Theoretical Physics Research Unit Seminar — Roman Zapatrin

0:00 Ahem, ahem, ahem. Yeah, well the speaker is taking heed of what you said. Yeah, I'm sorry, and if that will happen, I didn't give answers at all. Yeah, I don't know. In the end, because only once you're late. Why are you apologising to me that you've been far off? Well, because I'd actually asked you to, you know, to hold fire here. Well, I hope that he hasn't come late just on my account, and that's what I'm not supposed to mess up. No, no, no, he shouldn't mess up. He's not just coming straight here. He may, in fact, even go in. Oh, excuse me. What did you talk about on Tuesday? Not the first half. I thought... I began to see right, um... The second half was... Well, I didn't see this talk. I only arrived half, basically. What did you talk about in the first half? Um... To follow you. Well, yes, a very hand-waving, kind of qualitative account of the way that he thinks about it. He mentioned Rosa and incident algorithms in passing, but nothing that he said in the first half of the talk connected up in any well-defined way at all, but I can see it with incident algorithms.

2:30 with incidents articles, which is Keeg's question. Although they were mentioned in passing. The second half, things became a bit clearer because... He didn't really do the incidents articles. Well, as I said, he just mentioned them in passing. He didn't actually connect up really with anything that he was talking about. But the second part that was interesting was all this business about how you use essentially kind of information theoretic tricks to get answers out of, in a Hilbert space, of a system as to the amount of information that an external observer actually has about the states of that system when it is entangled. And from this, he thinks he can rebuild the apology. At least that's all I understood. I agree, I don't think it is a particularly brilliant idea. But the thing he said, which was really interesting, which immediately I literally saw Basil's eyes light up, even from behind I could see his eyes light up. Whereas when you said, well, of course I've presented all of this in this kind of information, I've been ready to come, Hilbert's face, probably like to do with entangled states and quantum computing. But really, I want to think about it all in terms of algebra, because that's really going on here. Yeah, fine. And there was no question-answer session, which was, well, actually was there for that, which Chris Eisham spent a lot of energy trying to pin him down, which algebra, which algebra? Chris Eisham always asks that question. I've seen him do it three times. Oh, well, it's OK. Well, in that case, he didn't disappoint. And he didn't get an answer, but I don't think he, in fairness, I don't think he really deserved an answer, given the level of... I think the quantitative ideas were quite interesting. Listen, before I forget, two things. First of all, let me give you all this stuff of volveos and peruses. And two, a letter. What's this very interesting paper of David Burns about table wrapping that you've sent around, well, parapsychology? Because I can't open it. Oh, you can do it, because that's been on the end of the problem. It's actually an HTML farm. What should I use to open it? I've tried everything. You see, this is just Internet Explorer page, nothing else. I didn't have anything on it. Well, I tried Explorer and all I got was... Well, it certainly wasn't plain text. I got something I could just about read. It was encoded for any time.

5:00 So I should just use Internet Explorer? Because when I click on, you know, open file, the window comes up saying which, which, um, no, things of machinery do you want to use to open it? You should, yeah. Okay, I should have used Internet Explorer. This is just a page. I think I probably tried everything about Internet Explorer. It was, uh, it was funny, it was, uh, Well, it was interesting. I was able, from one thing I tried working and I was able to read just enough of it. It was very difficult. He was being very rude about John Taylor, quite rightly too. What do you mean? I'm sorry, I've lost it, Keith. I think I... Oh, okay. I'm not convinced. There's about four more, which I would have copied had I not run out of copying papers. You've had one? No, I don't know. I've had a problem with my archive of Bill's stuff that is obviously relevant to what he means by getting what the hell is going on, except that there are about three or four more papers that I'll send you. Those, those are the most important ones there, and there's one paper by Ferrucci as well. Oh, that one! I don't know that one. It's kind of the end of that disc, which is fabulous. That's just about half a page. No, no, it was long. Have you got a disc, wasn't it? What's it? Yes, yes. Can you rename it? I don't have to try to glance at it. Well, it's fixed. Is that a SPIA now? The point about incidents, I'll tell you, is that I didn't understand that, in fact, The comment I made to you, I also made to Mike, so I can clarify it while you're very clear. Is that, I imagine the incidence algebra to be a structure made from what I think of as the incidence matrices. Yeah, that's what I would think, that's what I'm looking for. Well, well, I need to go back and understand the details a bit more, but actually that's wrong. Oh, wrong. Complex in a sense of cell termology. Yes, yes, yes. So the name incidence algebra is very misleading indeed. Okay, good. Well, I'm glad you're telling me that because I cannot have any sense of it in terms of I had only ever looked at this rotor algebra once when I first read Yana's paper, and I couldn't understand what it had to do with incidence. It's a way of making jewels, as you and I understand jewels, categorical jewels, if

7:30 you like. In a purely combinatorial framework where you haven't got any underlying topology or ontology or anything to stop with. You've just got pure structure and you don't know what it's the structure of. The rotor algebra is the dual. OK, well that's very clarifying. I hadn't understood that at all. It's really a badly chosen piece of terminology. They shouldn't have chosen the term incidents at all. It's very confusing, but I mean, I think it's close to what... I mean, people called it ROTA algebra and similar things. ROTA, R-O-T-A, it's named after the guy. So, I mean, that doesn't help me at all. I wrote it an awful lot of different kinds of maths, so now it would be... I was talking about... Well, that's, to be honest, the first time I saw the name, that's what I thought it was, I really did. That's seriously what I thought, I'm sorry, That's really what I thought it was the first time I came across the expression. I actually saw it written down first, so I knew it wasn't. Yeah, no, I'd heard the word, and for about two or three months until I saw it written down, I thought it was O-R-O-T-O-R, and I couldn't understand what the hell they were talking about. What the hell has any of this got to do with algebra or with rotations or at least that clears that up? Well, it does leave this other thing hanging in the air, I think you certainly could make an algebra out of all those incidents matrices, not just the ones which are on consecutive dimensions, but the whole lot, and think about what that would look like. I mean, that was the thing that seemed to me to be something no one had ever done before. Yeah, that is a very interesting thing to do. Yeah, I agree, that sounds a very interesting project. And the boundary operators would be things that lived, they would be the one-dimensional parts of those, but then there would be two-dimensional parts of those and higher-dimensional parts of those. and this which would be which would be related to the higher you know to the cut to the higher homology groups could well be related to the higher homology groups are you going to butt in and say that you've had a word with no i'm not going to say anything i haven't had a word with anybody i've been on computers all day oh god in that case god they are when they go wrong don't talk to me about it's just frustration you say that again too because i came in to download you need a stiff

