Calculation of Fine Structure Constant from Combinatorial Hierarchy

0:00 I don't need to go to this. I thought we'd get right there. Now, what would you do? No, you're never going to sit there. Let me just say a little bit of background about what I want to do this morning, because not everybody was present at my unnecessarily obscure paper earlier in the week. And in that earlier paper, of a somewhat mathematical kind, I showed how I got what seemed to be a very successful calculation of the science structure constant, to an astonishing degree of accuracy. since then I've had a great deal of help which I'd like to make public now my corner has aided me tremendously over presentation I mean I really think of him now since yesterday as the Alistair Campbell so watching the proceedings will be very much better than you heard last week and it also will have improved in content through discussions that I've had with both Lou and Arletta. So that's all I wanted to say about the paper. All that one needs to know for the present discussion is there's this astonishingly accurate calculation of a physical consequence. And what I'm out for today is to try and formulate a situation in which such a thing would be possible. Really, there are two senses. I mean, I want to ask how could it make sense for the sort of calculation I did to be correct, and there would be a subsequent thing. I don't want to talk today about the truth, but really it's about how it could be sensible that a physical constant defined in terms of, usually defined in terms of the length

2:30 constant and the charge on the electron, should come out of the piece of algebraic structure that I expose. I have a question which I've asked you before, but I'm going to ask it again. Is there any way you could apply the same argumentation to the reputational question? I haven't done it, so I can't say yes, unequivocally. It would be an incredibly powerful result. Thank you for that. I'll have a look. Two comments. We can't present it. Just one. You're using the same argument. Yes, well, that would... because then that would, um, back up the old, that's much more difficult, I think. The gravitational constant measures of zero-degree magnetism? No, and that would mean that we would be able to predict more easily than with the time-structure constant. Oh, that's right. You'd be talking to Alistair Campbell again. Yeah, people have, one or two people have tried something like this in the past, and the one thing I want to say a word about is, of course, Eddington tried something like this, and when he got his number, which wasn't as accurate as mine, but still it was an approximation, information, he then tried to justify what he did by connecting his work with very conventional physics, I mean by churning out the order of stuff, and then when he'd done that, point to one bit of the equation and say, there, there it is, you see, so what I got was actually the fine structure constant, hooray. This never worked for him. He never made it clear. Nobody could understand quite what he was doing. And that general course of action, I think, of trying to identify what has been calculated by going to the orthodox physics equations, is important, I'm not sure. I don't think there's any mind. The argument I want to make this morning, where this discussion comes in, is I want to try and put more flesh

5:00 on the bones of a general statement that Ted and I have said to each other at various times. Well, it's just that the prime structure constant is one of these things, we call them scale constants, which are more basic than other things. So they lie at the foundation of it, and so it's not altogether surprising that one could calculate them without doing the superstructure first. And the purpose of today's discussion is to help me to make a structure in which that statement which Ken and I have made to each other is actually a reasonable statement, because when one comes to analyse it, you know, not just in a happy conversation, What does it mean that some things are more basic than others? How can one have that concept in scientific theory? So it's to try and make that kind of thing precise. But I wrote these four small pages in a kind of sub-Fittgensteinian way, which were on the table, and everyone has been studying them since, I hope. Well, some people make RIOs view or copies here, if anyone would like them to... Well, so that's the idea that I want to flesh out. and the little things you had were an attempt to do it by relating it to things which Ted and I have done in the past. So if we could go, it seems to me, unless... Do interrupt, of course, at any time. This is supposed from now on to be a discussion. Where I begin by suggesting that If we're going to be able to calculate alpha, we need a special way of looking at what physical theories are, and this way of doing it was put up by us, but it was really put up by P in those papers on the concept of order at the very beginning of the sixth. The idea of scientific theory in a generalized sense, elements of a theory, it says here, 1.11, maybe observations, thoughts, sentences written or spoken, or manipulation with bits of the physical world.

