Concepts & reality

0:00 He also considers vibrations for objects or mammals with additional structures on mammals, usually defined by mammals. Sorry, is the other session in here? The parallel session? I see it. No, the other talk. So, let me just tell you that some of this could be phrased differently if you might want to assume candidates. But to me, I'm sort of saying kind of better at the set. I suppose category theory could also be really going to this way, but I won't do that. So we have some basic properties based on the set of x0. And to, I can say, the subsets, the power set of x and these subsets, I assign sort of a set of properties. So that is, the function there, I can already do that as I appreciate, but I won't probably use that language now. And therefore I look at another set, gamma-mort, which is a set of pairs of subsets and a kind of property, or you can say, state assigned to it. And then, when I consider subsets, so subsets with some kind of property assignment to it, or I also look at it as a lot of observables in this setting, then I have another function, B norm, which assigns another set, and that's what I call the set of bonds. So if it's empty, there's sort of no bond among these elements, if it's non-ending, you have to keep out the specific of the path forms and an element that set would be sort of a specific part. So, in the order of language, I think, x-part represents sort of systems, elements, sometimes also called agents, or when a lot of servers, states, properties, be not fonts, or interactions, and be not represented in specific fonts, or the previous we call results.

2:30 So, one particular example would be, I mean, these types that we may add on additional structures, like orderings, etc. And also, categories, we can consider two objects we have a set of fonts, namely the font of the mortis set. Another example would be what's called hypergraphs, for example, where you generalize the notion of a graph where you have, instead of just edges between pairs, you introduce general edges between subsets of bursts. And there's a whole theory of such hypergraphs, but they they just contain two letters, so I think that also will be extended in a hard way. Now, of course, this scheme can be iterated so that at the next level we look at a set of bonds, and then we look at their properties again by holding a one function, and And then you look at pairs of subsets of bonds and their properties, and then assign further bonds by another function, B1. But of course this is not an iterative procedure, it's not recursive, because in a sense you have to introduce new functions at each level. And that's sort of the art in a full structure to do that in non-period, in a interesting way. But I think this works and it can be iterated to sort of any finite level. And then we end up with a structure consisting of these levels of, let me, open bonds property assignments for observers, and what would be special for objects, and these are all the content assignments. And such a trickle, then, I like to call it the hyper-structure. Also, as I said, we could look at the subsets with more structure, like ordering and further or the replications or tallies, but I want to look at that here. And my basic claim is that I think that this very general scheme

5:00 captures the essence of the architecture of the general structures and organizations. In a way, it's not a specific structure, but a form of Ed Sein principle. Let me just also mention that for those of you most of Canada's theory, that commentatorially, this sort of extends a scheme of high categories that's called blocky love sets, where you look at one level, you can get down to the level below by sources and targets, and you have identity inclusion from the lower level to the top level. In this sense here, we're looking at one level, but we just have a prediction down to the power set, and successfully do that. And, geometrically, in a sense, the home mind is that sometimes in a lot of performance features, you look at cobordisms like that, and you have a direction from here to there. But geometrically, this is just the same as sort of having a bond between these. So, this is because these orientations, which are these, have an arrow in and arrow out, you can always adjust due to the duality of the properties, but geometrically, I think the profound thing is that you have a problem here. So, in a way, in this context, I'm saying in general, be-emphasizing the sources and targets, and the category theorists, that's like almost swearing on the church. And I once mentioned this at the category theory meeting where McLean was there. And the interesting thing, I mean, that was his 90 years celebration. And he would have been called and said, after all, he would be very upset. And he said, no, that's a very interesting point of view. So, let me give you some examples. Certainly playing tablets in this paper. and also higher cobordisms. What do I mean by that? High cobordisms are something like the following. You know, we have ordinary cobordisms, say, connecting these circles, a surface connecting, say, two circles here, one circle there. But in spring theory, you'd also like to have open springs. So you have to, geometrically, also allow more intervals like that connecting

7:30 in plus there. So that means that this could be an autism from two circles and two intervals to one circle and one interval, and this is sort of an open part of the boundary. And this is for the three-part of the boundary, or also in physics for what's called D-brains. So here you actually have three levels. You have, at the top level, the surface, sort of being the bomb. You have the circles and the intervals and the endpoints of the surface. That's what creates a new level. And let me, I couldn't attempt last night to make an extra transparency, because if you look at the open-closed first to the category. We actually have a very nice result there, that if you look at the geometric realization, you associate the space, as I thought, the bar speeds, and you de-look that, this can be determined very precisely because, for those of you who know the terminology, it's still with infinity of space, ct minus one infinity, plus certain modifications to do with Cp infinity. And also, this is the same as certain copies of Z. And this corresponds to the number of D-branes, B-power. And this is a mammoth transfer. So if you have a million of this terminology, and this is a consequence of a very famous result that we do at least in recent years by Watson and Weiss on the multiple projection. So, I'm just showing this that, I mean, the topology of two categories is absolutely non-pringual and relates to various pieces of mathematics. Also, at point C, I'd like to continue with hyperstructive graphs, that's extending hypergraphs, or what's called hypergraphs to another level of abstraction, mainly in the sense that we then consider subsets or subsets again, so we extend the edges to one more level. I mean, that's not very much. High-order logic, well, the bonds are sort of, and

