Anisotropy of biological spaces (part) / Anatoly F Turbin: Multidimensional Euclidean paradise

0:00 Genetic processes which are genetically inherited from generation to generation thanks to a genetic code and it is closely connected with a dimensional hyper complex numerical system which is connected with the anisotropy. ...of the corresponding multidimensional spaces and the principles of cyclicity. So, we reveal that living matter has got its own eight-dimensional algebra and has got specific forms of anisotropic regulation. And a mathematical basis for studying and modeling of genetic systems. It has applications in genetic engineering, in producing new organisms, in nanomaterials, where we come across unusual regularities of the states of matter, There are new types of neural computers and DNA computers and new types of cell automata from human machines.

2:30 But how can we find the non-Euclidean geometry of living when these living things are so different from each other. All the organisms from bacteria to birds have got the same... The same searches in the genetic code itself turned out to be surprisingly simple in that search and the series was searched. Then there was a whole network of it and we kept putting this thing into the hypothetical. In the mathematical basis of this genetic code, then it is possible to find the solution of the problem of the non-Euclidean geometry. It is a live relationship between Keynes and mathematics from his book. This has got in partnership with Kinetic Code and Determinants of Search and Provenance of a Leading Matter, the main points of the... We are interested primarily in the generacy of the genetic code. The details of this presentation and the subject can be found in my book, which is published in both English and Russian, and a series of articles which are given here, which I was commissioned to write these articles by a publishing house in the United States. I would like to remind you of the structure of the genetic code. The inheritance molecules, DNA and RNA, contain code sequences for... There are four bases, four letters, Z, R, N, N, I, I, I, I, I, I, I, I, I, I, I, I, I, I,

5:00 They say that the integral we do in life is everything by the letters, and that is which I don't know what it is. And then there are three pairs, where A and C are the structure of that M, A, G, R, O, C, F, and D. Scientists like Hofstra, Verger, and others proved that in four-dimensional, as compared to four-dimensional, there are six regular polyhedrons. Starting with dimensionality 5, the situation becomes... It becomes very interesting. There are only three types of polyhedrons, for example, in the dimensionality of five and, for example, three hundred and five. Schlafly proves that there are five or six symbols. It involves speaking about some kind of metric formula, which can use induction, dimensionality, induction. And we tried to classify six-dimensional and higher algebras and we got lost there with

7:30 And then in 8-dimensional, more than 50, there are some geometric associations, and we unexpectedly find out... Statements, which is like this, in dimensionalities of one or more, four or more, the number of key terms is infinite. This is something that is stated infinitely. Then Schleffle is different. And then we're speaking about, it starts working with four letters in some space, and one, and we take the classical... The classical definition of polyhedron, let's take its n-dimensional edges, and they should be regular, and the edges of dimensionality would be regular. Starting with the originality of the triad of polyhedrons, we started with four. The three groups fit in the n-plus or one-dimensional space. There are polyhedrons. In five-dimensional space, there are polyhedrons, the edges of which are polyhedrons of three-dimensional space, and the number of these polyhedrons is infinite, and you can imagine how many polyhedrons there are in five-dimensional space.

10:00 And the catastrophic effect is exponentially faster than the magnetic field. So the exponentiality is growing dramatically. The second principle we are using is when working. The first principle is induction. This is a regular, regular one from the previous dimensionality. We would like to see, sadly, as it is, whether it is regular or irregular, we would like to learn how to do this, how to see polyhedra, to develop in ourselves. We are trying to teach the students. I will see that in dimensionality of six it is possible, but there is some kind of hope to visualize this polyhedron. It's a number of uses. It is unique. It's very intricate. It's simple. And it is... It does... There were the works that had many uses. I'm not going to give any... Of course, we should involve groups and subgroups, unfortunately, theoretical physics do not know any finite subgroups except

12:30 Standard ones, except SO4, I'm not speaking about SO5, where we studied multidimensional groups, SL, algebras, where it was necessary to introduce SL groups. The topic is then starting with SL3 and this possibility is getting more and more lost and traveling into this trip, this journey into the multidimensional world. Alright, let us look at what we have in Giza. If we build a usual pyramid, a model of a pyramid, it is a two-dimensional square, and then this square goes into three-dimensional space. And the results in the pyramid. In the three-dimensional space, let us take tetrahedron. In three-dimensional space. It implies in three-dimensional space. Let's fix the fourth dimensional world, let us, we have this kind of frame, and this connects these things, we will have a pyramid. Next. And this is a prism. Clear. I built, I made a building, the basis of which is octahedrons.

