Embodied consciousness & quantum science / Category theory & living systems (& others)

0:00 The first one is that it has to be thought at the same time as reflection, so we're talking about self-reflection, in which the object is the subject known as the object of self-reflection. We can look at a simple word, a cat, or we can look at a cat as a convective object, a sensory object. These are three different operations that we can reflect on, namely, that is, the identification of a particular animal as a cat, the use of language that I use, and how I use it. These are different frameworks which are not organized in such a way that they stand side by side, but some of them are used together so that there is a complementarity between the symbol and the symbolized, or the representation and the representative, all in terms of the meaning that the symbol has.

2:30 The symbol is, of course, an accessory object, like the word, like the picture. We're going to see a picture here, and the picture we're going to see is Van Gogh's bedroom as he painted it, and then we'll see a reconstruction of that bedroom, which is done by Lafayette, according to the dimensions that occupy it. I spent the summer in Arles, and though the house is destroyed, it was destroyed during the war by bombing, the furniture, the details of the room, I was able to get from there. If you see a program in motion, hang it with a camera, and you will see three very short movies, one of the, they're all about Van Gogh's frame, and then the important one will be moving, looking at the room, the room that he's looking at, the room, how has he made it, what has he reconstructed architecturally. A man looking at it through the frame of the camera. What I want to point out is that the space in which we see things is not Euclidean space. And that is the point of what I'm going to show you. This is... Doesn't help. That's a house, a yellow house. The second one from the right facing you, which is the co-chamber, that's the best. I'm going to put a little bit of tape through another channel. That's important for some reason. I think there is no good enough of the same thing to be the second one from the right.

5:00 What is it now? I've hosted it now, I know it now. He studied perspective, and he has a long-lasting specificity about the importance of perspective. It's connected with the truly important things as we see things. And there is a very religious dimension to Van Gogh. He painted no religious pictures, he copied a few religious paintings, but no painting that he had originated is a religious painting because, as he said, it's too passionate. So, when he talks about the true shape of things, he's talking in a religious language. I could do a viewer. You see it's symmetrical, vertical and horizontal. The screen goes through a hole with a weighting on it, and where the focus would be the eye, looking through the frame, at the root, and then this guy is measuring where the screen goes through the hole, and then puts the dots there on that paper, and all of that is supposed to be a geometry. So is the viewer. Now, he had the picture frame made before him in an effort by his brother, so you would expect that the along the lines to the picture frame would follow the convergence of such lines to the central point, but you would not look at it in depth. Here is the window.

7:30 Is there paper on that? I think the problem is we need to dim the lights, but is there a way of dimming the lights? I mean the lights in the room. That's a bit better. All of these have been described as a place of peace and rest to attract artists to art. What I'm hoping is that is the entirety of space. There was nothing behind those shutters. Imagine yourself holding the shutters and what would happen to the roof. Most people would say, well there has to be something in the window. People in Amsterdam did not like that. Nobody published it to us without a transparency over it. Now, I'd like to tell you, before I show you with an open window, I'd like to explain something. Here is the famous illusion, the Miller-Dyer illusion. You would say that the top time was shorter than the bottom time. It is thus for sure that it is amazing to see the top line further away than any other way round.

10:00 You can't see it that way. There's nothing to talk to it. There's no flexibility in shaping space. But we want, mostly maybe, to set that up. See that further away. Now, it's that the specification is not ridiculous. It can't be that it's so. If it's further away, the top line should be long. We see it as shorter than the bottom line. The right way is to be curved to the end points of the two lines, so that the space is curved. Now what I want to show you is that the space actually, the curvatures can be quite cover-away. I'm going to show you an open window. There it is. Just accept that the shutters have been opened. Now look at the shape of the room. You see how the room becomes small, the room is compact, and now you see a much longer, not many of you see a longer world, but the room has changed in its shape, or its pattern. If you want to perform an aesthetic this way, ask yourself, is that a coaster, or is that a ring? When you ask yourself that question, you see the gears turning inside, so there is something going on in here.

12:30 As you say, that's a poster now. We do see differently, as we interpret differently, what we see. I'd like to show you a reconstruction, the architectural reconstruction by my friend in Ghent. There it is. I have put some of the elements from the picture into the room. And this is the Euclidean projection. Everything is the same in here. This was done by looking at and looking through his perspective frame, bringing the camera here, you can see him as fixed, and you are moving outside the room, the same thing in the picture at the end, I'm saying that the key arguments which he made up were assassinated, or recently, he's the black man who was the head of the engineering department.

15:00 You see what he's seeing on the left-hand side. We have a full screen of that. That's important.

17:30 Here, there's nothing non-critical that you notice, but there is where you change yourself. And this is what he sees. All of that. All of that is just introductory material so that you understand something that I'm saying. What I'm saying is that, as human beings, it's not looking at everything at work. We are, as adult teachers, definitely background. The earliest students certainly were concerned with the tasks that were nearby, on which they focused their attention, and some of the tasks were small and some were large. Let me give you some background about that. We looked at the world through binoculars. Involved are three separate angles. The top down, where it's in a bipolar light net, and there's convergence. Convergence gives chance, and the others give time.

20:00 These three angles are not all positive, but presumably are independent. If they are independent, they should be represented in a metric form by If you convert the x, y, z, the Cartesian coordinates using these three angles, you get cross terms. So, cross out the cross terms, and now you have a mapping of Cartesian space on these three angles. The net metric gives you families of dynamic spaces. The properties of those spaces are interesting to us because we watch and reproduce some of the things that we see here and that we see in the Miller-Irving. The interesting ones from that perspective turn out to be three-dimensional hyperbolic spaces, a family of three-dimensional spaces. But Rudabana, Newtonian, because it is virtually Euclidean, but how virtual, whether it's small or large, will depend upon the second curvature. The second curvature gives you how large that is in relation to that. These spaces are finite, meaning that Euclidean infinity is not on a finite number. So, I would say in fact that... Witten is mapped on the wall on the charters of Penrose Pavilion. When you open the window, you open to a huge space with dialogue on the outside, and the space is enough. It still wasn't ubiquitous, but a lot more of it was involved in the Newtonian zone of near-Euclidean character.

