Morning Discussions, incl. FW Lawvere — Choice principles, points functor & other topics

0:00 Yeah, if you can, but I don't know if we can get the sort of the end of that. And then we've got to draw lots for who's, well, the driver, the people who've got the, are on the license to drive, or the docket, have got to draw lots for who's going to go pick up their Corrie's wife. Oh, you do. Well, he's going to be ringing here sometime after five, but he won't be obviously when he'll be riding the train, so I think he'll probably be around sometime about nine, provided he... How long did it take you on the train? About two and a half? About that, yeah. About two and a half hours, yeah, so he gets a train run. Yeah, I'm not sure when the first train in the morning. He's due in at 5.30, is it? He's actually due in about ten past five. To where? Into Charles Dutton. Charles Dutton. Well known for his time. So you think, and then he gets a train ride. Well, if he's doing the sensible thing, it would be more comedy. He'll just get the train and drive. Are they traveling? Yeah, he gets a train without changing it. You don't have to go to Paris. You can just get a train directly from Charlesville. It takes longer, but it's more of a hassle then in Paris than having to get across. He'll actually be traveling in life. Yeah, I guess he said to me he travels very light. He just travels with his little backpack. So with any luck, he might hear around. I'm going to encourage him to get off at Laval if there is a train there. Where is Laval? Laval is about an hour and a half from Paris. Oh, I see. An hour and an hour and twenty-five minutes. It's almost exactly the same distance from here as Rennes but in the other direction. Are you going towards Paris rather? I can have a business meeting in five minutes just to discuss the... The agenda of the rest of the meeting, but maybe after the against the end. I think it's clear that he's only saying what he's saying.

2:30 And in fairness, he did actually send, by a long way, the most thorough and detailed set of suggestions for the topics for discussion. We should try and get away and just give ourselves a break one afternoon. I'm thinking probably the afternoon of Wednesday, and then we drive to buy our dinner there. Yeah, it's true, but we could not interrupt that. I mean, it's also an extremely beautiful place. But, yeah, well, I guess we can leave it until... Well, that's beautiful. I mean, I don't want to do anything at all to interrupt the discussions. That's right, I mean, nevertheless, perhaps a break. Thank you for your time, and I hope to see you again soon. Yeah, we can certainly spend a couple of hours looking around that. It seems, if the train stopped here, this could be a... Serious... What's that place in the south? Carcassonne. Carcassonne. It's actually known as the Carcassonne of the north. It is commonly referred to in the kind of the tourist brochures. No, but the Fouché Tourist Logos actually builds it as the Carcassonne of the North. But the Carcassonne has a railway line. Well, this had a railway line until 1944, but it was flattened by the Americans and they never rebuilt it. And this was quite unusual for a place of this size and beauty to be, to be for real. To be honest, yeah. I think it's one reason, I mean, you know, it's one reason I was able to get this house for such a fantastic price. Oh no, yes, it's just that it's a little bit... But it's also a little inconvenient. Of course, I drove it, it would make a lot of

5:00 a difference. Yeah, sure. And, um, but there is a period with us, I'd say. Yeah. Yeah, um, I think we'll, we'll resume soon, Pierre. Is he still having wimps? Okay. I didn't really want to stop. Question of the meeting? No consent? No consent. Of course. This works. By the glance of it, no. It's quite fascinating. Okay. Sure. I'll be sure. Yeah. There's a part here that's struggling around the different notions of second order. Yes, yes, yes. Yeah. What I see now is sort of the preferred notion. Yeah. Yeah. Yeah. Yeah. Yeah. Yeah. Yeah. Yeah. There are several candidates for who will work here. There's T-Squared over two times. I thought we had enough time to talk about the moon now. So, yeah, here we go, the moon. So, I mean, this is worth too much time, but I think that's the second order difference. Well, I'm going to take it on my shoulders as the facilitator, since I've already run the suggestion past Angus and Bill and Dee Collin, to suggest that we take as a relatively self-contained topic, just for the last hour or so, a theme which naturally comes out of the discussion of how one sees those promotions as fitting within the framework of algebraic geometry, which is the unity of the... Algebra, geometrical and logical conditions in topos are expressed by what Bill has referred to as the underlying unity of SUB, which is the separable, unramified, and decidable conditions for objects to be, respectively, very distinct in a topos, and how it also relates to this issue of...