15:00 And this is what I've explained. Now I'm building a five-dimensional key of the pyramid as a foundation. I use this four-dimensional hypercube. I go into the fifth dimension, then make connections. To the to the end. The sides are either pyramids or... They will be common pyramids, but they are four-dimensional. You can also see a usual, a standard pyramid here, too. Further. Now I have got a four-dimensional platform, and I am erecting a skyscraper. The stages are like this. First we made a base, then we go into the fifth dimension. Here it is, the frame. And then I build the roof. Here, here, here. We have seen this in Cairo. And next, next, next. Then we are going to skip the rhombododecahedron. And this is Kepler in his book, said that the rhombic deodecadron was referred to by Kepler as the honeycomb, the most regular geometric figure.

17:30 He knew the very work of five bodies of a plateau. This is the most regular geometrical figure which fills up the space in the most regular way. The most regular polyhedron here, and we get some kind of building at the base of which there is a pyramid to understand. For a better visual presentation I will show polyhedrons by Schlafly. There are five vertices, ten ribs and ten triangles and ordinary tetrahedrons. This is a self-dual figure, and it's the same, and it can be looked at as a pyramid, tetrahedron, then I go up, and if these ribs are equal, then I get a pyramid, but four-dimensional. One of the definitions of the regular in four-dimensional space, which is If we have what we have in trigonometry and take it into equation, then there are some other things here. Polyhedron is considered to be a parameter.

20:00 There is another... The definition of this, you are in your, you have shown the sky, let us imagine the four-dimensional sphere, we could find its center, and for example, look at me, I'm in the center of the four-dimensional sphere. And above the ribs and on the surface of the ribs, the ribs should have the same length or two-dimensional ribs will automatically go into triangles, then, well, I'm standing here in the center, and Distance, but distances are the same. The lengths are the same. They are halfway lengths to be the same. And in this case, it would be a regular polygon, sorry. This is a four-dimensional sphere, but it is not seen here. This is an analogue of, all right, this is just five, it is, is it from the point of view of theory of growth? It is, it is made in a symmetrical, beautiful way. And you will see hypotetrahedron here, further, now, this is nitrogen, this is oil of vodka.

22:30 10, 15, 120, this is the number of ages of the necessary dimensionality. Very interesting in five-dimensional space. Schlafly, there is a polygon which is a four-dimensional analog of the octahedron. There is no octahedron here, absolutely none, but it is assumed to be an analogue of the octahedron, one of the most surprising. Surprising polygons of Schleswig. We will base our considerations and thinking on this. There are six of them. Hyper tetrahedron, hyper cube, one hundred and twenty vertices.

25:00 There are six of them, and the sixth one has got 26 vertices, 96 ribs, 96 triangles, and these are the headrons, these are the headrons, real headrons. There are lots of constructions, very interesting constructions, it's not very well seen without different colors, oh no, you can see this octahedron here, we could miss out on this, skip out on this, sorry, the previous one, this is Schlafly 2. This is a Hupo-Oculus weight. This is a Hupo cube in 17 space with 400 something ribs and 560 cubes and so on. 280 hypercubes and 14 four-dimensional hypercubes. If you look at this, you will see a three-dimensional site here. This is to draw, to depict a hybrid, to decadron, it's very difficult, 600 vertices, such a work, we couldn't do that, fine work.

27:30 Now I am beginning to speak about the more informative part of this presentation. Why did we get lost in multidimensional space? The dimensionality is studied with four. There exists an infinite number of regular polygons, the three-dimensional edges of which are... You should understand the principle of induction and four-dimensional states, there is an infinite series of polygons, the three-dimensional sites, which are tetrahedrons. There are three structures, K, 3K, 3K, 3K, K, from 9 to infinity, super tetrahedron, which starts with, starts, which. No, it was proved that this is a regular test. Last year I spoke in Fresno, I made a talk in Fresno, and I mentioned Wales in a strange way, scent, scent. Another scientist into multidimensional world and he started speaking to what he had seen there, telling what he had seen there.

