John G Cramer: The blind men & the quantum / Dirac's hole theory (& others)

0:00 Excuse me, the speaker's actually started talking. But rather something that sort of suddenly dawned on me in Bexar at a conference just in June, when a young man called Coco came in and gave an absolutely brilliant talk in China, saying that quantum mechanics is essentially the And what I've done is to pinch some of the diagrams he used to try and illustrate what I wanted to do, and then we'll come to the one that I know Karl wants me to talk about to figure my way out towards the end. I hope it will make sense at the end of the day. I can't guarantee. But for now, what I have been doing for some time is that I've been thinking about...

2:30 Matter returning the space itself. Rather than starting with a given space time or given space space, let matter do it so you don't have a stage in which you dance but rather let the dance create the stage. Now you can do that with comic infrastructure, it's very galvanised that you did it that way back in the 40s. But when you come to a normal comic infrastructure, you can't do what you did because you've got no maximal argument. And so, thinking about that, someone occurred to me, well, let's have a look. What precisely do we mean by non-committivity? What precise feature of non-committivity is responsible for the problem? Well, you've got a common ex-impedo community, you've got uncertainty, and that surely is the problem. Well, then isn't just non-committivity that's the problem? And no, because you can live in a classical world, but we live in a whole world with non-cognitive operations. Try going through a door without opening it, for example. You will soon realise that the classical world is non-cognitive as well. Therefore, there must be something else that's in it. Can we have a look at what it is? Well, of course, what we're doing in quantum mathematics is we actually look at the eigenvalues, because the eigenvalues of operators are the numbers we get in the experiment. And the reason why we get the uncertainty principle is because you cannot find simultaneous eigenvectors for S and P with operators for S and P. So that problem, but all the symmetries, synthetic symmetries, rotational symmetries and so on, are carried by the operators themselves and not by the algebras. So sometimes we think the most important dynamics is on the operators. And somehow or another Paul can get these eigenvalues in, and these eigenvalues are the thing that causes the difference in the play around. As I say, Bob Coco came in to the conference at Brescia and said,

5:00 I could do quantum mechanics with a monogamous category. He didn't actually say that, he said, I'm going to teach you how to do category theory from the kindergarten. And no one believed him, of course. But what he did, he introduced the whole series of symbols. And he started putting these symbols together. They're not morphisms in a way, but these are one-sided morphisms that you want. So you can think of the text being represented by this arrow carrying an eye with you, that direction of it, and you can have the dual symbol going the other way. And think of these as movements of some kind, as processes. And, not thinking of these as practical health questions, because they're just symbols of the world, but two of the things that we know this needs to come as a satisfaction is that we've got to have that relation mapped onto complex numbers, but we can also stick them the other way around and we create our products. So what we can do is we can join our symbols together. Either they are all numberless numbers, or we can join all of their parts together to form a matrix. I thank Luke Cartman very much for introducing me to this type of notation. Okay, so now, suppose you've got a matrix A, i, j, represented by arrows from both sides. Optically you trace the sun over the eyes, and in this case you simply close the loop. You then trace it with an operator A, so here's your operator A, trace over your A, just as if you were with that, and close it. And that gives you the trace. Now then, the interesting thing that might work for you is you can actually cut the damn thing there. In other words, you can play around with these symbols to get expectation values and do quantum mechanics without getting into all the problems that...

7:30 They're all there hidden, please, don't get me wrong. But I'm talking about high-level language, which we can see what is going on without getting too much involved. Now I tell you, all of this is symbolism. It's really got a hooker. And also the word, what's it related by? It's not promised, but it's hammered out. If you actually want to see how this is all related to category theory, there's a paper where it sits in, it's a collection of, I think I've got the paper, of Sands, where they actually discuss this in all its detail. Okay? Now don't ask me to do it, because I tell it's introduced to it in June, and it's just that I picked up on its language, but it fitted exactly with what I was trying to do earlier. Now then, we can even take it further, and I don't think Bob's taught how to do this, and that is to go to Bob. I should just mention that what I'm doing here is I'm insisting it's a pure state so I can talk about whatever I want to hear. But what happens if you've got a mixed state, so you're getting more complicated situations? When you've got a mixed state, you normally have to have a density matrix, and I've just illustrated that two by two way. But you also ask the question, can I find a super wave function in which the trace can be written as an expectation value, even in the case of a mixed state? And that means you write this thing with, you've got to double the number of indices on it, obviously. And therefore, what I'm doing... I'm just saying that I'm looking at left operations and right operations and bringing them all round onto the left hand side, and there's a standard rule for doing that, and when you do that now, what do you get are objects with two arrows coming out of them. You're not squaring them, are you? Sorry? No, you just need two to label them, so you've got, this is a two by two, so there'll be two labels on it, one on the left and two labels on the right. And then, what you do again, you do the traces, as I've done before, and then you trace both ways, counting them up, and there's the expectation.