10:00 and then of course once once it got into that mode it wouldn't close down so i had to go down the back and close it down and when i open it up again it wouldn't open up probably because it was still fighting i don't know you're still fighting the uh you know i mean you you you think you find it difficult. I mean, he and I know just about everything about these machines that's worth knowing. It's still just as difficult. Is it? I thought it would be easier for you guys. No, no. Last time I had a problem with email, I finally verified this, that it was nothing to do with Birkbeck and it was nothing to do with my computer. Right. So what was it to do, a server? It was University College. What the hell did the University College got to do with it? What happened with this? I drove, I drove poor Keithy completely round the bend about a year ago, when my emails were done. After two hours, when Kevin came down, you know, I've been waiting, Kevin came down, sat there, didn't know how to open a Macintosh, no usual problems. And then he walked down the end, and somebody pulled the electrical plug out of his car. Oh, yes, well that does clearly make a difference, you know. You do that when you put the kettles on, do you? Oh, no, no, absolutely. You can't get anywhere near it, because he said he was just hanging out. I don't even use the kettles for someone to leave. people in this not legal first of all we thought they cut the they cut the wires because they redecorated everything you see i was running a router and i was going through you know i was running a room and it was changing certainly plugged in a couple of bits in the hub that were coming back this way and it was all fashion i didn't dream that there would be a something as simple as that yes were not connected to one part they decided they didn't make the other part so they filtered my packages but you know it's such a silly frustration and then my laptop you know i said go on last weekend a couple of weekends i've forgotten you mentioned the whole weekend i was trying shutting it down banging it opening it up banging it shutting it down banging it to try and yes on the on the kenneth moore principle the bloody good whack He came with a bloody good whack and he usually does the trick, yes. Well it's worked with the old television sets, a very good bash on this. So I took it in, got a telephone message this morning, there's nothing wrong with it. They can't replicate the thought.

12:30 So how does it put itself right between... God bless. ...banging it on the way in. No, you've got to lose contact when you bang it, you must make them back contact. Well, that was a standard British Army procedure, wasn't it, with the old valve radio sets that, you know, if they weren't open, just bash them extremely hard and, well, maybe not nine times. I hate forks that are like that, you know, that just go and then come back on again. So I say this, the whole weekend it was off, and I thought, well, maybe it's a capacitor loose, and I'll just close it down and cool it down for 24 hours, open it up, and they'll have exactly the same thing. you must be really badly a physicist under those circumstances because you know all the physics you don't know the engineering so you're really screwed well you don't know the circuitry yeah exactly well in fact in the physics we're always taught I was always taught that you open the box to see what's going on inside and I used to do that in the lab that doesn't work with Schrodinger's cat no and they used to get really cross with me because they said what are you doing inside that you shouldn't be inside there You know, treat us a black box. I said, well, I know what's going on inside there. No, you don't need to... You've got to break... I couldn't, you know... You're given a black box and you don't know what the hell it does and you're supposed to... Of course not, yes. Well, you're thinking like a physicist, which you are, a born physicist. It's like Maxwell, the famous story of... It's like Maxwell as a child. He insisted on dismantling his father's wristwatch and saying, I want to know the particular go of it, father. I mean, I do have a very bad reputation and never be able to put it back in. Where's this go? It was explained, you know, the mechanism was explained to him that he wasn't satisfied. No, I must know the particular goal of it, which is a great phrase. Have all kids do that, don't they? No, by no means. I think it is a sign, an early sign, that you're definitely... Come on, I ought to say, into everything. Even now, when somebody brings me in something that's not working, the first thing I do is take a pill to see how it works. Well, you're in the great line of Maxwell. Hello, Ria. as I say you're in the great line of James Clark Maxwell keep saying that it makes me feel good so you haven't had a chance to speak I'm sorry I know I'm tied up you've been the only thing is I will nag you about it mercilessly if you don't mind for the next month or so because if I don't get it sorted by the middle of March I might think why the hell would he be doing nothing yesterday

15:00 but yesterday I was seeing to my son's shower business in the morning so more but particularly a bit yeah is it got a condom on it just teasing I'm sure he's good, but I hope that you've got a virus, you're protected, aren't you? You've had all of the tests. This is up to date. This is up to date. I better move on that side because I imagine that... Yeah, but then in the afternoon, I had Melvin Brown here all day. Did you? We went through and we went through and we went through and we went through... Talking about... Sympathetic brain? Yeah, right there you. I nearly came up yesterday afternoon that I had all this shite with the tax business that I had. for another couple of weeks i also i owe a thousand pound tax not 150 i got another letter from them this morning saying and they found another 14 000 that they thought i heard which is quite encouraging no no no that i owed yeah no no well i mean considering that it was more than all of the income i declared for the year that they're asking i mean the income not the liability it's something that's gone completely crazy but i think the problem is that my accountant well i'm hoping and praying that they've got it very very seriously wrong indeed otherwise i may end up having to do as a runner well i hope it's not the irs winding you up i don't think they tend to do things like that but no it's not i mean they make ridiculous oh yes they do not in my shoes they make ridiculous assumptions actually in the sense not my mistake well i shall soon find out well i'm going to be bankrupt in actual just have to move it all very quickly to the cayman islands i mean this is big money man yes i know it is very big money we could have we could have done the mari conference you could have seven times i know and here am i i i i'm supposed

17:30 to be involved now now next year in in organizing and at least partly paying for this um this for the bill 60th birthday in fact i've actually got um a long email this just this weekend from colin mccarthy with uh the title of the talks he's going to give you know he's uh the um he and alberto have both already got their their headings and uh everything well you're contributing money for it oh yes i've already put up some money for it and i should be putting up that Do you claim tax rebate, have you? Yeah. Okay, good. How do you do that? Because he's got a good accountant. Well, I thought I had, until that's a very moot point. I'm not so sure right now. Do you need a tax rebate? Yes, if you do it. Yes, if you do it. Charitable donations to which any scientific conference certainly quite qualify as us. I put up the money for this thing. You gave my life on charity. so did so did some of the greatest minds of all time no problem with that no i got this i thought you'd say it was a business experience no no no obviously but you can get a donation to charitable or academic or causes oh i didn't know there was that there and get tax relief charitable donations to academic even number of years to my brother how much money he could save as he gave me some of them. Unfortunately, I think that personal family members are excluded and not disqualified. Otherwise, everybody would use it as an obvious scam and a tax shelter scam for the way of donating money to their kids. I mean, you cannot... It's a good special relationship. Yeah, you can give money to a foundation as long as it's a registered charity. Well, if Anchor is a registered charity, which it certainly should be, it should be. Well, it would. It was so messy that we didn't want to do it. Well, I'm surprised. It's normally very straightforward. He's here. Well, that's not what people tell me. Well, surprised. Are you guys ready? He's here. Yeah, sure. I'm just going to bring him up. Okay. Was there something in Oxford or something? Yes, there was. I didn't go to it, though. I was going to go. Did it fall so? Yes, it was. The Origins of Irreversibility. Dynamic Origins of Irreversibility. Clues from the second law. What, you didn't go to it? I didn't even know it was on.

