Einstein, Kant & the relativised a priori

0:00 Well, it's an interesting kind of history that Michael is doing, right? Sure, it's a very, very interesting one. The actual historical facts really matter very...matter some. They matter some, but you're quite right. It's rational reconstruction. It's Whig history of the best kind. And it's a very valuable project. It's a terrific project. But, as you say, I think it is that rather than, as it were, evidentially based. There's a lot of narrative history of science. But it's a great project and I think it's fascinating. And the more I think about it, the more I think about it actually, the issues that are at stake here. For instance, Poincaré, one thing which is, it does strike me, I think Einstein, in spite of the tribute that he paid to Poincaré, and clearly he saw Poincaré, rightly, as a great mathematical genius, also I have to say one that... He rather kind of felt his way on the subject in the way that Einstein also felt his way into it, but I don't know that he would ever have subscribed to that hierarchization of levels of structure of mathematical knowledge and of knowledge of the whole of natural science that Poincaré is insisting on in Science in Écoute. I do not think that he thought in terms of one level prescribing the first principles for the next in this ordered, this completely ordered and unrevisable linear work. I think he was, apart from anything else, if one really did think that, it would really not make, it would not seem to me to mesh at all with the vision that he clearly did have after the... Certainly after about 1920, 21, of the position of geometry. I mean, you know, I think he did actually have pretty well a geometric dynamic ontology towards the end of his career. But the 1905 paper, it's not geometry, but I mean, you have to make a definition before you can synchronize your clauses. Sure, sure, sure. I think it's quite possible he did subscribe to that view at the time that he got special relativity, but I don't think, what I'm saying is I don't think he would have subscribed, so far as he ever thought through his philosophy of mathematics and natural science as a unified package, that he would have subscribed to it any longer after, say, about 1921, because I don't think it can make sense of the way that he saw the first principles in mathematics and physics as a package. I think he was much more influenced after that.

2:30 That's my sense of the chronology. But again, I'd have to go and look at the sources. I think he is a very great genius, though, I have to say. I agree, he's not an easy philosopher to understand. People also say that I don't read German, that the English version of space-time matters and travesty is... Yeah, I've heard that it's a very bad translation. But I have to say, and I have more and more respect, the more I look into the... The unity of Vial's thought about the continuum, about the incomposability of the continuum, about his reasons for adhering to the intuitionist position, about his rejection of set theory, and his views on space-time, the more I see his philosophy of mathematics and natural sciences as a very powerfully unified, tremendously deeply unified package, and I really think Vial is an astonishing genius, and he and Cartan are my two supreme heroes. And I think that Einstein was much more in that line. I don't think that Einstein would have regarded these quite so... I'm not sure he ever addressed the issue, but I'm not sure that he would regard it as quite as unproblematical or straightforward that, for instance, that arithmetic naturally lies at the foundation of any sort of ordered series of their first principles in this thing. I mean, you could take the view... Were you there when Jean-Pierre Marcus gave that fascinating talk about the lottery charts? Well, this is of course fast-forwarding, but looking at what these people are doing now in category theory and in homotopy type theory, you can argue that it's actually geometry that may turn out to provide the first principles of arithmetic. That the very notion of being an object in the sense of being an element of a collection extension, the most primitive notion in set theory, is actually dependent on the prior. The geometric notion of being a closed and bounded component in a half-disconnected space, that without that you don't have any notion of object. In other words, this idea that every ingredient of cognition is in some sense ultimately the transposal spatial structure agent, which is really a very Kantian idea.

5:00 Um, oh yeah, yeah, I'm not saying that, but it's, but no, no, true, true, true, which I think may explain why some, well, some professors at least are not very happy about quantum theory and want us to go and reconstruct it or, or, or to continue to search for, search for some underlying, you know, underlying theory. Yes, yes, I agree, it does, but then of course, hey, hang on guys, I mean, you know, talk about the pessimistic, talk about the optimistic memory induction, I mean, that's very much true of Ptolemaic astronomy for a great deal longer than, it has been of quantum theory. Literally, our instrumentation's got a little bit better since then. And the same is true, and the same is true of all the music, so, I wouldn't say. Yeah, yeah, I'm, I'm, unfortunately, I've got to go dash. I'm going to dash back and then catch my train. That's what helps your wife too.