10:00 OK? This is amazing. And what is even more amazing is that Vaughan Jones has studied planar articles. And these damn diagrams are just satisfying the rules of planar articles. And Jones is dealing with monolingual algebra, which is why the connection is bad. Okay, I'm glad I raised you. Now the thing that really amazes me is the disruption of quantum teleportation. So if you've heard about quantum teleportation, you'll agree with me. Yeah? That's it. That's all the formulas. What you've got here is you've got an input state, and remember you've got an entangled pair here. You bring this variable to this thing and do a Bell measurement. And the other variable, which could be on Mars or wherever you'd like, He couples and produces an accurate statement, and if you know a certain bit of possible information, you can tell exactly what statement was put in here without any signal crossing between the two. This is just a diagram of the telephoto. And Robert's got a really good one. You can make these as complicated as you like, and they're a beautiful way of organising the whole structure. And here's something you can actually read, you can't get all of his lectures out, but you can actually read this discussion, showing how it plays on the tensor star category, in terms of... Okay, so that's a bit of an entertainment. It was remarkable what you said this morning, saying that one of the wonderful, beautiful pictures that you had was quantum reality. So you've got the categories underneath there and you're going to perhaps do something exciting with them. Okay. Actually, I was going to say, at this stage, Carl says, oh, come on, PJ, you've got this simple phone model in X and P. What are you doing with all this? What do you think you might be doing with this? Well, wait a minute, wait a minute, I've got one more thing to do. Now, why I'm doing this is not related, you guys.

12:30 Is that what I'm really doing is it's another idea that David told me many years ago. Split the lectures into two sub-lectures. And there's just one left ideal and one right ideal. In the mathematical terms, one's been operated from the left and one's been operated from the right. And these, in the mathematical terms, you separate these two things. You can separate these two things because I've got a... Has anybody got... anybody got... yeah. Oh, sorry. You've got an inner moment, which you put in between there, and because E squared equals E, when you put two E's together, then you get a matrix. So you've got a left ideal and a right ideal, and Carl, please gesture. Okay, that young lady used to tell me about it. So let's just finish. So you've now got a pictorial representation of something. Yep, so the clip of that figure is India. And I'm just looking at the left and right ideals of that algebra. And we know they are the algebraic equivalent of the wave function. So I've got rid of your wave function. Not really, but you know what I mean. It has a simple side. And it's this left ideal. Now if you think of these things as processes, then your side is really a process. It's a special kind of process that always has the same eigenvalues. And these things here, by the way, there's a thing in Dirac's third edition where he calls a standard cat and a standard bro, which everybody is not allowed to read. And they are Indian bones. You can actually identify them. Okay, so now then, remember one of the ideas was we get the process to produce a space number. Well, here's a preliminary example of it. He'd say the left ideal multiplied by the right ideal and you get... This matrix, for people who know about special elements, is the matrix of your space-time core. And what that is in terms of these diagrams is just that. You take your left ideal here, you take your right ideal, modify them together, and you produce.

15:00 Now, a lot of people don't know that that's a rotation group, but you can also do it with a synthetic group. Amethysts, synthetic spinners, and there are elements of that diagram of the extended Heisenberg algebra, you've got an extended Heisenberg algebra, by adding a purpose to it, that's called the algebra. So that everything is in the algebra. The whole quantum mechanics can be done in the algebra without any of the elements of the algebra. This of course is Bob's idea, I don't know where it's Bob's idea, Bob told me that there's a star traffic test category underlying this structure. It's the fact that, remember, the eigenvalues are the physical things, and what's the difference, you know, what's the important thing about quantum mechanics is those eigenvalues, not the non-computation per se. And the eigenvalues, say, you can either operate on the left or you can operate on the right. Now, normally we say, well, I suppose you get that. But suppose you have a general theory in which the left idea and the right idea are different. You need both equations to develop a physical and a transactional one. Transactional interpretations have come in. You can think about, in Feynman's way, the way in which the information is coming from the past, the progress of the information coming from the future, and where the intersections, where the actions. So, you know, you need both sides... Why the complex? That's what Penrose is always asking. There's something significant about the complex, more or less. The complex comes in because you need both the groups of operations and both the algorithms. Is it just supporting that idea? This thing where cars don't have any pictures. You've got a bone theory. Why don't you talk about that? What I want to do is to use what I've just said to motivate this argument. Right, now I'm not selling these as interpretations, I'm just saying, can we have a look at the descriptions of quantum mechanics in face-based, you know, because we seem to be violating the uncertainty principle in some way, because we're giving the particle, attributing the particle position and momentum simultaneously, but we're saying they cannot be measured simultaneously, and that's all we're saying are the uncertainty principles. Measure them.

