Morning talk

0:00 A lot of them are going to be conquered by such, by morphisms that preserve that structure, so in particular there's no universal one, one that sort of maps onto every other one. Yes, that's what happens here. This would be a model, what you're saying, or it would allow you to construct a model. Yeah, that's what I'm saying, that given a model of your theory... We can construct another category, which is these objects are all the SISs, and these morphisms are the findable maps between them that preserve whichever successor it was in each case, so there's probably no single one that maps to all the others. What I'm wondering is, is it going to do a similar bit on finding the reals? And then you can separate out the structures of the reals, considering that the final ones are pretty much the same thing. So you get my analysis of the reals. But the thing that intrigues me about that way of looking at reals is, really, Real number theory is about large collections of still finite collections of rations. Rations. Of collections of rations. So, yeah, so the distinction between irrational and rational is a kind of, corresponds to the distinction between large and small. Oh, yeah. So, something I think... There's a curious thing that fits in my belt. So this is in our own, we are counting our wits again, is that the resulting theory of the real looks so much like SDG, except it's SDG, but the trouble is you don't have the square zero into the decimals, and in a straight forward sense, you can get the sort of square zero into the decimals.

2:30 But we can't, we can't, I mean, what is, what's the principle, the truth, the sort of Pons-esque norm? It's not, it's the, it's the, it's the cancellation. We can't get that right. You can't say that two numbers agree on all of them for the test scores. Then they're in there the same number. Rationals can only be expressed by taking a large numerator and a large denominator. No, they're not. But they're new in a certain sense. That's the curious thing. But the point is, there are different levels of infinitesimals. So, if you take one level of infinitesimals, you can talk about infinitesimals inside that. And they're sort of new art. But the other thing is, because... The vagaries of what you mean by a, because it's vague what you mean by large, it's vague what you mean by infinitesimal, but the way we've set it up, it's not vague what you mean by the, even with infinitesimals you can tell whether they are, one is less than the other, thinking of them as rational, although if you... There's also a less-than-or-equal relation, modulus of infinitesimal, which has the effect that things infinitesimal with respect to that are not comparable.

5:00 So, there's something, there's some close connection, but we can't, we haven't been able to figure it out. I mean, there's... Anyway, the idea of syntactic... And if the main guy is synthetic, it's action-advised in terms of the geometrical categories, right? But you see what excited me was that I produced a purely arithmetical version. Germs. Yeah. So if I, but my idea was that I could produce a purely arithmetical piece, which is equivalent, because we're talking about defining reals here. So basically the final... Have you got enough? No, I've only got two, but people can sort of tell them in sequence. All right, well, I guess the first thing is I've been taught. Yeah. But, you see, that's what struck me. No, no, it's been built. You have to. You've been the second most talked about. Yes. Well, the two older guys. The two oldest guys deserve the place of honor. Definitely. Okay. I mean, it says that it is not satisfied with what you're teaching. Retrieving to the specker idea of the tree structure sets, we should be able to say something short in terms of the way that covering to a preventive, for instance, in this construction. Well, you could obviously rephrase this thing and turn to the epsilon. I want to invert this. It's enough. No, what intrigues me is that they're kind of naturally occurring in the dense form. In your smooth infinitesimal analysis, you don't even try to stick the ins with the outs. I mean, for example, it doesn't mean... Okay, so what happens is you get this other thing, R star, which is a different...

7:30 You're... the synthetic realists, that's what they are. The ones that sort of generate the total. Yeah. Well, I mean, typically it will contain as a sub-object the rations, you know, you know, the sort of constant abstract rations, you know, but what intrigued me was this business about, the business about integration, I mean, as far as I can see, what you needed in order to get a theory of integration. I thought this is what... As I understood it, this is what Anders was saying. That you just needed to stick in these area up to x integrals. You just had to sort of stick in integral zero to x, f of x, v of x. ...as a kind of primitive operation in order to get a conventional system of integration in that theory. Whereas in these, what Richard and I are doing, you just do it in the obvious... In fact, the Cauchy integral turns out to be quite adequate. You know, you just take an integral and split it up into n equal parts where n is large. And you've got something that almost fits the integral. And then you're just responding rectangles and they turn out to be infinite. That turns out to be in an infinite decimal. It defines the integral of the integral. My suggestion is that you talk about elementary extension only in terms of positive formulas. You don't want to have the usual non-standard analysis. You want something that's like it. That's something like it, where construction is not required. Preserving negation is a problem. But here, the negation is only a problem because of the presence of this.