10:00 high-order formal languages were a bond, a sort of parenthesis, that fit also in this picture. But I'd rather mention high-order cellular automata. In the cellular automata, you can see a sort of interaction they would write a cell. But then, And then, in certain situations like, for example, traffic networks and communication networks, also you'll have other neighbors interactions. So you'll sort of have an interaction between neighbors. And that creates a second level. And you could even have neighbors changing with time. So that gives, I have a student who is just finishing his PhD, this form, have written this thesis about this, and we have a paper that is in Cessna, the theory of advanced circumference systems, on these cellular automata. And I think that's to show you, for example, what it means. Here you have a sort of classical cellular automata, and in the lower row, you see that when you introduce these high-order groups, you get patterns, and actually it happens that you have not seen for ordinary cellular problem. So, one more level creates something entirely new. That's the point I'd like to make. And also, another thing is that, here too, this is an ordinary cellular problem. No, you can call that one. I'm just going to that one. What's happening here, this part here, sort of reflects the structure in the ordinary. And then you put on an extra layer, and then you see this phenomena here, which represents kind of periodic, regular phenomena. So, one of them, that's what we call crystallization in the pattern. And that reflects that even in sort of very complicated, almost random, chaotic patterns, all of a sudden when you put on another layer of order, some kind of order, and by iterating that, probably more order, and you may wonder if that could be relevant and interesting in studying, for example, neural networks and models of brain-like systems. So that's just a suggestion.

12:30 Another mathematical example that I've been studying quite a bit is what's called pi over So when you look at two factories of vector spaces, they introduce an ocean of two vector spaces. And in order to make here we consider sort of bundles of vectorspaces, here we consider bundles of two vectorspaces, which are vectorspaces or vectorspaces. This has to be made precise, and it shows that this is entirely a topologically different nature from that one. Actually, this is connected to a logically cross-call homology and the representative spectrum. For those of you who know, the homology is multiplied by the homology. And also, for the category theorists, I should mention that there's another version of this by John Van Aes, using in-terminal categories and defining the two ecospaces in a different way We use PN, which is based on the definition of Mr. A. Kalkawa and Kowalski. And we have just recently shown that by using IS's definition, we just get all the KT back to it. So it's, from that point of view, not some interest. Okay. I'm going to also introduce the notion of hyperbolic fractals. I can't want to make the details of that. And again, I mean, high-perspective graphs extending the networks and communication systems could be very interesting. I had a student doing some kind of experiments on that, actually looking at a very explicit tracking network concerning the flow between two points there, and then putting on high and high-perspectives and actually can see how that, in a sense, improves the flow. But that is, I think, the technology that could be interesting to look at. Also, modularized spaces, which in a sense is spaces of spaces, another example of this kind of idea of thinking. So there's also re-modelization. This is where you consider flows. flows. And, for example, that is, in a sense, an idea that's been used by Ehrman in his

15:00 approach to the Bank of Ray conjecture, that you can see it's actually a kind of space of structures and metric space, and you put on a flow of that space, and essentially heat up the metrics, and it follows the heat equation. So it's basically, the idea of this group is, you can see the space of structures, heat it up a little bit, look at the heat equation, and the equilibrium are the interesting geometrists. So it's a beautiful idea, but in a way, a second form of the line thinking, but at a very profound and manageable level. Also, I think, basically, I've been in contact with some chemists, and I think that high-order geometrists is, in a way, an ignored subject. For example, some people think of material structures built up by geometrists of geometrists. And basically I didn't realize that bone structure is very intricate, or very intricate, not because it's science, I think, from the two issues about that bone structure is basically seven hierarchical levels. And I think that at the moment, you get these within the world that one may be able to construct or realize some of these young methods that are not figuratively related. So, therefore, I think it's important for the chemists also to be able to give a description of what one might construct, because basically they tell me that they don't want the descriptions, They're just going to the lab and adjust the key parameters for the best. So I think they would be open to some kind of new descriptions. Also, dynamically, we make a lot of dynamics on the hydrostructures in the sense I mentioned, but I also made both the bonds and the properties kind of hen. And that's happened before, if I saw it on that. and, for example, especially making the neighborhood time-related to be a very interesting climax. And that's something that I don't think has been considered before. OK, so what do we mean returning to my kind of abstract matter? So that whenever we have a set, we may sort of be able to take that as the basic units of a hyperstructure and put on a hyperstructure.