20:00 Yeah, no, I didn't. I was planning to go to it, but then I... I was at about two o'clock. Yeah. Oh, I would have asked you to go to it and record it for me. We could have, you know, two of those with one stone. Never mind, one of those things. I was going to go, and then I got all this absolute shite... Remind you recording it just like that. About... Oh, I mean, I'd always ask the speaker, first but you know nine times out of ten they haven't got a problem yeah well some well some people i mean well video audio i don't know just just just just not just an audio and if somebody said anything else i wouldn't do it but um you know i mean no i was there that's who it sounded interesting it sounded quite an interesting talk it was the guy from i think he's from bristol was it was it a water no it was at all souls they always have them though it's it's the weekly seminar it's it's held at all souls every thursday pan was on his way down now on the motorway and uh he just came off the motorway gave me a quick call and he had no idea i was in oxford no we were it's what a very nuisance we could all have you know sort of paired up and as it were you know have all done one another mutual favors i mean you could have so it's also sort of fork every week every week yeah some sort of website or something yes it's again it's on jeremy vacanfield's philosophy of physics uh fixtures list which asked him to send to you he stopped the only problem is he hasn't been around much this term he's been making it to david wallace to send it out i don't think that he wants is terribly well i think david wallace needs he's very good that he he's very good philosopher of physics he needs a bit of a kick up the packet when it comes to uh you know details of admin like that like adding people's names to lists whereas jeremy is very good if you ask him to do it it'll just get down straight away a couple of emails from them about something well this is thing he sends out at least once a week and the last one i haven't seen anything for the last couple weeks well this came the last one uh that i got came back two days ago and it was just this week's and next week he usually he usually does about a fortnight ahead he does a preview for the term and then as things change he does he does them a couple of weeks ahead but the philosophy of physics seminar it is their main you know weekly seminar it's always at all cells it's always at four well less ones that include me they might have changed the time because of the speaker but but but normally it is a four o'clock at uh you know so either in the wharton room or in the old library it sort of moves around just but just between those two locations and um last week they had a very good talk by lionel mason from the math institute about uh twister theory it was a

22:30 pretty introductory talk with a lot of motivation and you know why should we take this seriously as as a rival to, to strings or to a, or to do quantum gravity or any of the other projects. And he gave some very, very, I thought very plausible, very interesting arguments. It's a long way up to Israel, isn't it? Not really. I mean, I find it very easy to get down. Well, if you're driving down yourself, then obviously... Can I just hop on the bus to Victoria? Are you there in 90 minutes? I think Victoria, for me, is a bit trickier than that. Oh, well, that is, you know, because it's easy for me, coming up from Epson. but the buses go every 12 minutes during the day and it's a very good service and it's 90 minutes usually on the button and it drops you right in the high so right back outside Queen's and on Seoul so you can literally walk in 2 minutes from the bus stop to where the seminar is you've obviously got it well organised yeah it is quite easy it's something that got interest to me is talking about yeah I'm really sorry I didn't realise you hadn't been getting them I was going to take a day off If I had known that you were interested, especially in today's, because I would love to have got today's, I really would have been very interested in getting a record of today's. This guy is the smoker, and you must ask him where he's allowed to smoke. Do you want to smoke now? Well, you have plenty of time, Roman, if you want to go smoke. Go on. Go on, boys. Anyway, just put your bag... I'm sorry, it's a very small room. Put your bag there, and hang your coat up. And then... You're going to need to use the board, obviously, aren't you, Siren? That will move, please. Not at this point, unless he's coming. No, he hasn't called me. Can I just squeeze behind you? Yeah, yeah, maybe we should... I'm so sorry. Maybe we should move there. I've got my back. And the back you could put down. I'm going to go and get myself a coffee. Anybody else want a coffee for you, Razzle? It's closed. It's open. It's closed. It's come back up one minute ago.

25:00 Why is it closed? Because there's no one to come up for lunch. It'll be back in half an hour. Oh, I see. There isn't a machine or anything like that. I've got a tea bag if you want. Oh, there's coffee up there. Okay, what matters? No, no, there is a coffee in here. This is not a coffee. Oh, a coffee. A sire? Garana. It looks horribly like coffee to me. I'm very suspicious. God, just push this under me. I don't disbelieve you. It's my private. Oh, it's your private coffee. It is coffee, but it is your private organic coffee. No, no, no, this is not coffee. This is garana. Lemon and ginger. Okay, I've looked for the pot of mine. you know I'm going to get it lots of cups in the kitchen in the kitchen that's just so same through the cold top but I don't know if it's good enough to be done no I am alright he goes down there he went to the toilet well I'm not sure whether I'm well he said he wouldn't So, I'm sorry, you'll have to smoke by yourself. I have no sympathy for smokers, having been subjected... Patrick, but I didn't notice you like me more... Sorry? ...if they stop smoking. I always like people more if they don't smoke. Oh, I agree. There's nothing to do with really smoking. You can't get happier than that, you believe. Yeah. I don't know how much Sir Patrick gets paid. a survey of academic salaries in Europe. Italy is top. Yes, they get good money. Three times more than we get. Too sickling, isn't it? Too sickling. There's Patia for you. Patia. In a moment. We will sit wherever he wants to sit. He always wants to sit here but I can't through. First. Well, he's a young boy, he could sit on the floor in half-loches or full-loches. He can sit cross-legged on the fine. Yeah, he used to sit on the floor in full-loches. I can sit up next to the printer.

27:30 This is a nice collection of people here. On the desk... Is there a mic? Because what is mic getting? Well, he said he wants here, but I don't know. I just wonder. Maybe he should abandon me. Okay, good. Now I completely hate you. Now you're completely refreshed. Do you want to drink? No, no, no. Do you want to drink? No, no, no. Do you want to drink? No, no, no. Do you want to drink? No, no, no. Do you want to drink? No, no, no. What are you proposing? Bistrup. No, Bistrup maybe. Maybe tea, maybe coffee, but he doesn't want to. But he doesn't want anything. He just hung out for a few minutes or so. I think maybe... There are two people coming. Just sit down, sit down and relax. Are you supposed to get to smoke? Yeah. Can you take him down to the smoking? Yes, yes, yes. I will go down with you to the smoking place, because she was a smoker. I was a smoker exactly one year ago, and they have the end of February, so I still know where it is. She comes up with that to get a smoker again. Yeah, she seems to have a strong will. Well, but there's different kinds of strong will, isn't there? Like, I mean, I haven't had one since Christmas, but I've had a few of the Christmas. And some people do it different ways to other people. Yeah. I mean, I've never... I think I took one cigarette once. my brother did nothing was sick well I just took out some people spending money on that and that is exactly what I did and threw it away I think twice the guy as well I've never had an argument I think twice the guy they actually are faster than cigarettes and then of course my asthma started why you smoke hmm that's why you smoke well that's a question that's always deluded me what people smoke well most people smoke for the effect of the nicotine but i thought it's something that they take it up because they don't know what the effect of the nicotine