7:30 So, I invite him to take that up and to give us an account of this. The SUD simply means that they're all three the same. They're three different. It's an unusual. Just to remind you that they are the same. But decidable is taken from logic. It's an object whose square has a diagonal map which is complemented in the most naive sense. This is a subspace of x squared. It's coproduct with the diagonal. It's all of x squared and its intersection. In the non-Hooleian world, it may happen that occasionally we have this, what's it called, decidable or decidable equality. The equality might well be decidable and other predicates are not. Shanyarol likes to call it separable because it's exactly the same thing. It's just the geometric expression of the idea that in number theory, ring theory, These are the repeated roots, and you separate the roots because we're not to get confused, so the S and the D are just too different. A lot of logicians work on that. Unramified is also the same thing, except that the word is typically applied in the category which is expressed as the categories over a certain object,

10:00 so that the separable objects over a given object, X, one says that the map is unramified. Grammified meaning, basically, if you start going along a curve in the top, then you can't suddenly separate into two parts, because being different and being the same are rigidly opposed. So, we used to think that it was an absolute notion. When separable, it's like it's an absolute notion, and when it's grammified, it's the corresponding relative. Okay. It wouldn't be fair to say separable is an absolute notion, but it might be a concept. Maybe it are all a concept. I mean, a scheme is a scheme. Maybe it's a scheme over a base. No, look, I'm not going to make it over a base. Now, that's when you define it as a base, and you're looking at it as a base. What came up was because, well, basically, Peter Johnstone had a paper which he called QD, QD topos. Q means quotient. It comes about in the following way, much more generally, let's say in a topos you can consider those objects which are SUD. It goes under many operations, sub-objects, Cartesian product, finite number, disjoint sums, and so on, but not under quotients, so they typically don't form a topos on their own. However, one can consider locally those which are the recipient of an epimorphism from an object that does have this, and these always form a sub-topos, so there is a... There's a, not a subtopos, excuse me, they form a subcategory which is a topos, however it's actually a quotient, because the inclusion, the obvious inclusion function is actually the inverse image function, the geometric morphism.

12:30 You see immediately, by what I said already, that it preserved arbitrary solvency. Given any object, to take the SUD core of it, which is just the joint image of all maps from all possible... Now, Peter Johnstone found a characterization which wrote deep topos, and he found that in terms of sites, so for which sites the corresponding topos could be, and it actually only depends on the category of any subtopos, and therefore the topology, the small category C, is locally, I'm sorry. He now in his book, in the elephant, he calls it locally decided. We call it locally separable, oh, I've got too many words, but the characterization is that the category C consists of epimorphisms in its own right, that is, its maps are not epimorphisms, there's a Yoneda embedding which inserts C into the total, it's not that the maps are epic taken in the large number. Epic is a cancellation property with respect to... A certain class of co-dominance. If you just take the co-dominance in the category C itself, this cancellation property should be true, and conversely. So this certainly includes the case where C is a partially loaded set, but this is a traditional case of sheaves on the topological space of D sets, where D is a group, because, again, the group obviously has a property that every map is, and it can work as a medium in the extended category.

15:00 So it's a kind of, in that sense, generalized space, because certainly two kinds of things that should be generalized spaces are cheese on a procept and actions of a group, and these are subsumed under this condition that's in the site all maps for. It would be, if you just, would be in the older, in the previous idea of Grotendieck about etande, which is essentially equivalent to every map in the site is monic. But in a sense, the epic condition of geometric and logical consideration, there's a certain way in which it's more general, because one feature, one drawback of the QD notion is that it's not stable under, so that if you have a topos E, and E slash X is QD, E itself may not be, even though X covered the terminal object, so it's covered, so it should sort of, sort of locally. There are now two senses, you see, locally in the sense of covering the topos, and then locally in the sense of there are enough maps into, you know, an object inside the topos. So locally, locally, I work this out. This is in the circle of my... The sites, this category C has a problem in using property, cancellation property still, and if you have a pair of maps... You can conclude that they're equal, provided there exists both a map before and a map after that have equal properties. So from those two equations, the sum map after red, it follows that the two maps themselves are equal. So that turns out to be equivalent to this thing of there exists some cover in the topos on which it's QD, but obviously it also especially indicates that if every map is monolithic, then that's it.