17:30 Then I call this set a piece of abstract matter. And also, the point is that this language even, I mean, you may formulate also the dynamics in the same way. So that, I mean, they may also be considered as, in this language pieces of abstract matter, in the sense that you consider the dynamics of dynamics. And, I mean, that's a very contrary of the question, because if you have a space, you look at the set of dynamical systems on it. And that's what we traditionally would have studied. But then, for example, a little study of quantum systems. physics. Physics, by using the idea of renormalization physics, introduced then the dynamics on the space of dynamics. For example, chaotic systems came out as tix points in that manner of dynamics. But on the other hand, if you go further, you may even get chaotic structures on the space of dynamics. And you might ask then, how to study these? OK, you then perform a second set of green optimization. The northern bigoties has fixed points, but then at high level. And this is mathematically tricky, but I think that is the fruit of the world. To start, please, one has to look at some specific examples first. So this is a setting where you have groups of groups, the reactors or reactors, the paladies or the paladies, And I mentioned, motivated by a book about Russell, Jokes on Jerks. And of course, logicians have been thinking about these high-level problems for some time. And just to show the need for the formulas in order to keep track of high-level structures, you may think about what is, I mean, we all know the jokers and love it, and you may talk about the joke, about the joke, still, it can be funny. If you talk about the joke, not the joke, not the joke, not the joke, then you just smite slightly, and when you talk about the joke, not the joke, not the joke, not the joke, no more smiles, and rather get ahead. But if you have a framework where you can keep pat for this, you can sort of have an observer telling you whether this is fun or not. I think that's what we need. And also in the social systems, I mean, people have studied societies of societies, also an example of abstract matter, and you may wonder whether even the system like our brain or brain-like systems will have this scratch. I would certainly think so.

20:00 Also, I think it's a very critical thing, like we've seen in some of these examples that students have been looking at, that communication and cutting networks, that if you have a set that you want to study, it's very useful then if you can find the hyperstructure, in this sense, to put on the set. Especially when you want to direct, say, a set of agents to some dynamics formed in a certain way. because then you have sort of control of the set and how it works. I mean, you may think of even social and political systems, I mean, if you want to act on a society, it's much easier to do it if it's a structural society than if you end in sort of a random society. if you want to win a game in a fairly chaotic system, the first thing you want to do is take some kind of party organization. And that would be simple. OK, so that is one point of view. And I think the interesting thing is then that this approach then it's solid, independent of whether the basic units are atoms, molecules, atoms, curves, surfaces, solids, or organisms. So in that sense, it is general, and I think it has an advantage of the general, because then it's more like a science principle than a specific scientific science, something that Randosius has pointed out several times. And, in a way, then we get these artificial worlds. And in these artificial worlds, the nice thing is, of course, that you can regulate the laws, rules, and processes of your pieces of matter and decide what kind of calculus you'd like to rule them. And I think that gives us the that is quite nice and modeling systems. And also, I think there is this idea that it's not just the matter of the system

22:30 that you have this kind of structure, but also the energy. And what do I mean by energy in some of these modeling systems? I mean, energy could, for example, be pre-time at the central processing unit in the computer program. That is what keeps the process going. And also, the hyperstructure in that sense, is a really advantageous point of view. Also, in artificial systems, like those that have been studied in artificial life, community, with the deconstruction and fabulous like abstract photosynthesis in this way. And even, for example, in connection with the production of non-materials, I think it's a sort of interesting task to give a genetic type production description of various kinds of materials and these new nanomaterials. Because, as I said, the premise gives a few parameters for the best, and then a description, I think, would be neat. And my time is out, so I will just end, where, in a sense, I.O. structures is, you may consider it, a never-ending story, because I mean, whenever you have a sort of constructed one-year-verse of male-verse, of course, the procedure may even be created to consider two-year-verse, et cetera. So, I don't think there's anything negative or problematic with that. It just shows that there is an infinity of possibilities that we can use, and how to use, et cetera. So, yeah, I think I can do that. Thank you. Any minutes for discussion? Yeah. So, yes? I didn't understand what you mean by violence. Could you give a definition, or example, or whatever you know? Well, I would say, let me take those examples that, Geometrically, I mean, I mentioned the spring topology. So if you have, for example, three surface, I would mean a geometric bond between those would be the surface having these three as a boundary. So a cobordism, in that sense, is a geometric bond between the boundary components.