17:30 Well, I don't know, most people say because you can't measure them, they don't exist. That's the assumption, I don't want to dismiss it, but that's the assumption they have. Okay, so how do you do it? Well, the model has already been mentioned twice here, okay? Very simple, just write the way you want genetics. And then separate, make sure you separate it, separate it out of real and magic. And there you get it. Very strange terms, the quantum potential. If that were zero, this would just be classical physics. But there's a new quality of energy, and a lot of people... Shelley Dunsting, I'm not going to touch him, I'm just going to... It's equal in some way, but it's come out of the Schrodinger equation, it's not equal. It's never been equal. When you've got something like this, physicists normally say, can I interpret it? What we can actually see is the approximation operator is widely there and I'm going to try and answer that. The other thing is just to quickly imagine that it's just a consolation formula. So once you start with a quantum probability, the boundary rules end up as a quantum probability. Nothing tests the distinction as in the transactions. Look at these beautiful pictures. Here's the two-sided experiment, and we've got Einstein's particles coming in here, and if you believe this picture, then the particles will come in at a certain initial condition and follow the trajectories up to this room. And then we build up the ensemble we were talking about with apparently a classical bridge. Now, of course, they will do the particle and really follow those trajectories. We can't say yes, we can't say no. This is the strange feature of quantum attention, because the light in between the splits and the springs, there's nothing there that you do, and yet this is the thing that makes those things hit, and then you've got, you know, penetration and barrier, and all the power that John talked about, he always explained it in terms of this point, and the non-linearity is in the quantum attention, in that extra energy. It's hidden away in there, you don't see it, because, as I'm going to say, it's in that higher dimensional space.

20:00 Okay, now we've got a second, which is the victim oil. And a very interesting story that I was told, that John Marko, who's a really eminent man in nanotechnology, said, I used to do approximations to plot the way particles go through systems using the victim oil. Everybody in the audience were attracted by the fact. And then he said, and this is the bike picture, and they all had the wrong one. Okay, as if there was something. What is the relation between the two? Are they totally different? Or are they... In fact, I'll show you. The bone is in the Witten-Moyalis. Let me show you. Now, the reason why I'm going down the Witten-Moyalis very quickly is where you write the expectation value as a classical integral. In other words, treating the probability distribution as a distribution in function space. No operators, none of that rubbish. And then we've got the particular thing, which is also called a symbol by the way, which is the equivalent of operating formula, and the way that you get it in the quantum mechanics is through these complicated formulae, and then you can work out the expectation values, and they are identical to the expectation values, the thing that you need to survive in is trying to interpret that as a probability, because it's negative, just in the way that the quantum mechanics products. Can it be complex? I don't know. It's all geared up so that it's real. I can't show it straight away, but it's real. Is there a difference between the two? To be honest with you, no. I don't know why people don't know this, but it's all raised in Moyle's paper in 1959.

22:30 The point is there are so many P's lying around, you don't know which P you're talking about. There's a bundle P, there's a capital P, but Moyard also has a mean value, P double bar, which is calculated in a standard way, using the formalism, and you find that his P double bar is just simply grad S, where you have R equal to I S. So his P double bar is just the first. Now you look at the transportation of probability, and you find he gets that equation, which is the same as the imaginary part of the Schrodinger equation, and, what is more, he looks at the transport of momentum, P double bar, and that turns out to be the Schrodinger equation where you put in your first equation. Mathematically, it's sitting inside the Big Neural Mathematical Theory, so one or the other way, you can see where they're related. From the mathematical point of view, the Big Neural Mathematical Theory approach is very important because it's really a deformed cross-analgebra where the deformation parameter is h-bar. It depends upon a star, one of its operators is your induction spectrum, you get a star from it, and that star is actually non-communicable. And so you're still carrying on an opportunity to do them all out. So there's got to be some left and right actions going on. Now the interesting thing is, if you take a commutator, and that's just a sign bracket, that's called a way-out bracket, but there's also a way-out bracket that lots of people don't realise is made by David Farley, who's worked a lot on this. So you've got these two equations. Now, they're interesting. Because if you take the classical limit, that is, expand to the order of h bar squared, you've got the fossil bracket.

25:00 And if you take the cosine and do the same thing, you get the ordinary product. So you've got the ordinary product and the fossil bracket, and then that's what I call the deformation of the fossil algebra. There is a problem with units between the White House and the paper, because one of them has an H bar and the other an R bar. Oh, that's me, that's me. You can get this. The plus versus the minus in that paper bracket, is that right? See the plus over on the left and the minus on the right? That's right, that minus always comes from there. It always comes from there. The plus is coinciding with the other side. I assure you this is not my work, it's absolutely not my work. We've got a lot of interesting values. We've got starting values, and then higher values that you get by this, could be arrows on the end, star on the end gives you the energy, but you can also have the other way, so we've got these arrows, and that gives you E2, and that could in general be different. And you've got the thing about it, it's actually, if I suddenly said to the back of two in the air, I'd agree with you, I'd lost it while I was doing this night in my little chair, there's going to be a fact that there's going to be a need of energy. Spatially, we have a ton of different kinds of equations. And what we would like to get is a sort of a looking equation, because this is a statistical distribution, and we'd like to see the looking equation sitting with us. The left one operates on that, time dependence, the right operates on the left, and you make the difference between these two lower your arm and you get the linear approach.