17:30 With every mathematician included in this locally, in some sense, the etendus are also locally QD, the first clans to epi and non-epi, obviously. That's, roughly speaking, why they came up there. And now, as I said, this notion of generalized space is, in fact, general enough to capture the main concrete idea of generalized space beyond these. There's a lot of trivial things about processing groups, namely the etal, the Petit etal topos, the Bernthalite is certainly of that form because one can show that we have proven this. Absolutely certain of the formal proof. I mean, I asked for advice and nobody, nobody was there. We have to reprocess it some more. But making sure I didn't miss some separability condition someplace, which I don't think I did. Yes, you take the Petit-Atal site, you look at just the affine parts, that's sufficient, right, because everything has an affine cover, you look at just the connected affine parts, and that's a site equivalent to the Petit-Atal site, which has no iron components. There you have the dichotomy, equal and not equal, and if you had the wrong thing, it would be dividing the domain into two parts, which you can't do because it's decidable. That's the basic dilemma about the situation I should have mentioned, but it applies here, because you assume they're connected, and that's, of course, enough for the site, because the sums come up automatically and are generated with it.

20:00 So it's just the fact that they are indeed CUD within the context that implies it's all a match. It's a kind of unique continuation of this. From then they were very reluctant to go to these kind of spaces. Natural, sanstrum, illogical, algebraic. What is very, very hard to get my friends to look at is the fact that he had two different kinds of topologies going. I mean, not only the generalized spaces, but also the categories of spaces, especially the analytic one. And his carton seminar about... Techniques of construction of analytic spaces. The technique of construction was, you take the category of analytic spaces, but you don't need to take a site that big, and you look at cheese on it, huge topos, and now you say, well, I want to construct an analytic space. It should be an analytic space which represents the whole theory of representable punctures. I want a space that represents such and such a concept growing out of the analytic function, the analytic space. I first show that it's a sheaf. It has to be a sheaf. And then, you know, you whittle it down to see that it's representable by one of these special objects, analytic spaces. You start by, you start by working, you know, in this much larger world,

22:30 Now, you can say that this is a category. That's an extra little step, which is obviously coming up all the time when you look at the schemes on schemes, the schemes on mathematical spaces and so forth, but obviously these schemes and scales should also be called spaces. They're very, you know, they may have more properties for special objects, but they represent concepts that arise in the study of the very special spaces. The beautiful virtue is that you can manipulate them geometrically, even as in the same sort of ways you manipulate them, even without using the word, which is constructing them. Do you want to say a little about how this connects with your own paper, your own JSL paper, 1987, the one, you know, which was the more philosophical version of which you published a set of... In a toughness with non-stellen sets where non-evident objects have global points, decidable objects are sets. And I showed pretty much, and that's why I said not only are they sets in terms of the motivation, but non-stellen sets, every object in it. The ones among them that are well distinguished objects are sets.

25:00 And so this was a real point to make in the 19th century. If we decide that things are completely decidable, then we'll get, as Cantor himself did, we extract these things, and then the world is mingled, cohesive mingling, extract these things. So the serious point here was to say, yeah, we've got these objects which are not all decidable, the classical spaces, and Harris talks about this, and Harris talks about it, and John is the expert on those sources. And one way to depict what Contrer did was he said, well, let's just ignore the fact that non-decidability of those treatments is all-decidable. Oh, and that was the other thing I showed. This is, in fact, a sheet of toposcript topology. So it's not just that you pick out the discrete objects. You can also map to them by saying, take the sheet of notation. And I said, that's Contrer's abstraction process. We'll take double negation sheaves. It's a topology in which every object has a smallest number, which is not a good condition. Well, that's not an essential. Is it an essential? I think in the usual models of SDGs, it's essential. Certainly in the usual one, but that's not a problem. Yeah, yeah, yeah. So I said, yeah, this is Condor's abstraction operation. He says, take any object and ignore everything except the cardinality.

27:30 Ignore everything except double negation identity, that is, take double negation sheets. In these models of SDG, those things will be decided of all here. They will be sets. They will form a category of sets. But it brings out the geometric meaning of Kepler's abstraction process. Yeah. Yeah. And so here we've got a nice precise model. I'm not trying to do SDG, but I'm saying, here's a precise model where the kind of reading we talked about makes sense. Yeah, well, I mean, the contrast, of course, is more general with everything, though. Specifically, it tells more different factors. Any kind of an extract is given and also... Well, you need stones and also two-valued if you want to get the two-valued category sets. Right. When you say category sets, the point is that it will behave. You know, like the category sets, it will be completely without cohesion, I mean, in some sense you see this decidable object is like a small step in the direction of discreteness, but the objects that merely have that property can still be very non-discreet, like a tall tower, but they are very discreet in the vertical direction. And also there is this infinitesimal criterion for acceptability, which is basically a space whose tangent bundle is always equal to itself. You're only talking about infinitesimal paths that are given. In other words, s to the power of t equals s along the diagonal path is the condition of s. Let's say, where an algebraic geometry enforces s to be the spectrum of a separable algebra. You know, we started just at the end. But this is the condition, you know, that all derivations into everything is zero, right?