25:00 Yes. And also in a graph, a bond would be sort of an edge. And in a hypergraph, a bond would be the set constituted between edges. So that would be subsets or vertices. But what makes them sort of, say, in a hypergraph, why you put them into sort of three rows of into one distinguished subset, that would be sort of due to external criteria. But for me, I mean, geometrically, think of the globalisms, I think that is the best one. Yeah? So that's a remarkable range of the possible applications, but I don't know if that's very many of them. But just to come to the two topological ones. Do you have actually used these hyperstructures to prove the theories about K-theory and globalisms? Or do you use high-category theory? High-category theory? Yes. I mean, you say high category theory is a particular case of this, but when you do it in the applications, don't you use high category theory? I mean, it's not just a question of the notions, but also the results. Yes, there are two topological examples that I mentioned. They were certainly within the same level of higher categories. That's what we asked. Yeah. They didn't use this more elaborate version. That's true. Though I think that there could be interesting topological applications going beyond that in this direction, which we haven't found yet. But on the other hand, the example that I mentioned, that's going to deal with advances in complex systems, is a sort of abundant, and explicitly, uses this office in a way that's not covered by that. So that is one example. There is another science where we have to handle multiple layers of complexities in computer science, and the vocabulary and the concepts are very different. We are talking about interface, message, event, answer, client-server model, and we are learning complexity with this concept. Not dawn, not matter. We want to hide. If we want to organize complexity, usually with a client-server model, an underlying layer is just answering to message, so underlying layer becomes a blank box, and we articulate like this one layer with another layer.

27:30 So, the question is not for me to have a mathematical structure, but to think about the semantics that you will use to handle complexity. And I think it's quite, here, I think category theory can be useful in the hybrid structure to handle complexity. But the concept describing does not fit complexity. Bones and interaction are not good intuition of complexity. We don't know the identity from one layer to another one. She must be defined from one layer to another one. So that's why it's a black box. We don't know behind the interface or it's done. So it does not matter. So redefining in a so-night way one layer from another one, I think is not a good intuition of the articulation of two layers. But my idea is behind this. So, I think it should be more interesting to look at what we already do. We practice in our exercise, articulation, if you have to design or analyse a problem in the business world, to programme it, we have to under complexity, and we don't worry about this concept at all, and we do it. Yeah, certainly there may be different points of view. I think on, I mean, say for example, geometric complexity, I think this is a natural way to look at it, but certainly there may be other ways to do it. What we do in computer science is certainly a natural way, because we need to... Yeah, and also, I mean, it may be possible to bridge the concepts also by... Yes, I mean, sort of, it may give you a sense that, well, that sort of bond may correspond to what you make for something different. And there's a computer program of hydrostructure in itself in the way you build up the various components of it's further. One more question. I completely agree with what he said. You, you're royal, not to be very useful,

30:00 but the conditions that they understand what you're doing. And that's why I started my question because I didn't first turn his bones. that is in the same direction where I come to this very complex system for one. And we need an approach, and we need a language, and we need to look more than that. What? I would say I agree. We have managed. If you give me a complex system, I might have some chance to stop you, because I'm not quite aware. that I understand that just because I know how to do it, but I can't transmit that. And each new problem in several fields is different from me. And if I could have something like this point, I would be very happy. But I can't understand it. For example, interactions. How do you define, how do you define interaction? Well, if we have, I mean, to say that two systems interact, I mean, if these are dynamical systems, I think we have at least a notion of interaction. Well, even in social network interacting in something very simple, there's communication ongoing. Yeah, but I mean, just to press it, say, in an explicit case, within sort of the space of dynamical systems and two systems and interacting is, I think, fairly clear that you have sort of interaction potential between them. If you can, say to your computer, it's fairly clear and do it. So we need, I'm sorry, we need something that we can newly understand, and that I want to write it down, and that the computer, the computer can understand it. But as it was suggested here, I mean, if you have a communication between these systems, you're going to come out in versus the other systems and vice versa, then that's the acceptable interaction of your system. Thank you very much.

32:30 Thank you. Thank you. Thank you. The coffee is out. Yes, it is. There is probably a cafe outside. There is a parent session and probably in the second section, and the other side wants to come here so that we have to rest

35:00 it exactly. Thank you. Thank you. Thank you. Thank you. Thank you.