27:30 A really interesting one is if you solve the two. You get this horrible mess which doesn't look at all inviting. It's a kind of anti-derivative of the linear side in there, so you can't collapse the two terms together. If you choose the wave function to be re to the ins, you have a look at that difference, it's still looking a bit messy, but if you go to the order h bar squared, you finally get this, so you've got this is the anti-commutator, this is ds by dt, so this is the d, and what is it? Just a customised formula. You need time? Well, just, you know, we've got a bit at the end of this. Yes, I understand. I'm trying to go as fast as I can. So now we've got these, let's do it for operators. So we're going to do it at the moment, the theory with the operators. And now what you assume is that there are two Schrodinger equations, and you say, one is, of course, the complex quantity, and the other, if you were just doing physics, but I'm saying make them different. So what you could do is you could sum them and you'd get a quantum boobie operator coming in, take the difference, and you'd get an equation of the phase, here's the way you've already composed, and you'd get the anticoagulant. And I claim this is a new equation which I've not seen and I'm willing to be told dreams that exist in the future, so I've not seen it. Gauge invariant and so on and ideas and the Bohmian artifact just drops out of it. It's too good to be true. So what have I got? I've got the operator equations here, and I've got the modality equations here, as you can see there. So the question is, what are we going to do with the projection operator?

30:00 I'll use this approach there, use this projection. Take the first equation, choose the projection operator to be F, choose a harmonic oscillator so that we've got a specific model to look at, and you get the conservation of probability, the whole equation from there. Do the same with the anti-computator. So the quantum potential arises because we're projecting onto some subspace, some substructure. It's the same thing, it's very similar to general relativity, where you take a curved space and you project it onto Euclidean space and you see that they're having a portal. So this is a parallel effect because you're trying to put it into the wrong... You can also do exactly the same for a mental representation. And I think that the big beef about Oman's model was that it destroys the SP symmetry. The SP symmetry is there. The reason why it's destroyed is that Oman took a positional representation and only presented that. Okay, so, and then what this means is that we don't have a unique underlying space through this algebraic structure. We have shadows. That's typical of what you get in logarithmic geometry. And I was talking to Freddie Van Westeren in Amsterdam just before I came here, and he has exactly the same problem with non-commutative topologies, that he has to project them into commutative topologies in order to talk about them. Okay, now I couldn't find any of you as I go, but in this bigger space is really where everything is going on. It can't be described in terms of base matters. But you can describe it in terms of those races if you're willing to project from this richer structure.

32:30 So you're forcing it into classical races. And what Melvin showed, Melvin Brown, the researcher, what he showed was there are many, because this is just a Fourier transform. This is a Fourier transform of that or vice versa. But there are fractional Fourier transforms. Look at that. Transform. It's a whole rich structure. And they all work in the same way. And so to sort of summarise what I'm going to show you is that you've got a non-commutative algebraic structure and you've got an aligned channel of variables. And this can either be discussed in terms of groups, in terms of the covering spaces, which is what Wilhelm Sternberg and my friend Maurice de Castellan does. You can discuss it in terms of general star algebra, C star or W star algebra. Or, now I've learnt, you can discuss it in terms of when I write a text or start a paragraph. The thing now is to explore those structures and see what we're getting within you. And then for the philosophical final over it. What I'm doing is I'm just putting mathematical form to David's original ideas. But here it is, because all of it is non-mathematical, which is based on quantum movement or its flux curve. And then, these are possible textbook rules. Mathematical structures that could possibly analyze that, but not Parasol and Intuition. Okay, thank you. I'd like to have some discussion. I have a first question on your first slide. When you write the uncertainty principle delta x delta p equal h bar, I have myself a problem with many papers because some people work only with h-bar divided by 2 and I assume that they use h-bar divided by 2 when the delta x and delta p are computed with variance in a statistical...