7:30 So we're stressing at that point that there isn't a sharp distinction between theory and experiment, it's all a seamless whole. You may be turning knobs or you may be thinking or you may be writing notes. But I think saying that theory is human activity, because all of them seem to be human activity, I mean pieces of experiment. I must make notes of what everybody says because otherwise I won't get out of this I think that of course it's obvious from what I've just said but which is quite commonplace amongst people who wouldn't take that sharp view they already have reached the position that the experimental thing has meaning only as part of a theory. There are no good facts. Now, the next step, we've come to 1.2, is that theory develops from a simpler to a more complex form. When it gets to a more complex form, and then different experimental results will arise and the point that we're wanting to make here is that if these higher results are different from the ones lower down, they don't invalidate the ones lower down because the ones lower down can only be tested in that simpler form of the theory that you have there if you were content with them when they are the ones at that level. One gets a more refined result higher up at a more complex level. That's not inconsistent with the other. Sorry. So you would apply this idea to, say, calculating the orbit of matter as well? Sure. Yes. Yeah, I have a trouble why I say this evolution is from a scene to a context, which is very complicated comparing with the next, which is like a conceptual mystification.

10:00 So, perhaps you mean something else. No, it's not a conceptual, it's just the opposite of a conceptual decrease of the elements you use. Of course, is much more intellectual development and much more theoretical elements than it is very simple on the conceptual level. I do not speak about the Copernican because the Copernican was not at all any development of the Copernican one, it was rather going back on a simpler level. In fact, the Copernican has been more complicated in both aspects as well as theoretically, if as well as in the model, then Copernican. Copernican just had an idea which later on proved successful in the physical view of the past. I think I'm sorry to interrupt you but I don't know if you believe if this theory develops at all, not now, I would agree that there is a development from a simpler to more complex theories, but I wonder what is this theory? Is there a hyper theory going on from Aristophanes or Hipparchos to Smolin? I don't, they are theories and they are killing each other or not killing each other, they are whole and left, so they go in steps. Yes, all right. This shows that we're using the word theory in slightly different senses and I'm intending to use it in what may well be an unorthodox sense in which I see a theory of...

12:30 which, to take the other example, which was, at one stage, was Newton's theory and then it becomes general relativity. Yes, if I might make a very quick observation there. Newton, it's all really classical Newtonian theory, But it's in a completely different coat each time, and it tends to get, well, more elaborated. And that's, I think, what you mean. It's still Newton's theory, but the axioms are the same, in a way. To go back to our letter's question, if you're thinking of epicycles in the, as it were, the final form, when they'd all been put in and then jumped to Newtonian gravitation. I can see that as a difference, but the example I would take about every cycle is, you know, when you keep putting in an X. That would be, that would be the development that you can't see. Yeah. Right? Yeah. Staying in the sort of human systems, I think the word in that first sentence that's bugging you is develops. Because develops makes... No, no, it's the sort of sense that it always goes from the centre to the... Yeah, that's what I mean. Well, develops gives that sense that it's always going up. Okay. Devolves. Well, not even that. I just... Yeah. The point that it's maybe bidirectional. I mean, it could be something like theories exist in both simpler and more complex forms. And there is this looping that they do. Section 2, and this is where our, this is trying to put some good sense into the idea that we refer to often in our discussions of process.

15:00 So I start with the construction of the universe from one point of view is by the process of experience. It's the universe of this world. Well, it's this universe as well, because that's what we're talking about. I mean, I'm not making a specific cosmological point here, but this universe of discourse... Can I have one? Yes, I'll let the answer. I'm saying that... I'm trying to get to the abstract position which I want to adopt by two steps. The first step, which really comes more or less directly from Kant, I'm saying that individuals construct the universe around them by the process of experience. Kant says this only, he puts the emphasis on experience. I want to put the emphasis on process, that you look around you and you get bits of information which you then somehow construct together to make the universe around you. That's why I said from one point of view, it's one individual. This is not what I'm wanting to use in the structure I'm building, it's to help me towards what I'm going to do. Can I say that? I do actually feel a problem that maybe just my thing believes that at any point will... Sure. I mean, the tabula brasa problem is one that comes upon me at various times, and I push to the back. When one's proceeding with one's life of constructing the universe, if that's the job you're doing, of course you've done a whole lot in the past and you'll spend it and so on. But you should perhaps, in order to pursue this sort of special case which I'm using as jumping off boards, I don't want to go in too much,