10:00 Comprehension. The negations of formulas are only problematic when you've got genuine global quantifiers. The idea is that these quantifier-free formulas are completely classless. Quantifier-free ones also do, in fact, contain these boundaries because of comprehension. But I mean, if you think about the negation of an unbounded global existential quantifier. All of this is expressible as a pi-1 proposition about the negation of what's inside, but pi-1s are really free variables. Pi-1s can be expressed as free variables. So that's... Well, okay, so my ambition originally was to show that there was a connection between these arithmetical, because there are no geometrical considerations going on, and smooth infinitesimal analysis, which is variety geometrically. Starting from two radically different standpoints, you arrive at the same conclusion. That's interesting. It might be that there are models of SIA that will also be models of this. We were thinking the other way around.

12:30 We were thinking the other way around. Yes, I mean I've never heard you mention the name before so I'm amazed, okay. I've never heard you mention Grassman before so I'm all ears, yes, okay, what, yes, yeah, okay, so, yeah, I know. I think he's pulling your leg. I'm pulling your leg. I've heard, I've never had a, I've never had a dinner with you without hearing Grassman. Shall we finish the coffee first and then perhaps we can come back together. Okay, so, so, what's your... See, Piano claims to have axiomatized Grossman's approach, but neglecting the fact that Grossman affirmed very definitely that arithmetic does not need any axioms, does not need any axioms, because there's an outright definition of what a natural number is. What does he say that was? Well, it's a little bit, you know, brief, but I think I can make sense of it. There's a following. He really involves a category of categories with the Vengeance in a trivial way. The point is this, that if you really see whatsoever, there's another category that you can call C to the movies. Where an object is an object of C together with the Vengeance of C. And the morphism is the obvious thing that we have to deal with that. We have this category. Now, in the forgetful time of the sea, we can consider hunters the way, given any object with an interval, producing another object with an interval, because the interval of the object is the same. But naturally, so it's required that this commute with all such apps. It has to be compatible with all the apps.

15:00 Well that's a natural number. The naturality, the way of giving a bigger loop from a given loop, is constrained by being compatible with all possible comparisons. That's the idea of a natural number. Well, in turn, you know, of course, this is going to depend on what category you have. Set is the one that, of course, means. Yeah. If you see where the category sets, you know, small sets, then you would expect that to be, really, the outright definition of natural numbers. I think about building a model. See, in this case, it's a play on naturality, because natural is an extremely strong restriction. Small sets. They won't consider all possible categories. So you can ask for naturalities with respect to arbitrary functors. Given an arbitrary functor, that will do something. It can do these things. And then you can require them. So A, that's the natural number three. The science of every endomorphism in every category, but now demanding naturality with respect locally within each category to all these little s, and locally to all the funkers, what else can agree with a natural model? The naturality is so restrictive. It's defining it directly in terms of iterates, directly in terms of, well, I know, but ask for iterates and... Oh, well, of course, of course, in other words... You don't appeal to the idea of iterating, but it just is intended to capture it.

17:30 We're somehow producing a new endo-math, but in a totally natural way, well, let's define that to be iterational, and then we should think about to what extent there's a more traditional way of building up. Of course, there never is, but you can see the whole idea of building up is really an illusion. Anyway, I agree with this. This is sort of the... I mean, the whole... whatever your views on these things is, the three dots are always illegitimate. Always illegitimate. So you can use them after you've explained what they mean in real terms. And so I think this is really what Grassmann had in mind, even if he didn't know that. But what did he actually say? I said something about it's something that you can apply to any of these stations, and there's no way to change it. But, you see, it gets more interesting. Okay, we've got to say you turn the category into all categories, but, as you say, it's reasonable to think it's just a one category of small sets, but already that would squeeze it down to the usual definition. What if you take finite sets? Then it starts to get interesting. Then you get complications of the kinds that you're taught here, because if you take the natural number, in other words, the natural iterations on endomorphisms of binary sets, you get a more, a more interesting structure, there's a sort of inverse limit of familiar behavior. So, yeah, so Bob Paré called them die natural numbers. But C-loop is actually, I mean that's what's, that's what sort of makes it clear that iteration is a part of it.