35:00 You may well be right. I'm notoriously bad at factor twos when I'm doing these presentations. I said I'm very bad at dropping twos or putting twos in where they shouldn't be. But what I would say to you is that you look at Robinson's proof. Do you know Robinson's proof of the uncertainty principle? Ok, well that is the one, I don't know the reference offhand, but that one actually does the whole thing rigorously, and you'll find the answer to your problem in that way. And second question, when you say that mathematics doesn't integrate, is that there is no unique solution in the space-space? There's no unique solution but base space. Yes, but it doesn't mean more intuitively or... It exists also classically, this fact. No, it doesn't classically. You see, classically the Q disappears. When you go to order h-bar squared, when you go to expand in terms of order h-bar squared, then all those merge into one. They separate that. So classical world is no problem. But my question is, are we living in a classical world? And if you take my philosophy that the physical processes actually determine the space, determine the phase space, then what I'm saying is that our physical processes don't determine phase spaces. A lot of the problems of trying to use phase space is that it won't go. I think this is where a lot of the difficulties in the interpretation come from. It's not forcing it into the structure. Which it is not appropriate for. It doesn't apply to the transactional interpretation, but I haven't thought about that particular point yet. I have one question. Okay. Have you both ever looked at Strodinger's original paper where he... No, no, I haven't.

37:30 Okay. His approximation in there is, before he makes the approximation, he gives the Strodinger equation. Doesn't he really have the equivalent of one credential in there because of that logarithmic... It's not there. The whole thing is bogus. The whole derivation is bogus. The whole derivation is bogus. And he realizes it because he's got an asterisk at the bottom of the page where he does an integral over what looked like a collection of analytical equations. Forks, because he's got the forks. And he says, I am aware that this step is not unambiguous. Not unambiguous. But if you want to see a proper job of this, go to Maurice de Gaussan's book, Newtonian and Classical Physics, which came out in 2001, and you'll see a brilliant discussion of what Schrodinger and Schoen have done, and you'll also see that this... I'm sorry, I don't... Can you hear that? I don't have the record. No, I do, you know, because I ran out of space. I can give it to you. This is actually coming from these huge deep sides at the top actually that are different from each other. Can we go back to 14.1? Tell me where to start. Okay, wait a minute. What are you looking for? What I'm looking for is to have something that we looked at at this time. Yeah, there it is. The issue you'd be writing is partial respect to time. Thank you for your time, and I look forward to seeing you again next time. You know, how you solve certain differential equations by doing a Darko transformation. And you looked at it and thought, I'm wondering about it.

40:00 It's a complicated thing to realize that. You could not be wrong. I'm not that familiar with that. But I'd say as soon as I find it. Okay. Excuse me. There's something very complicated. No, it's going to be strange. It's a PowerPoint. Thank you for your time. No, what I'll do tomorrow, I'll bring you the flyers for this meeting which you've got written to the speakers and writers. Are you involved as well? Yes, but what a noise here. We don't know what they're going to do with their full normal because they're going to have to face it. It's a big one. Screwed up from the beginning. Thank you for your attention. However, what I'll also be doing is to give you a call later on, because I'm going to have to leave tomorrow to go down there, since the speaker is actually still arriving. I'm going to try to get in with you, which is just going to go to the side of REM. But the meeting, I'll tell you exactly where it takes place. It is going to be starting on the 9th, I think the 10th, as we go there, at 9 a.m.

42:30 I'll put the word on the way. At the Econobal, but not in the hall. It's actually in the hall, but not in the hall. It's in the hall of the 45th. It's in the Sars-Jules-Ferrand, which is the big dance center for physics, number 29. Will there be in French? No, about half the talks are in English. In fact, I won't have more than half the talks in English. We have an entire discipline in French. Pierre Cartier in English. So it will be about 30, 60% English. It's 29 in English. That is the topic of our second part of the lecture theatre downstairs. Now, on the second part of it, I'd have you in the cell to see me, which is in the main building. But now I'll just have a little bit to do there, and this is just everything. But I'll bring the plans, because you've got all these details on the board. I've got to go down to sit down with the reception and the speakers, because they're calling them. I haven't even done that. There are also different fields of analysis, like mathematics, mathematics, mathematics, mathematics, mathematics, mathematics, mathematics, mathematics, mathematics, mathematics, I really disagreed in a sense, but they also didn't disagree, but certainly both said,

45:00 You get different results. That's the first thing that makes it so different from the physics of the 19th century. It comes from David Bohm's theory. If we didn't have telescopes, it would look like a whole rapture. Again, an instrument that allows us to see past the way we see it. I'm taking this one step further and saying if we didn't have lenses in the eye, Or other lens-like structures such as the cochlea, or hearing, and the skin, which acts very much like a lens-like structure, very similar, or ear, after all, is a part of the lateral line system of fishes, and turns out to be very much like the skin, or at least in three senses, they have lens-like structures, and there's some idea that... We didn't have big structures. The world would look entirely different. The world we navigate is in space and time. What is the world that we don't navigate on, what I would call a potential reality, rather than a good thing? That, basically, can be mathematized by a Fourier transform, because what Fourier shows, and all of you mathematicians, this is so, the way you think that you very rarely really think about it, what he says is that any pattern in space and time can be represented in terms of sine, cosine, or fringe patterns.

