MW visit Musée de Lorraine / bar conversations: FW Lawvere / lunch conversations: S Awodey

0:00 I'm now standing in the Museum of Lorraine, the Musee de Lorraine, on the afternoon of the 2nd of October.

5:00 I didn't recognise the jumper, I didn't recognise the new gear, which I didn't know about until I...

7:30 Yes, I've just been next to... Yes, they have some very nice... This is the private collection of this guy Stanislas, who was the Enlightenment ruler of Lorraine. What relationship he was to my grandfather, Marianne. I'm not quite sure how it goes, I think one of his sons is married. I know there wasn't any good at following those long dynastic families. Even by the times of the Enlightenment. And there's some beautiful microscopes. Yeah. It's in L'Indoire, the year two of the French Revolution, to defend the country against the invasion of the Axis Raids, which of course came right through here, came through Lorraine. And they took Nancy and Metz and Longley. And we're on our way to Paris when, of course, the mass mobilization of the people in what was really virtually an untrained, not a regular army, but largely kind of untrained militias. There were Jacobins, obviously, so there was a little bit, a slight historical distortion to call them red militias, but nonetheless they were the revolutionary, you know, product of the revolutionary, though they are masked, because all of the royalist officers were deserted, so of course they had to, you know, elect their own officers, so they were stopped at Balmy.

10:00 And that was, it was Conner who was the guy who actually organized the logistics, both of the mass mobilization and of the provision of depots and bases. He was a fantastic administrator, fantastically. Yes, I think he did his work on heat engines a little bit late, about 20 years later, yes. And what happened there, I'm not quite sure it was the same person. Oh no, it's definitely the same person, definitely the same guy. And he went out of, he became, he was disgusted by Napoleon, assuming the title of M. He would have not had it after Napoleon had proclaimed himself emperor. He retired into private life. In fact, he was regarded as politically very suspect. I think Fouché and Napoleon's police kept an almost constant watch on him. But then after Napoleon's failure in 1814, and of course the forewarns came back, an extreme reaction. When Napoleon came back in 1815, in the Hundred Days that ended at Waterloo, Carnot did rally to him. ...simply because, you know, anything was better than the continuation of the Hawthorne reaction, and he persuaded Napoleon, and Napoleon actually appointed him the Governor of Antwerp, the Ministry Governor of Antwerp, and he also, it was just a fact that they had last garrisoned for surrender, after Napoleon himself had advocated for a second time, throwing himself on the mercy of the English, and Carnot... ...continued to hold out in Antwerp for several weeks, hoping that there might yet be a popular uprising in Paris and that they might re-establish the republic, and once again start a revolutionary people's war with a mass of the whole people against the reaction. But it didn't happen. No, but by the span of his time, and obviously he was a, you know, a boy who liked acting radicals, but he was very... Very much one of the most progressive figures thrown out by the revolution.

12:30 And I say he left, he quit the portfolio in disgust and came back at the last minute. And then of course went on to do all that excellent stuff. He was a great guy. So that's definitely him. And I checked that out yesterday because I went through the brass card. There's another Karna, his son also was a politician, and later in the course of monarchy, but this is Karna, which I can never remember which is, the father is Lazar, and the son is... It's definitely Sadie Karno, the guy who did the work in thermodynamics, is definitely the same guy who was the... Organizing the armies, yes, the kind of genus of the revolutionary republic. We have a very interesting section on that, on the French Revolution in Lorraine, too. And quite a lot of the Japanese came from this area. But, of course, they only had about an hour and ten minutes before it closed. So I suppose from that point of view, that's fine with me as well. But they had some very interesting stuff in the last half century time, the 20th century time. Now I'm preparing myself for Wednesday when I have the awesome task of taking you around Paris and giving you a tour on the commune and the Liberation. Well, I would be very joyful either. I've never had to go to somebody who I quite wanted to do a good job for as much as a believer in cultural conspiracy. Well, not only such a believer, but such a hugely historically well-informed believer. Plus someone who's been, you know, so I try and pull out all the stops.

