the left side, we see that there are three categories. There are people who study mathematics on the right side, people who study mathematics on the left side, and people who study mathematics on the right side. In general, mathematics is based on one side and one side. So, you see, the first two are up there. All of these terms are already decided when you see them. The last ones are there, they are undecided and they will decide, they will vote right at the moment. They will vote when they enter the field. They have chosen, it's not random, but they have chosen to enter the field. You see, it's completely different. So, is it at the end, in the case of Bohr, when he is already a messiah, that we don't know? That's not a problem. In any case, it's exactly this little gap between the two that happens. Think that the same thing exists, but that it exists at all times. I don't know if you know that. So, I'm going to show you a little bit of my collection. So, we're going to start by putting a little bit of mathematics in it. So, well, here we have another subject. Apparently, everyone has seen this subject a little bit. So, by the way, I'm going to show you a little bit of my collection. I tried to put a few touches between them. I don't know if they are personal, but it's a common part. And in any case, I would like to try to present the things for the first time.

15:00 I'm going to close the door. I'm going to close the door a little bit. I'm going to close the door a little bit because I want you to be able to see a little bit in the pictures that we saw yesterday. That way we can see the structures that exist in a certain formalism within which we are going to work. We have good news that in this formalism, there is absolutely no problem at all. And in addition, we can see the elements of this paradigm to see if it becomes, in this paradigm, a certain reality. Because today, we can't call it a reality, we can call it an article of reality. And if we consider ourselves to be a reality, it allows us to cut into this paradigm whether it corresponds or not. That is to say, to answer the question of the art of science, theory, which is considered as such. I'm going to start by talking about the axiom itself. I'm talking about axioms because we generally talk about axioms and axiomatics and not about the psychological status of axioms. I'm going to start by explaining what axioms are. It's a presentation. It's also a good thing because it's called the axiom of the time of Potanac because at the time, everyone went to Potanac to see the sports. So it's good to... It allows people to have the same desire to go to the gym, to go to the gym, to go to the gym, to go to the gym, to go to the gym, to go to the gym, to go to the gym, to go to the gym, to go to the gym, to go to the gym, to go to the gym, to go to the gym, to go to the gym, to go to the gym, to go to the gym, to go to the gym, to go to the gym, to go to the gym, to go to the gym, to go to the gym, to go to the gym, to go to the gym, to go to the gym, to go to the gym, to go to the gym, to go to the gym, to go to the gym, to go to the gym, to go to the gym, to go to the gym, to go to the gym, to go to the gym, to go to the gym, to go to the gym, to go to the gym, to go to the gym We can see that there is also a change in the vocabulary of physics. By the way, there is a second formalism of the standard, namely the formalism of the matrix.

17:30 We must not forget, for example, that the matrix is something that has really become in the humanities, which is a bit too big. At the time, Weizenberg and de Waens were known for their knowledge of mathematics. Weizenberg and de Waens were known for their knowledge of mathematics. Weizenberg and de Waens were known for their knowledge of mathematics. Weizenberg and de Waens were known for their knowledge of mathematics. Weizenberg and de Waens were known for their knowledge of mathematics. Weizenberg and de Waens were known for their knowledge of mathematics. We didn't know that in the matrix there were numbers that could be used in mathematics. No, but they were used in mathematics. Yes, they were used in mathematics. Yes, they were used in mathematics. Yes, they were used in mathematics. Yes, they were used in mathematics. Yes, they were used in mathematics. Yes, they were used in mathematics. They were used in mathematics. What I know is that when we talk about topography, we are talking at the same time about the fact that Heidelberg came to talk about this world that we don't know, that it took him a long time to get to the bottom of the field of mathematical physics and telegraphics. And here, on the other hand, I am very happy to be able to talk with Hilbert in France, and with Hilbert in France, and with Hilbert in France, and with Hilbert in France, and with Hilbert in France, and with Hilbert in France, From this theory, a whole range of mathematics began, from the theory of the operator to the theory of the operator, and then a whole range of mathematics that began at that moment, or at least that we started to understand the importance of mathematics.