22:30 Space theory. Now this is an adventure to find. Go back to the one Helmholtz and Ludenberg, Rudolf Ludenberg, at the Courant of Mathematics in New York, at the beginning part of the 9th century, and that program to do research into the geometry of individual space, particularly to the present day, though it's pretty well to be figured out. For the reasons. The reason is that the people doing this research were persuaded that, to be scientific, they would have to think in terms of fixed curvatures. Now, I, being a hermeneuticist, should say, you know, that the curvature will depend on what the task is. James Gibson, about whom you like to know often, and a number of people like it, but they discussed it from the point of view that one's being a subjective. In other words, if you're looking at your nail, in fact, it's changing, or if you're looking at something back there, while the general structure of the space could be, I mean, they could be hyperbolic geometries at the same time, but the curvature is very different. If the curvature is our objective, then how do we do research for that? Well, I'm not going to go into that except that I haven't been able to persuade many people. But when it comes to experimental work aimed at discerning whether that kind of theory is acceptable or not acceptable for science, there will be that whole problem of what the purpose of it is. And what I can say is that the cultures of space are shaped by purposes. You have high temperatures. If you're playing soccer, that would be a necessary temperature, but those temperatures would be there a bit.

25:00 You'll find that in sports. Karate is a sport where the playing condition is that the goal is probably the game itself. If one jumps out beyond the limits of your opponent's visual space, you virtually disappear. So you can disappear and reappear if you would like. So the flexibility of the current choice of space indicate a connection between the structure of a space and the purpose and intention of the space. I love that. I'm persuaded that it is a fact that is continuous with the evolutionary account of species. And is visible, actually, in the everyday world. Mountains in the distance to the Rocky Mountains, they appear as a, and they remain there for twenty-four, forty-eight hours unchanged. But only when you get closer, you see the mountains open up. You can see that picture perfect. Skyline, when you get closer, the first block detaches itself from the second block and then the third block and so on. It's too sharp to move in a particular way, but it's great that these engineers are doing what they're doing, so I would say that we lack a trust in the Edinburgh University of Baker Road and we would like to encourage them to do so. Our vision is that's a matter of what aspect. The other aspect that I wanted to bring up, and I don't have time, but I can continue on this, is the complementarity aspect in which looking at the same thing, for example a painting, one can look at the painting as a spreader.

27:30 There's no difference in the physicality of the looking and what's looked at, but there is a big difference between what you're looking at and what you're intending to see. There is a change in your embodied structure, the symbolic representation becomes part of your embodiment. And when you're looking at the painting on the painting, the painting is not part of your subjective environment, it is a self-explanation of what you love and what you're looking at. And these two things, therefore, you cannot both look at what the painting represents and look at the painting as a work and a process together at the same time. It's like looking at the words, looking at the meanings. Looking at the words, looking at the meanings are two different things. And there's no physical difference, there's a lot of change in one's attitude, and because of that, and there will be, of course, a change in that attitude will be the correspondence between the physics and the mathematical system, knowing what kind of environment you're going to be in. And that, yeah, looks like quantum analogy, and then when you look at that, it can follow the same kinds of equations. That's why it's not the algebraic source. The algorithm itself has to break that down into different functions and break them down into other functions, so it's unnecessary. Do you want to say something first again? No, I want the light down so we can see your face when we ask you a question.

30:00 The shadow boxes that hang in the solar space, do you think that some people claim that the reason why the mirrors hang in the solar space is because the department used shadow boxes? First question is if you think that's true. A shadow box is essentially something like the way it used to be, the old photographs in the 19th century, you had a big box and you had a blended version, and you had a projected background on the screen, and what some people said is that they keep, essentially put together something that was projected, the image on this palette, and painted off, you know, essentially transcribed it. The empirical question is given, you know, you're given this thing that you're making an observation about, how do you decide the observation, whether or not the observation is consistent? This part of the general question about our business is that in fact your guesses are in a different direction. And that's the part I got stuck on. My takeaway from my theory. In that part, we come up with the title, the hermeneutic circle. Our process is a process and it has certain phases in it. And it's those, looking at those phases, studying those phases tell one what's possible and what's not. Ultimately, we use them in reviewing, whether reviewing old beliefs or new material, because eventually what we understand could be done in some countries.

32:30 It colors. What we see here, in the particular space that we see, is unconsciously produced. We're not consciously producing those spaces. So we are always structured in a certain way. We find ourselves structuring. Once we are structured, we don't need to take conscious count out, though we can revise it if it doesn't work for people. There are descriptive structures which are, we have to basically mimic what we may mimic by learning, building on structures that will become unconscious once they become conscious. That's one kind of concept. They're very specific, which are scientific concepts, meaning they relate the descriptive concepts to one another in a very small way. And they're very different. They're very different. Modern views of language are divided into lexicons and grammatization. Grammatization are the long-term, theoretical relationships that we accept as the structure of the world. And the lexicons are the placement of kinds of objects within our consciousness. And then there is key matter between these two. So for example, one time, the mathematical can become lexical and so on.

35:00 So there's a latent force between the lexical and the grammatization. One being long term, the other being long term. And these are the structures that we're talking about. How would we be talking about the neurological representations of those things? The linguists would be talking about, let's say, Betsy Kahn and Brahma, and the psychologists would be looking at some of the security of the earth, and... Subjects, you know, what they see, what they don't see. We've had transport of modern inventions. The photography has constantly changed in our perspective. Apparently, we've lost all the time for this. You know what you want, but you don't know what you want, but you don't know what you want, but you don't know what you want, but you don't know what you want, but you don't know what you want, but you don't know what you want, but you don't know what you want, We start with, as I said yesterday, look at two, their hands are all about the same size, even though their ankles are tended by a face close by, it's much more clear that there's a lot of correction involved by the brains involved in making that correction, taking the distance into account. So, I think you can think of a lot of this stuff automatically, but it is a matter of practice, also, in the way that perspective is used. There are a lot of angle of respect, and there are, in fact, several standard students who would sit there at the front of the room and get a whole set of terms. But the vision, the moral of the story is approaching the scientific way to do that.

37:30 I didn't talk about insignification. All insignificance becomes part of our embodiment. But when we use them, it has to be a skilled person. A skilled person, the instruments of his body. If you're not skilled, these are, from the outside, you wouldn't know. You could act as a scientist, a doctor, or a doctor of religion, and you couldn't know what you would be doing. You wouldn't know what you were doing. I think we have to stop now. I mean, we're coming up to the end of the time. Thank you very much. I think there is a talk about category theory and meaning systems. I'm going to swap them and I'll have some more discussion afterwards. Okay. As well.

40:00 Okay, we talked about sports a couple of times. In fact, baseball was mentioned. I want to talk about, at the beginning of the example, these sports-motivated kinds of sports that actually in other parts of life are particularly notable sports to acquire a level of biological computation that is, at least to me, absolutely amazing. Let's suppose that we designed a robot that had direct access to the most powerful creative computers of the current generation must be a sketch of a baseball line, not necessarily for Americans, but just in case, so around 30 feet on the side, we have a diamond, with a back machine, swing it back and hit a small baseball. That is thrown at tremendous speed by the pitcher up to 100 miles an hour, which is a dumb idea to get you, and then swings are back. These are the lines of the field, and out here are the outfielders, who catch while they're hit in the air sufficiently far along the ground.