15:00 Just explain to me the origin of the human shield. In the 1870 war, the Germans took part in the war. Yeah, that's right. The frontier was back between here and Metz, in fact. Exactly. Exactly halfway between. I mean, I'm trying to tell you something kind of gigantic. Oh, is that? Now that's interesting. That's the story I was given, yeah. That's perfectly plausible, because I had known that the Babylon in those styles had originated. But as a reaction to what the Germans were doing, what I haven't heard, that sounds very plausible, but it's quite interesting to go to the Met, which of course was a German city for 50 years, and you look at all the developments, the various types of problems between the 17th and 18th century French architecture. And then, I guess, I don't know, I think I've got near run and extra, which is a huge railway station, which is... Is that true? Yes, I think you actually have to go through Metz to get to Paris, I think you have to go north, I think the line goes north through Metz before it goes to Paris, I think that's right, I think you do go through Metz, well maybe more than one way to go, I'm pretty sure, I think what I'm trying to say is that there's a lot of people who go to Paris, there's a lot of people who go to Paris, there's a lot of people who go to Paris, there's a lot of people who go to Paris, there's a lot of people who go to Paris, there's a lot of people who go to Paris, there's a lot of people who go to Paris, there's a lot of people who go to Paris, there's a lot of people who go to Paris, there's a lot of people who go to Paris,

17:30 This railway station which the Germans built, which they completed just before World War I, but which was actually built because they needed these huge railway stations for the requirement of the German army, which was a need for the civilian population of a city the size of Metz, and it's one of the four or five biggest railway stations in Europe. And it's absolutely vast. It's designed to basically handle an entire army corps, to pass through it, to deploy through it. That was the reasoning for saying that. The Great Channel General's task had a huge amount of time protecting its railway platform. Thank you for your attention. Actually, we didn't get anything quite early on Saturday, aren't we, so we might as well slip you into one of the modern works of that day, and then pop back on a Tuesday. Yeah, well, it's so easy these days. That was the only thing, the only error I could detect in your otherwise absolutely magnificent talk. Namely? Well, of course, you can if I now will come faster. It was certainly Shulman-Maxwell, but they are in fact not. They are not closed without a concern to the pathos-connected space, they are in fact connected, as indeed all these programming things, all these poor, wretched... Thank you very much for your attention.

20:00 All of these things are clinging underneath the tracks. Well, several have been killed, because of the incredible danger that's been in those trains that are moving at over 100 miles an hour. But they're that desperate, obviously. But in addition to the two train tunnels, there is also a service tunnel, which is also intended to serve as an evacuation hub in the event of a major disaster. Which is large enough for vehicles to drive, to address. It's close to the hub, it's only used by the service personnel. With that you can, in principle, you can walk through. But of course there are all sorts of physical barriers along the way. You were standing on the other side of the table. No, no, no, no, no, no, no, no, no, no, no, no, no, no, no, no.

22:30 That covers the set of all those greater than or equal to the two distinct up-close sets, but they should become, they should grow less in the category. You just get ordinary real numbers that take me that long for whatever to become true. I remember you saying that you thought the up was semi-continuous. In some sense, the written structure is more relevant to the model because metric space is in various places where variable metric space is parameterized by something. Then typically the metric is a semi-continuous structure with a parameter, not a continuous one. Can you tell me some of that? That's the reason why I don't know. Thanks. Well, how do you explain something new with suburban railway, especially calculating the minimal cost of journey? Well, that was just sort of an elaboration of the rich category theory built on the semi-continuous real solid as a closed category. Yeah, right. That's the least cost, a two-step process, knowing that costs are going from here to here. Given that you must use those two processes, what's the cost of going from some point here to some point there? It's just the impingement of all possible sums, the impingement of taking over all points in the middle of the thing, which is actually matrix multiplication, if you realize that anything is a sum, a kind of sum, and summing is a kind of product, actually it's the tensor product in the, in the, in the, in the, in the, in the, in the, in the, in the, in the, in the, in the,

