Marco Panza talk

0:00 But also, of course, there is no doubt that conservative literacy is present, so we can discover that it is historically based on data that is made in the present. It is certainly a myth that in the Soviet era, metallic mechanics is also a definition of neologism. According to that myth, Jung's thesis provides, indeed, a definition of natural networks that can't be squared with a y-axis. This is the way that natural numbers are perceived, that scientists establish that natural numbers are things that result from concepts, and my comments expressly result from the judge's perspective. It is not my intention here to discuss the legitimacy of these views, but rather to focus on the identity of others in a kind of analysis that squares and is clear. And so the question, where it was, was asked in the forum. And our definition may be such that if you are told the same thing that it has to solve, I, Patrice, can't, I will not, I will not answer it, but I will, I will discuss it.

2:30 But what I think of, you know what I'm saying, depends on the fact that me,

5:00 it does not arise in me to understand such a notion that is closed to history. To insist that the general principle of the world, the barrier between mathematics and science, from the start, is just to say that such numbers become explainable, they are, and the warning is that some number of values that observe the education is to characterize the number by right-sides of the principle, which states that the number of values explained is important.

7:30 The application is to do something else that the theory does not do. The application is external to mathematics. This is the contrast. If we are not in the same way as today, it doesn't mean that we solve the problems at the same time. So it's a narrow answer with the theory of mathematics that we have done so far, and the applications of mathematics are immobile.

10:00 This is right and that is not right. That's right anyway. But they are not mathematics, they are knowledge. Now, round the corner. In some of the courses, the focus is on the reality of mathematics. There is simply no substance in mathematics. And the translation of the language is not for the people or any other people. And besides this, you are going to be able to do this. And even if you don't know anything about statistics, here is a code that has been built, a sign that in our a priori, they've trained. Imagine. In the analysis, they basically divide. Now the cost is net. The problem is to justify, say, the adoption and the fabrication of the space that they can create is enough to lead to the sense that there is no doubt that people can't do it because it does not satisfy God.

12:30 They are going to say, okay, I don't think they are going to listen to me. It's not justified. So, framing is completely wrong. We are so, it's only a very vast problem. It's a concept. And we keep judging by our statement. The entire development of the right chain of conceptual continuity as classically conceived, the density and confidence of the range of possible values and parameters is simply not manifested in the application of the law. Rather, the flow of constant formation grows with the development of the right chain, a classically manifested continuity. So in the case of mathematics and algebra, we are competent, in the case of algebra we are not. But probably I don't. No, no, that is not the point. My point is to not explain the fact of the frame. There is a problem that we could think about kind of indirect empirical definition of definition.

15:00 Actually, I don't think that's right. I don't think that's right. I can see the problem.

27:30 One thing, there's arguments about infinity, that, okay, every measurement is finite, etc. I don't think it goes through. Can we discuss quantum mechanics? It's a question. Okay? Keep it at the bottom, because it's important to discuss it, but not now, because otherwise... I think the application of quantum mechanics... These are the specifications of these topologies in mathematical physics that are described in this article. Military education is so important that we define that attraction.

30:00 That attraction should be open to all. More of the concepts of mathematics and mathematics are displayed in the general concept. The underlying use of mathematical physics is characterized by the fact that it is one part. Now, the corrective application of the explanation of the use of physics is the function of math. The areas that define the last element of the quantum domain are more or less in the right. In this time, it is not shared by the sorority of the right. Physical properties of any kind do not, and hardly do not, exceed the aspects of the quantum domain. It does not mean that the capital forces do exist. It seems to me that it is not necessary to fulfill such an argument that the relationship should intersect. Otherwise, the application of the theory... The structure of the structure is not the same as the structure of the technology. The structure is equal to the structure. The structure is equal to the structure. The structure is equal to the structure.