37:30 Thank you. What is it? What is that? What is it? What is it? What? Okay, we're going to start now with the song. Next session, with Professor Eresman and Dr. And as we know, we have half an hour for this whole thing, and then the bottom of an hour for discussion, right? So we try to keep the time to date another session. It's difficult with all these . So, Professor Erisman wrote a book on that book on that book on that book on that book on that book on that book on that book on that book on that book on that book. So, thank you so much. You did a good job. So, we are speaking about the black men. So, here, the idea of what I'm saying would be to describe the model of human rights. Yesterday, a lot of us have spoken of the matter of human rights, and that of the human rights of human rights, more and more properties have been obtained from animals, and then more and more properties.

40:00 Now I will give a smaller slide to explain how a physician, a mathematician, myself, a human mathematician, myself, are trying to find a model for emergence. and that they have something to do also with the commonwealth class. So Charlotte has always thought that mathematics at the base is an understanding of everything. And in the 18th, in the 60s and 70s, we thought that mathematics was not something which is only format, but it was really something which could uncover the structure of everything around Africa. And it was not just a sentence, we say, like that. It was really something, really good and mathematics was really a sentence. So we thought that we would have applications, but we were always just working on the mathematics and so that could be applied and could be really after change to do. And so all of that was mentioned in mathematics. And when we do one more moment, one of my friends, my friend, John Dichon, I asked you, my teacher, students, if you could help us from all the day-day problems, health problems, you try to make new deaths in the Apple. So, we need to do an hour away from that, and after the death of Charles, he helped me to go on, which was difficult, since we are clearly completing the work, and to form a round of mathematics, with mathematics, our internal language, and our communication language.

42:30 And Jean-Paul suggests that I write, that I edit the complete works of Charles and that I have the comments, which are created in the four parts of the time. And he also had to be organized somewhere on category theory and at this occasion we had discussions and I tried to explain what was category and why category could be interesting. And he proposed that the work of the nation of capital, and at this time, in France, there were much thought about the benefits, because there have been many complexity organizations because of books, which have been written from them, there were books by Dabobit on the There have been also books of contemporary complexity and so on. And so we decided perhaps to give time to use some ideas of technology theory to model Islam artists. And this is not completely at hand, because if we think of mathematics, mathematics are being developed, but initially, of a very practical way that we can leave, our union and government wants to measure things, and so on. So, many mathematical versions have been introduced by mathematicians with some view of the real problems in physics in particular. For instance, when Charles had developed the notion of production, it was in relation to his problem in relation to his history. And so, for a little bit of force, were inspired to charge by reflections on the lecture of

45:00 time, two types of times seen by Bersoll and which are made in discussion with Lombard just before the war. So, mathematics seems to have something to do with the real world, which is completely natural, since our mind, peace of soul, and our body, and our self, are a child of faith, art of the new reality. And now, why categorical? Why categorical? Why are they interested? They are interested. So, Roconcon asked this question. Why is it so important in this time? I think it is because mathematics, a category theory, is not a domain of mathematics. It is a domain of mathematics which is at a border with mathematics. It is a domain where the categorization reflects on the way that the mathematician reflects when the research works in mathematics. So in some way, the category theory must have something to do with the way our thoughts, our minds can operate. And so, if we reflect on this, you see that the category, the basic capacity of our man, and really what is at the basic category theory. This, if we think of the category, so what does man, when he has, is not different. The first thing is to do everything in a category, in a category, no matter what. Then he tries to find, to study how these different subjects and their interact with them. So, we are, this will be made by the interaction, by the arrows in the category. The arrow, I can speak, not of morphine, but of arrow, or of links in the category. And then, we want to interact with the sequence of interaction. And our different sequence of interaction may lead to the same piece. That means that this is exactly what we all have in the associativity.

47:30 What it means, the associativity of the component of the category is a way to differentiate classes of sequence of interactions which have the same functionalism. So, the top of the category and this is exactly, are describing objects, relation between these objects, and the way, and the classes of sequence of interaction, exactly. Another characteristic, which is very important in the evolution of adaptation of man, will be to consider not just one object, but to see several objects acting together. So, this we asked to be represented, but this is the fact that several objects work together, and they are represented by the patterns in a family of objects, an eye, and some distinguishes between men. So, the collectifaction of this pattern will be called collectivity, and it means that there are interactions from each NRFN, and such vats, which are applicable with this language link on the back. We have several collective genes and another possibility of our brain is to optimize something. So among all the possibilities of interactions that the collective interaction of the pattern is the one which is an optimal one. This corresponds to the construction of the coordinate. So the process construction in category theory just means that among all the quality things of the pattern, we have one which is the best one in the sense that every other one factors uniquely truth. So, you can see it's exactly what is done. Now we can also think of the pattern as the internal organization of M, and M as complex subjects. And in this way, we see the thing from top to bottom, and M is a complex object, the pattern is an organization. And we see that we have two properties of the colony, one with local, local because it's just put together, bind together to the matter, but also local, since it has been constructed that any collective link of the matter must be different.