42:30 Just to give you a rough range, so this would be around 135 feet or so. Senator Buehler would probably be playing around here, so he could run in and catch a ball that's hit just outside of the inning, and he could run out and catch up to a blocked ball that was even high in the air, and he could just run out, sort of keep an eye on it, and catch it. But the attempt was made by the famous baseball player Willie Mays, who happens to be playing. Now, Mays, playing especially close, always hit with just a glance. Now, for a dead center field, let's go back to the example of a robot. So we have a robot, you know, that has access to the crane, it can see this tiny little ball, hit, and with just a split-second glance at the trajectory, taking into account the fact that wind can affect it, the ball might be hit with spin, etc. With that glance, it has to go across. The field is the appropriate spot and be prepared to receive it at the appropriate moments. I don't think that we would be capable of building anything close to that, even within 50 years of today. But May is going to do it. The question is, how is it possible to perform computations? The term I used in the paper book conference is exquisite. So, how is that possible? That is not merely, but unreasonably accurate. Where is the unreasonable accuracy of the rigor of computation?

45:00 I've got feedback, Jerry, that's not wrong. I mean, this is an account of calculus, computational abilities, and biologists. Well, it's just feedback. I mean, there are advantages. For instance, if I stand here, like this. I'm setting a little piece of wood that's a little bit tricky. I can do this because I'm using feedback. If there's no feedback, perhaps you can hear the ball. Maybe you can even somehow sense its position. Even though we can't quite account for that according to the normal physiology, it may be that there are other physiologies that we don't know about yet. The average baseball player uses feedback willy-nilly. So here's what I'm saying. Yeah, we've got to be looking and seeing where it is, but many of you just ran out on a dead record, not just in sports. In music, dance that goes on to music needs to end at precisely the right moment. Now, there's a lot of rehearsal, and you can say that's how it works, but dancers can do this when they're hearing music just a couple of times. They haven't listened to it many, many times. They barely know it, but they just sense the rhythm unconsciously. I'm going to finish a highly detailed piece of choreography at exactly the right moment, so it's the coordination of space and time that strikes me as a wonderful phenomenon that deserves a lot more study. Now, what I want to do is to shift gears and talk about some category theory. I don't complete theory by any means as a cartoon, but it seems to me it's important to have cartoons that capture Essential questions as opposed to highly detailed studies of things that are static and interesting.

47:30 Aspects of biology that I hope to account for are gestalt, perception, and synergy of action. The question is, what is the relationship between perception of the animal and its environment, between biology and physics? Is there a way to use mathematics specifically to categorically look at this question? This is a generalization of the notion of Agilent Puncture. Since this is a somewhat unantiguar theory, I won't define Agilent Puncture, but I will more or less sketch the idea in this context. With topology, one of the things one studies is the universal coefficient theory. It relates cohomology and homology, and it tells you that there is a natural short exact sequence. I'm going to show the end of it there. Which goes from cohomology to the homomorphisms of cohomology into some dictating regime. There is also a space called the Idaweber Plane Space that represents cohomology. That is, there's a isomorphism of biphromatism. Once again, it's natural. Which gives you a map of the homotopy classes of maps.

50:00 From topological space X into the Eilenberg plane space with the cohomology. Putting those together, you get a natural transformation, which is an epimorphism, not an isomorphism, from the mathematics into the Eilenberg plane space on the left, and to homomorphism, to homology, to the group on the right. The algebra in the plane space is a weak and bright adjuvant to homology. Above I've shown the usual categorical picture, so ab stands for categories of linear loops and homomorphisms. The topological space is a homomorphism for homotopy classes of maps. So homology maps top my homotopy with linear loops. Since... The maps that are on the top introduce the same homomorphism between the parts of the alien groups, and the Einberger plane space maps the alien groups down at the top, and what we just saw on the last slide says that the Einberger plane space is a leap right element to homology, which I indicate by this symbolism k to h, from k to hn. Unlike the ordinary autonomous is symmetric, so to say that F is a left adjoint to G is the same as to say G is a right adjoint to F, but here, since we're using epimortisms instead of isomorphisms, there's an asymmetry in terms of size, so this would mean that K is a right adjoint to H, but if I put the bar on the other side, it would mean that H is a left adjoint to K, or is a left adjoint to N. Now, the connection of this, one connection of this with what I started with, is that way back in 1961, perception was a wonderful area of study in biological science. Christopher Seaman, if I had a little more time, I'd love to tell you about this very simple topological model of the visual fields in the brain.

52:30 And how this is used in this simple model of how objects on the right get, their images get mapped to the side of the brain to control the right side of the body. And of course the same on the left. Objects that are central, coming toward you, go mapped to both sides of the brain and therefore are handled, also mapped to both left and right sides of the body. And so there's an immediate... Neurologic difference at very basic level. So I'm looking at the peripherals that are coming in from the side as opposed to the center. All this, the visual computation is intimately linked with the survival of the organism. I'm not saying that evolution and evolutionary history are not very, very much a critical part of it, but what I believe biology has been not paying sufficient attention to is the necessity for mathematical principles. To understand the biological computation, Brian mentioned earlier, paradigm shifts. I've been involved with paradigm shifts and a number of them now. I recall the first board and research conferences that I went to back in the late 70s and early 80s. People said that, the biologists said, I went to theoretical biology slash bio math, and the biologists said, computing? What do you mean computing? Well, that's gone away, and biologists now all pay homage to the idea that biology computes. Well, if there's computing, it seems to me there must be mathematical principles that play a role. It's incredibly egotistical to imagine that humans are the only possible way of mathematics to get into biology. We are biological, for sure. Math may be something that exists on the quantum realm. I believe there is a platonic graph, but the math I really know about is a math that human beings have gone out into that ground somehow brought it back to use the rest of us. So it's biological, and if nature can come up with mathematics to get human beings, who is to say that mathematical principles cannot be utilized by nature correctly without the necessity of humans to use it?