30:00 Let us may continue this talk. He saw there 27 worlds of different lengths. He took four of them and made a tetrahedron. The frame of a tetrahedron. Then he took three more. He took six to start with. And then he used these six to construct a tetrahedron. With six rots that he had, he added three more, then he made it into a closed structure. I am in the center. I have nine points in a four-dimensional sphere. I locate the points so that the distance to the center is all the rods will equal and if we the tetrahedrons would be irregular. And the construction is finished. Then this is his next structure, his seventh polygon. This structure is 30-30-10. And he made this figure out of the rods he had.

32:30 At the first sight it is very exciting. No, no. No, I need the... Now, following the principle that the dimensionality... Is a polygon, a three-dimensional regular polygon? No? If you see the infinite, infinite series of regular, four-dimensional polygons in the... In the form of deterrents, then in five-dimensional space, there will be... The two-dimensional sides of which would be the tetrahedrons from this picture. We have exponential rules of the class of regular polygons. Now we could build octahedrons. There is an effect of illusion. And when I start explaining, they see there, they see a tetrahedron there, they start seeing it there. And not to waste words, we can start with 13 vertices. And tetrahedrons, instead of three, we will have four K, four K, four K, K.

35:00 I've instructed it, but there is also echoceratons, which one has to Schlafly. It starts with 24 vertices, a series of polyhedrons. With the four-dimensional sides of which are octahedrons. And then if we start with the figure with starting with 41. The structure is analogous to oil bunkers. All three-dimensional sides of the world are tetrahedrons. We could speak about deudecahedrons. How much time do we have? By analogy, in an analogous way. If the nationality is five and half, could the speaker speak into the microphone, please? I am sorry, very sorry. And instead of three polyhedrons, regular ones, I get... You could find them really exciting, especially if you do them, make them in colors and look inside of them. If you wish, there are lots of them, lots of pictures like this, several hundreds of them, are one of the most exciting, yeah, and this is a super series, which resists in one of the hero-wishes of algebraic geometry, the madras.

37:30 All the polyhedrons of this series are regular, and the vertices can be seen as quaternions with some kind of algebraic components, but they do not form groups or anything. There should be a group of symmetries, and they, the symmetries of these polyhedrons, are finite subgroups of infinites, of finite groups in SO further. Then we found another way of effective visualization of these speakers, the theory of numbers, quantification, a usual form. The sum of n x squared is equal to this, and it is known that if n is the dimensionality of space, is equal to 4 and above, then according to the theorem of Lagrange, this... This theorem has always got a solution. According to the Bachelov range theorem, any integer can be represented by the sum of not more than four O-squares.

40:00 This equation has always got a solution. If we use any term to describe the number of equations, then this is the point of n-dimensional space. In the sphere of radius, let us use these vertices, and it will give us perfect polyhedron, and now we have a possibility of visualization of multidimensional space, at least. In my office I have got one polyhedron which has got 192 vertices, I can imagine what kind of figure I will be able to make in two years time. This is in the class of polyhedrons before speaking about different types of polyhedrons. The polyhedrons which I have used in this polyhedron circle, you can easily calculate the group of symmetry. This is the equation which corresponds to and depending on the right part, if m is equal to 1, this polyhedron is a polyhedron which is a dual, a dual to cube that is consisting of three polyhedrons. Now, four-dimensionality space. If m is equal to 2, then the theory is true.

42:30 In four-dimensional space, it is Schlafly's polyhedron, could be called a mega-octahedron, starting with four-dimensional, until four and above, Biafontein polyhedrons are regular polyhedrons. Two- and three-dimensional sides of which are octahedrons, and in five-dimensional, mega-octahedrons of Schlepp Lake. Let us take Diophantine polyhedrons in four-dimensional world. Let us look at... We are giving an example of Diophantine polyhedrons in four-dimensional space. Then we connect, make connections between them, and we get a polyhedron with four vertices, well, 40, sorry, vertices, no, 26, 26 vertices. Schlafly had 24 too. Then, if we are using the method of different type, we have to move the axis, and then we cut out what we do not need. Here we have the 1, 1, 1 point, and then... And then a number of signs or two zero zero zero and this is a quaternion The octahedrons are seen here.