20:00 No, I don't, but it allows you to explain what iteration is. We use it as a representation if we grant the existence of a natural additive moment, then it's the frontiers from that moment to C. It's the same thing. Well, of course, yeah. So when we represent it in terms of universal properties, we get to an additive moment. Again, with the quantification over all C's. Yeah, because, I mean, I've heard you say it a million times, but that is absolutely right. That drags subjective, idealizations of subjective capacities. That can be placed in, you know, if you say, what do you mean by the next one? You know, how long are you allowed to try to do it? You know, all this kind of stuff. That's what Brian Rotman was. I could do something that's kind of crazy because it brings all kinds of extraneous considerations. Basically, that's the idea that you could just say, well, just go on forever. And then that explains it. There is a loop. Excellent. Sorry to disturb you. Well, no, I think in the same direction. Good job. No, it's not. No, it's on the outside, John. Yes, it's an absolutely beautiful idea.

22:30 It's just, I just think it is the dramatizer of any discrete state without the system. Yeah, in any category. In any category, yes. That's the proselytizing of anything just as discrete states. That's how I think of it. Yeah, I mean, it's literally, let's say you talk about all finite categories. There is this sort of natural numbers up there, absolute and everything, sort of a platonic ideal of all possible attempts to keep on going. Yes, that's what I'm talking about, the inverse number. But structurally it shows that it doesn't have to rest on these ideas of completely discrete infinity at all. Oh no. It's there, as I say, in the master construction in a completely objective way. I'm deeply impressed by the fact that you... No, what's the root of all evil is extrapolating capacities beyond where the, you know, in a sort of ideal sense. The ideal, that would be idealism. Oh, but I mean, the real line, you see, is not evil and bad and evil. That's one point. The idea that you construct the real, that is the line that you're going to determine. As I said, it was Aurelius who read this thing, and then the 20th century. That's what the old minimal theory is all about, really. You can have very good models of the line and the plane and stuff like that without having the natural number present.

25:00 It means that the theory can be decidable. The undecidable, that's where it's coming from. Once you sing off the natural number, you mean the rationals, then they're all only real. Because the rationals, again, that's sort of the idea. In other words, there's geometric and there's objective and subjective evil, you see, in the sense that the undecided duality theorem is subjective evil, whereas the piano space-building curve is clearly objective evil. So you have both kinds. It isn't just... What about the just the fact that, in fact, physics only makes use of rationality? It only makes use of rationality. There's also a point that physics seems to say that there's a limit to divisibility, modern physics. So, isn't it conceivable that physics ultimately will be discreet? Modern physics doesn't have a uniform thought. In fact, this has been said since the 20s, but nobody's ever proved it. Nobody's ever offered a plausible mathematical model. So in all that time, we're all powerful mathematicians. So it's just a speculation, a speculation that we're all somebody's experiment. It seems to me, it seems to me it's really heavily ideologically rooted. I observed that the Scientific American in January of my year, I think it was 2004.

27:30 There's a long article on the front page. What is that? A picture, a picture. With that, precisely that assertion came with Space and Time is to Speak. The latest results show Space and Time is to Speak. It went on for many, many pages. A year later, the January issue had exactly the same article. Most of the same pictures, just a few words changed to deal with the fact that Otherwise, exactly the same article repeated twice. Something I've never seen before, that they thought it was so important to repeat it twice. Now, what wrote it? Do you remember? There was a guy at the Perimeter Institute who also attempted to name the... Smolin? Smolin. Smolin. The only citation, the only thing in the bibliography to legislate some kind of publication to support this... One thing, namely an article by John Baez, which I believe was in Nature. It was about half a page. If you can deduce in that half a page anything like a proof of a big conclusion of all space and time, it's discrete, and you're much, much better than I was. I was on this extremely flimsy basis, and it was so important to have a long article published twice. So, do you take a view on the matter, or do you not? I think it's almost surely false, I think. Probably space and time are further divisible with the advance of technology. Well, if it turns out not to be the case, then this analysis of mine will sit happily on top of it.