17:30 when it's first few instances of life, there's a lot of hardwiring. I have firmware in the DNA. So where do you still get more from? There's a lot of hardwiring, yes, but the hardwiring there is designed to grab more. Okay, so the tabula might not be Raza, if you see what I mean. It might have a structure on it, but you've got to write into the structure about what you find out about the universe. so I don't have any difficulty with this at all I simply know that how we gradually pick up our individual view of the universe at the point I think that I was making is that it is an individual view in any way we make up our view and it is actually quite difficult to communicate your view to anybody else that we're discovering But our disagreements are not so strongly related to different experiences because mostly we don't even have so much experiences. The difference are between the models or even between ideologies attached to the models. And I again have difficulty because I couldn't even imagine how the construction of an universe ever could arise in experience. I simply would, I think the word is refuted. That's why you're a philosopher. Yes, that's true. It seems to start in a sense historically in this way because the oldest cosmological concepts are mythological concepts and they are not in a pretty easy sense derived by experience, if there are also elements of experience, for example, organizing the life by bringing it, or making it organized by the planetary behavior.

20:00 Let me try and be a bit more precise about, an example of this would be that, one, which probably everyone would agree in the construction is that we have a lot of experiences coming in and we systematize those by saying that the world has three dimensions. Now that is that construction of a three-dimensional world which I'm appealing to here. But we are the three-dimensional objects just from the beginning before we have any experience. And again, it is, you know, I had to speak about actual existence and I always try to make a sharp distinction in order to what you now want to bring it in some correlation. You know, we live in a three-dimensional world, but there always comes a moment what that means. 90% of the people won't care about and think it is stupid and, you know, half, I don't know what it is with the oldest theorists. I think they killed most of them, but some survived and became priests. And it is something completely extra added because all the other guys are very well in three dimensions and good in killing the priests or scientists into coming. They are much better in killing than the scientists they take in a while and then they become better in killing with other means. They have no problem. So I think you must not, in any sense, construct the universe you are living in. And these people which do not construct the universe... When he's talking about modelling, that's why he's using the word construction on that side. I understand very well. If he comes to me when I'm a nipper and I say, there are all these corpses, that's my model. I doubt the ducted element it is.

22:30 That's what I'm against. But I can move on. Because there is only half an hour ago. Any resection by the eyes or other organs? So a raindrop falls on a rock. The rock has an experience, no. No, but you see it fall and it splashed. So then you assume an observer who makes distinctions? Yes. In this particular bit of the... No, in this particular bit of the argument I assume... Distinctions made are beyond experience, in the sense that many distinctions can be made upon it. Agreed. But I don't want to be tied down too much because I'm just using this as a step to through the next bit of the model of having the experience is put into a more abstract form. Well, it's not got rid of, but I'm not really wanting to be tied down to this one observe. This is slightly analogous to the situation where you look at mechanics from one point of view, and then along comes Galileo and says, oh, you might be moving. So you need a transformation to do that too seriously. I'm talking about one point of view here, in order to get me going. What I want to say about this is, this is, this process comes... Well, the process involved, as Lou has jumped towards, is that the university divided into two parts, which could be called known and the unknown. Could you call it something different? At this stage I wouldn't want to, Ted. Later I do want to, because at this point we're talking about, from one point of view, a particular observer. And I think what he's doing is things are becoming known to. No, you'd rather not. I think all this becomes, to me, utterly clear if we put the word conceptual in front of the world. They're taking the world, the universe, literally. What you're talking about is an individual's concept of gradually building up from experience. Yes, I am.