47:30 We have space and time over here. We do the transform and other things as well, including the earliest one that was built, and when we do that we get energy over here in the spectral domain, has a tremendous amount of... Let me just do a few things here. But before I do that, I want to bring up a little. When I started writing a book on perception, there were very few things that people would read about in all of the perception literature.

50:00 But one thing everybody did agree to is that our lenses of the eye do a Fourier transform. That everybody agrees to. And lenses like we have. So that was sort of the starting point. The next question though is if the Fourier transform does for our lenses do the Fourier transform, and on one side is space and time, what on the other side is a spectrum, what... Where is the spectrum and where is the space-time image? And it turned out, with several avenues of research, that the spectrum is out there, which is what David Bohm was talking about. Our lenses are in the spectrum. That does not mean that there are no objects on them. It simply means that what comes to us in the sense of the radiation that we perceive Touch, what we perceive deals with oscillations, but that is in the spectral domain. But just so that you have some idea of what this really means if you turn it on. Can you all see that? What do you see?

52:30 I like that. It's a whole thing. Except for when you're at home with your neighbor. I quote a little bit of it, it's in the fifties. Some of these chicken pox are very interesting. I think there will be another one within the next two years. I won't be able to give you the details, but if you need it, I can send you a letter.

55:00 I can send you a letter. Thanks. A theater that sounds great. Then when people come in, with their overcoats and hair and clothes on, the concert hall sounds very dull because the refracted and reflected sound gets absorbed. People in what we hear get frightened, which is all I'm saying for vision. So that's point number one. If I accept that, there is another thing that when I became an undergraduate, which is that instead of having a lens, I know when I was beginning to have to use glasses, ordinary grocery store reading glasses, and I left them somewhere and I couldn't see and couldn't read, what I do is very simple. I just took my finger like this and I could read. Before that, things were blurry, like the holographic, which you saw. And we can actually do quite well on Paris-Walter and Alexander.

57:30 Now, if you can do that with a hole, maybe what quantum physicists find when they talk about particles... It's due to the fact they're using a hole or a slip, a very fine slip. It's an artifact of that particular instrumentation. The main difference is, why don't we think in terms of waveforms and not get into all this particle stuff that gives you all the problems of the words, after all, before you transform? So the question then arises, why are people, like quantum physicists, so besotted with particles? Because, and they are, I've read quite a few books of quantum physics trying to explain to the layman, and in one book they said, The weirdness of quantum physics goes away if you use what you could think it comes away for. The last part of the chapter where they have explained this and shown the experiments and so on and so on, they say, and you know, it's so weird that we have particles, we have to consider particles. Having just said, if you don't use particles, it isn't so bad. The point is this, and that is because in the 20th century, DNA wasn't central to statistics. In the 19th century, statistics began to dominate what's going on in the black art. Before the early part of the 19th century, people were talking about fields. And that was the excitement of the ideas that were... These came on during the 17th century, 18th century, in the Enlightenment, then became fruitful by the development of concepts such as force and fields, and that really had a tremendous explanatory, we began to have statistics which dealt with populations, and that had a great, 23, I'll have to go to the 20th century, I think this...

1:00:00 These were so useful, psychology, astrology, and so on, that people started thinking solely in terms of things and statistics. That's why some of this weirdness comes in, if you just go back to basics. Now, what part of the deal is this? Why do we even have to worry about this when we could just talk about it? By the time you get to the visual cortex, when we use vision as an example, it's true of the other as well, the program is mathematically by God the work. Before that, for telecommunication, for telecommunication, he wrote things about how much he could compress a message. He picked effectively so that we wouldn't be using a gigantic table when we needed to. He came up with this analogy, which instead of, as we've already touched on, either space-time or space-time and space.

1:02:30 And so forth. And he called these elements here, he called them logons. We call them logarithmic functions, but the other thing he called them is quanta of inclination. And he did this because he said it was the same mathematics that Heisenberg used. And so we have here a way of talking about not only the material universe, but also the communication. Which is the basis of our mental universe. And it turns out, when we get to the visual cortex, the disruption of the receptive field of a single neuron, a field that brings in all the excitation, all the signals from the outside world, is describable as these functions. That's what the Hilbert space is. And so right at the beginning of the processing of the brain, we get into the problem of is it frequency or is it spectrum or is it space-time, and you have that choice as the processing of the brain goes on. As you go forward in the brain, just next to the visual cortex and other systems together, there are motor systems. I would tell you that if you stimulate those parts of the brain, you get movement. Eye movements, speech movements, body movements, and so on. So when you bring in movement, you then can get from this Hilbert space into objects, really objects. The theory that describes that as this root theory. There's a long history to that. We talked about that it was started by Planck, Leibniz, and Leibniz, or invented by Leibniz in order to explain object perception.

