Spin networks & anyonic topological quantum computing

2:30 It pays them just enough to keep them from starvation, I think that's it. Keep them lean, treat them mean and keep them keen is obviously his business philosophy, as it is of most Russian entrepreneurs, but there was one young guy, he was about 30, called Oleg Yerman, who I was told... I'm not, by other people, you know, not connected with this group, is expected to be the algebraic topologist of his generation in Russia, and he certainly impressed me as being very, very smart guy indeed, and there were a couple of twistor theorists, one of whom struck me as being completely batty, yeah, yeah, one of him struck me as being amorous around the bend, and he gave me a long letter to Penrose, which he wanted me to deliver. which he asked me to read through first and I did and I was a little bit embarrassed to say Well, quite honestly, it reads as if the whole thing has been written in green ink, you know, by the kind of mad woman who writes to the Prime Minister about, you know, the Martians who have, you know, taken over the body of her pussycat and are now projecting death rays from the television set in the corner. Well, that, yes, what I said, it sounds exactly as if it had been written in green ink. But if you want me to deliver it, I, you know, will do so.

5:00 We're all, apart from this very bright young algebraic apologist, we're almost all working on Klinzler geometry, which is a particular, almost obsessional concern of this guy Pavlov, is what he got his PhD in. I think that's the one bit of math that he does generally know a bit about. He had his figure in various parts, in logical parts. I'm very unconvinced that there's anything serious in it. But he was a kind of precursor of not-well-founded set theory. This is discussed in Peter Axel. Ah, I didn't know that. So he was quite a polymath. He worked in many different fields. He was a bit of a polymath, and apparently he had a bit of an altercation, perhaps. A bit of an exchange with Gödel, where he was sort of claiming that a lot of times he'd anticipated Gödel, and Gödel was sort of probably doing more interesting things, and Gödel was rather, was more brusque than usual in his rebuttal. It's usually very difficult to get Gödel to say anything about Goethe. I think apparently the issue of priority of his incompleteness is sensitivity. I'm not surprised. I think being accused of plagiarism would be... No, it wasn't as bad as that. I think it may seem the point that a lot of people just did not take a long time for his work to be understood. It was misunderstood by various people, including... Even including von Neumann, for instance. ...Samello. No, Samello did. I guess it may be a bit... But that's very interesting. Well, I'd like to know more about things, but certainly the geometry, the geometry is interesting. I mean, the basic idea is pretty straightforward. You just have a definition of angle and of line elements and the metric function based on hyper-complex number fields rather than on... Oh, no, no, no, no, not at all. He's standing by trying to base the generalization of metric geometry based on the hyper-complex number field. Are you guys leaving now? Yeah. Yeah. So maybe we should... Yeah, we'd better make a move, haven't we? Can I just finish this? What's the time now, Bob, when he's waking? Two o'clock? Yeah, for a thought. I need to put my bag in more office. Oh, you've still got an hour and a half.

7:30 Thank you very much for your time. Thank you for your attention. The man who takes his coffee seriously, even though it is Brazil rather than Argentina, which is the place which notoriously has an awful lot of coffee, because he's actually Argentinian. Don't mention Brazil. No, no, no, I wasn't going to say that. That's right there. Don't mention the coffee in Brazil, except the table sleeves. Oh, it's worse than that. Have you ever met Madeline's wife? She is called Sibyl. She is. Sibyl Heiley's wife is called Sibyl. Well, I'll tell you one reason why I wouldn't have sued her for libel. Because Sibyl Heiley is exactly like Sibyl Heiley. You never run a hotel? I know, I know, to the best of my knowledge and belief, they never ran out of hotels together, they never ran out of hotels, but in other respects, I have to say, the marriages, she is exactly like, don't you ever say that, please, don't ever repeat that, don't you ever repeat that, or if you do, don't ever source it to me, but I'm sorry to say that Sybil Heine is exactly like Sybil Heine. I learnt that, I had to say, I really fell around laughing. The payoff of the Tensor Geometry Program, if there is anything in it, is that you have a generalization of the metric tensor in GR from 10 components to 35 components. ...that you might be able to find a physical interpretation for the additional components in terms of fields other than the geometrical. So the payoff is, you know, some kind of framework for unified field theory.