32:30 The structure is equal to the structure. The structure is equal to the structure. The structure is equal to the structure. The structure is equal to the structure. The structure is equal to the structure. The structure is equal to the structure. The structure is equal to the structure. In other terms, if you might have understood the practice, the use of them has to have made a difference. The capital definition of the future does not make a difference. It suggests a much stronger understanding of the pseudo-extension of mathematics. In other terms, the education of the 24-year-old is required. The real standard of speech is read from language. It is not by debating, arguing, negation. All the implications of mathematics are the cards in the game that you can't have without the theory of mathematics. An occasional friend said, look, real numbers are not numbers. You have to know that the variables make something substantially different than the final preparation of your family or home. Real numbers are numbers of a substantial difference between one and the other. For number of numbers that are unbound, that are non-regenerative. So real numbers are... So there are numbers in two, in a number. There are numbers known in a trial, in a second.

35:00 There are numbers that are made from real numbers. So nothing of this, so to speak, money, has not a physical value of geometry. You understand? Because the quotation made of a white number shows quite well that it is made by natural numbers, real numbers. In the second case, rather, to say that there are numbers of essential people, it is indeed to provide a much more real understanding and to find the answers to these questions. They are metaphysical, so to say, they do not give to real numbers the right organization of ideas, since they do not exist.

37:30 In the third case, it is a case of natural numbers. If last, really, is there another potential point to show that the logic cannot be the same in the two aspects, but again, I don't know, three minutes, so I don't know it, and I presume the point. So we have to, to now, we have to do a very clear interpretation of the question portraying that I'd like to never know, only to reach. It's a matter. And according to this other service, it's exactly the same information, it's exactly the representation of others, me, because when we try to measure the medium of water, we exactly reduce it, try to imitate it, and with the mathematical object, exactly, we have a chemical wave, and we say, okay, now I have to do this, and so on, and so on, and so on, and so on, and so on, and so on, and so on, and so on,

40:00 We admit that we are talking about a too much demanding construction of science. Constructions are simply using binomial symbols. We know that every natural number can be approximated by an alpha of 0 to 1. And so we get, in a sense, for example, a natural number, but a number of n. A number of n and a succession of 0 to 1. A succession of 0 to 1. We can simply use, for example, properties of numbers. We can take here properties of numbers. And it is so, it is the property of numbers that all the numbers, the values, each alpha e is one.

42:30 e is one for each table. We can do it. But we can even not do it. The natural numbers are not provided. I was sitting at home. The natural numbers are not provided. I was at the same time with the logic. Now we get over there. You just can ask the student how to say what they want, and it's pretty easy to do, yeah, it's time, it's a work of art, but it's very important. You can define all of them now, but it's not there yet. We can only define them in addition, in operation, and it's getting darker and darker, and they're not completed by then. So there is a very simple definition of mathematics in our science.

45:00 Just concerning this argument that there is no reals empirically given, no reals, real numbers, empirically given, because... No, there is a number not empirically given, so there is no truth. I think there is a clear sense in which they are, of course you are right that we need kind of procedure, but about this infinity argument, of course what's going on, we just assume something about... Potentially infinite, how say, continuation of measurement. This is how this infinity goes in, right? No, no, no, Andrei, it's not that way. The answer is not that we are trying to measure this physical object using A, B, C, or D. We suppose that we have a root that is very precise. It's already in the biggest position. But let's suppose that my root... I am very precise and I can use it in a very precise way, in terms of one, two, exactly two, not exactly two, so really very, very precise. Two, three, then something is infinite. The point is not that the distance is infinite. The point is that there is no empirical way to distinguish between converters and non-converters. When you say that it's converters, it's mathematical. Yeah, that's correct. It's not empirical. I know, but my point exactly is that just assuming this kind of, say, stronger hypothesis, stronger than we can possibly get, we make, say, physics based on real numbers, and then this physics gives very good fit with, you know, kind of best... It's not true. It's not true. You make physics based on real numbers. Why do you make application to real experiments? You use real numbers.