55:00 Be that as it may, if we're going to emulate principles of biology, we may, we'll certainly need to find mathematical techniques that we can use to instruct our machines and our programs to do that. So Tiemann had the interesting idea in his paper that visual perception is somehow related to homology. He also talked about these issues of, that Carl mentioned, scale. I think he was talking about moving and driving and moving and seeing a huge image that you have no problem seeing. Forgetting about it. You can go inside and just think of it as a person. I think the effectiveness of television as a hypnagogic is largely related to its smallness. You would have to sort of get down inside it and be distracted. McQuiggan had a lot to say about that. So, in perception and action, we follow him as our model. We'll have a weak line adjoining X to some functor N. And we can think of X as being exogenous. So V is a biological category. I'm not following the subscripts here, but there's no way to suppose that if only one pair of functors is involved, it could be many, many pairs. I'm also not saying anything about what the category is going to be. I don't know. I want to keep it as general as possible. As I said, it's a cartoon. It's hard to assume, for a couple of reasons, that not only is x at least where n is, but it's also a right inverse. That is, I wrote it as nx, but of course this means you compose from right to left. So it means first you x, and then you n. That's the identity. It turns out that if you know the language, this will say that the co-unit is also the identity. But the union is another story. So we have a natural transformation, P, indexed by C and D. It's an epimorphism, and we furthermore assume that this epimorphism is actually given by applying the puncture, N, to the morphism.

57:30 And this is, by the way, all of this holds with the example of the item of plane space as a weak, bright atom to the model. Actually, you don't need to assume that X is a functor at all, let's first assume that X is simply a function on objects, such that there exists an epimorphism from the mapping in the category C, from object C to XB, etc., as I wrote it there, which is natural in C, and that means that we've got a certain commutative diameter. So far, I'm only using X as a function on objects. I haven't said what it does on morphisms. It turns out, if you can extend it to morphisms, the notion of Witten-Wright-Atom, as you said, I do the citation details in the paper on autonomous proceedings, but it was part of my thesis in 1970, a long ago. But actually, the notion going back a little further, As I learned later, he didn't do much with it and I wasn't sure quite where he was going with it. I was using it to solve some problems and I was great at topology, so I knew he was going to do it. Since, but not very specifically, the notation is sharp for those who haven't seen it. It just means post-composed, or let's say pre-composed by now. All this says, most category theories are just a very fancy way of saying that things do exactly what they think they should do. No surprises. So you can extend what Miranda and I noticed, and you can also independently notice it, that you don't need to, you only, when you're defining arguments, it's enough to give it on the object and you can fill it in for the morphisms. But what's different, or what we catch on this, is that you don't get a single morphism, you get a family of morphisms.

1:00:00 So, that's here, that if you have a morphism beta, from an object in B to another object in B, Then x of beta is not a empty set. The reason it's not empty is because it comes from the fact that the macro is an epimorphism. So it says there's a factorization, but it's not unique. So weak adjoinments is like a weak code limit or a weak limit. It says there's a certain kind of diagram. You have a factorization, but you do not get a unique factor. And a functor is a quasi-functor that associates a function, an object, and a morphogenesis. It carries 9% more business as a quasi-prunctor if one belongs to the other one and it gets along in composition to add it to the bottom. And if you do this, then you make X into a quasi-prunctor and it becomes unnatural in the other category as well. An example of a kind of theorem you can prove, you can show that, and this is essentially in that paper thesis, but we're going to explain it later. If you have a weak right answer, then if you have a diagram in B and you have a partial utilization of it, then you can extend that utilization. If we think of this in terms of action now, this is saying that we've already partially continued an action, that we can continue the action in some suitable fashion. I was thinking ahead, but I wasn't watching my feet. I noticed that, at least even for myself, when I do some things like thoughts, it's because I'm not thinking about where I'm at. However, that's an occupational hazard when one does mathematics. Classmates in graduate school actually walk into a wall and seriously hurt themselves.

1:02:30 has studied exactly this kind of problem out of the curriculum room. So what John Lowe did in his laboratory was that he had someone seated in a chair and they're reaching for, that is, a simple cylindrical form of this bracelet. The object is very rapidly rotated by an ensemble to a different position. And so you have to adjust your movements. People adjust the movement in a very particular way so that when they grasp it, they grasp it so that the wrist is more or less centered, so that they could do it by merely changing the wrist, but that would mean that their arm is in an awkward position, not a good survival mode for a critter. Awkward position is when you slip and you break something. So in fact what happens is you expend more energy than necessary. We turn other parts of the body in order that when we grasp it, the contact is centered, so that it's almost a martial arts kind of biology, but observable. We started with, well, coming back to this notion of action and perception, this is certainly a wild belief, not justified by any kind of new data. I don't claim it is. Where we have both action and perception going on simultaneously. After all, in speech, you have to prepare. In many bodily movements, you have to prepare before you do it, but you automatically prepare. It's quite unconscious.

1:05:00 There's a lot of perception in terms of co-limits, and assuming a few others, we'll better talk about syntax and semantics as an adjunct pair of some groups. So, it seems that there's some consensus that this is not completely crazy to be using as a model of biology for some biological processes. There might be a number of different actions, but they will all be perceived as giving the same thing, as in signing your name. In fact, signing your name seems very much the same, but you sign it this way, or you sign it that way. Bernstein first wrote this. The cites are in the paper. It's really quite an interesting... How do we do that? Because the actual set of neuromuscular actions are very different. An experienced driver who has never had to park a car on the left-hand side of the street as opposed to the right-hand side of the street, not an experienced driver, but if you're experienced in parking in the city where you have to do parallel parking, you can immediately, without any effort, switch from right to left and park on the other side. But not all of this, how that kind of synergy of motion is coordinated. So for biology, what my aim is is that independent catalog theory appealing discipline.

1:07:30 For biology, it seems to me that different types, we have to ask how are these different principles actually put together? Neural networks, differential equations, how are they connected to one another? If, and indeed, if we want to use computers and software for any of the biological decisions, how would we do so? We know that some things can be pretty well modeled by differential equations. We have to know what are the parameters in the differential equation, and when do we switch from one form of the differential equation to another? That is, in biology, there are many stories, typical stories, a cell provides. There are, as Rene Kahn points out, these octypal forms. So there are simple stories. These stories can be told in the best and kind of categories. We have objects, and we call them organisms, but in computer science they call them messages. They have object-oriented software. So it seems to me biology is best understood as a totality in this. Nevertheless, the level of a cartoon, or perhaps a totality, if we wanted a cartoon that relates biology to a cartoon, it's always fun to think about it. Thank you for your attention. So, I think we now need to go to the next page, which is about the mathematical aspect of biology. Going back to 1976, by the time I was 29.