7:30 Um, of course, I've got to go. You do? Yeah, I'm on my train. Thank you. Good luck. Thank you. Um, look, I'm really sorry I haven't shown a lot of property. My property's darling. I haven't got rack art the other night. So wind down for a second. Can you just send an e-mail just to confirm that we're recording all that stuff for DVDs? And I still owe you the other DVDs. Oh yeah, that's okay. I wasn't expecting that. When you get a chance. But let me know when it's done. Did you get good recordings? Yes, very good, very good. I'm sure. I've got to copy all the digital stuff onto DVD. I've got some audio tapes. Yeah, yeah. I mean, just tell me what you think. Yeah, I've got that. So I'm a little bit, a little bit off of that except for the first three songs that I've got to do. Okay, and I've also sent you the abstracts for Boston now that we've got them. I think it's very interesting, some of those. Okay, hang in there, ladies. Have a safe journey back. You too. Please do. There's a quicker way out. Yeah, much quicker. You're going towards the train station, aren't you? Oh, it's much quicker to go this way, then. Even without? Yeah, especially without, I would say. Unless it's extremely heavy. If you go that way, you're going to walk three sides of the block. What's three sides of the block? It's three sides of the block, so I'm going to walk on a rather, you know, gravel path. Yeah. Oh shit, oh bloody hell, don't tell me, oh wait a minute, no, no, no, no, no, no, no, no, no, no, no, no, no, no, no, no, no, no, no, no, no, no, no, no, no, no, no, no, no, no, no, no, no, no, no, no, no, no, no, no, no, no, no, no, no, no, no, no, no, no, no, no, no, no, no, no, no, no, no, no, no, no, no, no, no, no, no, no, no, no, no, no, no, no, no, no, no, no, no, no, no, no, no, no, no, no, no, no, no, no, no, no, no, no, no, no, no, no.

10:00 Thank you for your attention. Ah, yes, that's where I'm going to go and try to get myself in there, to catch my train there, so you don't see the way I'm going to go. Sorry, I didn't mean to interrupt. Well, I had seen it before, so I just wanted to... Thank you for watching. The worst way of teaming up is because you don't know who you're talking to. I do what I want to do. The guy I think is so amazing. Thank you for your attention.

12:30 The old collection of mathematics is now part of the collection of mathematics, and it has become a part of the collection of mathematics, and it has become a part of the collection of mathematics. Thank you for your attention. I was also told that the natural history museum is on screen. Yeah, I think I'm going to try and get that this afternoon. Because I've got ten hours to kill before my train, so... Um... The strike starts again next Tuesday. Let me finish my project, sir. The sarcasm he boasts is that he's managed to make the trains not run all the time. Oh yes, I think so. They now absolutely and reliably predict that you're going to drive my car. You're very wise. You are by far very wise. I'm speaking last night. I just want to ask you a question before I push off. Thank you for watching this video.

15:00 But we'll be about to have phenomenology and logic, back in about 1966, in a lecture called, uh, by Peter Jekyll and I, um, on the taxi, called The Fault. And he's gone on and on and on about how one might think of, and this is really a kind of phenomenological analysis, it's pure philosophy of math, but that's all a kind of rigorous phenomenological standard, but how one might think about the primitive ingredients that are actually centred in the religion of mathematics. Perhaps a rather obvious point is that quite a few tend to be reflective about cosmologies or basic notions, except that without the notion of them, you could argue that they can take a very strong and inalienable position in science and mathematics and mathematics, but without our being able to be as close to that as most of us are. It's certainly that there is a possible connection between the motivations of the mind and the movement of the mind, and the movement of the mind and the movement of the space is something that I recommend. It's a very much a speculation, but I think it struck me that there was an interesting parallel. Yeah, you may want to have that one. If not, then I can send it to you when I see it.

17:30 Oh, I've put in a couple of minutes. No, just time. It sounds absolutely fascinating. Yeah, well, I think it's absolutely right. What's the algorithm that first allowed the rhetoric about the connection between a minor and a program? Oh, yes, yes. I think the two talks are going to complement each other. Now what I'm going to do is get on the film and see if I can't really lean on any of the class. Well, he is very nice. He has, oh good. We spoke over the phone, though. Oh good, oh good. So he knows, and he's sort of a very, I mean, when he told me that he's a nice person, he's very nice, but you know, things happen, and sometimes you just don't know why. Something like that. From his point of view, it just happens. There's no reason to like, find out why. Well, dare I say it, well, yes, true, except that by the same, dare I say it, by the same reason that Michael Taylor and Michael Friedman are still completely wasting his time, I think Einstein would probably have given exactly the same answer. So Einstein would have said, hey, this just happened, I wasn't thinking about it, I wasn't thinking about it, all right, all right, I wasn't thinking about it, and maybe later, after I've been talking to Herman for a little bit, I didn't get it, but I didn't get it, the idea is, the idea is, the idea is, I don't know what idea is coming out of the kind of integrated philosophy of mathematics and natural science, but this is still, that doesn't make any of this interesting. And the fact that Daniel Kahn might say that doesn't make George's talk one whit less interesting. I find that sad, if you think about it. Well, I'm not sure we'd put it that way, but it was quite well-developed.