30:00 As I say, there was no actual theory of the Philippines. There were just a little flimsy enough people to have got defeated. No deduction of quantum mechanical laws of motion on the definition of state or anything. Total speculation by this Templeton fellow citing another Templeton fellow's... Well, why would a temple be interested in making space time finite? I think that one study of the history of philosophy, it was found to discover why this is so illogical. Well, it certainly was the view of the Epicureans, who were hardly in good order with Christians. There's a general aim of religion with idealist philosophy and submission, but it's an awe. So our ignorance of the mathematics behind these two articles, or this single article, is supposed to lead to awesome acceptance that it's some kind of viable conclusion. Or even if it's a completely established fact, which is certainly the way that it's presented in common. I mean, I think everybody's honest about it. You find math professors in Bristol thoughtlessly repeating this. Modern physics thinks that. So that's how powerful it is. Who's a math professor in Bristol saying this? I don't think so. I've got a prejudice against infinite anything. But there's lots of... the infinite is ambiguous, though. Discrete infinity is only different than continuous infinity.

32:30 It's just because traditionally since the ducting models of the continuum out of the discrete infinites, but that doesn't mean that's what... In fact, I think Dedekind himself, my impression is, Dedekind himself started with the idea that there is a continuous line. And proceeded to make constructions behind it that mapped into it, you see. Right. I mean, that's what, if you think about it, that's what Cuddax is. He's thinking geometrically. Yeah. He's thinking geometrically, and he says, okay, how do we paint out the geometrical background? We only have one of the considerations. So, I mean, first you identify the points with the... I mean, the idea is that there'd be a real number associated with each point. So then, he puts it in terms of splitting up the real. You can either apply it to the line, or measure the line. In other words, there's the concept of real cuts, starting with the line. Then you find, well, among those are the rational cuts, and then you find that the latter are dense, that they should be, or at least that it's reasonable to hope that they will be adequate. But, but you see that's not, that's not necessary. Well, I mean, but boy is Dedekind's, Dedekind's construction, Dedekind's construction is more geometrical than the Cauchy construction. Right, right. I mean, it's more geometrical. Because the other thing, approximations are going to have to be approximations to something. Yeah. And the Dedekind's thing is, oh, if you cross, if you try to cut a line... You're going to pass through a point. Yeah, in fact, the Cauchy idea sort of suggests, well, there's this approximation procedure, and later we figure out whether it approximates something.

35:00 I mean, it's that same way that, you know, Piano arrived at his space-going curve. The approximations are utterly simple, and the individual approximations are utterly... It's simple, as Ironberg was fond of pointing out, that an automaton at a very low degree of complexity can compute the successive stages, but then the idea that there must be a limit is basically this intervention of the discrete infinity into the presence of discrete process, the continuous. So he actually, if I remember right, he defines that it's basically... You can do that, but it's, you know, there are even several geometrical ways to picture the successors. Yeah, but presumably he would have thought that defining it by means of a convergent series made its existence beyond all doubt. Maybe that was his psychology. But I think it's kind of bad that Keanu gets all the credit. I mean, basically, the two guys that really figured it out. The piano, simple piano. A piano gets credit for it because he just stuck it on. Well, actually he inserted it in his version of Grasmont's referential geometry. Yeah. He claimed to be the interpreter to the Italian-speaking world of Grasmont's geometry. Okay, so he wrote a book. He wrote a book on that purpose, but then the introduction includes... All this is claimed that he's axiomatized Grassmann's arithmetic quite against Grassmann's assertion that there's no axiomatic arithmetic. Well, Dedekind's, I mean, if you think about it, Dedekind's structures are a much simpler thing than piano structures.

37:30 His point was that once you've specified the Dedekind structures and what the piano structures are, you have no choice at all, because you can use recursion to do that. Just simply writing down recursion equations doesn't give you a function, doesn't define a function. Oh, oh, yeah, about that, you see. This definition that I gave you here, the natural numbers, these sort of doubly natural things, well, clearly they are on the face of it an additive monoid, okay, but it's not clear that they have multiplication. So you need, you need a similar bit. Different level of definition to get the thing, to get the rig with the vision handbook, you know, so that's something interesting that even from the objective, from the naturality point of view. So this is kind of like one of the high-number systems that's just got success. That's all you... Well, it's got addition. It's got addition. It's got addition. You certainly can compose and find that number of times. Yeah, yeah. For example, . It's going to be a community of thought. Again, there's a very notion of naturality. Of course, there's a big generalization of nativity. But yeah, you get it. It's an additive moment. Well, it's something else. Ah, ah, ah, ah, ah. Well, I was saying, given any category C, you can construct another one. These objects are in the world. And now you can consider functors. On that, which preserves the underlying object, x, and that gives an attitude moment, because obviously you can compose certain C's,