30:00 Because the space s to the t, of course, has figures of all kinds of shapes, so it really has to do with maps between two rings, and all derivations are all zero. But then, there's a further thing where you introduce the Grudenbeam topology, which is typical, but then you restrict that to these simple objects. And you find you get a boolean topos, namely the Yawa topos, because the restriction of the topos. For example, let's look. I mean, we're discussing about stochastic sections. Of course, any finite field extension is a stochastic section. This just means the bigger one is a vector space over the bigger one. And so there do exist many linear maps which can be chosen. So that topology, although it's not boolean globally when you restrict the cyclical objects, it turns out to be that so-called bar topology where everything is a covering and that gives all of the boolean atomic, atomic boolean, which is basically the all-out surface. So the separability idea combined with the cyclical topology gives actually a much stronger idea of discreteness. Still we know, while we've been acting, that otherwise this is the street. Yeah, well, I mean, if you have a Nellstone... You've got to follow this guy somewhere. I mean, there are versions of the Nellstone Zots which don't require the global section. Yeah. I mean, reciprocally, what you have is that this, these, the street planes are both reflected and co-reflected. So a general cohesive space has not only a Cantorian set of, quote, set of points, but it has equally a set of components. And connected components. And these are two functors which one is left and one is right, adjunct to the same inclusion, so there's a natural map of the points to the components.

32:30 And so the Nostal and Satz should say that that's an empty morphism, roughly speaking, every component. Because components are always connected by any component as a point, except that it isn't a global thing if you're not talking about it. Abstracts, abstracts, abstracts, abstracts, abstracts, abstracts, abstracts, abstracts, abstracts, abstracts, abstracts, abstracts, abstracts, abstracts, abstracts, abstracts, abstracts, abstracts. Going in the same direction, from X to the A, the A to the X should still be an epimorphism. So no, in other words, no actual existence. That's the property of epimorphism. It's called internal choice.

35:00 You see, even the Guggen models with groups tend to satisfy that. But then, this isn't about the global section, because if you apply the global section structure, If it preserves epimorphs, then you would get a real point out of that, and a real point of that would be a close choice. There are two sort of, you know, internal arcs, which is very strong, which doesn't imply that the epimorphisms actually have sections, it's just that in some internal logic sense of what it is. In fact, there's a paper by Albert, is that right, Colin, did I get that right? He also makes one understand better the relationship between and the relative uniform separability conditions. I mean the definite term. Well, I'm sorry. Uniform whatever. It doesn't sound like definitions. What was it again? Uniform relative uniform separability. Relative? Uniform separability. The Chinese thought his perception of the house is Hausdorff, that it's slightly stronger than Hausdorff. In terms, he has about six different versions of extension of economic conditions in the internal. The SUD condition is way stronger than Hausdorff, in one point of view, because Hausdorff just says that the diagonal map is a closed map. We're saying it's a coping map. I mean, there's no topology as such around, but it's in the spirit of...

37:30 The guy will be cloven and merely closed. Is that what he's talking about, that he's stupid? I will happily lever out, but yes, I think it will be that. I said there's no topology around. There's no specified notion of open and closed. We're talking about objects in a category which may or may not be anthropological territory. There may or may not be a category of spaces, and even a category of spaces may not be. My feeling is that really these are two different terms. It's unfortunate that the word separable or separated is used. Separated is used for Hausdorff. Schemes are separated pre-schemes of the previous. Now that's been reversed. So the separated basically means the diagonal is closed. It's one thing, but then to say that we have this logical decidability of acceptabilities is another thing, and so the fact that they go together. I don't think there's any context in which they become the same. In other words, this is not one of those cases where there's a single very general theory of separation. I guess that's part of it. I don't know. I can't think of it. I can't think of a separable polynomial. There are two things might possibly, but that's sort of too special for me. It just seems that the use of the word separated has too widely... separated, which cannot really be united, these two things.