25:00 That's all on the web. That's all on the web. My paper, my 1973 paper. Well, Metric Spaces. Yeah, Metric Spaces and Post-Campus. Do you have that paper? Yes, I do. Well, anyway, anybody can get it now. It was published in a very obscure journal. And on the other hand, various people have been using fragments of it, you see. I felt it was quite important to realize it's a whole thing because these fragments don't mean much unless you see how they fit together into a vast, compact... Anyway, you see the TAC, you know TAC, Theory and Application of Categories, Electronic Journal. Oh, well, sorry, this is for a minute. Oh, I didn't know about this. Previously we had the JPAA, the CAIE, the ESMOND. Yeah, I knew about that. And the Brooklyn one, the earlier, yeah. I suppose I haven't picked that up because I look at the discussion. Well, it's the same, it's from the same center, the MTA.ca, Mount Ellicott University. I have to put my hand up to say it's about six months since I did the last look at it. Well, no, the journal has been published for at least five years. That's not that bad. I have many, many volumes. Yeah, cool. Anyway, they instituted a new section called... Well, it's not called that. Well, that's what it is. It's called Tapping Prints. Yes, and metric spaces and class categories.

27:30 I certainly deserve my point of speculation. I do have it. I was one of the many questions I was getting at. I was preparing on it. Anybody can read it. There'll be some developments. But actually there have been some very exciting developments in metric space theory itself, which should be seen in this light, for me. I have two thick books. This one, let's use the famous Russian man. Yeah. Yeah. I mean, the IGF. And the other one is by . They have found a definition of curvature that's worked in a general metric space. One should not go around putting special conditions on methods. Try to find a good definition that has some sense for all of them. Or for something, because there's a, there's a, I mean what my paper focuses on, maybe it's not the only thing there is, but in fact there's great power in the unity of all of them. And this is lost if you start making sort of ad hoc assumptions, hoping things will go nicer if you do this and that. You should try to find the definition of what NICER means that's meaningful in their own metric spaces or in these spires. So I found this for geodesics, by the way. The whole concept of geodesics is basically to co-monad on the category of all metric spaces. Given any metric space, there's a sort of best covering of it, which is the geodesic re-parameterization. Re-metricization. Basically, it's the direct rule of all intervals, so this combon ad is what's called the adequacy combon ad. So again, of course, the notion of adequacy is the adequacy of additions.

30:00 I don't know. It's actually fascinating. I must try and learn about this. This was recognized around the world. There were two aspects. The intellectual aspect was important. There was another one. It was recognized early on. Well, after all, we wanted to play. There's an ordinary metric space of a special form. And so the, you know, because you take the input as well, you take the geometric, so many geometries can be understood comparatively at the end of the network, and then you sort of begin to overall highlight what you saw. So I think there's just an ordinary metric. And actually, some of those metametric is good by... by... by... by... by... by... by... by... by... by... by... by... Grusman, Grusman, Grusman, Grusman, Grusman, Grusman, Grusman, Grusman, Grusman, Grusman, Grusman, Grusman, Grusman, Grusman, Grusman, Grusman, Grusman, Grusman, Grusman, Grusman, Grusman, Grusman, Grusman, Grusman, Grusman, Grusman, Grusman, Grusman, Grusman, Grusman, Grusman, Grusman, Grusman. But it's always compound names, isn't it? Well, I like them. I use them in English, you know. Well, of course, I know. Right, so... Well, that's the idea, you see, that any space with shells are kind of... The transportability of the triangle, that is, if you have two triples of a point, which in their own right are isometric, then there should be an isometry of the whole phase of the other.