40:00 meaning it's not exactly, a certain category of small sets, but then you can also globalize it on a category of categories, any functor. Here, you can require that you have this for each category and for each object in it. But that system is my explanation of adjustment. Nothing to do with building up, necessarily. I was saying that that system is such a supernatural thing. Clearly, I have an additional opinion about it. You expect that it does happen, but you make the assumption that it doesn't. I don't know if this would be a good opportunity, perhaps not now, but perhaps this afternoon, for you to give us a wider exposition on the whole grasp and theory of extensive and intensive quantum, which is something that I would very much like to hear more about, particularly in connection with some of the things that you wrote in the 1973-1996 papers we were discussing last night before we got back in. I don't know if Astrid made this remark about the... I was already saying that there was a natural number of these. Yes, yes, he was saying that, certainly. And I wanted to ask about that too, but you also said something very interesting about the more fundamental of the two ways of analyzing the structure of the modes of variation. So it's not just about the sum of all these parts of quantity. Parts of the domain actually is varying by the theory.

42:30 But the whole notion of the terms of quantity and their variation. Well, I don't think we want to launch off at that. I'm going to have to get home before too long to feed my brother off today. I've got to keep an eye on him or he won't eat. Well, thank you. I mean, you've explained pretty well what I'm trying to do. I mean, I'm quite happy for you to look at it in any way you want to, as long as you see what I'm trying to do. I mean, you might even explain it in a way that it would take me some time to figure out what was going on. That won't be the first time. Beyond this naive idea of an abstract set with an end in mind. Which is what I always thought was the basic approach to natural numbers by inverse limits along these coverings that you talked about. If the object has all this extra structure that's not necessarily preserved by the end of that, you get an incredible possibility. Oh, yeah, I mean, it's obvious. That in this theory that you've got finite version of recursal on any finite linear ordering onto an endo-path with respect to an endo-map on a given set. I mean, you can do, I mean, that, that, I mean, it's, the natural numbers are assuming that there's a sort of universal such thing. Right. That's what I say, the inverse limit around projecting that. Yeah, yeah.

45:00 I was sort of always thinking that you might as well normalize these things so they stop at the end. Well, no, you're leaving it undefined. Your finance sets are not closed under the operations. No, no, these are operations coming. The things they're closed under are these local successor functions. But they're not even closed. I understood that the sigma comes from outside. There's something that applies to the tree structure. But the sigma, the individual finite set L, is not closed in any way. No, it's closed. There's an intuitive sense in which L has got its own successive function, which is a matter of its field. Exactly. It's not defined at the last moment. It's left undefined. Whereas I was thinking one could normalize it by redefining it at the end just to be a cell. Yeah, you could do that. That wouldn't introduce any undue constriction? Because the point is that it's the global operation we're interested in. We're interested, I mean, basically, what we want to say, what does it mean to iterate this thing, a finite number? The answer is contained in this definition. We were talking about for a long time what it meant for sigma to generate l from. Sigma coincides the internal successor function on the field minus the last element. So it goes from the field minus the last element to the point. So it just coincides, you take away the last. That's saying, giving a local...

55:00 Yes, but the problem is that you can't wait until you've looked over for a position that stands in the middle. I can understand that, but at the same time, yes. There are also a number of different types of mathematics, such as quantum mechanics, algebra, algebra, algebra, algebra, algebra, algebra, algebra, algebra, algebra, algebra, algebra, algebra, algebra, algebra, algebra, algebra, algebra, algebra, algebra, algebra, algebra, algebra, algebra, algebra, algebra, algebra, algebra, algebra, algebra, algebra, algebra, algebra,