40:00 Yeah. ...unramified. Yes, sir. I mean, unramified is an old... Oh, yes, yes, yes, but it's not good. It's a property of a map. It's a property of an object in the category after it's over. That's such and such a thing. No, I mean, it's... We have another, we have another notational trick. The French word for unramified is in, in, in, in, in, in, in, in, in, in, in, in, in, in, in, in, in, in, in, in, in, in, in, in, And therefore, of course, in any category, the category of neat objects in any category automatically has a property, because they have both this property, all over the world. In other words, because any non-zero thing mapping to it wouldn't necessarily map ethically, and so the two things are equal.

42:30 I mean, sorry, they are equal because the tone structure, the direct image part of the QG reflection of the general picture. You see, we're cleaning up the general object, so dusting off the stuff that's sticking to it, and taking the really neat part, so out of this we can make a whole. We commonly say that you've been taken to the cleaners, but your money has been taken. But you see, your money is around the superficial aspect of your body. Your body is still there. There are all sorts of layers which are all functures in the same sort of general pattern because you know exactly what means, that's which category you're in, so if you change the original category you'll therefore change the notion of what the natural reality is. I take your point. We've come to the end of the day.

45:00 It turns out to be the same thing. Yeah, that's right. Yeah, okay, that's kind of, I don't know exactly how this works in general. If you take any topos, this QD reflection, Yeah. works for the right adjunct portion of the head. It's extraordinary, isn't it? On the other hand, you always have the open negation T, which is a subtopo. Yeah. So you have a composite from geometric morphism going from Now, what you're saying is that, under your assumptions, this was an isomorphism between a quotient and a sub, but I don't know exactly when this might happen in general. This would help a lot to understand this bureaucraty business, too, if we could freely say the same, for example. In fact, you see that you have the forward and backward maps, and sometimes you even have the essentiality and the localness and so forth. What is a quotient topos and what is a subtopos are distinct concepts. Occasionally you might have it retracted or all the same, but especially in this case. I have to apologize for the horrible immediately get to get around to two of my questions. Why do I have to be detained? In concrete cases, what you construct at first, it indicates an essential purpose.

47:30 You may then pass species where it's no longer available. The thing is that the sort of intuitive inclusion in many of these examples. The relationship between the infinitesimal is talking about the, if you have a finite dimensional algebra, the whole kind of infinitesimal object, that you get actually an infinitesimal object, which is the standard sheet conclusion, you see, the sheet conclusion is always this bright edge one, you're actually getting quite another global space, you're getting one which is very, which is informal in character, right, kind of in character. It contains the same information, but it's plugged in in the opposite way into the world. So, this is not ever easy to point out. These are actually just two different industries in the street, but with structure. If you can keep you to lunchtime. Yes, no, you said it then. I'm sorry, the English, your clock. Yes, true, true. Being literally, literally, the English used very highly in my childhood.

50:00 The expression lunchtime and then drop. You think a change would be in English music. No, no, no. So that gives us three hours. And I thought it would make a very self-contained and natural way of concluding, if it's okay with you, to discuss the ownership of growth and decon points. You're okay to raise some issues about that. I agree with what you just read. Well, I certainly agree. And perhaps a satisfactory definition. What's this? Well, this is something about stochastic sections of... Where one branch goes to infinity at some point, does some branch going to infinity prevent them? Well, no, but here's what happens. So, is it one double point? Yeah, this is, I'm thinking of this as the imaginary section of the line. This sheet has a branch that goes to infinity here, and it's two-sheeted. It turns out that this account's exceptions are determined by any polynomial over the line that passes through that point. Where the one sheet disappears, it has to coincide with the other branch. Because it can be anything. Anything anywhere else? Any polynomial function will do, as long as it crosses the diagonal. And any polynomial function has some weighting of these branches.

52:30 But here, it has to do with all the weighting. Why is there any more? It has to be that. I guess what you're saying is that it will be that. There are sections, and they're all that. Thank you very much for your time. All of the above are on the cradle, so I have to leave it downstairs in the corner of the room. He'll ring when he signs at the airport. Let's see if I can find him. It's all right, I'll be up too. I wouldn't leave the store with you. There are plenty who would come by bus. No, he will come on the train, and Colin and I are going to drive to meet him. Okay, okay. If he gets something, I'm not casting sections. I don't know why he should be in this one. That's why I'm not casting sections. Thank you for your attention. I think that would make it agreeable to that suggestion. Well, it's an atomic function. It all substitutes for having been able to do an absolute number one. Thank you for watching. I like situations where it makes sense. It turns out that slowly, slowly, the moral of the problem is that it's not always the same.