32:30 So this is, of course, strongly just saying, you know, transitivity of a point, or even on pairs, but if you have it on triples, you see, then the conclusion should be that the state really is... Classical examples. It's either Euclid or Lomachevsky, and that's all the three possibilities. Well, then you see, well, of course, it couldn't be quite two. It would be the universal covering space of a given space, which is one of the three possibilities. So Griezmann does prove this under certain assumptions of what kind of space... It's totally on the global metric side, but it's very special. It's a nice space we've been able to think of. But the transportability implies one of the three possibilities. There's kind of a tradition of putting a lot of special property models, but there's a counter tendency in terms of if you put the hypotheses correctly, then you don't need special assumptions. So what has been discovered, I think Alexandrov originally made a suggestion, but there were many attempts to... The design notion of curvature in a metric space is not a Riemannian approach, but a government approach, and this one apparently was successful in the extent that the whole thing worked, developing a theory of it, and I think it would work for other theories as well. Of course, of course. I mean, this is what I mean when they come up with them. Recognizing the affine structure of people. There you go, yeah. Yeah, they still, yeah, yeah. That's another. I guess I got that on the ground. And there's this striking thing, you see Gromov. Among many others is this, among many others there are, an interesting idea that we've been given two lessons today.

35:00 There's a distance between them, and I would like you to see the difference somehow. But it's unbelievable, you know, some ordinary scientific writing, if you'd given independent writing to someone, you couldn't possibly derive anything from that. You all would have said it to yourself. But no, there actually is a double-definition. I was going to say, this is the category, and since the category is the enriched categories for a single V, the question makes sense for general V, not just for V equal to real numbers, but can you make the category a V category for itself, a V category, I think. I wrote a little introduction. I certainly don't have that, and I do want to try and have it, at least because I want to make sure it circulates before the end of the lecture. I certainly will download it. So I go to the NCA at the same site as the publisher's category video. I'll certainly download that. I think I have a problem because I haven't put the text in. I need to put some stuff on the webinar. Oh, you're right. Yeah, this would be awesome to do. It's a city there. Do we have room for one more? You know what, my plan is we'll catch them shuddering. Ah, that's not a bad idea. Yeah, we're eating at eight, aren't we? Yeah. And actually, I haven't even looked at the map, I've just got to do that last little time. Where is this past Colonel Fabian? By the way, you know who Colonel Fabian was? Ah, he was the military commander of the French Communist resistance. In the course of the course of the course of the course of the course of It's very important that it's in the history of existence and one of the grounds we've played a crucial role in the Liberation.

37:30 We can tell you more about him when we go out of their door, I don't care at all. Is it not? We're from their world. No, it is. It is very interesting. I'm very interested that they have a square. Well, of course, he wants the Cossack as a costume, obviously, because it's part of the team. And, you know, the Greek world, although it's structurally made for the poor, it's not going to be a great deal of work. And it wasn't what we thought it would be. So he is regarded, I mean, pretty well across the whole political spectrum, except on the extreme right. I'm going over here, and I'll put the camera on the mask, but that would be a little... Unfortunately, he didn't survive the war very long. He did, he did, he did, he did survive in action. But he's, he's, he's, he's, he's, he's, he's, he's, he's, he's, he's, he's, he's... There's a metro station in Paris where you had to actually set up the headquarters before the liberation, for which you directed the liberation in Paris, actually in the 17th century as well, which of course was Paris-Pas-Couin at the hands of the opponent of the people by a revolutionary uprising before the legalist army division, which of course was specially sent in by Eisenhower and the American forces. All of this was sent to the city, mainly to make sure that officials were able to ensure that order would be restored and also order meaning about disordering the government. Order meaning, priority number one, disarm the government, which de Gaulle in fact spent several months manoeuvring to do. And of course, in the end, it was sent up and told that he was not going to do it. He was not going to do it. Yeah, it's a number that's apparently important in the hands of the people, and the people led by an armed revolutionary government that might have come to this point in the 40s, I think. Tofus, the German commander, of course, actually insisted that the army of the Allied troops, because he refused to surrender to the Communists, In fact, he would very shortly have no option anyway, because the area over which he exercised effective control had been reduced just to the whole summer weeks,