10:00 Well, it's interesting the idea that we're trying to build additional structure into a four-dimensional metric geometry rather than add dimensions. That's a completely different approach in the twistor theory. It's not a totally different thought. In the sense that both of them are going down the opposite route from the root of the string theory, instead of adding additional dimensions to the geometry, you're trying to build a richer structure, possibly into the likehead structure in the case of the twistor program, and then directly to the metric in the case of the Fensler geometry. By the way, Basil has a very interesting line on the twistor program, which of course he was in a... So, this was the creation, and Penrose was in Birkbeck before he went to Harvard. Yes, indeed, they were colleagues at Birkbeck for the first ten years of Penrose's career. And that was where all this stuff that he was talking about was going on. The same time Basil used to talk to Penrose almost every day. And he had a completely different line on how one should define Birkbeck, coming from spherical, hyperbolic spherical geometry, and connecting it up with his interesting clip-it alphabets, Full descent with twistons, which goes back to that time, which didn't involve having to use all this machinery from complex analysis, you know, the upper and lower portions of the holomorphic sphere, that Penrose uses is a conceptually and technically quite different approach to defining twistors, and arguably one which gives a much more intuitive understanding of, for instance, the way the black picture drops out, the connection with the... And also, arguably, provides a way of generalizing so that they more naturally connect up with quantum theory. I think it's extraordinary the way that those ideas, which unfortunately Hylian only published in two or three papers back in the early 70s, have been completely lost sight of, and the mainstream development of twistor theory has just rolled down the Penrose Road. Thank you for your attention. Thank you very much for being revisited and for examining it. By the way, I understand from Blue that there's a meeting here next week, which kind of wraps up this quantum computing month,

12:30 indeed as a Newton, yeah, which Penrose and some other people are... That's the one I want to go to. Do you know the date? Exact date. I've got to be at a meeting in Paris on Wednesday, which has nothing to do with this category. I'm going to Paris on the 13th anyway. I'll go to your meeting on the 14th. It'll be pleasant to see you all. So it's not such a bad idea to go out for the evening in Paris with a person from New York. But I'd like to try and get back here for the... Well, that's what I want to find out, whether it's a double booking, isn't it? By Foslaw it will be, of course. Yes, yes, absolutely, I'm sorry, absolutely. To gird our loins and get the coffee. As you say, don't mention Brazil. Whose is this? Is that Lord Tony? Okay, go, go, go. Are you planning to come to this Corp of Bob's? Do you know where it is? Nor do I, nor does any man, except... Do we know exactly where Bob's talk is? Okay, well can you physically point out the computing lab? But which of these buildings is the computing lab? I don't even know that. Well, this is all a bit hopeless. It's on Thompson Avenue, and you would have to go to reception and ask which one. Is it? I'm not, haven't been in Cambridge. I'm so sorry for interrupting. I know that both Lou and I wanted to go to this thing. Okay. Well, best of luck finding it.