55:00 Well, I proved this here on Piper A's way. I proved that you want to do the logical method. But you can see from the way it worked, it's always the same. I go round the world. It's always there. Perhaps it's a slightly different dialect. It's a different culture, which is a photograph of a function, but nonetheless, yeah, I think that... I was trying to figure out... And one thing I had hoped you could come up with. Perhaps in fact he will come up tomorrow in the general discussion. I think I'm ready for that. There are quite so many points that you can see in one position. I don't know if I've seen his... It's an extraordinary memoir. It's a story about the child we know that he wrote in 1973. This was just during his visit to Brussels. The actual ring of the moment gave us this series of talks. Very well. And what others might say is usually more about classifying toposes for different theories, which theories have had a classifying purpose, which, as Bruce said, has been effected eventually. Essentially, it bypasses what you can think of, because it's just so incredibly powerful that you can see everything in terms of limits of which theories have had a classifying purpose. Which, of course, in a sense, you know, don't trust us anyway. These examples were bypassed by him. He, he, you know, wasn't doing it, I'm talking about. Think about how poor he was. He was not within the sets of the alphabet, you know, or a blackboard, or a normal telegraph. He didn't spare any of it. Of course, he made the worst ones, actually. I think James Webb, for example, said a little bit about that. Thank you very much for your attention. So the y-squared has to, um, y itself is now determined by that. I wonder if that makes me possible. Higher powers of y are associated with that.

57:30 So you've actually had many, many, many, many, many, many, many, many, many, many, many, many, many, many, many, many, many, many, many, many, many, many, many, many. Number two. He is from the north of Germany and has extensive research in the Lumen Bay, something about the family background. Yes, it's more of a personal experience. It's not a scientific background. It was intended to be a study of American things. Yes, exactly. What Scharau does is to research the family background, his father, his mother, and so on. Well, of course, we'll read it. Let's start with a very nervous sort of story, because I'm not going to be very cautious with this. I'm not going to be very cautious with this. I'm not going to be very, so very strict, acidic. I'm just going to sit here. I'm not going to sit here. I'm not going to sit here. I'm not going to sit here. I'm not going to sit here. I'm not going to sit here. Was it near Lodz? I don't know. I doubt it. This is somewhere in the east. No, it's not. I don't know. It might be. At the time it was Ukrainian. Yeah, yeah, yeah. But it's just a quarter of Belarus, Ukraine, and Russia. I know the border of each of them. Well, of course, it transforms the time. It's related to the time. And I think I have to take one witness, correct me if I'm wrong, but I'm not sure either way. In other words, oh no, you must have been Rasmus. You must have been Rasmus. You must have been Rasmus. You must have been Rasmus. You must have been Rasmus. Yeah, yeah. Thank you for your attention. From 1905 to 1910, he was released from jail and was re-arrested and participated in the revolution, I know. But he was, of course, he came from this very strange city.

1:00:00 I don't know what to say. I don't know what to call him. I don't know what to call him. I don't know what to call him. I don't know what to call him. I don't know what to call him. It's very interesting. The strict Hasidic Jews are obviously the we frees of Judaism. Well, it's interesting, let's say. It's time for one... Why is it the same as Lubavitch? I mean, not exactly the same as Lubavitch. It's similar, isn't it, actually? Lubavitch is an Hasidic sect, isn't it? And then we were invaded by... The Lubavitch apparently, in the section of Brooklyn where they live, there's a tremendous tussle going on because it's become a very fashionable area with lots of hip-hip-hip-hip-hip-hip-hip-hip-hip-hip-hip-hip-hip-hip-hip-hip-hip-hip-hip-hip-hip-hip-hip-hip-hip-hip-hip-hip-hip. A London Jewish community who were proposing a real cave out of London. They were going to do everything. There was this business in Hempstead that they wanted to act. I don't know what it's called, I mean, well, Comet probably does, and Pierre, you'll certainly know. What is that thing called in Orthodox Judaism where you have a particular area which is marked off by... The boundaries of the area are marked with particular signs on holes or on trees or other features in order to indicate that this is an area in which some, it has something to do with the observance of, you know, I can't remember what it was. Well, that's what originally it was. The tail was the boundary that Jews would cross socially. This is something much more specific. There's a technical term for it in Judaism. I sometimes used to get the Jewish Chronicles and they always banged on about this because it was a big tussle between Haskell and Kigate Council whether they were going to admit them to have this.