1:05:00 We found that part of the brain that is involved in that is just around the sensory input there. We've definitely been far, and then we go still further forward from that. Away from the climate projection errors, you get a still another set of mathematical categories that are not yet categorized, but they are abstractions from objects, ways of putting objects together, but not to form categories. That's as far as my own research went, and then Edelman has a... And so on and so on, which I think is on the right track now, exactly as you said, but I think it is. Now let me go back to, let me just show you one other thing that I haven't always seen. Metaphor for how the brain works. You need to remove the mother sheet. Maybe I should get new sheets. Hold on a minute. They use the camera as a metaphor. Some of the receptors here, these are the keys, they become very, sometimes lots of readers. And again, very topologically, anatomically, connections to the cortex. The way anatomically the receptors are related to the cortex here is the same as in a camera where you have shorter or longer strings. The distances between the strings are not as fluid. These are the things that are important for us to be able to mix up, and I think that's what's important.

1:07:30 And one is, in your case of attention, you talk about neurons. The ECG probably has nothing to do with neurons, per se, unless these ten greatest processes were oscillating. And they're patches of these oscillations, and that's the result. I think so. I keep talking about dendrites, dendrites, dendrites, so actually it's not a space problem, it's a dynamic problem. And that is sort of the social movement. I'm just going to add to this because there's a very main interest in this topic. First of all, it's a very important topic. He was talking about matter, he was talking about momentum. Physicists talk about matter. That's what they're doing. I mean, that's what they're doing. But there's something else up here, and that came into the 19th century in terms of some dynamics, in terms of radiation. It was talked about here in terms of energy. And different ways, forms of energy and then different orders of organization, entropy. I like the idea essentially that entropy is talking about possibilities rather than being just disorganization. It may be disorganization, but that problem is a very tough one because of non-linear dynamics and so on. And if we try to find out the particular strain, let's say, of neurons, pulses, mini-rambles, we'll come back to that. But anyway, that's what happened in the 19th century, then in the 20th century.

1:10:00 In the 20th century, the measure of information was to get the same mathematics that were mathematics and the measure of uncertainty was the measure of entropy, the same mathematics as the measure of entropy. I'm talking about not the content of what this is about, but the form. The mathematical form was the same. So we have here, up here, communication, and we have radiation. We're dealing not with matter, but with energy, radiation, and communication. And in a way, this highlights, this diagram highlights what... This group I've been talking about so much that they have a Cartesian cut, which is a cut between up here and down here, and we have the Heisenberg cut, which is from here to here. I don't like the word cut. I prefer the word relation because, as Descartes himself said, He said in philosophy it's important to make a distinction between the computer, the thing, and the material universe, and that's what this is. But he said, in a interchange with Princess Elizabeth of Romania, he said when you go to the store, you don't have to worry about this, because you have a union. Considerations such as these developments are feasible arguments to technically algebraic measurement of material.

1:12:30 So, I really am obsessed, and I would like to simply say, think of this as a relationship among Penrose-Hawking and Heisenberg relationship as well, The degree of precision is that it doesn't say you can't measure them simultaneously, you just don't get to the same precision level. You can talk about the ground, but there's a little bit of surface. And this surface is different from the surface you measure. I think it's a lot more difficult than you think. Now, how do we learn? What we've learned so far... We've gone all the way, very nicely, to categories, but the category theory is lacking this diagram, because this diagram, in modeling the dynamics, I would say, is a more complex section. It is a slice, but this is static. This is dynamic. We've learned a lot about this part, but it falls short when we're trying to think dynamically, because... Now, said it simply, God does not play dice with the universe, except he does. He plays, but Einstein was talking about, you know, a six-sided figure with numbers on it. That's very determined. The point in the throw is nice, you have how many? How many alternatives? I'll leave it to you. I always thought it was about 12 factorials, but I've been corrected. It's not quite that many, but almost that many alternatives. And that's where nonlinear dynamics comes in. This is where we begin to get categorized and categorize theory. My next step is to try to... I have already done experiments back in the 50s showing that information is not what we process. We process meaning.

1:15:00 And mathematics involved there was sampling theory, that we sampled with what information is, communication theory, or materialism. Sampling theory, having this very beautifully set of experiments selected in order to show that the number of alternatives in a situation make a difference, and they should make a difference in information measurement theory in a linear fashion. They do. It's a very complex sort of formulation, but... The solution that I know of the data, which I couldn't understand, but somebody suggested to me that sampling theory works, so I went back to him and I turned out sampling theory worked fine. But sampling theory is just one step. It's not yet categorized. And that's the next thing I have to try to work on, is to see what the relationship between sampling theory and quantification is. The whole thing will die if you do not know. From the actual steps and recent data, I said this morning, we already have data showing that in aging, the electrical activity of the brain forms more and more complex. So we have that information on how to get the complexity to the particulars in this one. I'll say thank you very much. Two short questions for this person, or one long one. What about putting the diagram back up for a moment, that last diagram? Three. Is that over there in the special? Time and frequency, weight, length, and precision. Here's time, here's frequency, weight, length, and frequency.