15:00 Well, they want to drag me over there for some reason, I think, because Bob has got something. Yeah, but do you know which of these buildings is a granola lab? No, nor do I. There's somebody around here who would look for it. Well, no, because he's still got it. Can I ask you one quick thing? This meeting next week on cotton field theory at the Newton, what date is it? The 14th of September. Damn! That's what I was afraid of. 14th to the 17th. Oh right, we'll talk about that later. Bob's talk? No, that's exactly what I'm trying to find out for us. For some reason, they insist on shooting off even though it's half an hour before it starts. If I don't follow them, I won't be able to find it either. They're coming. They're coming. It's just they have no idea where to go. I'm sorry, I don't mean to keep Bob and the other chap, Kosta, whatever his name is, from the coffee. But Lou will have no idea where to go if he doesn't follow us. If they follow us, then... Yes, but if we hair off at lightning speed, they'll lose us. There speaks a man who has worked as a tour guide, you see, I don't know, I have to move to the speed of the... No, no, no, I'm not going to be reduced to that terribly naff, I don't know, but I do know there is the sort of speed of the slowest ship in the convoy principle. Well, this is all very grandiose in comparison with the, you know, but I still think that your facility in Oxford is much more stylish. Well, I have to say, as modern architecture goes, that's pretty good. I like that. I like that even better than I like the Newton and the social and mathematical sciences, and I like that too.

17:30 Why is it that almost all the good modern architecture in England is concentrated in Cambridge? Why have they got the man who did this to design the Scottish Parliament building, instead of that monstrous abortion? I spent five years in Stockton and the whole time I was there there was a hole in the ground. It's a damn sight better looking when it was a hole in the ground than what they put in it. Not to mention the corruption involved, the staggering amount of corruption. The Scottish banking system is extremely gruff. It's an awful lot of Russian mafia money is being cyclised through it at the moment. I seriously question whether Donald Deere's death was a natural cause of it. Well, the fact that they found something like two million sitting in his bank account has never happened before. The London media never bothered to investigate this properly. All right. Could you ring Marcella for me, please? Are you going to do a C20 tip now? Well, it is for the seminar. Actually, could you ring Marcella? We can all have a cup of coffee beforehand. I'm Michael Rye. These days I live in France, in Fougere. And I haven't had any sort of academic position officially since the early 1980s. I wrote my alphabet here in Cambridge 30 years ago. God help me, almost 40 years ago now. And in fact did a retread. I changed to the philosophy tripod after doing part one and two. Because I knew I was not going to hack it as a research mountain course, I became a philosopher of mathematics instead, did a PhD in history and philosophy in London. I taught for a few years and then got back into life altogether, ran a business for 25 years, invested some money in property, sold that the last year, a couple of years ago now, bought this big house in France where I now organise meetings and foundations of maths and physics and have a thing called the It's horrible for a software apprentice to attempt a mathematical physics project, which is a horrible mouthful, but if you create a foundation in France, a brigade of academic foundations, you have to give a very specific, you have to give a name to it.

20:00 What is the objective practice? How do you apply it? Well, there are about four or five parallel activities. One is to organise about half a dozen workshops every year, small workshops, so ideally no more than eight, nine, ten people. Very carefully chosen, allowing much more time for discussion and sustained base-based interaction than the average short scientific meeting, and usually devoted to a single topic. The second is a series of interviews, the first one of which is kicking off in June this year, with... Mathematicians and physicists who have, you know, the opinion of yours truly, whose work has been decisive for the mathematical conceptualization of their field and for the overall shape and direction of the subject in the last 30 years or so, and for each of those people who are subjects of these interviews, the interviews will be conducted by a panel of five or six interlocutors. Obviously, people with equivalent expertise in the field. We spend about a year preparing for each, discussing how much time to devote to the particular aspects of the subject's work, and they will run for anything from 10 days to a fortnight, but obviously paced carefully, so a certain number, a prescribed number of hours every day and breaks every four or five days for half a day or a day or so out for relaxation. And the idea is that after, you know, two weeks of really intensive debrief, all of this is recorded and webcammed and then edited and put on the web. And we've got the first one. Oh, this is the copy, is it? Right, lovely. The first one is going to be with the Lobbyer in June this year, and then Pierre Cartier, the French-Armourite geometer, in December. Hopefully we'll be able to do Roger Penrose in sometime early 2006. And then I've got three other threads as well, including supporting some research students. And there's this little archive which I've been recording now for over 30 years. That's since the early 1970s.