57:30 There are actually many parts of these like experiment papers that are secured that can be stored in another place for one year, they can still apply to string theory, because string theory can be done if they're stored for one year. So if you find an experimental position, by the way, it doesn't make sense. In fact, they try to elucidate people from outside. You know, perhaps they have a certain policy that they want people from outside rather than from inside. Well, actually, there is a one-year difference between a model in college And this is the one that offers which of our studies is starting from August and the three of you should look it over for me and I'll see where it's taking you. You can see August is going on quite a bit. Yes, yes. Yes, yes, yes, yes, yes, yes, yes. No, in fact, it's more that the oldest and the oldest, and the deadliest are spreading. ...which is that they... Exactly. That's it. It's totally cynical. It's revolting. In fact, the tactics of the piece have become, under new labour, have become far more vicious, and the readiness to resort to lethal violence has become much, much more distinct than it was even in that first period in history.

1:00:00 So, in fact, I will have to stop for another period of time. For instance, hecklers. There was this one man who... I mean, in the 1950s and 60s, people would heckle politicians in public meetings. It was a very well-established tradition of political life. Any politician had to know how to deal with a heckler. The practice under Mosley, when Blair stood up to speak at the party conference, of course everything was so tightly controlled in terms of the scripting and the television cameras and the minute management, but there was one man in the hall, he was an elderly German refugee, had been a refugee from the Nazis as a child, and he was a lifelong member of the Labour Party, and he got up. Not scripted, not on message, not part of the entirely pre-scripted television production to the heckling and to object to the Iraq war. And he was immediately, not immediately, he was beaten up on the very floor of the party conference. And then dragged outside and arrested by the police. I don't want to talk about these people. Well, even 20 years ago people would stand up and heckle speakers at public conferences, let alone at public meetings outside. But now, it is not the case. Speaking of heckling, in the last 20 years, the movie always begins with a common warning. Do not speak in silence. Completely, completely or completely muffled and made to feel very, very serious. As you were saying, Varma was not described, according to the movies, as a villain, even under the fascists. These people were always making lively comments and tapping on the screen and trying to get the whole experience and that's completely surprising to the lives of the people.

1:02:30 I went to the movies in the 70s and 70s and it was still there very much but I went there for repartee and to make witty comments about what they were saying and what people were saying. It was all part of the experience. You don't blame the time, you don't blame the time. His father said hello in the morning. I think that's true, isn't it? The psychology of mathematics is still to be found. To figure out why that's the case. When you go to sleep with a protein, you wake up and you're kind of unconscious the whole time. Yeah, you kind of need serious consciousness. I used to learn pieces of mathematics. As soon as I got stuck on something, I went to sleep for one hour, and when I came back, I saw it automatically. There is this technique to other students of the conservatory, but unfortunately it didn't work for them. But can you go to sleep whenever you feel like it? Yes, I can either at any time, or at least when I feel like it. That is a great gift, yes, you're very lucky. Because the unconscious is very active, that's why. So the brain re-elaborates a lot, even though you don't see it. Perhaps it's the fact that when you are conscious, you should organize your brain as well as possible. So I need to include in your brain the main highway things, in a way, and after you have organized everything, you can sleep and the brain works for you, and then you can make plans for recording back. As you can see from the classical rules, as everybody knows, Poincaré is still one of the forces and functions, but there seem to be many, many, many illustrations. Have you experienced working on a problem? Oh yeah. Or just literally the solution came to you when you were not thinking about it? And also some pieces of memory that come...

1:05:00 Also, when you don't expect a break, you are already in dinner, and you remember something like a detail that you saw three weeks before, something that, ah, that's what... So, you know, that is a practice thing. There's a similar property when you're trying to remember something, forcing it, but you don't know exactly the barrier. It's the same with maths, if you hear it. Concentrate right now, in fact that could be the barriers that we get. But suddenly when you remove all those barriers, suddenly I think you keep going. But it would be interesting to investigate whether one can increase these abilities, you know, for the common population, because if one were able to discover the real mechanism behind these unconscious things, many people would be happy. Because in my experience, when I talk about my experience to people, they are pretty amazed. They say, how is that possible? And I would like to teach them. So perhaps it's something personal, but also it could be something more objective, don't you think? I joke, well I joke the first thing about neuroscience, and it's a very, very disjointed subject. I mean there isn't really a discipline called neuroscience, there are a hundred or a hundred and twenty different fields, each of which... Contribute something towards our understanding of brain function at some level, some of which has contributed something towards our understanding of brain function, some of them I think probably are relevant to us, I mean they've done these things, they've now done these things, we've been honest with you about this for a long time. The studies of which parts of the brain, which systems within the brain, are in use in particular intellectual tasks, I don't know how far they can pass, but certainly in listening to music and in... It's quite interesting actually to see in the studies of mathematicians when people were doing, say, areas which are more clearly geometric as against areas which are more combinatoric.