47:30 No, no, no, no, listen, listen, no, no, no, that's, I think, that's just all. In a sense, we just cannot, how say, take out of physics just one little thing like any particular measurement. I think it's just kind of wrong analysis, because what's going on in physics, of course, you're... Every kind of, as people say, theoretically laden, right? Any kind of measurement, whatever. So we have a theory in mind. And most of theory is contemporary. Now we are thinking, oh, probably we should accept something else than real numbers. It's interesting. But a lot of physics is done on real numbers, right? Is that what I'm calling for? So it's not independent of mathematics? So you cannot interpret the application constraint as a... Why do you apply to interpret the application constraint for concepts? We have solved that question. Solved that question are things completely independent of mathematics. How is it? Let's suppose that they exist, right? Of course, we can avoid them. But we are completely neurobiologists. No, we are not neurobiologists. But for the sake of the argument, let's just suppose that we are biologists. So exist, solved that question. Solved that question. And so, they are completely independent of mathematics. If they are there, we do not need mathematicians to explain what they are. I think that is real. Perhaps we don't agree that they are there. But if they are there, we don't need mathematics in order to explain what they are. But what? We cannot say the same with the object of physics. We cannot say the same with the object of physics if they are there. So there is no way we can explain them. Is that clear? Is it possible? There is another point. When you say real numbers are ratios of magnitude, is it your claim? No, no, it's a claim. Say, traditional notion of real numbers as ratios and magnitudes, exactly. And people like dedicating why they intermediate because it wasn't satisfactory for mathematical reasons. I think I'm able to say that in my interpretation, Frege application for real numbers and application for real numbers is not only a constraint concerning the organization of mathematics, it's even historical.

50:00 I think that part of Frege is that we have to respect history. In this sense, I think it's important to connect OITO because OITO has explained to us exactly what the difference is between mathematics and physics, and this difference is essential. In a sense, I think it's essential in my interpretation. There was something very strange in the story about an age, about Descartes in the end, and it was to put together mathematics. But the classical distinction between other magnitudes that was the base of classical mathematics was the right of physics. And so we have to carry that. And the right definition of mathematics is a definition that reformed it. So I think it's real. It's a historical fact. But if I remember correctly, people like Dedekind, I think he just saw it as a circular definition, so that's why... We can correct them. We can do that. Quantity. Quantity is full of quantities. After that, we will define a ratio of 100% But that's because it's a degree. In this sense, a frege is 100%

52:30 We can do the same thing, that is to say, natural, relative, rational. Real and expansion, but the point of this is that it is no longer a distinction between real and expansion, it is a norm of magnitude. The natural norms are essentially the same. It is said that the non-real is the one that can pass through. We can hide what it is, we can hide the importance, but we are going against it. Third possibility, we can pass the real to the expansion, but not to the rational. We can have the natural to the real directly, without passing neither to the relative nor to the rational. Directly from the natural to the natural, in a way that is very simple, because it has... Don't make use of the sense of agency, the sense of center, the sense of series, nothing. You tell me, I'm more interested in what you propose. It's a problem to demonstrate that... No, I don't think so. It's not because we define them in a way with these infinite series, it is necessary that there is still a lot of action afterwards. It's a bit of a work of fiction. No, that's exactly what I'm saying. So, once you have this definition, you have to... No, no. I mean, there's a lot of techniques. We can look at them together. In any case, the idea is that you have defined the logic of couples. Couples of natural numbers and properties. And then you define... A natural number that belongs to the whole of the world is an infinite sequence of entire numbers. No, it's good. You define a natural number... And then you define the history of multiplication directly on that. And that's what you can do, it's slow, it's complicated, and you can do it. To show that the history is defined in this way and associative, it takes 10 pages. There is nothing to discuss here, because I have already asked for it.