30:00 nicotine is do they so they just take it up because it's it's something that you people do grown-ups do no not at all i smoke gladly for the effect of the nicotine i like the effect of the nicotine well you do know but i mean when you first started you didn't say oh i like nicotine let me try a cigarette not in those words but that's what it came down to no the very first cigarette that's not true this is it you see I mean if you because you do get I mean it's sort of addictive I won't say it's you know it's very addictive it's seriously more addictive than heroin little down to that I mean, I was in company where, you know, my mother used to have those little tins. You remember those tins, I've probably, before your time? Little tins of Navy Cut of 50 cigarettes? Yeah. Was it 50 or 25? I can't remember, quite a lot. And we had to keep them in India. We had to keep them in tins, you see, to keep them dry. Those tins fascinated me. Well, both my father and my mother carry around these things, The smell, the smell of tobacco I find very pleasant, but not of smoking, it's the tobacco. The tobacco, and they used to smell, you know, because the first time the tin was opened there was a tremendous aroma. It's a nice smell. That is a nice smell, I agree with you. I would assume smoking was an extension of a lot of children's dummy. Well that's one theory, to put something in your mouth. there are I'm sure people who smoke for that kind of reason yes I think that's true and I think it's also probably true that most smokers do that a little bit like if you're a smoker and you're in the pub and you're having a conversation and I don't know there's sort of some level of stress or nervousness or something I'm sure there's a bit of that goes on with most smokers anyway but then everybody does various things They do when they're nervous or whatever. But no, I mean, nicotine is quite a strong drug. It's certainly stronger than coffee. Or tea. Oh yeah, whatever. Especially if you're smoking all the time. Or, you know, relatively all the time. No, I saw my mother trying to give up. It wasn't murder.

32:30 I would like to see cigarettes illegal, personally. I mean, I'd give them a chance, but I'd like to see marijuana illegal. Yeah, well. I mean, the... I want to tell you, Mike is here. He's supposed to make some coffee. Oh, right, yeah. Only Roman's gone down to get a cigarette. Yeah, he said he was getting, you know, well if he's an addict then it's only in a sense where he tries to get himself a fix before him. Yeah, he only snags a lot. Yeah, he only snags a lot. Yeah, he only snags a lot. Yeah, he only snags a lot. Yeah, he only snags a lot. Yeah, he only snags a lot. All Greeks snags a lot. Actually, all Southern Europeans do. It's basically once you get the Mediterranean, the Chinese do. The Chinese do. The Chinese do. The Japanese do. Yeah, much more healthy diet. Yeah, much more healthy diet. It sort of balances it up a little bit. Well, this is making the very sweeping assumption it's making, isn't that, here? I have no doubt about that. Yeah, I have heard some strange defences, I think. Mike Manfey's a good one for defending. Well, John Dawling had an entire line on how, and he's quite an expert on Bayesianism, as to how the epidemiological evidence was terribly flawed. if you already get the chance on that subject. Nearly? Well, that must be the only thing that Owen and Roger Scruton have ever agreed about! Er, Owen had a relation, or a friend, a close friend, who was very involved in that, and... Well, I've seen John Dornhill who was talking about as well. At the same time, that doesn't mean to say Owen thinks that smoking's safe. No, of course not, no. I mean, I think very few people in their sound life would say that smoking was a good idea. however there's a lot of a lot of the evidence is terribly fluid yeah well that was the line that i was hearing but anyway i certainly had no intention of taking it up what i am going to do as i say is drive you around the bend as well the next three weeks about asking if you can i know it's difficult for you because you're no longer in that as it were an official position and i'm obviously a it's a non-standard procedure because i thought that when i retired i'd be nice and relaxed and wouldn't be hassled i'm sorry you're the only guy i can turn to if i didn't hassle you and have time to do everything i wanted to do it doesn't work that's what bill says to me as well he's been more he's been more stressed out and more busy since he returned than he ever was when

35:00 well i'm i'm thankfully i'm stressed out and busy on the things i want to except when computers go Yeah, yeah, so it's pretty well. But, um, no, the only thing is, I either drive you around the bend, or I drive these guys around the bend constantly, sort of begging, er, you know, copies and things off of them. Because I want to get Pan sorted out as well, because he loves the, er... Well, what do you call, apart from... Research... Associate Research Fellow. Associate Research Fellow, thanks. they are off hello fellow fellow why didn't i say oh i'm just going just going where is it on any research and i think i might be going to start again what you're talking to um melvin about uh you know what i talked to melvin about was how stupid i'd been and how obviously trivial this whole subject really is which subject simplex extractions i don't think it's trivial at all well if it is then i'm very very very dumb indeed because it took me a hell of a long time to get my mind now i've now got my no disentangled quantum mechanics from the mathematics right well that's a hell of an achievement that's a highly non-trivial achievement highly non-trivial achievement because in my mind everything directed from quantum mechanics mm-hmm right in other words it was that if you didn't know what quantum mechanics was you wouldn't be asking those questions that was that was my mind because I'm sympathetic and metaplectic and I'm not so sure about that I think they're an independent roots of independent features of interest about those structures that have nothing to do with quantum absolutely that's what I've got clear I've now divorced the quantum mechanics per se from the actual mathematical structure that is there regardless of whether quantum mechanics is is is valid and this whole business is the symplectic camel camel would be a great independent mathematical interest if heisenberg would you know have never lived this would have been extremely you know about the symplectic camel Symplectic camel? No, obviously he doesn't, yes. It's a kind of cigarette.

37:30 No, no, no, not a cigarette. Well, here's a fine mathematician that's telling the story. Yeah, a camel is an animal. No, I understand, but it's a symplectic. It's a symplectic camel. He's your symplectic. It's one of your countrymen who is doing the theorem. Robots. Oh, yes. You know him, but you don't know the camera. Oh, sorry. No, this is something that, uh, Maurice de Gosson, the Jean Marais student, our student who did a PhD at the Jean Marais, introduced me to it, so, and it's very interesting. Yes, we're just real, isn't it? So, again, what I'm going to speak about is that in a way, it may become everything completely wrong. Everything completely wrong. Because I didn't try to get into it. I've had a bad experience over the last five years, that I have done something for myself, and there's such a great session that I'm about to do. Now I see some indication that it is very difficult, so, again, may I nevertheless sometimes use just by the reasons that how I... How you told me about it, yes, okay. Because part of these activities, when I just came to this quantum information group, So, I was just thinking that my basic idea was somehow to introduce this notion of virtual intent. And then somehow to introduce something like a position to this silver space, which are quite uniform. You cannot say that one vector is better than another vector. And if you have just a simple space, you cannot say is this a product vector or is it not a product vector. All vectors are equal. Then we discussed it with my colleague Paolo Zanardi and as a result he has written a paper about PPS, he called it, in terms of product term. It was recently published in Physics Matters and it turned out that he did not want first to introduce algebra, he wanted to do it just only in terms of super space, but he was forced

40:00 I guess he was forced to introduce some algebras because suppose even you have a hinkert space, you may even fix a basis there, but even if you fix the basis there, you still cannot say is it a product basis or what is it, you have to introduce something which you have to call product structure, but how can you, what are your means to do it, only if you say that I am doing some local operations or this particular operation, is it local or is it not local. He introduces it in such a form, he uses C-star algebras, and Ruz simply copies just in, so, when he had big huge space space, and space is the algebra of all, you know, for all, you need square-faring dimensions, simply a whole linear operation, space space. And then, if there is given a tensor-product structure, if it is given, then we can consider algebras AI of such course as 1, 2, I'm going to lose the notation, but I mean that it is the algebra of linear operator in particular, ah, I don't get the right. Yes, of the law, of the top. It will be more precise. And here, somehow we'll just introduce, in terms of algebra of linear operators, this notion of terms of product structure. What I did not like in this construction is the following, that, for example, because his definition was so rigid, that if a hidden space has a dimension, say, 25, it means he can introduce a tensor-coded structure. Because, just because 25 is 5 times 5, I was trying to promote this idea that even if there is a space of dimension 15, and they consider an algebra of operations, not all of the operations, my life is, that nevertheless he can view it like something multi-partite.