22:30 Oh well in that case it's not, I'm black in that case because there's no milk. I find it difficult to believe that there isn't a bottle of milk somewhere in the building, but I could be wrong. I'd say no more. I mean, I haven't seen... academics and organization are not terribly well-known. You did, yes, yes. I wanted to talk to you. I think before hearing you talk about that in... What is it, what is it, what is it, what is it, what is it, what is it, what is it, what is it, what is it, what is it, what is it, what is it, what is it, what is it, what is it, what is it, what is it, what is it, what is it, what is it, Anyway, that's the outline project. As I said, it was a long interview with various people in the country, UK, Australia, and Cartier, and conferences, meetings, workshops, and seminars going back through the early 1920s. ...which very badly needs to be transferred. All the latest stuff in that 1995 article is on digital anyway, but all the other stuff is on old audio tape, which is clearly up to date, and it's badly needs to be remastered and just, you know, to do this often, and that requires... And if I could get through some of them, then once it was out, it would be the most interesting part for me to put on the web, which gives me some value. It's much more practical every year. I've been financing it myself for the last three years. Unfortunately, I don't have the sort of job financing, it's quite single-handed, it's much longer, so I'm looking around to see if I can find some support.

25:00 Thank you for your attention. I definitely recall hearing you talk. I even remember that logo on the cover. Yes, it would be Oxford then. It must have been, maybe it was. Might be sometime in the late 90s or... Subtitles by the Amara.org community They knew that was where, didn't they? It was in Oxford in 2002, of course it was. The question here is, I've really remarked on unification, but that's what people like us don't do, and I have to agree with what I'm saying. Well, I'm seeing implications of how deep the unification comes out, and obviously what Lou was talking about this morning, but also, actually, in this little meeting we just had in St. Mary's, it's astonishing how many converged lines are starting to converge here. I mean, there are also, of course, lines of research in pure algebra involving a kind of unification of symplectic and orthogonal characters. and algebra, understanding what's really going on in the present, non-competitivity, topology, and pure, and enjoy in this interior of, of, of, of, of, of, of, of, of, And the difficulties that there have been in putting that into effect in physics rather than the scope of mathematics.

27:30 There's now a whole area called defamation quantization which deals with a kind of geometric quantization approach, but with a property that deals with the properties of the double covering. It's called defamation quantization. It's a related sort of geometric approach to computational physics. And there are all sorts of really beautiful results in analysis that connect up with this to do with modifications of Liouville's equation and the compressibility of volume elements so that the constant actually pops out. You get the whole thing out of pure mathematics, it's really surprising to see quantum mechanics as broadly out of a deeper mathematical understanding of classical Hamiltonian dynamics. To do that you have to paint in these deletes from the wave function and treat it as charged energy and current. And you do that with minimum performance. Well of course that's exactly what they do in this kind of Hamiltonian approach. They're trying to treat the wave function as charged energy and current. The underlying cannot be written down. You don't get the right equation to do the right thing if you try anything hard with it. You put that together, and it creates a closed causal model, which is called error. It's got a quadratic type of form in it, plus a bilinear interaction, which gives you the cubic area non-linearity, which is necessary to gain, to get solid-tron, you can't have solid-tron, you can't have amplitude or regulation with anything less than cubic structure, you know, one of the, one of the, the second degree comes from the, from the solid stuff, you know, like this. The forces of these directions always go in a quadratic order.