20:00 So, there are four actions. The first action is that an ISA, a system, And decrypt, to be honest, we are going to have to do a demarcation, by measuring the vector space. So, this is a space marked with a square. This is a dimension that we are going to have to find out. We are going to have to find out the dimension of the vector space. This is a vector space. This means that we can add and multiply a complex. Add and multiply a complex. And here you have the definition of the vector space. So, the definition of the vector space. This is the first question. It has the letter H at the end of the letter H. The answer will be given by the direction of the dirac. We can put it anywhere in it. It means that the direction of the dirac is the direction of the direction of the dirac. And the direction of the direction of the dirac is the direction of the direction of the direction of the direction of the direction of the direction of the direction of the direction of the direction of the direction. So, that's it. It's written by an academic.

22:30 So, if you find that in mathematics there are two things. Sometimes we say that an state is a system that we call a ray, that is to say a modulo-mitral vector. So, I'm going to say that an state is a vector. So this is the axiom 1, which is equivalent in some ways to the notion of space in the future. So the axiom 2, on the dynamic side, is that the dynamic tells us that the evolution of the system is to become, not something that acts on the vectors, but something that acts on them. In the case of mathematical physics, the matrix is immediately conserved, i.e. the matrix will remain the same. What does this mean? For example, if you want to know if a matrix is a sphere, you have to ask yourself the following question. And a matrix is created by a collection of numbers, matrix elements, coefficients, which are the numbers of the inverse and the inverse of the inverse of the inverse of the inverse of the inverse of the inverse of the inverse of the inverse of the inverse of the inverse.

25:00 And of course, the humanities, which is immediately followed by science, because we have the evolution of the linear and matrix system, and the fact that it is unitary, and we can say that it is the result of the conservation of the system. I'm not going to talk too much, because we won't have enough time to talk about it. So, this idea that there is a conservation, in the same way as in classical mechanics, there is a conservation of the volume, of the space-time, for example, in the Euclidean theorem, for example, in the Euclidean theorem, for example, in the Euclidean theorem, for example, in the Euclidean theorem, for example, in the Euclidean theorem, for example, in the Euclidean theorem, for example, in the Euclidean theorem, for example, in the Euclidean theorem, for example, in the Euclidean theorem, for example, in the Euclidean theorem, for example, in the Euclidean theorem, for example, in the Euclidean theorem, This is an example of a matrix with no structure, but with the structure of an equation. This is an example of a matrix with no structure, but with the structure of an equation. This is an example of a matrix with no structure, but with the structure of an equation. This is an example of a matrix with no structure, but with the structure of an equation. This is an example of a matrix with no structure, but with the structure of an equation. This is an example of a matrix with no structure, but with the structure of an equation. This is an example of a matrix with no structure, but with the structure of an equation.

27:30 This is an example of a matrix with no structure, but with the structure of an equation. This is an example of a matrix with no structure, but with the structure of an equation. This is an example of a matrix with no structure, but with the structure of an equation. Mathematics and mathematics, mathematics and mathematics, trigonometry, trigonometry, trigonometry, trigonometry, trigonometry, trigonometry, trigonometry, trigonometry, trigonometry, trigonometry, trigonometry, trigonometry, trigonometry, trigonometry, trigonometry, trigonometry, trigonometry, trigonometry, trigonometry, trigonometry, trigonometry, trigonometry, trigonometry, There is a system that is very far from you, you have another one with you, so for the moment they are independent and I don't know if you want to put them together. So let's say we have a third system, which in theory formed this system, you see that here it is in a state. How will the third system be described? You don't want to go up to all the I don't know if you know what I'm talking about, but I don't know if you know what I'm talking about, but I don't know if you know what I'm talking about, but I don't know if you know what I'm talking about, but I don't know if you know what I'm talking about, but I don't know if you know what I'm talking about,

30:00 Well, you're going to have a third history, and a third is going to be given from the geosciences. In fact, it's a very heavy term. It's a very heavy term. We're going to see what the cancer product is. So, the cancer product, at the beginning, it looks like the Carthaginian product, in the measure of the cancer product. So, if you have a space H1 with the dimensions m1 and a space H2, you can see that this space has a base vector. So, you have to keep 1, because 1 is m1, and the vector 2 is m2. So, what do we do? Well, we consider all the components. The vector of the form 1u equals 0. The idea of this tutorial is to tell you about the H1 space of the tutorial, its message and its dimension, L1 plus 1, L2 plus 2.

32:30 So a base that I would make, it would be the whole of the book, I will use it as a salary formula. All of this will be equal to delta u delta y, delta x and y, and delta x and y. And if I have a vector u in H1, u will be a sum of u and v. In addition, we have a product of the vector A, without definition, the vector is coordinated on the base of the coordinate. So it's a bit of a formal lecture, but it's a bit of an important thing to understand. It's an image of the whole of quantum mechanics. So, it's not his speed, it's not his speed, it's not his speed, it's not his speed, it's not his speed, it's not his speed, it's not his speed, it's not his speed, it's not his speed.