42:30 He told me that it's completely unphysical, and he didn't want to be engaged in it, but I don't keep it in the paper. After that, again, I have encountered this paper by Dürer and Sirach. May I tell you the contents of this paper, the classification of weak states, because just generalizing it, But I have some hopes that we can get subsystems. So, suppose we have a Hilbert space. This Hilbert space is a given . And this index i, i, is a set of subsystems. Now, if we have a density operator here or here, then we can ask, is this operator separable or not? Just with respect exactly to such this tender product structure. May I remind the definition of what is a separable operator? Yes, so it is introduced in two steps. So, first step, introduce decomposable operators. It's not necessarily a basic operator, any operator. We can speak about any operator. Decomposable means that you can represent your operator as a total product of operators, each of them acting here. And the operator is called separable, but separability, of course, applies only to density operators just by that reason that if you consider arbitrary operators and arbitrary linear combinations, you seem to forget all the operators. So, let's speak about density operators, positive operators, and it is called separable if you can somehow represent it as a convex combination, it means that these are in 0 and 1, times such tensile products, rho 1, 1, 4, 10,

45:00 And it turns out that there are some density operators which are not separate, and they are called entangled. Entangled. Entangled. Entangled. Now, what was the idea of Deux and Therac? They would like to classify all density operators here, in this big space. And they talk, well, suppose our operator is not separable with respect to such big decomposition of our space in third or quarter. But maybe, with a bit of a variance, we consider the same space, but we group, make a grouping of some of the factors, so it becomes the third or quarter of less number of spaces, but the dimension of spaces is bigger. And we can ask, maybe with respect to such the composition, it is separable. Of course, if it is separable with respect to this composition, it will be separable with respect to any. But not, not, not, vice versa. Please interrupt me at any moment, because I don't want just to be like a speaker. I just need to be understood at this moment. So, the first step was just simply, again, just not me, I don't know exactly the paper, but introduce it as I see it in a more, I should say, algebraic way. No, please, be free. Now, again, it was stated by that let us consider all possible such groupings and regroupings of this tensor product. And then they realized that any such regrouping, because we do not care for the order of multiples, because they are all I think I mean if you exchange the multiple the results in space and they claim that all such possible regroupings are in one-to-one correspondence with partitions of this set of subsystems. So you have this set of subsystems I, I, one, two, and so on

47:30 And you may consider different partitions. This is one partition. For example, if I make so, it means I make a finer partitions. So, this is all, now, if you consider all partitions of this plate. Partitions, you suppose you just knock it with a hammer and you will say, that's a partition. And you see that partitions may be, it's called partial order on the relation of all partitions, because some of them may be comparable, because, really, if you knock once, you get some picture, and then you may knock twice, and you will get more refined picture. However, you can take two different screens and knock them in between, and you will see that they are... You cannot compare them. One is not weak, and not terrible, the other one. So it's like a partition of a set. Since, simply, simply, you can see the whole partitions of this set. But these nested are occupants. No, the collection of all partitions, it has a very good algebraic problem, because it's not just a partial, it is a lattice. That is what it means, that if you take two partitions, you always can find exactly one least upper bound and exactly one greatest lower bound, two partitions. At the lower end, and up and down, I'm thinking, yeah, I know. Here, at the very top, is the partition which corresponds to the particular position. So every point is the partition, as strong as possible. At the very bottom is just the whole, in the whole. And everything is intermediate to here. And the property to be, to be a, we call stronger, I don't know how to call it, you know, look, this is in fact not a partition, it's just a set as a whole. Yes, it's just the whole set. The first floor above, what you have, it's all bipartite splits of the system. All bipartite partitionings, yes. The next floor, it's all tripartite. And so on. And on the very top you have bipartite splits, you cannot split it anymore.

50:00 Sorry, it's the maximal refinement of the partitioning. Yes, yes, yes. And this is the maximal element of this lattice of partitions. Now, it is... I'm afraid that I will overload you by different mathematical objects, but... So, at the end, you will put sort of short context... I will try... What is the point now? Because since I did not yet finish this, I do not know. Maybe something of what I am telling you is redundant. I do not have to speak about it. I do not know yet what do I have to use here. So now we can introduce the following thing, which was not introduced by Durant-Serra, but it is directly follows from the paper, and we may apply it to algebra. So, let us take the set of all sets, all S, and the set of all partitions. Then, for any element, for any set, and for any partition, why? We may ask, is it separable this state with respect to this partition, or not, yes or no? And what does it mean? It means that we have a relation. We have a relation between two sets. It's just as general in our whole degree. We have a relation between two sets, between the set of straights and between the set of only partitions. Now, we can look for the following thing. What are the equivalence classes of partitions with respect to all possible local transformations? So, we fix a particular state here, and we We ask which partitions are separable with respect to which partitions this given S is separable. You can get, for example, it is separable with respect to this, to this, to this, to this, to this, to this. But if it is separable with respect to this, it means it is automatically separable to everything that is below. Just because if we have a product of many elements, of course we can group them and

52:30 can I ask one quick question is this this doesn't have to be a finite set or is this a finite set in the case of this everything that's in your right now is it a finite set ok so if it's not necessarily a finite set then this partitioning that you talked about got to have you the condition you've just you've just stated is that equivalent to to the actual choice is equivalent to what topologists call relative uniform separability no just just a moment you know considering what i'm speaking about what is finite infinite this the no no no the set the set that you're talking about here the thing on which you put this the thing on which you're defining these equivalence relations between the partitioning no you know i guess i i i have to It should be fine. It should, right, that's what I thought. Because, you know, what is the reason? It may be not fine, it may be not fine, but in such case, we have a freedom in determining this. It is not neatly defined, because you must define something like a topology or... Yeah, yeah. Well, that's my point. It was done by Aysen, but it is just a possibility. I'd like to know more about the Crescentian quote. In infinite set, you cannot speak about that. Because at-end the code, with respect to a particular structure here, or a topology or something, you must impose on this. If it's just a set, you... But it's infinite. In the case of this lower diagram that you're talking about now, you can't even put classes of your partitioning, unless you're using the trifects, unless you've already got relatively uniform separability. That's why it needs to be finite. By the way, I would like to mention, if we were once, that if we would have algebras here instead of partitions, in such case, we could introduce something which will not require any additional structure or set of indices. How can we do it? Because, unlike Hilbert Then, algebra are, they have really suitable elements called unit element. And we can consider all kinds of products for which, which contains finite number of elements which are not equal to 1.