30:00 This is very interesting because it seems to carry some echoes of what the people doing this Hamiltonian geometric quantization approach, which is actually also where quadratic form shows up as being the absolute privilege without that. But then you have two systems. You've got the system of degree wave and the system of maximum wave. And this one multiplies that one. It's a coefficient wave. And that's the third degree. That's the third degree in the process. I'm mostly not familiar with the terminology you're using, but it sounds... It sounds as if there are some very interesting connections here between the ideas of your ideas and the ideas of these people like Chikov and his definition of what I say. Would you be interested in coming to give a talk about this in either way? Well, I think we probably wouldn't be having another workshop on quantum physics for another year or in England. Well, no, I was thinking, why not come down to London and to Basel? Why not come and speak to Russell Hiley in Birkbeck? I'm in contact with Keith as well. I was thinking of meeting him on Tuesday or something. I'll leave you around on Tuesday. Well, Keith's always difficult to pin down. If you've seen him, give him my best wishes and say we spoke. I've been trying to weave it in because I feel I have to find some good hits. Well, I would say maybe sometime in the new year would be the best time, so maybe in January or February and chat to, yeah, but why don't you talk, but don't leave it to Keith to talk to Basil, because with the greatest respect, he's not very good at doing things he says he's going to do, now don't repeat that, don't repeat that, please don't repeat that, don't repeat that, he's, if your best bet is proper to get directly in touch with Michael Hyland, who's phone number I can give you, or... I'd be very interested. I've still got your email on there. I've still got your email, I think, in my database from last year, from a couple of years ago. Yeah, and have another one of those and I'll scribble my coordinates on the back. I haven't got a card at the moment myself. Probably because I just changed my email. Okay, as good as any. At least you can't, at least if your system crashes, you've still got a lot of backup.

32:30 It's alright, I've got... This is fine. I'm very much an old fashioned pencil and paper guy myself. Here we are, our famous last word. What happened to my... No, it's okay. Here it is. That's all right. That's my computer. Yes, but that will be on my old email, which is no longer valid. So don't mail me on that. Do this, which is because I disconnected from my old email, because it was just so clogged up with spam and junk. And this is much better, which gets to me all the time, because I'm afraid I'm too impoverished to have a laptop, so I just use Yahoo when I'm away. Thank you for your attention. I think you should definitely come and talk to AMPA and maybe to TPRU as well. Thank you very much, that's really kind of you. I'm sorry, you obviously had to go through an awful lot of time and bother to find the milk. I'm sorry to put you to all that bother. That was very kind of you. You'll have to tell me what's going on here.

35:00 I mean, the proof of that, yes, that's quite agreeable. Mechanical engineers take this quite seriously. Have you seen this, do you? Tractors and all that kind of stuff. It's a rather interesting, collapsible, reassembleable structure for this. It's got a million members and it's got some intents and ligaments and all that kind of stuff in there. And you can make things that look like buildings that will assemble in about 20 seconds or something like that. Gosh, right on. Right on. Anything, anything which would, yeah, over the flack of that, yeah. That looks vaguely reminiscent of Julian Barber's model that he carries around with him of his, I don't know if you've ever seen his... You may know the following, but the physical models are... Subjecting is symbolic of some of the stuff that Gordon has been trying to put together in these last years. This is not the name I'm afraid I recognise. Gordon Pants? No, I don't know who it was. I don't know. Nick was working with him. I was very surprised when I was in Paris the other day at an office of a colleague of mine, a friend of mine, who is director of the philosophy of science department at the Ecole Normale Supérieure and who is certainly a very bright and hugely well-read guy. There's a course on category theory at the moment for philosophers at the Eccle-Nomale Superior, which I'm involved in supporting. Anyway, he was in his office, and what did I see on his shelf but the whole of a complete photocopy of Krong's thesis and his book on sensor analysis for electrical networks. Very, very, well I think it is beautiful. Of course, the mathematical apparatus is... In the sense that, you know, there's obviously an awful lot of things that have happened since, but the guiding ideas, I think, are extraordinarily beautiful. Well, it was specifically in the context of electrical networks that he produced a bit of the work.