40:00 The reasons that you can understand from the nature of this were extremely, extremely cooperative. They did push for the proclamation of the republic by De Gaulle, but of course De Gaulle wouldn't even do that. De Gaulle was the derivative basis of De Gaulle's claim to power. The public had never legally ceased to exist. The nation had absolutely no legal status. Although that might carry out the damn thing, given the, I'll be frank with you, the exception of that, let's just say, it should really go on for years. Well, it's fairly relevant, as we all know. But it's slightly different, because I have the front page of the Manute, not the original document. ...which was actually produced on the day after the liberation by the Democratic Party party, which is the People's Journal. Incidentally, when we do our little writing for the thoughts at the moment, I can actually show you where the presses were, and which they produced during the occupation, because it was produced continuously under the motions of the chairman. But the mood order which Freud gave to the party was the militancy party, you know, when the gold entered the Paris. The cry was to be first, you know, vive la France, and then vive la France, and then, third, vive the gold. I don't need to go out of bag, because I don't want to say much about it, but I don't need to go out of bag, because I don't want to say much about it. No, no, no, absolutely not. They were very, very much, as it were, you know, fresh and playing the role. Well, they didn't play the role. They were having marketing problems, obviously. No, of course they didn't play the role. Nonetheless, that was the, that was their main edge. It was quite an incredibly minimalist position, considering that at that moment they had the, you know, the conference people behind them.

42:30 The most important principle for anybody else is called the actual liberation of the interior of the social complex. And the British political system is kind of the same. Churchill went on making all these more generalized points than that. Remotely, on the board, he picked up a little script from a 16-year-old boy who lived in Canada. He put it in his way of referring to the FBI, the people who were trapped in small groups. Well, remember, they were the Brits getting ready to go into Greece and crunched the resistance there. And they were rather annoyed that the Germans didn't remain there. The whole point was that the Germans had evacuated to Greece. You know, they had to go in and do the job anyway. This is why Churchill spent the Christmas of 1944 in Athens. And the very French way is where the British Prime Minister could be in the middle of what was still no world war. The destruction of the University and the instillation of this puppet royalist government had actually been known in a popular place forever and didn't have any kind of historical control outside that, and many of the historical control within Athens was because there were two different divisions. These have been ordered to ask exactly as if you were in a concert city for half a thousand years of progress against certain problems. These are people that have just liberated the world. No, the history of the Liberation and the period immediately after the Liberation is very, very interesting, really, because they might be the site of that question. I'm really looking forward to giving you a little quick thorough apparel of what's on there.

45:00 Well, the space just as well. Oh, yes, you didn't know at the time. Oh, that's interesting. No, the Greek Civil War. No, I think it was a British crash that was done after the war. Oh, no, during the war. Oh, yes, during the war. Churchill himself actually went with the Greeks. It's a very high path indeed. In the course of the course of the course of the course of They're clearly trickling down into the absolute truth. Oh yeah, because what do you think, it wasn't just the self-doubting that ended up in mathematics, it ended up in all of Europe. Here is one idea, he was a scientist in the United States in the 1900s, fortunately he was also a monk, but suddenly he was in the area of the 12th and 17th century. But to the extent that Churchill sent his only son, and he was Churchill's only son as his representative, the head of the nation.

47:30 These are some of the key terms that are used in mathematics and physics. Thank you very much for your attention. How zoomed that man is zoomed, and what's out of that man. Hmm. Anyway, you better get back to the rest. Well, I'm afraid there are any stories, but, you know, not necessarily historical analysis. That comes weird, but I'm looking forward to going back. Thank you for your attention. Oh, she was one of the last girls to always go to college. Yeah, like a 19th century girl. She was the name of a funder of a dental department at Southern Wall. No, she went to a secondary school. And I don't trust her at that time. They said that that was the reason that Clayton sent her back to Paris rather than to London.

50:00 It was because it was in such incineration for her to be internationally known that when she looked at that, she was beyond a good chance by a government. Just because she had so many favourites. Thank you for your attention. But before that, probably I'll mention this to you, that I have a strong suspicion that the link between the Araman and Nikoyan, which is potential and laying away from the argument of the theory, that you haven't learned so much, but it's extremely interesting to notice that it's one of the strongest. Thank you for your attention and see you in the next lecture.