55:00 And all the rest must be equal to 1. And in such case, it's a kind of natural structure which will not require anything on this set of I. And in such case, we had to consider the set of all finite partitions of I. And in such case, it will be a lattice again. So, again, you see, it's a very direct, just the semantics push, push, pushes us to answer. Because when we have algebraic, it becomes easier. It is, by the way, my very general principle, just to feel where the semantics pushes itself and just to follow. Well, so, now, we'll stop at this point, yes? We have the set of all partitions, we have the set of states, we have this relation, and what do we see that? With any state S, we can associate, we may call it an order ideal. Sorry, what was that? What the ideal in the lattice of partitions? Yes, yes. Order ideal, not a lattice ideal, but an order ideal. Order ideal is a very simple thing. It is such a subset of this partially ordered set, that if you have an element there, everything that is below is in this. But not a lattice ideal, because if a lattice ideal, I should require that the upper bound should hold partitions, And it was just demonstrated in the paper that there are states to which you can have this split, they are separate to that split, but it can take the refinement of all the splits, but what it is not more than the same. So this is where you think that's there? No, no, unfortunately. Oh, yes, man. And I have another, it's right somehow to get simplicity from here, because otherwise everything will become much easier, you can get more geometrical pictures. I did not succeed. But if you say, if this thing is there, so then every subset is there as well, so this sounds to me like scenarios in this sense. Ah, yes, yes, yes, yes. According to definition. So this is possible, sorry. Just, just let, let, let me understand this. Yes, you may, may, may consider it. Yes, yes, yes, in this case, yes, yes, of course, it was exactly what I tried to do, but the point is that the vertices of these simplances are all bipartite splits of the system.

57:30 And, again, I could not find, manage to find any direct interpretation of what are this, anyway, all bipartite splits, all possible representations of our system as bipartite. And that's why, since I could not find any picture of this, what was the meaning of these vertices, I would not relate these things with simplices. It's the first thing. And the second thing is that, again, using simplicial complexes could be good if we would have some differ, they would be very different. But here, if you simply have this lattice of partitions, it's fixed just by the only number, one number. So it is too rigid structure, and again it indicates probably, unfortunately, because I like simplicial complexes, unfortunately, maybe normalization. Why do you insist on a bipartite split? Because they are, this lattice of partitions is so-called atomic lattice. Atomic it means that any element of this lattice you can represent as an upper bound of a collection of these small elements which are not equal to today. But these elements are exactly bipartite split. Just for this particular... Would it not work if they were tripartites? No, because how can you represent a bipartite spree as a refinement of a bipartite spree? No, you must have below the coarsest ones, which you cannot already make. Look, you have such a kind of structure of lattice. I would like to tell that any element from here is represented as a joint of some elements from here. But they must be just from the very below, because if I would like to say that any element is a joint of these elements, these are not, that I have to take something which is the lowest. but the longest are bipartite splits or of course you can look at this picture just the other way

1:00:00 around and consider everything as if you are living this to this but these are the splits of the following forms that you have this big set and you just unite two elements but all other are separated i see how what does it mean in terms of partitions of our future multi-partite system is every i i have very silly question and i apologize because everybody understand what is Why partai, do people understand? Because I don't. Why partai system? I simply don't. Could you please tell us? I don't know, maybe you know, but I don't know. I mean, because you see, this sort of... So I'm thinking about splits or partitions. I have this set, I. Yeah, I mean, I don't understand this word, bi-parti. You understand? It's columns. Something which consists of bi-parti. It's a two-element partition. One minute. Something which consists of bi-parti. Yes, so you, you feel why, or you, I feel, for example, we are a multi-parter, we are a 1, 2, 2. I can know what the name word means. So, so, do you understand why, do you understand why a tripartite wouldn't work? Yeah, I think so. Alright, next one is... Alright, but you want to explain it again, I'm sorry. Let me explain it again, because I, I, I have to explain it clearly, because as a right side, it means that I, to me it's a matter of things, but if I cannot explain it, yes, I don't understand myself. So, I would like to, for any split, for any, any split, to tell them this split is a refinement of some basic splits. And I don't want to have too many basic splits, but I want to have the minimal number of basic splits. Oh, if you say it's minimal, then that answers the question, but you weren't insisting that it be minimal explicitly before. Why does it have to be minimal? Is it just a desire? Look, look again. For example, you have a linear space.

1:02:30 You would like to represent a vector as a linear combination of some basic vectors. Of course, you may consider big systems of vectors and representative vectors. It is suitable for many points of view to consider a minimal system of vectors using which you can represent any vector. But here just the desire is of the same kind. I did something very similar to this on simplicial complexes, which is why... Yes, of course! And the point was, I deliberately was trying very hard to make it not bipartite. I made it arbitrary. Because I thought I wanted generality. But then you're going to... In such, in this case, look, the bipartite splits are points. Tripartite splits are edges. In general, what are the bipartite splits, what should you call them, they are redder faces, and so on. But I'm sorry, I don't understand the answer to that question because that seems to contradict what you, I'm now being completely naive, I'm missing something, that seems to completely contradict what you just said to our letter about not being able to get simplicial complexes out of this construction. Isn't what you just said the definition of simplicial complexes? I'm not able to get a reason of this. It is not trivial, but it is, you know, the problem is the terms of product structure of Herbert's price is too complex to be represented by synthetic compacts and so on. Okay. You know this, this, now I know it's first part of it. Sure. We have a fixed tensile product structure, we do not vary it here, and even with respect to this fixed structure, we have such a variety of states, of the structure of states. But this variety of structure of states, it involves some structure on the splits as well. And what is essential, these invariant elements with respect to which you cannot distinguish English if you have states in your disposal. They look like this. They are all their ideas. Let me check, I'm not completely sure that this is especially complex, because if they are complex, I feel like...

1:05:00 I remember that there could be some problems with this dimension, maybe it's not so well defined. So this I remain open just by that reason that I didn't want to work with the fixed kind of product. And I wanted to pass it to algorithms. But in here I simply took some hints, how to approach this, the definition of multipartiteness in algorithms. So, may I try to proceed? Sure. Because somehow, you see how the states are classified with respect to this dual relation of separability. Because suppose you have fixed this order ideal, and with respect to this order ideal you have some set of states If you take something bigger, it means you will take a proper superset, no, a proper subset of this set of states. Because the stronger partitions means I already have less states. That means that the set of states itself automatically acquires the same structure. And it is worth just the statement that equivalence classes are just these equivalence classes which are between two, which are not separated by audiences. and I can clear all of this. Now I will repeat this in a more general way for algebra, so... I believe I understand what you're saying. That picture you've drawn on there is less clear than that. You made it for me. Maybe next time, five years we used transparency. Five years ago I still had a big list of topologists and I had one transparency.