37:30 In fact, his big book, which is the thing that Charles de Looney has got, a photocopy of, which I've never seen except the copy that Keith has. ...was actually published by the Institute of Electrical Engineers, the American Institute of Electrical Engineers, I think in 1939, and he actually met Cronk, he met him in his last years, about five years before he died, he had quite a sense of correspondence with him, and I think sometime in the 70s or early 80s, yeah, I can't be sure, I think... I think he was relatively young when he published, you know, Tensor Analysis for Electrical Networks, which was 1979. I think he made some of the books on his network theory, topology and all that stuff. Well, of course, Keith has to be fascinated by that because it's his way of getting the holographic principles. Of course, he's also fascinated by the connection of ions, in fact. Or the theory of the waveforms and the waveforms. He thinks that. You know, the key to understanding quantum theory. I don't think he's right, but I think it's a very interesting research program. It certainly is well worth doing. Well, Key, the key to my interest in the whole subject is his work on quadrophenics, quadrophenia, and on sound systems. Because he was working as an engineer for, I think it was 3MI or, I don't quite know, I'm not quite sure which company it was. But he was basically working as an engineer on sound systems for one of the big new music companies, I think it was TMI, and that was where he became fascinated by quadratonic systems and then the underlying mathematical theory and then by Huygens in foundational quantum mechanics and the good honest technological learning to go down into doing quantum theory. And then build up in a piecemeal way. Yeah, well, it's a strategy which actually is almost always complementary to... The top-down strategy is kind of grand mathematical schematism, or schematization, but it actually creates a pair of powerful constraints in winnowing out the good ideas.

40:00 Which, as we all know, there are ways of interpreting quantum theory which quite definitely don't satisfy Hawking's ray, to put it mildly. The engineers are absolutely right, I think, in their instincts there, you know, and they go back to the coast, you know, and there's a boat, you can take, and then you can come up the other side of the river and you can have fun and drive it. I'm not about to go into that, you know. I'll go up to the edge of the river in the jungle and come down the other side. This is called bridging the river. No, that's a very good analogy for the way, the different ways that mathematicians and philosophers think and the way that engineers think. But I think it's very interesting because calculus theory, which is my own particular area of interest, is very much... I think in some way it does embody the kind of engineer's way of looking at mathematical structure, prepared to fend that clay. I mean, on one level it's high abstract machinery, but on another level it's actually very much piecemeal bottom-up. OK, right, let's go. Thank you again. The main of the Argentinians, I think that's the oldest of all people. Oh, even you don't know? Good. That makes all of us. Well, you could just give the seminar here if you wanted to. We're all here and we don't know where the bloody room is. You could just have it right here. Did we just follow you, Bob? No, I think I... Oh, okay. We can talk for a while. No, we stay here, I think. He's just pickpicking some stuff from his office. So you're here for a while? Just for three or four days. I wanted to... There was a BSPS meeting in London last night, which is the Society for Philosophy of Science meeting, that I wanted to go to. And it's the birthday of a friend of mine tomorrow, who lives in Luton. It's the birthday of a friend of mine tomorrow, who lives in Luton. And it's the birthday of a friend of mine tomorrow, who lives in Luton. And it's the birthday of a friend of mine tomorrow, who lives in Luton. And it's the birthday of a friend of mine tomorrow, who lives in Luton.

42:30 So I thought, you know, why not go and get here and hear old Calvin, you know, banging on about spin networks and stuff again. God knows, he might have something to say this time. Pretty good, actually. No, more to the point, I might actually get my head around hearing it. No, it was very good talk. But you think this thing on quantum field theory is from the 14th to the 17th? You were just saying, the thing that you were telling me about in Puget that Roger is speaking at, and you're speaking at it as well, or is it just...? This QFT thing, here at the Newstown, is the 14th to the 17th. I'd really like to get that. The trouble is, that clashes because they've got this meeting in Paris on quantum computing, which Bob is speaking at. Well, I think I see a way around that. I think I might see a way around that. Thank you for your attention. I think you said that there would be a program of that meeting on the Newton website. I looked at it the other day and I didn't see it. I might just pick it up from you this afternoon when I give you back your overheads actually. You see I probably won't be back in Couger now between now and then. Thank you for watching.