20:00 Yeah, I dare I say it's a little bit like Einstein and Michael, but I still think it's that overrated. In his eyes, 50 years later, he's still a very worthwhile scientist, and while I recall that he is now, but he was... So he didn't wake up on... I'm quite sure he didn't wake up the moment that morning he got the actor in front of him and say, Hey, I've just seen how Cacker is very... I've just seen how Cacker is very... I'm sure he didn't do that. I'm sure he didn't do that. No, I think that particular point he actually never saw. Yeah, yeah. Like I said, I don't think... But the whole thing that he did... Thank you for watching. So open up, it's possibly in the discussion session. Or even if it doesn't open up, it's not one-on-one, you know, you or Colin will be proud to be part of it. I've heard stories about him, which is not very likely to be extremely general. The story about how he... He came into the department one day, and somebody saw him underneath the windows of the math building, and he hadn't been in place since he was in college. No, he's not in college. No, he must have been in college, I guess. In that case, definitely must have been in college. Stanley Cox was a guy who had to show the world that he's a genius. And who particularly isolated one very crucial piece of it, a bit of an adroit pun. The conceptually the thing that you really need to make it is going to be that the framework I really

22:30 And then almost immediately after he published this work, he was clear to some very smart people very soon after that, that adjoint was absolutely fundamental and central to the understanding of mathematics. And that is the dimension which is so fundamental and central to the way that category theorists do think about structure, which all these people who call themselves mathematical strategists, who write about structure, like Stalin, Reznik, Shapiro, have just completely messed up. They just haven't bothered to go, oh, what do mathematicians themselves do? What kind of structure do mathematicians, when they're dealing with structures of really... I'm ready to do it. I'm sorry to say, I do think that it's shockingly responsible and it's the kind of thing that comes from philosophers and mathematicians, top mathematicians, real mathematicians, in a way that in the last 30 years, the philosophy of physics has become, because now people in the philosophy of physics are absolutely expected to be able to speak, to be able to do, to be able to do, to be able to do, to be able to do, to be able to do, There is a complete interchange of both the conceptual and technical discussions on a basis of complete mutual respect between the philosophers of physics and the best of the physicists. I was just going to say, until we have people like you and Colin around, I'm also going to

25:00 Thank you for watching this video, if you liked it please subscribe to the channel and give it a thumbs up. I've heard of all of this before. I think it's an extremely, um, I think it's a fascinating, um, I don't think that makes it any less interesting. Yeah, but why not? There's the intellectual division of physics. No, he doesn't have to be the last person to say that he was. Yeah, he's quite clear about that. It's using, I'd say, it's fashionally reconstructing, I guess, of the game, and it kind of brings it into a little bit of a particular subject in general, which is to read, to know, to talk about, or to read, well, really, I guess, to read in modern science, I guess, in science, and to send it to a child. I think that's extremely interesting. Yes, Einstein was much more competent. Yeah, yeah, I agree. I agree. Einstein didn't have a, I haven't fully developed it today. I think he did actually think more than that. He had read a lot. He had read a lot. I think it's precisely about the algebra there. I have respect for you. I have respect for you. You actually believe in pragmatism. There are also many other fields of study, such as mathematics, geometry, algebra, mathematics, physics, physics, physics, physics, physics, physics, physics, physics, physics, physics, physics, physics, physics, physics, physics, physics, physics, physics, physics, physics, physics, physics, physics,

27:30 But if you look at his, if you recapitulate his profile, there he is, he's guided by, he can't really. I don't want to give a very good account of what he is, but he is guided by some kind of vision of the way that the first principles of mathematics and physics go together as a package, and the way that Weyl was much more specific about it, so I don't think he had a lot of support for it. The change of perspective that you can trace in the life of Schubert was largely coming from that. Yeah, there is this sort of correlation between the great beauty and truth, and then there is this end element we've talked about in a while, and that it is somehow inscribed on the origin of the studies in the entries, but there is some sort of slogan. If you want to get someone to do some vaporing then and revise it. To revise it? Wow. That's a story. There was a college that avoided the dream, but it was very, very evident. They were expecting to make it. If they were only allowed one vocation, all their other work would be lost forever. What was the one sentence that they would leave behind? And I did compile a course on them, and I'd like the members to take any questions they may have.