50:00 So, the polimic operations are both local and global products. And now, why it will be very useful for describing emergence, is because not only one pattern has two units, but the same object may have two different organizations of which it is a polimic. And this, we see, that is what we first think characterizes the image. But first, since we have defined objects, raw and non-complex objects, to have this, we define the area. So the category will be called the article, If the different objects are partitioned in different levels, such as one object is the colony of at least one pattern of lower-order objects. So we have many problems. But up to now, I have those of one category. In fact, if you look at a system, say, for instance, you want to model the brain, we will not have a unique category. Categories in subjects are somewhat static to our object, to our intervention, and in the way. But in dynamics, you want something which has some dynamics. If we think of the brain, the brain has some neurons at the moment, but later on there may be some neurons which will have new formation and so on. So what do others take into account change. So, we will not represent the natural system by the data of one category, but by the familiar category, each category corresponding to a successive state of a system, with its objects representing the components of the system which exist at the time, and the links between them corresponding to the interactions which are, in course, around data. And we have to be more than just a family of categorists, but also how we go from one category at T to that at T5.

52:30 And this will be done by the data, the transition from the third category to the other. So that means an application which is compatible with the data of the category, with the IELTS category, but it is only possible to tell you that some objects here may not exist, still exist after that, and on the other hand they may have no objects and so on. So, we have a nervous system defined as a family of technology, which comes from the middle. Now, we must take into account that an element of the natural system in the brain will be not represented just in this model by one element, but by the sequence of the successive states. And this can be an invariant, at least you are just one neuron, without the fact that the internal organization, if you think, for instance, of the adults or the molecules will show the role, changes much more the ability. So that you are, you know, stability, different on one level and another one, Now, the other dynamics is different. You must have different time scales depending on . Now, in a young people category, we want to know what are the good interactions between patterns. If we have two patterns here at the level 1, there may have families of interactions in their components, which we call a cluster, which are such that they correspond to some interaction, local interaction between two patterns, which are the property that if the two patterns are a polymine and an I, they are binded together into a link, which we call a simple link, from the end to end. So this kind of links between higher order objects, between the level n plus 1 in our levels, this kind of links can be said to be dedecible links.

55:00 Niels Barthes with the diverse cultures as well done with the difference between the visible beings and those with charis. Now, we have one comment, which is, we sculpted only to the natural age. We are saying that there may exist two patterns which are the same qualities. Now in this case, suppose that we have the symphony from n to n' and the symphony from n' to n' to n's. The first one binds the cluster between the two patterns here, the second one binds the non-attachment cluster. In some cases, there is a cluster between rows and the composite of simple symphony with simple symphony. Then, the problem of convergence is the characteristic of convergence, because there may exist in some categories, and I think we will see the example in the natural system, that we have two patterns which are non-equivalents, which we call non-equivalence, which are the same coding. An example would be, the same ago, there are two different internal organizations in electronic properties. So, in this case, we have links from n to n second, which are not simply. So, at the level of M, you cannot explain this complex list by interaction between the components here and the components here, but, however, they completely depend on the whole structure of the lower level, since the fact that these two factors at the same point, have taken just into account all the properties of the law. So, we have here the possibility of defining something which is an emergentist recutionism in the sense of Marianne, mango. So now we want to go further. We are saying that in a system we have an evolution system, we have a change of state.

57:30 However, in a natural system, this is a central state that depends on what the law has called the archetypal, the four archetypal changes, birth, teleth, polyglom, cishol. In our category, it is that some objects will be added to the category, this is birth, some others will be suppressed, and we give some patterns which have to be binded, this is called corrosion, and also some patterns of which the colony will be dead. And now, there is a categorical construction which allows to describe exactly, if we are such something we call strategy, the data, there is a construction which means the best way to realize the objective of the strategy. in a completely described way, and in fact, this construction is a particular type of the construction of the prototype of a sketch of which I have alluded yesterday. So now we have the complexification of the category with respect to the particular strategy which is defined. Each object are both from the category which have not been suppressed. There are new objects, one new object from each pattern which are in demand. And so that becomes a new object, other because it's collinates. And among the links on these new objects, there are both simple links which bind clusters which are in the category of cats, but there are also necessary complex links as soon as there are two different patterns in the first category, which are the same links. We call category, we say that category satisfies the multiplicity principle, when there is such multiple objects, and we call complex which, the passage from one of the patterns to another, which are successfully.