1:10:00 We looked at the various stories involved in Piaget's developmental example, and we took table tennis as an example and analysed it. One other point, and it is happening today, but if you want to use a ball, you've got two degrees of freedom of direction, so you just have to move the ball. We also include the idea that mathematics is an installation of processes, by your criteria, the most comfortable process in our comparative process of chance of action itself. And more recently, the idea of particular abstractions... There are a lot of situations in which the exception of the puns determines the method that is used to solve the problem. Nothing is obvious. It's pretty disgusting. It seems to be an interconnection between blindness and personal procrastination. In procrastination, you can prepare your original thinking so that it doesn't mean that you don't know what works and what doesn't. Words don't have time to do that. Could you explain the way that this weak adjunction is supposed to be a caption for a biological phenomenon? I'm not really understanding what you're looking for. The X represents action, the exogenous author. N represents perception, endogenous. Another factor is an action that is consistent with preservation of coordinates or limits, and so one will say that an action to preserve the limits is to preserve the coordinates. But in biological words, what would you have with the thing that is mathematically... In biology? I said I don't have any... I didn't claim that I actually have a biological example.

1:12:30 But let's see, you did say too much of Xn because the unit, the identity. What would that mean? At Xn, that is, first Xn is the identity. And that would say that the result of acting and then proceeding is seen in the identity. So you would expect that... That it's simply a tautology. It's still human. It doesn't mean it's a... It doesn't say the opposite of course. But there's some idea behind this model. Well, the notion of which is something and has a weak mind actually, as a perception, goes back to Regimen in the early 60s. So it's not entirely new. And also, Laver, in the early 60s, had the notion of syntax and semantics. This new perception space led to an actual ability to predict a position given the perception of where you are in the visual space, how to do what William Newton did, which was to take one set of data and extrapolate it to be in some place at the right time and have you see both the right place and the right time. Prediction is in fact a very difficult thing from a dynamic perspective. Because of her data, I had to get a wider degree of uncertainty in where you're going to be. I mean, quantum coding is all about good prediction models. But mathematics, working from a perceptive space of predictions, would seem to be a real connection between biology and category theory. If we find that, we can implement it in a computer and try it out. This isn't that level yet. This is just, the idea is conceptual. To my knowledge, there really isn't any... There's a whole lot of arts and theory that accounts for the relationship between perception and action and that's all that I'm trying to do is to find some sort of cartoon of the relationship between perception and action. Not yet in detailed computations with it. I believe they can be done, but I haven't done it yet.

1:15:00 The last 30 years or so tell of what the model project does based off of Dunstine's work, in which he did a fluid analysis of joints and redness and redness, and he did a fluid analysis of the conceptual alignment of the model project and of the images of achievement and frequency. Schrodinger's cat. Schrodinger's cat. Real cat. Schrodinger's cat. So in the natural field, you have neurons that respond to particular gradient spacing or movement types. Everyone responds to, or to the weight of things. Things do. But it is, in a great many ways, polygons. I'm going to be all I do. I'm going to do what you're talking about. I'm going to do what you're questioning. I'm going to do what you're questioning. I'm going to do what you're questioning. I'm going to do what you're questioning. I'm going to do what you're questioning. I'm going to do what you're questioning. I'm going to do what you're questioning. I'm going to do what you're questioning.

1:17:30 I'm going to do what you're questioning. I'm going to do what you're questioning. I'm going to do what you're questioning. That's what you're missing. The conceptions, first of all, can be found in Peter's lecture. Unleash the image of the structure I am present to the world with its own features. I touch. I have the purest sense of sensibility, of muscle, of action. So, the question of seeing is determined by the sense of reality. My mind is building a specific sense of reality. I don't read, but photonics can read. I can't do it on my own. You cannot see the scene in this equation without body, in the sense that if you take the point of view of pedagogy, you take a story and try to explain the scene. At one time, things happened. So it's not also a main scene. It's a result of an agreement, a sense of reality. You take the story of the major, and that's the start. In the interest, seeing happens. So you can put between parentheses a real, no questions about the real, no question about the subject. You can create what is the structure of seeing, in the sense to expect the prototype to be present. That is part of your plane of analogy. So, I know that we are a bit at the point of science. Now, Oki said we can do science of perception in the distance. There is a prototype of the present. He said prototype correct, and then in the book. And we can do science of this prototype. We can try to discover this prototype. Any way to represent the world, we have a canonical structure. We want a dark room. I think a dark room is to try to get this canonical structure of a sense of reality. So, it's far from trying to understand our algorithmic neurons. It's highly information to build a section, and nothing to resist. It's another approach, another way to understand, and we can do much more with this science, a new science, and try to use the possibility of this science, because some things have a bit of a sense, and it's too far.

1:20:00 At the moment, science, we are just explaining the story of the leader. Let me respond to your question. One of the things that was interesting when I went through the work from my thesis of Alzheimer's and thought about and put it together with the idea of perception, action, and abnormal clusters, which actually I developed in the 80s. I realized as I started to write out the equations, I had things confused. It took a while to figure it out. And there were a couple surprises. One of them is that you can have X followed by Y followed by Y, and it must be epimorphic. It must be onto you. So what is that telling you? Is that consistent with anything in biology? Actually, it is. If you put a person into an isolation tank, so they're receiving absolutely no external input, they nevertheless... There is a little bit of evidence in the reading then that the mind requires input that from the fact that x followed by n is 1, that means that not only is x 1 to 1, but n is onto the morphisms. At least that category in which I'm going to introduce you to, our main biological category, all kind of microorganisms in the physical world. Okay. My commission, I'd like to make this about the colloquium that starts in Paris tomorrow.

1:22:30 This is the program for work with if anybody wants one. Okay? So you're level focused. If anybody wants to do it, there's a way to do it. It's for work. You're supposed to do it. You're supposed to do it. The first question is, how does the theory of quantum mechanics work? We need to associate both the formal logic and the logical-formal logic following a path that is quite long and in the sense that it is forced to be interested in modern discourse.

1:25:00 In this case, if you want, I would like to make an intervention. I do not intend to avoid the category theory, but to see to what extent physics can benefit from the theory of the category theory. So, I would like to start by showing you the general picture of our natural plan in a few minutes, because it is very important that we think that the theory of the ensembles can help us in the future. We started with the theory of the ensembles until we met Mrs. Esma at the Ecole de l'Enfant Claire. And at that time, the problems that we were trying to solve... We have been transformed from this moment. I will show you my intervention. It is a question of a brief report on the complexity of psychiatry. We have reviewed the different ensembles. We have encountered the evolution of the theory of memory-based systems, and we have been able to apply it around the central plane, which is the location of the entity. And after this meeting, we have been able to consider the application of this theory of categories as observation tools for the analysis of complex pathologies and the analysis of complex structures. And after, we will see the consequences of this. Let's talk about psychiatry. Psychiatry is a relatively recent discipline. It has only two centuries of existence, and it is particularly important because we have a variety of different currents. We have a very important number of psychotherapy techniques. In addition to that, the fundamental of physics is very common and very new. It cannot be reduced to the logic that we have. We are therefore obliged to propose to it, and it is always from an approach-approximation perspective that we are obliged to operate. And this is going to pose a lot of other problems.