1:07:30 I don't know if the technologies reached to the point where one would be able to distinguish clearly between a population of different parts of the place. There are different kinds of intellectual function in mathematics. It would be interesting to talk to some of the people who are doing the cutting edge work in neuroscience. I have been pressured a lot. Very, very big claims are made for advances in neuroscience which when you go and study it more carefully turn out to have been hype. By the way, I have a speculation on the reason of the conjecture. I think the reason that Smollett can somehow get to the belly with printing almost the same article, repeating this claim about... Science has shown that space-time is inherently discreet, is because, and without even bothering to produce any kind of argument, is because people have been softened up so intensively in the last 20, 25 years at least by the quantum physicists, people doing so-called quantum gravity, telling them that the Planck, this whole argument about the Planck length. Being some kind of inherent in the world demonstrates that because of the uncertainty relations between the metric tensor and the energy of that scale proves that there must be some kind of ultimate granularity to space-time and that is now so established in the popular consciousness of people who read general scientific publications that Smalley doesn't even feel he needs to repeat that a lot longer. Everybody's supposed to know that, that's absolutely given, but the smallest scale of space-time is 10 to the minus 33 centimeters. It would be a great pain to kill it if they didn't know about that. Do you want any sauce for your now warm pot? No thanks. It's alright, it's alright, don't you worry, usually we heat them up down here, because you've never actually heated pot before. You'll be alright without the sauce, yeah? Everyone else okay? Good stuff. What this has to do with religion, I mean, I was hoping...

1:10:00 But you would come up with a sharp formulation. I wish I could. No, but the key point is this, that if this space at the time, or the streets, how do you get from one point to another? It can only be due to God. The outside. The outside of work. Otherwise, there's just no way to get there. And that's the whole idea. It's not going to get from A to B. I mean, I'm, you know, I'm not, I'm not, I'm not, I'm not, I'm not, I'm not, I'm not, I'm not, I'm not, I'm not, I'm not, I'm not, I'm not, I'm not, I'm not, I'm not, I'm not, I'm not, I'm not, I'm not, I'm not, I'm not, I'm not, I'm not, I'm not, I'm not, I'm not, There was a whole theological position which I don't know about, with occasionalism, which was developed particularly in the 17th century, which did, in fact earlier in the Middle Ages, it's frightening that the Greek atomists, the people who did actually believe in the space time were. As John pointed out, they were regarded by the Platonists and by the early Christian Church as their chief intellectual parents and were associated with materialism. Um, so... Well, I don't think... Discreteness of matter. Well, it's... I don't think Boltzmann figured it out. It's based on... Uh, it's not much cheaper with...

1:12:30 It didn't... Discreteness of matter was discreet either. Yes, just that it was a very useful model at a certain level of the Maxwell principle about screwing up and screwing down. But no, you're right, because that was actually used as a theological argument, that if there was ultimate granularity, then there has to be some principle notion for notion. There's at least one, Occasionalism, which I think is also developed in Mislen in Theology and Mathematics too, which says you've got to bring in God because God is the picture, it's a little bit like Machia, all you have is configurations and you need the passage of time and ultimately illusion, but God is just giving the illusion of passage by reaping of the thing, you don't know what that means if you don't believe in passage. Yeah, in fact, the Julian Barber theory of time capsules is actually really, as far as I can understand what he's saying, really a revival of some of those ideas of the occasionist metaphysicians who did believe that people had to bring God to explain motion. So maybe, yeah, maybe it is something. It's actually not very structural, is it? You almost don't have to talk about that at all. It may be a medieval argument, because you may be very much interested in reviving it. Oh, no. Because look how interested they are in reviving all the other medieval stuff, like possible worlds. Right.