1:00:00 So, this competitive list of multiplicity principles, in fact, we are primitively called the degeneracy principle because it is exactly what Edelman defines as a degeneracy principle in his book, Unremembered by the President. And more recently, Edelman and Tonnery have made some assumptions that this would be apparent in the image. So, it's a complexification process from the interaction. And here we can have a sequence of interactions. As soon as the multiplicity principle is realized, we have more and more complex objects which are formed. So, in particular, if you want to model the cognitive system, we will say the first category will be a category of neurons, but for the cognitive system, we want not only to have the physical brain, generally, the simple assemblies of neurons are not neurons as a So that we will have mental objects which are obtained by the complexification process. And this we call cat-neurals, or category-neurals. So the mental object will be represented by class of different assemblies of synchronous assemblies of neurons, as it has been shown in neuroscience, that the synchronicities of the nervous are realized, what does the metrologic technique with a long time? And if we have such a higher category of neurons, it can be later recalled by different ramifications, the difference between the pattern of which it is called me, and then the pattern of which it has to be unfolded in several steps. Now another property of our mind is that we have possibilities of memory.

1:02:30 So, we have a possibility to learn some objects in our environment, to learn more and more complex procedures of behavior and so on. So, we are trying to enable this system and not a bigger anymore. We want also to see how the strategies are chosen. We have said that the general state, the complexification with respect to the strategy, but we must have the strategy. So the strategy, we have autonomous. So, one of the capacities of our range is that we have internal, we are not something external, which we direct us. So, for this, we suppose that in the economic system, there have been several sub-systems, which we call co-pagulators, and which will direct altogether the dynamic of a system. In the brain, for instance, the co-regulator would correspond to some area of the brain. There are several levels, it would be just a column, a neural column, or it would be much larger and so on. And how it operates the co-regulator? It operates by, at each time, laboring the partial information it may have on the system, enforced what we call it sans-shape, which is described appropriately. And then on this scale to which CR has some admissible strategies, in the already of the later he can take numerous strategies, he chose one of these admissible strategies, then he sends comments on the strategies to effectors, and then after that, there will be comparisons between the with what is expected, which is modelled by the complexification of the landscape with respect to the strategy and with the new landscape.

1:05:00 Now, for instance, how the memory will be developed in this case. So by determining for the difference here, we have to think of an object in the memory, which we call record, as a model, an internal model of something, for instance, of an external stimulus. So it will be constructed to, we have here, an external stimulus, for instance, or an internal stimulus, which is seen by receptors. Now, the difference here is, for example, the thing of the blue triangle, and here, the color triangle, and here, the shape triangle. Each of the different aspects of the stimulus. And then, the strategy will be to memorize the stimulus if it is not yet known. So what I will ask is that these patterns of aspects there are actually good. So the record, the irrecore, record relative to the following instance, will be here. And now all the different CRs work together and the higher CR which controls the 3 CR here, for instance, the higher area which controls polar, polar and also size, shape, size and sense, will also form this whole record, and the record of the stimulus will be obtained by binding together all these records, so that it is the quality of the different records, they adhere to the transfer. So this record is not something that can exist. We have a possibility of multiple effects. It can later be somewhat modified without changing the record. So that is not something completely fixed, but that complex identity. Now, for IRM, we will have the possibility of looking together classes of such records and by forming what is the concept of the record, for instance, the concept of blue, and not only the blue, but in particular, this will be made by the intermediary of the by taking a limit of the pattern of agents of the CR, which are activated by the stimulus.

1:07:30 Now, in the gallery, we have another concept that can later two different things. For example, a blue object, a blue triangle, and a blue circle may have the same different limits, but the same concept. And these are different instances of the concept, and there is a possibility of shift between the two different instances of the concept. Thus, we have a semantic memory, which is formed in this year. Now, there is another part of the memory, which is the procedural memory. The chart where we have models of behaviors, models of the strategies, this will be represented by formal units, here in the procedural memory, which are patterns of programs to our effectors. pattern which is then memorized by the code unit, which is called the effector. And the procedural memorials will be constructed by the iteration of the process to add limits, not the code unit, but limits, you know, projective limits of patterns of already constructed strategies in the framework. Now, such a procedure can be ruled by an external stimulus. Suppose we have an external stimulus, and we want, for instance, an object which has to be taken. Then we have the object, and then we may have the antiquatory from the record of the object to a particular strategy. And so, the record of the package will be done like that, and it will activate the different comments of the package. Now, we are saying so that in this way, we have a cognitive system, which was presented by such a memory-wracking system based on the category of neurons, and successive complexifications of this category. And this category is a multiple object because we are already at the base of the category of the rules that itself, we consider, are obtained by complexification from the category of the rules, where the multiplicity principle is known as we have said.