25:00 Right, right. Or maybe a group concept. Well, he's coming on to group later. But for an individual, the conceptual universe has to be identified. I'd like to just pursue with Ted a moment why known and unknown are objectionable in this two-point. Well, all right, so that's a reasonable reply. My prediction is to talk about the system in an abstract form, not the universal form. or in any kind of objectivity can't be introduced without really presupposing a form of the objectivity if you talk about things being known or unknown. I mean, if you said that they were... if you said that they were seen in the course. Anyway, you asked me what... I'm sorry, I shouldn't... No, that's reasonable. I think to some extent the point is that you've already got further than I have at this stage because you're wanting to work towards an objective view more than one server or something like that, whereas I'm proceeding in a rather pedestrian way a little at the time and generalizing. Well, I'll go on to 2.2 anyway. where the critical idea is a sequential one, that it's a process. Things, entities, may become what I've called known. Just one word further. Really, I've characterized your objection to the argument in this format that by starting in this way and then generalizing, when I've generalized, my starting point will not be a possible one, and so I'll generate an inconsistency. At least until your next lecture and look at it from this point of view. This sequential character of the theory has to be built in from the beginning. So one result of that is that what we call the theoretical description, some people might call the mathematics of it.

27:30 But we don't use that word when we can help it, because it brings up all sorts of overtones. I mean, for one thing, it frightens philosophers, and also it implies a whole body of orthodox mathematics, which we're not necessarily taking on board. The theoretical description has to change as the process takes place, and at one time we toyed greatly with our intuitionism, but we now are not actually taking an intuitionistic approach, but we are being careful to develop the theoretical description. Because the theory must build in this sequential character, just be… It's always the same, is it what you're saying? It must be, yes, the process must be… I mean, what I'm trying to say here is, oh well, yes, but you mustn't just say, of course it's a process it happens and we learn more about things. We've got to build this process nature into the theory itself. The theory has to develop as the process proceeds. So would you say that your own mathematics is going to non-conceptivity, non-associativity? No, I'm not quite sure whether that would be, yeah, maybe it would. In 2.3, I go to the next stage, which I thought of as overcoming the problems that Ted has been raising to the earlier stage. When I say correspondingly, the construction of a more objective universe is by an abstract process. And I thought this was what we were asking for, Tim, an abstract process rather than known and unknown. Yes, yes. Do you mean by an abstract process, a process of abstraction? Or an abstract process? I mean a process of a more abstract kind than the one I was talking about up until now. 2.31 is probably, need not be put there,

30:00 but my natural weakness would have led me to say by an abstract process of experience. So then I put in why I mustn't say that, but maybe some of you wouldn't even have wanted to. But if you start saying that, then you're losing the drive towards the objectivity. In the abstract process, the universe is again dividing it into two parts, but we don't use the words that Peg's objective to. One of these parts will be a finite one, and the other might not be. I don't know if it corresponds to my knowledge here, because there's only been time for certain numbers. I think you are still a little bit captured in this. There is the thing in itself, the unknown, or in parallel, and then this is a nice collection of conceptualization, which we are aware of, and you remember, I think, that I said that Kat is sitting on the fence, and I'm afraid four times, two hours later he would fall down. in the naturalist camp or in the era camp. In the end, it is a painful thing to say, not the past. It depends, of course, as an objection of the past. Yeah, I take your point. I'm good about that. I mean, in some ways, if someone says I'm sort of a bit calm down, I'm quite flattered. But then taking into account your paper, whatever it was, I'm more uncomfortable. Okay. So, when entities come into play, then one can draw inferences from the results, from the statistical analysis of those that are in play, and these inferences, we, in these inferences, we, as I've been telling now, when he did it, always assume that we've generalised the Ergodic principle that one will do statistical analysis of the model, taking the view that probabilities are to