35:00 It means that there are vectors, not only in the form of a vector, but also in the form of a sum, a sum of m and m, given that we impose on our theory that we have the structure of the vector m, we impose on our theory that we have the sum. These vectors are written as much as possible, they do not work that way, but we have the sum of our theory that we have the structure of the vector m, that's how it works, that's how it works, that's how it works. These are really exactly the new vectors of quantum mechanics, those for which you could no longer think that you have put a system 1 with a system 2. You really have a system 3 that will no longer have any interpretation of the term. So we will see it later.

37:30 So, two states like this are what we call intrusive states, in English intrusive states. These are states that cause problems. So, why do we have to have intrusive states? Why do we have to have intrusive states? Well, precisely because when you are going to act... If a state is formed by the evolution of all the systems that were together, if it was evolved by a sinister matrix, by a sinister matrix in Einstein, then it will preserve this factorization only precisely if it is free. The two systems, I don't see the interaction. The interaction of the two systems must automatically mix things up and be able to go from one state to another, from one state to another, and so on and so forth. So we come to factorization, and so on and so forth. Generally, in general, we have to create states. So, if you want, the beauty of formalism is to allow us to explain the experience of some of the speakers earlier, but also to create this structure via the states that we are talking about. We will see later the link between this particularity and the perception that we have in our situation of probability of a particularity, but that is not the case. So all this makes the social system, the industrial products, and when you discover the algorithm of teleportation, you will see that the point is a bit unremarkable. That is to say, it is exactly what it takes and it is just what it takes. So you can absolutely not move to the other side, and there is a possibility that we will not move. So, we did the first four sessions, and in the fourth one, we did the second one, and in the third one, we did the fourth one, and in the fourth one, we did the fifth one, and in the fourth one, we did the sixth one.

40:00 So, for those of you who are still watching this video, I recommend you to go and see the physical and mathematical books. Because in mathematics, we're going to look at things, we're going to look at things at a level that masks science a little bit. The fourth relation is the one that I talked about in the black box earlier. The fourth relation refers to the shoe. If you want to make a shoe, you can make a shoe. We will talk about this in the third class, in the third class. You make a shoe out of a system that uses the capabilities of the system. So, in any case, we are used to, in classical mechanics, to attribute a particular dimension to the other dimension, and so on and so forth. So, when you say that Venus is there, you say that Venus is there. Why? Because you have created a position. So, the idea is that in our production, not only in our production, Einstein created a quantity, a mix of realities, a quantity of something that we can measure without intermingling with other things. It is not a cube that expands with other things. It is absolutely necessary. So, there are a few measures that we can use. First, we take an observable. An observable, like the first one, is an atomic matrix. The idea is that the atomic matrix is based on something that is real. All of these are not complete.

42:30 So, we have a non-complete. This is what we see in the real world. This is the reality of the real world. So, the trace of the position of the universe in the real world, this is what we call the term of the field. The term of the field means that if the point is the same, the position is the same, and so is the expression of the real world. If we have a matrix in the field, the mathematical method of the field is called the technical decomposition. In other words, One of the least important of the three is the definition of the definition of the definition of the definition of the definition of the definition of the definition of the definition All of these terms are related to a vector of life when there is the same vector of life, but in a different language, the language of life. So, this is the fourth case. This is the fourth case where we have to use the observable as soon as we have used the observable. So, to calculate the measurement, we define the following thing. This is the equation. Once we have calculated the measurement, we will have two choices.

45:00 Obviously, when you measure something, it must have a result. The results of the lecture will be one. You will obtain the results of one of their types. For example, you will continue to see the results of the other two. The results of the lecture will be one. You will continue to see the results of the other two. For example, you will continue to see the results of the other two. The results of the lecture will be one. You will continue to see the results of the other two. The results of the lecture will be one. You will continue to see the results of the other two. The results of the lecture will be one. You will continue to see the results of the other two. The results of the lecture will be one. You will continue to see the results of the other two. The results of the lecture will be one. You will continue to see the results of the other two. The results of the lecture will be one. You will continue to see the results of the other two. But if you have learned the language of life, you are sure that after the system of the state of mind, you will be able to learn the language of life. And so the chance is that you will learn the language of life.