1:27:30 In addition to this, we had a personal experiment 50 years ago in Basque Country, where we gave psychiatrists or fundamentalists These were considered as mental diseases because classic psychiatry consisted of organizing the blurry psychiatric world, the folly at the time, as we said, into mental diseases, that is to say, in synchronicity with the entity, which were blocks, in a way, isolated from each other, and representations on which the psychiatrist travels. And then, the next step we took was to go to the hospital in the first service in the General Hospital in France, and from that moment on, we had a surprise, which was to see that the dead bodies were no longer trapped in mental diseases such as neuropsychiatry, but became much more polymorphic, much more moving, because they were in permanent contact with the surrounding environment. And so we had to reformulate psychiatry entirely. And for this, we thought that the best way was to look for dynamic combinations first. And these dynamic combinations, it was obviously necessary that you have a new instrument of comprehension and action to approach the world beyond the pathology of math. We have two others. The new method that we have learned, the systematic method, is based on the scale of observation. So the scale of observation is as follows. At the bottom, there are two domains of instincts, one of them is constantivity, then the domain of polarity and volatility, and finally, the domain of the territory. We will have to divide these groups into three groups, of course, and each group will have two groups of forces. For example, the intellectual domain is automatically represented, synthesized. With these instruments, which are called antennas, we can use the phenomena observed in each of these levels with a computer language.

1:30:00 All of this is constructed from the arrows, the round, the square, the triangle, etc., and we have put them in the computer. And at this point, we have discovered the functions, the great functions, which are not only the levels that we have demonstrated, but also their integrations, their internal and external communication. And finally, self-organizations, self-regulation, self-organizations that result from them. But it is clear that the advantage is not only in the individual, it is included in its environment. And we will also have to take into account the elements of the environment. And for this, we must first commit ourselves to... The levels, the scales of the plane have an integral role in the sociocultural environment. So we have used this internal environment, in an educational environment, in a socio-economic social environment, in a cultural environment, and we have stopped at the physical environment. It is in a way an observation tool that allows us to fully reform all the identity, in the common and the sub-common of all. The only thing is that there is a big problem. We don't know why psychiatry has evolved in different levels, in different currents, according to the times, according to the territories. So we had to try to understand this formation, this new knowledge. And for this, it seemed to us that we could use the notion of living together in a world where we were suppressing the foundation, the axiom of foundation in a certain way, and we have transformed our chain into a tower on the next level, namely that the superior level of the mental synthesis joined, if you will, the most elementary parts Psychological functioning and all that we have placed in a set of psychic currents. And we have thus reconstructed the history of psychiatry, which began in the 18th century

1:32:30 with the development of the psychotropic society, as well as the French Revolution, in passive psychiatry. Then there is psychiatry based on psychopathology based on the foundations underlying the mental centers. We are now in the field of bio-instincts with psychoanalysis, the idea of ​​artistry in what we find to be the most humanistic field in the world. Biological psychiatry, behavioral psychiatry, then philosophical discovery, a field of philosophy, moral psychiatry, and science. And finally, we have ectopsychiatry and antipsychiatry, which are opposed to the classical psychiatry. And finally, we have the technological evolution in the middle of the 20th century, which are obviously cybernetics and informatics. It is the technological evolution that brings psychiatry towards a transdisciplinary and interdisciplinary psychiatry. So, this is the end of this lecture. The evolutionary source of the evolution of anti-patriotic knowledge has an inverse sense of the constitution of social structuration. And this has been important because we wondered to what extent the things that existed between the evolution of the observation system and the evolution of knowledge could not, from knowledge, know better. The observation system. And it is then that we have a conference system of Mrs. Reisman at the École Normale Supérieure, with which we have presented almost the same presentation yesterday, and which really gives us a solution to the problem. Analogically, because obviously we do not hide the identity, they are analogies and concepts. And we have addressed at that moment The most elementary problem that exists in physics is scientific employment. So you will ask me why scientific employment? Because scientific employment is a phenomenon that is normal in the end, where each animal, as it can, finds its existence around it, and it is a logical rule that when it is very intense and it goes, it will unbalance the rest of the system.

1:35:00 So, that's where we get a little bit into the category. When we are psychiatrists, we listen to the stories of patients, we have doctors too, and we try to see the links that exist between the psychosis and the fear. However, when the patient is exhausted, if you examine him, you notice that when you lend him this plexus, plexus is a contribution of the neurodegenerative system, which is 100 neurodegenerative. And when you put it on his stomach, you hurt him very badly, you have a pain. On the exosceles also. It's very heavy. And if you pick it up, it's a very unique citation of the skin on the projections of the globes. You light the globe and you make the Ambroise disappear. There is therefore a link between the Ambroise phenomenon and the synaptic civilization which is represented by this solar and epic exosceles. So, we wanted to transfer this to our catalogues. And according to Schumann and Griezmann, we find that this place is a kind of physical tension, that is to say that it is a ball of the stomach constructed by acid and calculations. And it is obvious that at this time, this wave will also evolve, and it will evolve in different ways. In other words, over time, this physical manifestation will transform, that is to say, it will create fear, but it is not a construction manifestation, it is not a distraction, it is an impasse in the process of manifestation. We therefore have here two different aspects of anguish that are nevertheless, that are always part of anguish and that are raised in a simple way, as Madame Teresta said. However, this anxiety is destined for anxiety. Why? Because it is retarded. Anxiety and anxiety are two manifestations that can be repeated, that can be repeated, that can be encrypted, and that can engender and engender others. There have been schools of psychiatry, the French school of psychiatry, which has been denigrating since the end of the 19th century.

1:37:30 They claimed that anxiety was physical and anxiety was psychic, and therefore at different levels. When Freud arrived at the end of the 20th century, he took the German language of the concept of anxiety and its anti-term. He said that at that time Freud had mixed anxiety and anxiety. And then, in the middle of the 20th century, the American school was retreating on it. O'Neill's pragmatism was well known. For the art of economics, you have the avalanches, which are called botanical attacks, and botanical attacks involve physical anxiety plus anxious phenomena, and the states of anxiety for the art of economics also involve physical phenomena. So you see that there is a shift and the lines between anxiety and anxiety have been changed. If we listen to them, we listen very well, very sensibly, and we are forced to better understand the differences between language and science, and with this theory and category, we understand that things can no longer be possible, which is why science has become much more difficult. If, for example, we pass anxiety, anguish, all that, a little random, there are things that we don't understand very well. I have also written a book called Compia Vectis, which can trigger anxiety, but we don't know how all of this works. And if, in theory, I give you an introduction to the categories, the problem is clear. Why? Because we found the levels at the bottom, that is to say, the top, the topology, that is to say, the summa, where we found the BQ. The evolutions of the anguish, and above all, you can find the psychic effect with the mind-sickness effect. Activate the vision, the classical vision.