45:00 And, unfortunately, it is not quite well seen here, cubes. This results in the classification of polyhedrons in a multidimensional world. A polyhedron is regular. If it is regular, not... And do not completely fill up the space like an octahedron. Cubes fill up the space. Tetrahedrons do not. Octahedrons do not. So it should not be self-dual. Polyhedron, irregular polyhedron, and self-dual tetrahedron is Polyhedron is homogeneously regular and the main, the central definition, polyhedron is considered to be perfect if it is regular, so dual, and fills up the space. And equal to four, the perfect polyhedrons, strange as it may be, they are connected with the solution of the 13th sphere of Newton, and I think, well, we have got lots of pictures, but thank you very much. Fortunately, we physicists cannot get lost in the microphone.

47:30 We have been doing lots of work in multidimensional doing research in multidimensional multidimensional spaces and we know quite well that when we use use space the dimensionality which is If space-time is more than three and space-time is more than four, then additional dimensionalities will be different from the classical n plus three dimensions, or one-in-one dimension. And if we get into this world, six identical synapseminar worlds will not help us. Your world is not Euclidean. Can I enter the microphone? After my presentation three days ago, I fell asleep and looked into a multi-detachable. I tried to figure out the polyhedrons in my head. I was bleeding and then I went to the hospital to explore the dimension of hospitals and they said, you know, after your doctorate, you, you spent a lot of time eating and that is why you are trying to, you are trying to reimagine what you could not imagine and you should go ahead and take Atomogram, tomography, then I just... Let us the task of tomography is M, where tomography is made in the inter-dimensional world with a tomography called working in three-dimensional world.

50:00 Do you know a solution to this problem? I think the first attempt in this direction Hasn't been taken by us in the current way. We are drawing in light colors. This is thermography. As I switch on music, it's open when I draw this. This is tomography again. May you use whatever is available. Whatever methods you would like us to use. Maybe there is a method of representing multidimensional polyhedrons, including regular ones, here we make kind of an album of these polyhedrons. I will try to do it. I cannot see this clearly. Maybe it's where the text begins. Did I get it right that there is an infinite number of regular polyhedrons in a two-dimensional space? The three-dimensional sides of which are polyhedrons from three-dimensional world and going up, this is the principle which cannot be proved. This is an attempt.

52:30 After the introduction, and they seem to be successful, a heuristic principle, that's what I call it, could you repeat your two theorems that you've formulated? First I give the definition of a perfect polyhedron. Okay, let us leave it out. The theorem that you formulated, any dimensionality, the speaker says, the theorem, the person asking the question says, the theorem... Does this theorem has got some numerical estimate? What do you mean by numerical estimate? I described the number of vertices, the number of sides, the number of ribs. We are speaking about polyhedrons. What kind of estimates can you give me? But the difference between the theorem of pure existence and the theorem which gives numerical numbers, do you imagine the difference between them? The polyhedron, which is described by the formula X plus 2, is a polyhedron of regular form. I will ask another question. I will ask a simple question, one of the last phrases in the report.

55:00 The problem of contact numbers of internationalities do not exist, because there are two million of them which are known. For some dimensionality, they do not exist. Look at the table again. I'm sorry, I would like to stop this discussion. You can discuss this in private talks, too. And we are asking questions of general character. One more question? I have got two questions, in fact. I would like to understand where Schlafly's logic doesn't work and the theorem of Schlafly's right is correct. Symbols and five-dimensional and above. We have three types with levels shaped as symbols, and you do not have symbols. I do not use them practically. You cannot use them? You do not need them? I do not need them. Okay, we will discuss it privately. The theory of Lie algebra's simple numbers. Four series of infinite and five limited. In the theory of catastrophes, does it work? A very good question. In the theory of packages, if you wish. To write, to draw a regular multidimensional polyhedron, you use a diagram which does not give any geometric representations.

57:30 We come across different groups, infinite groups. And there is some connection between them. Thank you. There might be more questions after this presentation, which concerns many of us. And I have heard interesting information here. And I think since the speaker is here, you can come up to him. Today or tomorrow and discuss the questions that you are interested in. Now I would like to... I think our agenda is over. We have fulfilled our agenda. And thank you for the interesting presentation and now we will get to the closing part of the conference. I would like to give it to Mr. Parker. I can see that everybody is going to be anxious to get to dinner. So I think he wants to say something.