1:10:00 So we see that the emergence of higher and higher complex objects, higher and higher category neurons, is in fact based on the laws of quantum physics, since the fact that at the level of the atoms we have a multiplicity principle depends completely on the laws of quantum physics. So in some way, the element of higher and higher complex objects and the element of higher and higher cognitive process, mental objects, cognitive process, and so on, depends on what you play at the basic level of the quantum law of physics. So that we can say that we have this way, so I'm going to leave between the two ways that we have to do in a formalized sense. At the basis, we have quantum physics, which is given in this way, to have multiplicity principles. And at a higher level, we have some things which act in a very global way, which is very Now, I have not much time, so I just said some quick work on how consciousness could be put into this term. So we have to send another way of the human system. And we suppose that there are some records which are much more often activated and for longer time, and that they are, for instance, the behavior, natural behavior, and so on, and they form a part of the memory which we call the archetypal form. And this will be developed during the evolution, during the convert form, by adding more and more objects to the influence of the different crs, and always with a latitude, with a switch between different instances of the concept and a switch between different decompositions of each instance.

1:12:30 So that the archetypal core will grow by taking into itself other nearby records and so on. And then this artificial record can be thought of as the inter-identitative memory of the animal and as representing the cells, not as planned to develop this idea. And so, we suppose that in this particular article as geometrical structure, given by France, what we call France, only there is no mix between the elements, and for the categorization, the France would define the topology and the topology on the article. Now, consciousness will be only dependent on the activity of the architectural law, because we define a conscious process when there is some kind of bourgeois events, for instance, a fracture because the different strategies of the differential are not coherent. And at this moment, we have served our attention, which will activate the archetypal core, and this activation will retroact and complicate to flow through the different needs of the different plants. And this will allow the formation of what we call an extended landscape, which can be correlated to the global workspace of many of us. And on this extended landscape, it is really possible to do two processes. One, a retrospective process to find the course of the unusual element. and so I'm going back into the past, the real past, to, because the accent doesn't get a lot to read through. It takes out of the memory for some distance. For instance, if you have a year, you have, you can just after the end of the block,

1:15:00 and we have also a prospection process in which, thanks to the fact that we have, it will remain cyberactivated for a long time. We can perform internal landscape where strategies can be virtually tried of course for the organism, and this process allows to develop long-term strategies, and not just for one step. So, we see that all this is based on the fact that we have this emergence through the multiplicity principle. So, in the memory of the system, we think that naturally the construction of this is for us not the most general thing we can do, it is very possible that we should be somewhat generalized, for instance, employing more general infrastructure, but it has the property that it just points exactly to one reason at least of emergence, this complexity which cannot be reduced to simple. Thank you.

1:17:30 I can't hear, can't at all. Would it be possible to repeat the question, for the speaker to repeat the question? Because I don't think any of us were able to hear that. Sorry. Sorry, could you just repeat? We've been able to measure the complexity of the EEG, the electrical activity of the brain, At the same time, that behavior becomes slower and slower in problem solving as we grow older, the EEG becomes more complex. It becomes faster and more complex as we grow older. So we have measures now of complexity of the electrical antenna frame, which fit. So I expect that, in fact, in this model, there is more of the time, which is not time enough to develop in, but the time programs are much better than the problem. Yes, ma'am. Will it be possible to get to work on your site? You have our website. Our website is on the first page. There is one website where there are several of our papers, and they also, on the website, many of the papers are completely printed on the website. I understand that your papers are on the website. Because there is a problem, it is done with the director, and we don't know how to put the director, this kind of thing, on the website.

1:20:00 That's an interesting question. But if you want, I may give you a CD with this. Yes, can I do that? Yes, we could have a look at that, because I found your slide, but I couldn't agree with everything, so I'm sure I'm all going to do it, and I'd like to work on it. So, I have this first question. The other question is that you have a technical problem. And before the technical problem in the beginning, you have something very local, but I haven't, maybe this is my life, and we are in COVID-19 because you have the same thing that you have in the middle of it. And in talking about science, we are at the law, which we didn't actually understand, but in fact we don't know how to do it, we don't know how to explain it. You see, you see. So, what have you done for you? For what? How are you going to share in China? Yes, in China, Hawaii, you know? It's a... I don't know. Yes, I understand that. We don't know how to do it. If you have a solution, I don't know. I don't. Thank you. Thank you.

1:22:30 Thank you. Thank you.