1:40:00 You have to make sure that the game allows you to regulate the situation. That is, you can play with simple and complex games, and you understand why, when you calm the physical anguish, you can very well calm the psychic effect. But otherwise, if one is specific and well-accompanied with it, you can very well act on the physical field without having to act on the physical field. So the problem is clear, if you will. And in addition to that, we have to be careful of what we say. That is to say that, if your physical experience makes you feel like you are still in the real world, you can have the idea that you are still here. And finally, the subject of the lecture, the subject of the lecture, the subject of the lecture, the subject of the lecture, And if you establish links between physical representations and physical representations, you can have obsessive phobias. And if you have obsessive phobias, when you work on physical phenomena, you can, it's a simple link, it's normal, and you can bring together both the physical phenomena, that is, the phobias, and the obsession, which is a physical phenomenon. If the psychic effect is related to affective-partial conflicts, you can no longer rely solely on the psychic phenomenon to end the obsession. And the obsession at that moment becomes prejudicial. So you see all this clarification which is dominated by this categorical conception. So, as we talked about this, we said to ourselves, well, if it works, we send it to the SAT. As we send it to the SAT, it is the supplement of a lot of mental problems to intervene in a lot of problems. We will also be able to generate all the mental pathology. When you research, it's not just a certificate, of course.

1:42:30 So, in this research... We have obviously thought about the principal logic of the problem, and we have obviously used the systematical pleading, we have used the pleads that you use in theoretical theory, and we have obviously disposed of them in geometry. But there is also a much more important problem, if the psychiatrist not only writes the holes to identify himself, he is obliged to penetrate into the holes. If we consider a patient, if we consider a patient, if we consider a patient, if we consider a patient, if we consider a patient, Obviously, because it is necessary to know, if we want to treat the narrative, it is necessary to know what is underneath the layers. To do this, it is obvious that, so, I will not go into too much detail, but it is necessary to know the values of the scientific, evolutionary, artistic, and intellectual fields. And, however, it is difficult to talk about mathematics, but what we call mathematics, or the language of the word, is the excitement, it is a big word. You can excite yourself physically, mentally, you are in a different world. But the classical theory is very different. There is what we call the same part. That is, you can excite at the physical level, be very calm at the physical level. You can be very calm at the physical level, be excited at the physical level. You can have a very high level of activity, a very high level of joy and sensibility, and nevertheless be calm, quickly, and so on. And this led us to believe that there were centers of regulation at each level, since if you are not psychically excited, you are not physically excited, which means that you have a regulation at a physical level that works well, although at a psychical level, it doesn't work anymore. And it is also evident that if the whole subject remains calm, adapted to the situation, A level of global regulation, we have been encouraged to distinguish the centers of global regulation and the center of regulation by level.

1:45:00 And this has brought us to a level, to a central level of regulation that made us think exactly of the artificial law of Mrs. Pérez. So we will generalize this in the following way. They will integrate with external dynamics and we are going to have this central reference medium, let's say this central reference medium that we are talking about to translate into the language of Mrs. Petzmann. And then, at each of the other levels, we are going to have the centers of regulation and they will be in relation with this central reference medium, which is a retrooperative level, which will constrain the psychic regulation system. The whole network, in a way, flows in the field of mathematics. And so, we now have another very important thought instrument, which is the process of decision. It is obvious that everything we do in life is based, or voluntarily, is based on decisions. So, we have a systemic author, who thinks that the decision is to be taken into account in between. An internal system and the external environment which is complex. The only thing is that the internal system is unidirectional. So we have to figure out how to adapt the complexity of the system to the complexity of the external environment. And so it's a problem of decision. In the world of science, you have here the clinician, the patient, There are functions that are in the clinician, in the patient, negation between the clinician and the patient, negation in the motivator, negation between the clinician and the motivator, negation between the clinician and the motivator, negation between the clinician and the motivator, negation between the clinician and the motivator,

1:47:30 You have observed the method I used to observe these terms and the diagnosis that follows. In other words, the approach to the classical case is a very elementary one. And this elementary one is quite useful, of course. And when you approach a fundamental problem, you can approach it either in a classical but effective way. But you will have the advantage that you will be able to go further and you will have the disadvantage that you will not be able to go very far because you will stay on the description, you will not enter into the structure of the whole. If you have made a systema reference, you will have the advantage of going further and further. And you will have the disadvantage that all your lessons will not follow your way of doing things and your problems are a modest reduction. In other words, you will have a double. These are possible decisions that are not at all the same value. It is therefore another type of decision, which is a cross-cutting type decision. This cross-cutting type decision can be explained by the fact that, in the case of the following nation, you will observe, and we have seen, your beliefs and the decision to learn. And the third type that will appear there, which will be the hidden thing, the hidden principle, which must be eliminated. We have here a... You start with the trigonometry, you follow the trigonometry, you have a decision that is already more complicated, which is already very important. And this requires a lot of psychiatry and a lot of mathematics with students who are very bad at it, very bad at specifying, and it becomes extremely complicated, for example. It is easy to say that schizophrenics have a certain amount of hallucinations, mental dissociation, etc. But you have patients who present themselves as schizophrenics, and if you see that in their behavior there is a slight possibility of depression, you are forced at that moment to rethink the problem according to another one. And you have the surprise at that moment to find a new diagnosis, as long as it is the first diagnosis, but not the second.

1:50:00 And you are in a good situation. And we had a lab like this, which sent us the diagnosis of schizophrenia. We noticed that there was a small increase in the number of symptoms. We took it differently. We abandoned the first treatment, which did not work. We gave a second treatment related to the new given diagnosis, and it increased by 5. So we had to associate two different studies. All of these terms are used in this scheme, which is a simple scheme, a crossed scheme, and which is turned back to give a final diagnostic. So when you are convinced in your decision that there are different possibilities of decision making, you find these three possibilities in the language. An elemental model, a crossed model, a complex model. All of these concepts have been brought down to the bottom of the list. All of these concepts have been brought down to the bottom of the list. All of these concepts have been brought down to the bottom of the list. All of these concepts have been brought down to the bottom of the list. All of these concepts have been brought down to the bottom of the list. All of these concepts have been brought down to the bottom of the list. All of these concepts have been brought down to the bottom of the list. All of these concepts have been brought down to the bottom of the list. All of these concepts have been brought down to the bottom of the list. All of these concepts have been brought down to the bottom of the list. All of these concepts have been brought down to the bottom of the list. All of these concepts have been brought down to the bottom of the list. All of these concepts have been brought down to the bottom of the list. There are two missions that will take place. The first will be the integration of all these factors and the decision will be the integration of all these factors and the decision will be the integration of all these factors and the decision will be the integration of all these factors So, once we had these elements in hand, we were able to address phenomena that we didn't understand at all before, namely, what we call an etalix. An etalix is a state that mixes two different maladies. If you will, you can both excite and deprive. And it can be understood, it can be understood how?