30:00 There was certainly when they had distinguished visitors that were asked to meet with them. Do you know that there's a website? What? What do you mean? I think one client. Formed one. Formed one. I did one. I did one. Formed one. See, see, see, you must be connected to it. You must be connected to it. It would be fascinating to look at all the different key terms. I hate to say it, but I think it is. They want you to soundbite, counter, and so on and so on and so on and so on and so on and so on and so on and so on and so on and so on and so on and so on and so on and so on and so on Necessarily, he was possibly good at anything else. He was undoubtedly very good at mathematics. I think a little too good, but yes, he had his talents. He had the learning power to do great things. I couldn't lie to him. But you don't need to know that. You've got to tell him you love mathematics. You've got to lie to him. But you don't know he loved mathematics. Thank you for watching. I hope I've become a little bit more sophisticated than all of our assistants have been. He went into the nearest bookshop, and he looked there at the shelves of physics, and he saw this book, and he had an excation like that, and he bought it, and his claim is that he finished it before he ended it.

32:30 It's just incredible. It's just incredible. It's powerful. It's a car mine. It's possible. Anybody who knows, anybody who knows, you know, from the book before. And, of course, it's got to be either very, very big headed or very, very smart because they could be both. Let's write the story about Peter Johnston on top of this bit. Well, the original one, the first one, the first one, and even the last one. Well, of course, the second one hasn't been finished yet, but the first one comes through. But we hope that he can work on it. I'm Johnston. All right. He can learn that, he can very, very much touch. He is the only mathematician ever to have learnt tolmphs theory from Johnson's book. Well, Johnson's book is pretty, pretty tough going. It's really tough going. It's not public. This, of course, has the unfortunate consequence of being a very small number of philosophers, at least 95% of which are from Darwin, about which you don't like to hear. We do meet the really good interviewees. We have several, but they don't have the same coverage. It's very, very hard. I think one of the best things to meet you is actually that book by Gonzalo. Thank you very much for your attention and I hope to see you again soon. There are a number of different types of mathematics in physics, including quantum mechanics, quantum mechanics, quantum mechanics, quantum mechanics, quantum mechanics, quantum mechanics, quantum mechanics, quantum mechanics, quantum mechanics, quantum mechanics, quantum mechanics, quantum mechanics, quantum mechanics, quantum mechanics, quantum mechanics, quantum mechanics, quantum mechanics, quantum mechanics, quantum mechanics, quantum mechanics, quantum mechanics, quantum mechanics,

35:00 Thank you for watching. Oh, well, that's a very, very good question. There are lots of examples. And it's almost always underlining the point that it's the cohomology of mathematical structure that's carried by the domain that's really doing the interesting, well, that's conceptually crucial to the way that these... It's a very, very, but it's, I'm much stronger than you, but I'm almost very, you know, better. I'll let you have a look. But it's a safe time. It's just, you know, it's a story. Yeah, that's true, that's true, especially in the Christmas time. I mean, that's true, that's true. But I know how to explain it, but I'm not quite sure. Yeah, it's a struggle. I agree. I agree. It is a very nice way to start, but it gives us very much of a vision of something that never shows the connection, which was indeed the context of the Genesis development. I'm going to do it straight by hand, so I'm just going to follow you. That's what I'm going to do. Go ahead and run straight.

37:30 So I think we do need a very much consensually oriented, historically oriented lecture. Well, you took the words right out of my mouth. Thank you for your attention. I really am looking forward to it. You're still going to keep the side glasses on. You'll have to have something easy to wear. Yeah, but as long as you keep them on. Because I just think that's... Since we're talking about the soundbite, the world of soundbites, that is the soundbite that I want to take away. I have to take away one soundbite. I don't know. I don't know. I don't know. I don't know. I don't know. I like this book, I disagree with it, but it's a nice book to read. Thank you very much for your attention.

40:00 I'll see you on TV. All be well, provided that nothing bad happens. Um, you'll see me up here, can I help you on the 29th? Of course, it's probably a little ungratitude, but that's not a problem. Fantastic. I'll see you on the 28th. Oh, that's all the pictures that I've seen. Thank you for watching this video. I'll send him an email tonight, just in case. He must have seen it. All the same, a personal invitation would not come to him. He's a pretty neat guy. Anyway, so see you in Boston. Have a safe journey back. See you, take care, see you there, take care.