1:02:30 As I said, it has something to do with the ritual observance of the Sabbath. Very strictly Orthodox Jews require that this... Any Jew entering this area is expected to be observing the Shabbat very strictly. I don't know. But anyway, I'm not sure. I mean, I read it very hastily. It was probably in the gallery two or three weeks ago. But the implication was that this group was growing and very united. And they basically wanted to build themselves a very good society. Well, it's a very common thing and very tough in religious communities. I've heard quite a lot about these speakers, the Assyrian Jews, and as indeed the Wefrees and of course the Mormons, is that they are a very strict respecter. I mean, they regard it as duty to have as many children as possible. They're living biologically bare. That's simply so. There should be more Mormons or Assyrian Jews. Actually, the Wefrees don't seem to be quite so bound up with that. They carry lots and lots of children. I think they tend to, in the open, they tend to settle down more shortly than the rest of the population. Well, he's not over the screen primarily, so it's not, I think, as far as I know, he's not, he's not terribly over the screen, but his family do, and I think he comes from, I don't know, the 6th or 7th, which is, in modern times, in Britain, it's not, it's about, but we freeze, I should say, just to think how much Scots give to the... To the splinter group from the free, independent Presbyterian church, which was itself a splinter group of the original splinters in 1831 at the time of the Westminster Confession. So somehow it was free, so it was weed free. That's right. I think there's something which is even adjoined to being a weed free, but they're the kind of, you know, independent weed free. They're the reformed, independent, free. But the main Presbyterian church split into three factions, I think in 1831, they split into three main factions, essentially over a theological issue, it was also related to their relationship to the state, but it was mainly over a theological issue, the nature of grace and the nature of salvation, whether grace was the solution to salvation or whatever it is.

1:05:00 So when you save yourself by words, can you know whether you're saved? I think there's no question at all, but for a good columnist they all suppose it's not true. I even believe the rest of the class found out on that point. Well, even after that, it's not a yes or no question. For some people, are you elect? No, I'm kidding. For other people, you could be elect. Oh, no, it's not that. It's just that, you know... Your good works are a sign, are an external sign of your being elect, and they're not necessarily salvation, I'll tell them, and they're certainly not sufficient. I think that's the standard Calvinist position, that these guys split over something much more, a much more suspicious theological issue than that, and having split into three, The smallest of the factions, the ones which basically fell back on the mainstream, the cells split again, and then one section tried to reunite with the section that had split off, and there was a further split, and the weak trees were the ones who were left, and they are regardless the kind of strictest and most powerful Presbyterians, they're the ones who, you know, if you, if you just kind of, you know, you just don't. There was in fact the Lord Chancellor of England, who in fact became the Lord Chancellor of England. He was a mathematician. Indeed. Not only was he a mathematician, I believe he was the last. He was a very distinguished person in the UK. He was a member of this extremely strict.

1:07:30 I'm a fanatic of the strict Presbyterian sect, although not, I think, the very strictest. He was expelled. No, he was the Lord Chancellor of England, and one of his most senior colleagues, a fellow judge, who was a Roman Catholic, died. And he went not to the funeral mass, that would have been quite unacceptable, but to the man's memorial service. And that was enough for the Wefords to expel him. He went to the memorial service for a fellow judge who was a Roman Catholic. That was enough for them to expel him. Because Roman Catholics are followers of Satan. The Pope is the Antichrist. He is, you know, he is the antichrist, he is the devil. The bishop of Rome is the representative of the devil on earth. If you have any dealings at all with his followers or his wealth, you're damned. And this man went to the memorial, not to the funeral mass, that would have been your funeral mass, but just to the memorial service, and that was enough for him to be expelled from this world. Well, I mean, this, I'll tell you, another story, it's not... Why not? I never had any contact with him. No, no, the mainstream Presbyterians in Scotland are also very mild. This is an extremely small, specific group of researchers who wrote a bit of it in ancient. And so they remain a mainstream church in terms of... No, no, no, the people who expelled the Chiro are a tiny splinter group of a splinter group. Speaking but on the different places. The south of the determinant and the north of the determinant. The Baptist too, of course. But even in the pedagogical dictionary, there is a spirit of the north and the south. Well, was it the Baptist? Well, it was the Methodist who split over slavery, wasn't it? The southern Methodist went off. I think it was in the 18... it was not... I think it was in the 1830s.