1:52:30 And we have different forms, different descriptions, of the forms in which the excitation is carried, in which the vibration is carried, in which the excitation and the vibration are combined, etc. And you immediately understand, in this way, I repeat in this way, that if you have an excitation at this level, a vibration at this level, an excitation here, another excitation there, you will have to see one by one, and things are clear. It is important to understand how the pathology is constituted. There are so-called statics that pose a very complex problem. And the most important is that of schizophrony and the way in which it is tested. We were in the atmosphere of the atmosphere a long time ago. We were looking at American research samples. And we found out that there was 60% of schizophrony in American pathology. So, these are all references of Tainos. And for that, we have to understand what we call in France the typical states of manic or depressive states, that is to say, the state of excitement and depression form a joint disease, and we define the typical. If, for example, you have, for example, an excitement there, and a depression there. After this explanation, you will have to see a table of contents that is apparently dissociated from the analysis of schizophrenia. So for us, it was not necessarily schizophrenia, it was a different thing. But it would have been better if this reference point was human-attached. How to say? Psychosomaniacal-depressive atypical psychosis could simulate a psychotrony and not be a continual psychotronic psychotrony. It would be necessary for everything to be together, and it would also be necessary to have a representative model. And the consequences are very important, because a psychotrony is derived in a few months, a few years, a year.

1:55:00 So a psychotrony takes months, years, and the first year. So it's capital for the idealist. So, from this point of view, we could explain all the mathematical theory at the level of these theories, but not in a blatant way. The theoretical theory is indisputable. We could, at this point, go further and try to better understand the psychical containment. And the psychical containment, there is a very big problem that is more and more evident to us, which is the integration process. We don't know exactly how things work. For example, at the National University of Paris, when we ask the question, but when we go from a symbol representing all the arts to a polemic, we have to go back a thousand times, the problem is the passage, how do we go from the symbol to the object of the symbol? So there is a loop that is made, and that is a problem for us as psychiatrists. And finally, we have a relatively simple rule, which is the chromatic phobia. What is a chromatic phobia? If you cross the street, for example, with a car, there is a speed limit. You are caught, you are afraid, you have a constriction of your mind, you are anxious. At the same time, you have the presentation of the street, you have the presentation of the street that remains to be crossed, and you remain stuck in place. From this moment on, there is no more rain. And you can continue to go through the others to find out more about them. And then, with this book, we will continue to film in the same way. When you have an emotional shock here, but you have a non-creative system, you can't touch it. And so on. And you could, through an approach, try to better understand what constitutes this block that prevents us from being able to pass through it later. So, this is obviously a way of exchange, and we were told that it might be possible to go further to understand consciousness, which is consciousness, which is a very good thing. And we can't have all the consciousness in a block, it's not possible. But if we already love the reflexive consciousness... In the fields of logic, intuition, etc., we can still progress with this theory.

1:57:30 We are currently working with a Swiss logistician, who is the post-administrator, who was the chair of the University of Boucher, and who was the director of the Boucher University. We have been working with him for many years. And we are happy to say that we can, at the moment, always evaluate. I would like to represent this part of the lecture in the following way, which is to try to understand the irrational logic and the active logic. We are everywhere, in several fields. We have the field of biology and we are in a field of subjectivity. But these two fields remain within a cultural field for which we belong. Our references are more general, and in a case where there is obviously a contextual field that will also intervene all these other aspects. And through the intermediary of this theory, we come to understand how we have a common narrative between the inaccessible analogies, that is to say, between the automatized mechanisms and the sensory resonance of the logic. We can describe the philomens, the philomens of water and the philomens of water, which will mix according to the objects in the pillar, in a protological way, which will give us the logic of the cloud, then the logic of functions, and these logic of functions will depend on the nature of the object. So, according to the prevalence of the philomens of water and the philomens of water, or with that, we can have totally different intuitions, intuitions... Sensitivity, media, if the sensitivity film is good, and of course, if the rationality is good on this platform, it is good to have an academician in the room who can do it clearly. And we have to build a formula and a formula. Of course, all this is not a point that we have to work on, but it is a goal of the future that we hope to achieve. In other words, this category theory, which is not the point that the psychics do not master, of course, but it is a help that helps to better enter into a psychological culture, to better understand the structure of mathematics, and not only in the laboratory, but also in the community.

2:00:00 So the benefit for the psychics is that they can, with this approach, have better targeted treatments, and therefore much more efficient. L'intérêt aussi, c'est de voir que cette théorie lui permet aux psychiatres d'aborder les phénomènes d'une interdisciplinarité, ce qui fait plutôt que d'aller un peu au hasard à l'affection du classement. Voilà, un peu gros sur le bout. Peut-être une dizaine de minutes pour questions. C'est impossible parce que je parle vraiment anglais. In fact, it's possible. Do you have any idea of the metaphors behind the graphs, the structures, the fields, and so on? Or is there a certain modernization behind it, or are there any metaphors behind it? Well, there are two things. The first is that the citation is an intangible language. In fact, it is still an intangible language. So, you never know, if you want, if it is a metaphor or if it is a... The second point is that with these steps and the analysis produced by the students on a very large scale, all these researches last 40 years, including the initial studies, the observation scale, I made a roving system. So, there are still some invariants that are not purely mathematical and that answer a certain reality. What I presented to you has still a value of modality. It's not just an example, but I would be happy to say myself what is true and what is false. But we can't do otherwise. Yes, you know, because at the moment, as you can see from the information, the technical risks of sending an academic lecture, what are they, or what are the steps to be taken?

2:02:30 They are a structure for the French language. So, who knows? When I build my graphs, I do it from the invariant functions that I try to extract. And once I do it, it helps me to work on the clinic. And there is a very curious area, you know. When a graph is well built, I am not alone. I know that in Saint-Denis, it is built that there is something that is not in my hand. I am obliged to show that there is a human place in my hand. I am obliged to work on it. And to repeat the observation, etc. And to repeat it. There is always a gap between the public observation and the law. We are in the middle of a representation of the law.