32:30 be assumed equal unless you've got reasons to the contrary. Er, should we not? It seems too technical Tony in the sense that I wouldn't want to draw those descriptions. Yes, that's all you want to say. I'm happy with that. That is a regenerating, we take some objective, are there? Yes, I know. Good question. Not ones you could use. So, a partial answer to this would be that I'm trying to construct a description which would allow for a number of observers to observe the same universe and compare their results. That's only a partial answer. I mean, I think probably... Are statistics necessarily the others? Even for the one observer, because it only has a finite number of entities at any stage have come into play. I mean, he can look at those and say, oh, there's twice as many red ones as blue ones here. And then he can infer that the whole universe consists of twice as many red ones as blue ones, but this is a statistic. Nothing in absolute circumstance for this reason. No. Right. Right. If you take 2.3, 2.31, 2.32. I don't want to hold matters up. I'll write all things down. But what you were saying is the idea. So you have no interest in objectivity, but you said something. Yes, the idea of 2.3 could be interpreted as... One meaning of being more abstract is... It's not the norm, but that is the way of... Thanks, I've got that down. Good. In this abstract process, since one no longer has these labels like known and unknown, the entities might go in either direction.

35:00 I think, really, that I might, because time's getting on, I might say, well, shall we leave three, take three for red, unless anyone's been through the paper and thinks that there's something in three that they want to form this. The idea in four is that there are certain numbers around, and I've called them stale constants. To stress how important I think they are, I put it in capital letters. And the crucial thing that I'm wanting to get at in thought is that there are these things called scale constants. People haven't always known that there were. The idea just began to develop a little in 1899 with Plum, but a proper emphasis on them really depends on Ted who had taken aboard the essentially strange character that these constants have. The person who came a bit near it was Dirac in 1938 when he noticed that they fell into what he called in three groups because people, you know, some of them are order, one, some order, ten to thirty-nine, some order. He's going to get towards this notion, but I think it's only we who have emphasised the extreme importance of it now. Yes, I think that's part of the story. But I think Planck glimpsed something more than that when he was noticing these facts. Which, of course, I mean, the fact that a set of dimensionless quantities for mass length and time was possible could only exist once Planck's constants had been constructed because you were needing to make them.

37:30 But I think he glimpsed something more. He put it in an odd way. What he said was, by these means you could make absolute units for length, mass and time, which would be common to all cultures and all communities in any part of the world. So he was looking at a particular generality which they had. It wasn't the non-dimensionality in the sense of MLT or 3.0 that I was involved using non-dimensional concepts. See, what worries me once people talk about modelling is, it's just a personal worry, though. Then I think, oh yeah, you often get non-dimensional things. I think of the people who do hydrodynamics, and they say, oh, you know, the Reynolds number is so-and-so. They construct non-dimensional things, but I have to somehow say, no, that's not the sort of thing I'm thinking of. Mine are more fundamental, somehow, and it's that more fundamental that I'm trying to get to in this discussion. Well, now we're getting more onto familiar ground. As I say in 4.2, one such constant is the so-called fine structure constant, which it got that name for historical reasons to do with the fact that the old quantum theory was absolutely obsessed with explaining sharp spectral lines and the fine structure of those lines. It happens to turn up there. It turns up in lots of other places in quantum physics. Now, I go on from there. In section 5, I'm just referring to Durant and Eddington's attempts to do something about that. I think that's, we can skip that and see if you want to interrupt more when I get to six. Well, the nature of this document is that it does get easier as it goes on.