1:10:00 They split because the Methodists in the UK, of course, were very strongly anti-slavery. Wesley was one of the principal allies of the world of course in anti-slavery. But in the United States, not to the exact date, but the southern Methodists... I don't think they, you know, I don't think they actually condemned the ownership of slaves, but they certainly wouldn't say, you know, there definitely is a strong biblical government, nor do they own slaves themselves, because, well. By the way, there's another, there's another question. Yeah. Do you know the president? Oh, yeah. He said, well, because he said, no, it's a labor system. And then, you see, there's a, well, there's a solid answer. But he asked me if, who was the principal author of the Chronicle of the Atheist and the Architect History of Mathematics, and it turned out, in reality, and I think this is quite a number of you, Oh, but that might have been because they were on the right side of the spectrum. Either they refused to accept a paper like that, or not to admit it, which was a freeze.

1:12:30 In the course of the course of the course of the course of the course of No one will remember whether it was the object who acted after us. And in fact it was because they were no longer part of the teaching, they were no longer a sport, they were a thing of the wild. So he had two, so he gave one to Mr. Ed Holmsher of the Methodist Center over there, and his name was Ed Holmsher, and he was one of our connoisseurs, and he was one of our connoisseurs, and he made it, he was already a Methodist, and he was a non-capitalist, and he's a definitely honorable visiting friend of mine, and he had a vision, and he had a vision, and he had a vision, and he had a vision. That was the point of delay and then we're sure to see the good ones, the good ones, and then go on about that. But he's proved that there are other kinds of chances, things like that, which were a joke, a joke, but he had, he had. He had some very good lectures at that time in England and Samoa, not in the West Camp, but I think it was further across all the dissenters like John Barnier. So, it must be an absolute phenomenon, not only the problem of England's age, but it was going on for some time, with some choices and others, but it continued after they restored the king, I mean, even though he did that, they still went on with anguishes. And of course, I mean, they put a deal, basically, right there, well, they want to see history and the way they want to discuss it, the channels, the world, and there's no way that you want to speak of it, you'll have to speak of it only one moment.

1:15:00 From having met Sperry Speckhardt, I didn't know that there was such a thing as the Southern Metaphysic, and the people didn't agree with the Southern Metaphysic. I mean, I read a third-year student of yours, you know, and he said, well, he said, well, he said, well, he said, well, he said, well, he said, well, he said, well, he said, well, he said, well, he said, well, he said, well, he said, well, he said, well, he said, well, he said, well, he said, well, he said, well, he said, well, he said, well, he said, well, he said, well, he said, well, he said, well, he said, well, he said, well, he said, well, he said, well, he said, well, he said, well, he said, well, he said, well, he said, well, he said, well, he said, well, he said, well, he said, well, he said, well, he said, well, he said. If he would at some point be king, he would then be on the spectrum. Well, I don't know. I mean, I don't know by far. But he, I mean, why would he be on the spectrum? Actually, he was not even on the spectrum until... In fact, when I was in Melbourne, in general, I was told it was a fact. I was told it was a fact. And then, then, then, then, then, then, then, then, then, then, then, then, then, then, then, then, then, then, then, then, then, then, then, then, then, then, then, then, then, then, then, then, then, then, then. I wouldn't have never heard of it. It's like traveling to a museum, it's like you'll take my word and I'll know where you were. But then into a new experience that hasn't been bad, literally, I mean it's all the way through the world. This is where I did a lot of my science problems, I did a lot of my future and third year, I did a lot of my chemistry, I did a lot of my chemistry, I did a lot of my chemistry. And then he was killed. My mother always suspected him of the first kill from the very day. It was from the head of Gaddafi. But in fact, I know him from his grave. And then Gautama, I mean, when Gautama was there, Gautama was in the clover quite early. He was in the 60s, I guess. And in fact, he had Gautama as a soldier. He died when he was 14. And then Gautama, I mean, he killed him in the end. Gautama came to me and he said to me, you should join him. And I said, just to me.

1:17:30 I hold a letter of my due for a good price. I will send it somewhere to the Ministry of Education for you or for whatever reason. Didn't you say that you were going to be very loud? Oh, he's speaking already. That's all. It's a mission. It's a due then. It's very direct. I can solve it. I see it. It's 50 hours behind.