55:00 For the students, I have very good answers. All the answers are very good. But I don't think I have very good answers. But wait, because there is a question that arises. What do you do for the Archimedes' actions? You see, in order to have a theory of reality that is useful, you have to reintroduce it. But the Archimedes' actions are the Archimedes' actions. We haven't talked about that. The Archimedes' actions are done under the basin. What do you do if you don't have a marketing action? What do you do if you don't have a marketing action? What do you do if you don't have a marketing action? What do you do if you don't have a marketing action? What do you do if you don't have a marketing action? What do you do if you don't have a marketing action? What do you do if you don't have a marketing action? What do you do if you don't have a marketing action? What do you do if you don't have a marketing action? What do you do if you don't have a marketing action? What do you do if you don't have a marketing action? If you show that you are an operator by using tools, tools of strength, as a foundation and all that, you can do it. You build objects, you don't need a foundation. So, over time, even when you build objects, you need a foundation. There, you have a way to build objects that doesn't use the foundation. And then you use the foundation to build objects. It's the same thing. But on the other hand, I think, I repeat, I haven't finished yet, but it's much closer. Otherwise, I would have forgotten all that. You can also interpret the actions of a machine without using convergence, by thinking, for example, of an algorithm that shows that for each n-n-couple, you have an operational procedure that allows you to construct multiple n-n-couples, and then you simply show how to construct them, and you show that for any n-n-couple, you can construct them in this way. It is very important, it is clear that when we have these n-n-couples, the entire length is the part... The whole part of the numbers and this infinite sequence of images, we can treat that, as you just said, totally in a simple way, without talking about the convergence, I agree quite deeply with that, except that there is always the problem of when it's big, it's continuous, there are the new ones that end at the end, there is this small technical problem, delicate, but that's not the problem, why are we building the numbers? It's for completeness, that's the main goal anyway, so obviously the convergence is there, we can't limit it to infinity.

57:30 We want to fill the gaps that exist in the antinaturals, that's the goal. We can't say that we avoid convergence because if we have an infinite number of antinaturals, the antinaturals originate, it's zero, it starts with zero, but there is no end. We can't consider that the end of the antinaturals is the same status as zero. We can't. So that's why we put everything that is at the end. When we have one more, we can of course reason clearly. By saying that we manipulate the series of natural quantities as a kind of rule, which is not true, but no, we forget, we say that we push, but we return to the potential, we do not return to the potential, in the end, we do not return, we do not return to the convergence, in any case, that is certainly not true. There are infinitely more mathematicians than me. No, let me finish! Let me finish! Let me finish! Let me finish! What they are saying is that we have witnesses. This is the work they are doing. If I think that I have finished correctly, when I have done the same, If you and I are the same, I will pass the test together and if you find that I am wrong, I will deny it, and if you find that I am right, I will reject it, because I am the same. The goal is to complete. The goal is completeness, and so convergence is the foundation of the notion that we are trying to define. That is the goal. Where do you think you can find what you're looking for? In the mathematical field? When? What can you do? In the mathematical field? When? In the mathematical field? When? In the mathematical field? When? In the mathematical field? When? In the mathematical field? When? In the mathematical field? When? In the mathematical field? When? In the mathematical field? When? In the mathematical field? When? In the mathematical field? When? In the mathematical field? When? In the mathematical field? When? In the mathematical field? When? In the mathematical field? When? In the mathematical field? When? In the mathematical field? When? In the mathematical field? When? In the mathematical field? When? In the mathematical field? When? In the mathematical field? When? In the mathematical field? When? I was speaking French, sorry, sorry. So again, there is no mathematical gap. I'm not attending the mathematical gap. I do not think that there is a philosophy. Because I'm not, as a neurologist, to say, look, the definition of mathematical numbers or U-principles is better than the definition of Europeans

1:00:00 because U-principles is analytic. I think that the future of mathematics, as on the new principle, is a nice, essentially different. And I think the same with my officials. Don't think that it's better, in some sense. It's important to show what we can do to arrive strong. We can see where exactly for the construction we need stronger systems. I think that my approach, because show exactly where we are in general convergence. The state of natural numbers is infinite, and you consider that the potential infinite is an actual infinite in this context. Never forget that. It's second order logic. It's second order logic, but anyway it's infinite. Of course you can say second order logic is a way of mathematics, so in a sense it's okay. I started with two thoughts, that the phrasal, the natural numbers, and the real numbers should be separate. The natural numbers, the phrasal numbers, and the real numbers. So the thought was that the natural numbers, they're used for counting. We do justice to the application when we, through an abstraction, we start with the concepts, and we're able to find the concepts, and then we extract the numbers. So the idea is that this abstraction really does capture the essence of the natural numbers. It's not my idea, it's not the neurologist's idea. Yeah, that's the neurologist's. Exactly. Even not the greatest idea. Yeah, exactly. So they're neurologists. Yeah. Well then, well. Yes and no. I mean, Craig does insist on what the neurologist is.

1:02:30 He has traction.