1:07:30 Now probably I have to draw a couple of partition letters to show, because I have no place. Yes, really. Well, let us try to make the best, let's make the best. Let's really try to... ...to research it rightly, no? I mean, is everybody aware what is the context of the problem? I was just going to ask, I mean, where are you going? Can we get back to a broad view? Could you take some short broad view? What is a multi-partite? So I would like to introduce the notion of multi-partite structure. Now why do you want to... You're perhaps asking a question... Moment, moment, I'm asking now. Now why do you want to introduce multi-partite structure? Because, what is the count of them? What is the motivation? Several, several motivations. The first one was, as I told, in Imperial College, to bring some background for our quanta-topological activities. Because we get spaces containing points, regions, and causality, but how can we test that something is located in a different place? which consists of some systems or some entities, and I would like to have some, maybe not experimental, but in terms of state, in terms of something measurable. How can we perceive this multiple dynamics? It's the first part of motivation. The second one is this activity is related to quantum computation, because there is so-called De Vincenzo checklist what is needed from a quantum system to play a role of a quantum computer. It is just exactly the list that you must select some operations which are local, which are easy for you to access. Then you must have some restricted class of integral states which you also should be able to furnish. access to local operation, to any subsistible, it's just something like four or five.

1:10:00 So at least, my basic idea was that maybe it's not the first way just to try to make various kinds of experiments, to trap ions, nuclear magnetic resonance, and so on, but you need to look around, because there are instilled strays in terms of slow temperatures, there are many systems which have infinitely many degrees of fluid. The point is that maybe we can somehow organize the algebra of our observables to work with the systems in such a way that, from our point of view, they look as if we have five antennas of qubits. We don't care what is the inside. Maybe they're not five qubits, but maybe it's just some liquid which is up to zero. But for us, just for our traditionalistic means, we would like to see it as if it's five qubits. Yes. And just from this kind of purely structural characterization of what you need for the system to be a computable... Yes, yes. ...computable in terms of the theorem of quantum computability. No, no, not computable. To play a role of a quantum computer. It means that on which you can implement quantum algorithms... Yes. Yes, to be an algorithmic. Okay, that's what I meant to say. No, no, no, not to be an algorithmic, but to be a carrier. yes yes to allow you to implement it understand what it has to do with this observable topology of space-time because what is common that I don't What are the problems? For example, when we consider quantum state teleportation, it is very difficult for us to entangle remote states. So it is hard for us to perform remote and entangled operations. Now, if we have some operations in our disposal, maybe we could somehow arrange them, all of them are more or less easy for us, but we could somehow structure them in such a way that some of them we call local, and they really play the role of local operations. Some of them we call entangling operations, and they really, from the point of view of just that number of observables which we would like to have, they would play the role of You asked for the big picture, can I give you a sound bite for the big picture and tell

1:12:30 me if this is wrong? You want to get your elements from your operations. You want from the operations, you want to get your algebraic structure and from the order ideals, the reducible representations in the algebraic structure, you want to get your elements, you want to get your points back. Is that what's going on here? To get it, I don't even know more, to simulate. To simulate, or to get back, okay. I, I, I do not say that it is a . No, no, no. It looks, looks to me as for an experiment, but it looks like multiple. Right, but there's some kind of diagramming the, you know, the lines of, you know, the flow of structural intelligibility in the notions involved here. You're treating the operations and alongside the operations the algebraic structure as fundamental and aiming to get back the topological in a more narrowly sort of space-time geometric sense of topology structure out of that. you know now now right at this moment i'm definitely not ready to speak about space then because now i'm more or less could be able to speak about space just a partition of space because there are not events it's a region in regions in space yes and again my basic motivation that i don't i want to have operations they don't have space states what does it mean i I further an operation and the states seem to give me some numbers, give me some statistics, to sweep away these intermediate things. Now, I have tried to introduce the notion of this virtual multi-partite structure, the ML multi-partite structure, and an autogram. Again, try to mimic this, somehow to take something from the tensile product filtered species. Again, we have this archival. And I consider the collection of this sub-archivaless, such that it generates our algebra, and such that they are disjoint. Is it, is it span, linear span?

1:15:00 Yes, yes. No, I, I, yes, yes. I agree that they generate between the two neural algorithms and the other one. What I do not require here, unlike the situation with human spaces, I do not require the elements of this algebra to commute. Because usually when you have the analog of the structure in human spaces, Yes, you can, if you have AI and DJ, they also form something like AI times one and something, and so you run DJ, and they always do communication. However, I would not like to make viruses. And the reason it's a problem is that I'd like to stay to keep myself operationalistic, because it may happen so that we have not all states are in our disposal, only some states. And with respect to these states, what we do have, this operation may commute. We cannot feel it. No correlations will occur. Maybe there are some other states which we did not measure. They may not commute. That's why I would like to avoid this requirement. And all any such collection, that is this set and this collection of algebras, I call a multipartite structure. I am a little bit puzzled because the whole idea of tensor producting is to actually get things that do commute. I can emphasize that I would like that they would commute but only with respect to my operational needs. Because, for example, my aim is to simulate, suppose I have operations which do not commute. Again, return to the representation of this object as operators in that space, that suppose they, in fact, they do not commute, but I, my space of states which is available for is in just a subspace of the whole space, and in this subspace, this is new. They commute from all factors which are available. That's why I don't want to put the requirement of commutativity, just because it is not testable.

1:17:30 How do you test that the two operations commute? Because you are checking by the result. I don't want to reduce the termism here. That's why I'm ready to expect that sometimes it commuted for a couple of years and then once they end up commuted. I forgot such a scale. It's the first thing. The second thing is that it is not, I don't know, it's not needed. So why should I do that? Do we have any structures that are like that, even like that? Like that, but of course it's exactly the tensor-products branches that are full. You have a different space, but similar tensor-products branches. They all are special case. They're a special case, yes. Do you want to look at something more general about that? Yes, yes. First, I would like to... General, and second, I would like to have to speak about algebras, but not about particular representation for them. Sure. I mean, I'm totally in agreement with you on that. and to communicate, basically, just in terms of possible, so I'm calling it from there. I don't have full sympathy with... but you see, my thinking as a physicist has always been that somehow you have a definite algebra but somehow by doing statistical averaging you'll get these things. They'll be non-commuting at the more fundamental level, but then if you statistically average into regions then those regions will be committative. So it will be a kind of an approximation. But you seem to be suggesting something much more than just an approximation. Is that right? You know, it seems to me that maybe we are speaking about the same things. Maybe, maybe, maybe I'm wrong, but again, if I would like to translate it to my language... I'm trying to translate it to my language. Only something which I could call macro-states are available for us. Right, and those macro-states commute? The states do not commute. The algebra which you use to... Yes, yes, but the operators with respect to the states do commute. But how do I check commutativity? I simply, again, introduce the notion of the computable state. Now, let's introduce the notion. Yeah, come on, let's go through this one.

1:20:00 I have to follow all the things, but without the notion of tensile force. I think, you know, I can do that. Alright, this is what I wanted, this is what I'm interested in. So, now, let me introduce something like, Capiton Mu, it is a set of all multi-partized structures. Now suppose we have even multi-partized structures. Now suppose that we have a state. What is the state of an algebra? It is just an element. You take an element. If this element is positive, this should be positive. If this element is a unit element, this should be equal to 1. That's all. But now, what are these? A i. It is a subaltern. Means, if I take an element from this A i, it will be an element of A as well. And I can calculate, oh, something of P1. I can calculate, it is a number. I can calculate, oh, of P2. It is a number. I can multiply it. Or, you can take the product. So, this is a well-defined solution. Now, again, I take the same A1, A2, and so on. This is a number and this is a number. So I think it's just, I think, right the definition of independent variables. Yeah, yeah. What is an independent variable? It's a probability, independent probability of a problem. Yes, yes, yes. This distribution is product of this state, but when we are speaking of distributions, the state is a decomposable state. But I think that if it is equal, then it is decomposable.