40:00 The hard bits I think are at the beginning, and I've had some help from you about those for which I'm grateful. Yes, but there are some key points. The question, could different formulations produce different numbers? I mean, that is a very, very important question. You're referring here to... Yes, indeed. I mean, this is what always amazed me about the Dirac paper being published in the Proceedings of the Royal Society He said, oh look, we'll take these numbers and we've got them look back all into three groups. And surely some referee would have said to him, well those numbers have turned up as a matter of history, but suppose you reformulated your electromagnetic theory or whatever, by taking logarithms of everything or, you know, doing everything. quite different, not just, they wouldn't have been of the same order. But they would have been connected by a transformation, wouldn't they? Oh, yes. I read this as saying, yes, but perhaps you could reformulate your physics in some way that these numbers might be different. And if you find you can't, then there's something fundamental about the numbers. Yes, I do. but I don't think you would be able to find it. No, because you think those numbers are fundamental. I agree, I can't run. Okay. Yes, they really do fall into these groups, but isn't it strange? I mean, what I'm really saying is in Dirac's 1938 paper, he does mention that it's strange, but he doesn't really mention just how strange it is that the way that things have been done produce these numbers, whereas you might have thought if they'd been done differently they'd produce numbers of a considerably different kind. you use it's something to do with physics but also of course

42:30 you could take up Mike's other point that if you could manage two numbers or three numbers which are apparently different and not connected then you would have it even further nailed down because you can toss down the gauntlet and say alright you explain it You're taking up here 5.3, yes, which is, because, let me say a word about 5.3. I'm saying, well, I'm not going down either the Dirac route, which was kind of, I think Fondi in his cosmology calls it a council of despair, to just say, oh, well, there they are in groups. And I don't want to go down the Eddington route of saying, oh, well, I'll work out the hydrogen atom wave equation and do it my way, and then I'll find this number comes up in it. That's where they put alpha, and I've got 5 over 137. So that, because that, I don't believe that route is actually feasible, that's why no one's ever understood it. So, then I've got, as it were, two bits of justification to manage. One is to say, and that's what this whole thing is about, say how it could possibly make sense to calculate a number. I mean, if only Viv had been here, because obviously he's had to go, he would have jumped on me for thinking I could sit in an armchair, work out a number that the experimenters find out. Who will be dropping out of it? Billy. That was Galeos Welchman, as he once described himself. That's part of it. But then there is also a kind of slightly subsidiary thing that, OK, if people are prepared to think that I could do that sort of thing, how do I know I've got that one rather than one of the others? and admittedly I suppose this is perhaps one of the weakest points in my argument, that I do that by saying, well look, you see it's that one, because it's about the right size. Yeah, I mean, that's my problem. It's pretty near. But if you could manage two of them or three of them, you begin to say, well look, I've got various pins stuck in this board.

45:00 The trouble is, in some peculiar sense, which I don't at all understand, this one's the easy one. And it's taken me a number of years to get to this point. So, but I accept your... Yes, if we can do more, then... I mean, Keith suggested gravitation for constant. That ought not to be terribly hard. It's like 10 to the 30 down again one, doesn't it? I mean it. Pierre's book professes to do a whole lot of these things. Or the various papers he cites professes to do a whole lot of these things. Okay, the arguments are not all coherent and so on and so forth, but one feels one is treading towards some kind of truth. Yes, yes. He finds a lot of consonants which I don't actually know about. I mean, he says what they are, but I don't know what they are. And that makes it, I find it sort of inhibiting to argue about them without a bit more background. I'll stop now. Do you need some ten minutes more or one hour? No, I certainly don't need an animal, but I could go just a little way there, into six. I draw attention here to the fact that this one particular constant has turned up, and in what it turned up originally in Frederick's construction, which turned out to be closely related to the concept of order ideas which Ted and I had earlier. This one constant comes up by the process which is described in six of discriminating between entities to see whether they're the same or different and labeling them. And then when you have these closed subsets of entities which is go up a level by subsuming them under a single element. Now that process gives one constant.