1:15:00 Which is just that they want their name to be associated as, because of the kind of reflected authority and curiosity it gives, with what they take to be the most advanced, the most sophisticated, the most mathematically, Sophisticated, prestigious physical theories at the time. Even if they hadn't figured out a specific theological reading for those theories, they'd still like to have their names as well on the research proposals because that gives them some prestige. That's why they're so keen to get people like Hawking to come and speak at conferences sponsored by the Vatican. Speck is pretty well completely cynical about it. I'm presuming there must be somewhere, shall we say, religionists who are very unhappy about the unprecedented. Yes, I think there probably are. Religion accepted. Yes, people who don't share so much, what they call the kind of toolkit field of mathematics. We know what we want people to believe, now let's find what shiny new gadgets will help impress people. No, I don't think that people are much more serious than that.

1:17:30 Not even slightly, it's almost completely banished from the current analytics of this. I mean, I guess it's, they're sort of pariahs now. There are people who do this, plus food religion, but they tend to . So, people have . But Oxford has its, it has a chain. It's a pretty much a dead philosophical subject. There's still debate and things that are unjust and there's sort of many things. There's nervousness pretty much. They're gone. I think there are things that you might, you know, feed into as being off the scene. Psychological bent of religion. Nothing that's a part of the religion. Just about everyone is delivering a walk down the side. It was so curiously a few people in philosophy of mind. Right, so they have the most difficult job to square the materials. Yes, exactly. I mean, there are still perfectly sort of serious dualists. Yeah, well, there are a few of those, I think. Dualists in the really rich, strong, extenuated sense of dualism. In the United States, it's a bit different, because in addition to the Catholic trade, you've also got these actually intellectually very backward looking.

1:20:00 For instance, there's this whole school of so-called process theology, which tries to base itself on Hegel, which argues that they publish a journal called Process Metaphysics, in which I'm sorry to say that David Byrne and two other people used to occasionally publish their work. Wilder speculations. It seems to be a kind of attempt to bridge traditional Christian theology with something more like Buddhism. Could you have religion without God? Yes, if you dress up the notion of God in a sufficiently subtle way and then reintroduce it by the back door. There's a man called Hartshorn who was very influential. He was their guru. So that these sorts of particular sciences, philosophies of particular sciences, that's what that's interested in. Metaphysics, traditionally conceived as largely a dead subject, though again carried out by the chemical ecologists. Yes, there's a general rejection of the idea of the first philosophy. The first philosophy is some overarching framework which one can articulate and within which the exact sciences would then be inter-fit with that project. It's public, it's completely around. Now the slogan is that philosophy is just the hand-made opinion of the sciences.

1:22:30 Yeah, sort of looking into those assumptions of science as a task. Not to extend it. That's, yeah, that's the subject. Except philosophy of mind. No, philosophy of mind has become a habit of mine for two years. That's true, that has become a habit of mine for two years. But there are still some, there are people like Colin McGee, I was thinking of, you know, the so-called new mysterians, who obviously do a job, who still are convinced that the solution to the hard problem is that they will just say that consciousness is ineffable, which is just another way of saying it, it's an impractical mystery, which is another way of saying it, you know, bringing God or something. It has swung a little bit too far in my mind, I think, but one of the obstacles that the scientists have taken sort of as data and all philosophical theories about them are supposed to be attempts to make sense of them rather than trying to take the underlying phenomenon and try to make sense of it. That's the reason for the huge authority of these alleged or widely regarded by the media as unchallengeable experts. But it's still trying to recover from the fact that there was system building going on since the late 19th, so it still doesn't quite know what to do with it. In Australia, he writes all the books. Yeah, that's right, yes, he's one of those people. He also writes, yeah, he's one of them. He's also, revealingly, and I think this is certainly no coincidence, he also writes quite a lot about the so-called philosophy of cosmology, about the philosophical implications of cosmology, and particularly about the multiverse, and that's probably the subject he writes. That again absolutely doesn't surprise me at all.

1:25:00 It's a very strongly anti-materialist position because, of course, if there is some possible structures, in fact, it's a subtle way of reintroducing Russell's neutral feminist position. Well, that was just a bit of polish. It really is. Hello. Hello. Would you want one? That's very kind of you. Am I allowed to? Thank you. Thank you very much indeed. That's very kind of you. Thanks.