1:17:30 Waves are now. Waves are now space-time fluids. They're not over here. Waves, particle dynamics, belongs over here. This is something that is taking away. I got kicked in the hand by David Bowie recently. Seven or eight times, seven or eight times I made a video to do waves of electrons. That's what we're going to be looking at in the next chapter, the proof of mathematical physics. Mathematical physics is also a configuration study. Mathematical physics is a way of thinking, and maybe it's a teaching. But, what you said, Mark, yeah, there's just some point that could be mentioned there, particularly in the meeting with Rose Calderon, that there's some argument which says that Lee wasn't really thinking about these groups, that he was really thinking about the group Because we've reached a position here and a position there, and we're transforming from one to the other. And I think that's the version of what I like about Charles Ellison's extensive work on the development of the groupoid. And also, it's mentioned by Connes that Heisenberg invented quantum mechanics by looking at the groupoid of transitions. These are a group of symmetries. Well, the glucoid is going to have one of the like categories which we have already looked at. We have a sort of spatial component, which is a very important point. To normalize the symmetry here, there is anything that seems to be there. I suspect that I was talking about something which I don't understand. Yes, sir, if you have to go into equations, you want your first group, then you can read the topology section. Groups, very good. These kind of groups, they have a lot of cases in them.

1:20:00 And then, what category was Adi Mahatma Gandhi, Adi Mahatma Gandhi, Adi Mahatma Gandhi, Adi Mahatma Gandhi, Adi Mahatma Gandhi, Adi Mahatma Gandhi, Adi Mahatma Gandhi, Adi Mahatma Gandhi, Adi Mahatma Gandhi, Adi Mahatma Gandhi, Adi Mahatma Gandhi, Adi Mahatma Gandhi, Adi Mahatma Gandhi, Adi Mahatma Gandhi, Adi Mahatma Gandhi, Adi Mahatma Gandhi, Key terms may include analysis, computer fields, analysis of the personal state of the human body, the formation of the human body, the formation of the human body, the formation of the human body, the formation of the human body. Because in the canonical, classical theory, the mathematics of impermanence processes is divided into, what I'm saying is that group theories, especially in the other kind of theories, which are much better, which have much more freedom in talking about these purposes and processes. I guess we have to talk over with the staff a little bit first. Where do you get the skills you need? I mean, do you have the body parts you're using at the university to, yes, how do you get them to deploy? That's so hard. Do you have a position for that? Yes. We're all on the same wavelength. It's really... I'd really like to go after your point about time. In the way that you use one second of the wave picture, I mean, how do you deal with things like mass and circles for m-parts and so forth? It seems like mass is the reason why we don't like particles because they have these things stuck to them. Remember what I said. I mean, I do see that there are objects in the universe. This is what?

1:22:30 Which perspective do you want to use and why it's difficult for you to think if you're working in a psychiatric situation, because of this person's perspective, that person's perspective, they don't perceive the situation in the same way. And so you've got to have some way to get out of it. ...seeing things in only one form, even if you measure it right, or whatever, in any one of those aspects. Yeah, I think that, yeah, I think that the mistake is when you say it's weird because of things. It's weird because of some ones that are making them, who are making them, you know, neither. That doesn't mean that I just want to teach you. That's why I'm teaching you. That's why I'm teaching you. It's a sense of order. I think that's what Patrick and I are trying to change the way in which we look at all of science. You know, we're making it. And let's have fun with it and not worry about weirdness because it won't fit that completely different perspective. And things like particles, that there are certain horizons that work for us, work surfaces that we reach, within which I'm looking at this room, and as far as I can tell, pretty well we all have the same size heads, but if somebody gets a little further than this... At the end there, it's already a little difficult. Then this comes, and we have no one part of the brain is involved in giving you that kind of measure. And within that is the focus. But then if you try to apply that to the wounded, it's that kind of thing that surfaces or arises within your certain respective force. And that's not how we do it.

1:25:00 Of course, those perspectives have to revolve. Well, I just have to say that reductionism is kind of fun, too. Oh, I know. So you take an approach and you start to push it as far as you can go. Category theory, the wave theory, the particle theory. And you just push them real hard and see what they can do. It's understanding and acknowledging that they're probably not going to go the whole way. It's a quiz sometimes because there's a lot of other problems to make, but Exploring Alan's machine and their data. Thank you very much. Thank you for watching.