47:30 If I go a little further along it, I hope to get to a gravitational one, as he suggests. But at the stage which I've gone to, it gives one particular constant, and one sees already in Frederick's original discussion that it's about 137. So, according to the rule in 5.3, you say, oh, well, we know which that one is. It must be 1 over alpha because we know that's quite close to 137. And then we feel confident to refine our calculations better we can do and the amazing thing which has come over me this year is that if you carry that refining process as far as i know how to do you get exactly the observed value of several significant figures so the original i mean my argument here is the original identification is now a slightly different way. One is saying to start with, oh, this is about 137. Oh, that must be one over alpha. I don't get any credit for that at all. I'm just recognising that it happens to be the right number. So that gives me no credit. But then, the next step was David McGovern said, you see, Frederick wasn't quite right because he got this artificial constraint to three levels. And if you take account of that in the probability, then you get a better approximation. Better in the sense of nearer to the observed value. And this, MacGuffer's change, didn't take the 137 away to the 180 or something like that. It just all to the decimal point. You say, well, you know, I'm obviously on to the same concept. And now some credit is due. Didn't get any credit for the first thing of Frederick's. I mean, this is hard on him actually because, of course, certain sense, in the ordinary sense of the word, it deserves credit to have spotted something like that. But I'm giving that up for the purpose of identifying the cost. And the next one,

50:00 you deserve a bit of credit for that. Then we looked at it from the process point of view and noticed that there was some defect in the construction. When we put that defect right, sure enough, the decimal points changed a little bit and got nearer. And then finally, In the English which I talked about this year, I noticed once again that we haven't done it quite right. And when we did it this time, we were bang on as far as the experimenters have gone. So all of the time, we're relying on this first identification to tell us, yes, that's the constant work. And if I may use the longer term, what you have done is create a system. That is the way I've presented it. To some extent, that's just a statement of the actual, it's a historical statement. It would have been, you know, all that Frederick, well, that's not Frederick because he started from such a specific position. but from the time that Ted and I took it over and started improving as we did in the book we could have gone straight through to the end if we'd been as clever as you but we weren't so it's taken a while so I mean I don't object to the word, I don't have a sort of nasty objection to sausage machine but it isn't like it's not a sausage machine it's an aggressive Can I just put a spooky idea to you, which may interest the others, the explanations as to why we think most of the matter we can see from telescopes and things is sort of, so that you get plus energies and minus energies that are exactly the same for elementary particles, or elementary fermions at any rate. he, Rhys says well this is a bit of a mystery isn't it but he finds that you only need to change one of them by a tiny factor, I think it's one in ten to the nine or something and you've got enough matter or antimatter if it's an anti-universe left over at our stage, now going back to Dirac's theory

52:30 with the square roots and things this seems to be suggesting is Okay, it means that the matrix which represents mass is not, in the technical sense, degenerate. It's not quite degenerate, which it is in Dirac's thing. That must be a number, because you're talking about a constant times a matrix whose eigenvalues are plus or minus one, you see. So you add that little number. Now, the first place in physics where I think the fine structure constant comes along and is entirely respectable is in... So, if that was to be more realistic, there is one of these small numbers tucked away, which makes the matrices non-degenerate. And maybe that's the key number, because if you put that number in, you not only have the fine structure constant, maybe, because it only fits together some way, but you also have mass range. Sorry, can I just correct something Tony said? Historically, that's not the first respectable appearance of fine structure constant. because Sommerfeld had already... Yeah, I don't regard him as very respectable. You don't regard respectable? Oh, okay. It's respectable from his point of his position in the scheme. Yeah. But respectable meaning completely quantum mechanical. Ah, I see. But even Dierer used the correspondence principle, so even he's not entirely respectable. That's right. In the spirit of Keith's suggestion, My understanding of the state of play with Grammity, if I pick, is that there is agreement that in some way, using the word involved with respect to . Now, if one was courageous and rather than saying, you know, which Pierre offers us so we can see, is it 3.00 or 3.00? We were so courageous years ago, but the lower ones, I mean the three and ten or seven and so on, don't seem to agree very well, so with increasing age, my courage has drained out of my, bottom of my boots, as Sheridan puts it.

55:00 Yeah, and so at the moment I'm just confining myself to one where I think I've got to really cast no answer. Instead of just saying I think you're going to thank me, I expect, our letter, but I was going to say I think we ought to reverse the process on this occasion. And I thank you for the comments that you have. We'll start with that. Oh, perhaps I can start with that, yes. in 20 minutes