1:22:30 Yes, yes. Now, what do we know? We can, if we have a collection of states, and if we take any convex combination of a collection of states, we make again a state. But now we take all the composable states and we take the convex hull. Sorry my questions. Yes. I allow mixtures of the composable states, and I call them the state set. OK. Reasonable. No. It is unambiguously defined. I don't have to introduce anything new. Now, suppose I am given a state. Then I can ask, and I am given a multi-partite structure. Then I can ask the same question. Is the state separable with respect to this multi-partite structure, or it is not separate? This, I have to tell you one thing. Even for the simplest case, this is a mathematical question which is not answered. Of course, for this more complicated case, it is not highlighted as well. But again, more modular this, but it is just a quite definite mathematical question that no not of the level of material and so on so it should be anyway this this is again an ambitious well-defined relation so if you are given a state it is acceptable or it is nothing you can see and again they have quite, quite the same duality. Isn't there any general theory in algebra which is answering this kind of question, because this means when, when we have this equation? Which kind of question? This? Yes, yes, I mean when this equation is studied, so then it means it's separate. I mean, I don't know... It assures that there is no general theory. Does that mean it's the way it's actually... depends upon this... this multi-partite structure? Is that...?

1:25:00 Because I ask this question with respect to this... But you're doing it for... Yeah, but you're doing it for a fixed... Yeah, for a fixed... But look, now I have all multi-partite structures here, I take any multi-partite structure, any state, and I can ask, is it separable or is it not separable? And this, as I call this, is the main duality between states and multi-partite structures. And what you are thinking of next step, I think from the right to the right to the right. Now, so what you're complaining about is you don't have a way of thinking of answering that question. Yes, yes, yes. But perhaps... But in a way, there is a way of feeling, because the answer is yes or no, so you've got only two possibilities, you think. I can describe it generally. It is a relation between two sets, and if I have a relation, I can introduce the so-called Moore closure, I can consider closed subsets of states, closed subsets of conceptualized structures, I know what to do with all this, but I would like... it's quite purely algebraic i should say next level algebraic things like not external choice very generally but they already quite forget about particular structures of this and i cannot catch what i cannot catch is just how how do i use that it is just not a set but it's really a collection of subalgebra such that they are disjoint you know it's it's a bad mathematics if it does not constraints which I introduced at the very beginning. At this stage, unfortunately, I am now. Yes, passing it out here. Yes, if it is, of course, I'm following this paper. I would like, maybe, you could think something, how could it look, not physically, but operationalistically, and you might look at some pictures, because it may prove this unsemitic way. Oh, Jesus. You have some pictures. You have some pictures. Well, I mean, you see, the truth is I'm not sure... I mean, I think we're all in the same boat here, whether we're not partitions or physicists, if we try to come through this with some physical intuition.

1:27:30 i mean this is the problem that that that you know a number of us have been sort of banging our heads against the brick wall i mean we're hoping that you guys you mathematicians will actually give us a clue and you're coming to us and saying perhaps we will give you a clue you see the the the way the physicists would would would the way i would say I don't know, I don't blame other physicists, but you say that somehow at this point it seems as if some new structure is required, and it's not clear what that new structure is. This is the problem for the physicists, you see. I'm quite sure that this structure exists, I think I have to look better. That's why I'm asking for some physical, you see maybe it's more similar like something. Well, how would it happen with the cities and such? It was quite okay, quite hard. They were in number series, I think, quite hard. I was just speaking to my colleagues at that time, I worked in the economical university, and quite occasionally one of them said, Oh, what do you do, what do you do, what do you do, what do you do, what do you do, what do you do, what do you do? That's why I came up with the... But what do you really want? I mean, what is the purpose of that? What do you really want to get out of your algebra? Look, now we have this huge algebra. We have no access to all equations, but we have somehow reconstructed this huge algebra as a potential. This big algebra here has a very big set of states. Again, we do not have access to all these set of states, but we have some of the states in our possession. Then, again, some of the states are, in a sense, easy for us to maintain, some of them are wars. Yes, some of them are very fragile, you know. Yes, yes, yes. Yes, yes, and I'd like just to put the things in the other way around. So I call, I simply call the states which are easy for me, I call them separately. But if I call them separately, I must provide the separability structure separately with respect to what? Then I take this simple state again, I simply repeat as I did with... ...tens of products, but only on this level of multi-partized structures. And then obviously you'll try to recover the elements between which you can distinguish with those states, separable or non-separable.

1:30:00 So we've got a generalized notion of elements here, which takes account of the non-separability of these states, from a physicist's point of view, what constitutes a measure in that way? Yes. And also, because we've got all these entangled states, we can't do anything with the entangled states, but we always reflect them in some classical... Yes, yes, yes, yes. And I said, we don't know how to do this. We assume, you see, we assume that there is this. But that's what you're doing here, though. But what I think might help, I can't say, but I think what might help Romare, is if you were to say, concisely, you're the best person to do it, what it is about the Hilbert space framework that you think is inadequate to express the most certain aspects of the structure of the state space, and particularly of the pay space. What it was, for instance, to DeRoxel way back, when he said that, you know, the Hilda space framework was too restricted. You've already tried to do that with Roman. You've already talked about that. We talked about that at T, and I wasn't getting anywhere. Sorry, I didn't know you'd already talked about that. I went down the wrong direction for Roman, because, you know... You didn't tell me you'd already got at the speaker before the seminar goes on. do that to fix things you know smoke filled rooms before the way i i came and arrived at this was was first of all there was a philosophical background and the second thing that i came to it was whenever i was using the quantum formalism it seemed that i was not talking about objects i was talking about process and that's where the sort of physical ideas come I was talking about transitions, I wasn't talking about things existing as such. Transitions, but you only have to put some mathematical object which stands for just transitions. Yes, and they're the algebraic elements. That's where the algebraic structure comes in. To me the algebraic is not about observables, it's not about, it's actually about process, which is... And it's from structures like the idempotence in the algebraic. I go back, sorry, I go back to the beginning of the last century with Hamilton and Grassman and Clifford and people like that, who were arguing that algebra is actually a description of process, of movement.

1:32:30 Hamilton had this paper called Algebra, the Algebra of Pure Time. He said, what am I saying? Well, you see, he doesn't like it. I, I, no. It is about... I'm coming from a very different way. I understand that, but why... Because, if you... why... why do you take two... Because, to me, the algebra which, and you poo-fooed this idea, was that the linear combination is the linear superposition, and I need that element. But look... I need a vector space, in other words. No, I was speaking about measuring, for me, just to add the value, to add numbers. If you are speaking about processes, what is multiplication? It's quite straightforward. You do this thing, you do that. And it's a whole sequence, and it stands for a sequence. No, just the product. Yeah, but the product, to me, is a sequence.