Morning discussions

0:00 Thank you very much for your time. He actually really did try to consider the general and quite systematically, and then try to develop a kind of general framework, I mean, a framework for dealing with general algebra. He mentions it in 30 years of foundational study. Let's look away from the full conceptual explanation of this vision of Hawking. He said he thought about the other treatments, and I don't know the other ones. My basic claim is that most of what's been done in neuroscience logic is intentional, actually, the fact that we take the inverse integer, i.e. the substitution, of, you know, a provocation combination, and that's, we look how to substitute, and so forth, which has been turned into, you know, Toko's logic or bar-exact category logic, whatever the fact would be. You can view sub-objects and you can take union intersections of sub-objects and you can map another object into your object and take the pullback which will certainly contribute to the intersection and in many cases also the union. So this pullback is essentially looking at the solution set, the function and you have a subset of antivariate and multiplicative whereas the logic is an extensive problem.

2:30 You know, I'm just saying that there should be a parallel development of extensive logic and at least some of these, I'm sure, systematizing by logicians, you get all sorts of alternations of things that only about a fourth of that would be fitting into the narrow idea of a coherent function. But still, you know, it's interesting to know... The basic things they keep considering is of such a nature. It's a kind of extensive quantity. They start off with something that's not even a totem, but once you've embedded it in the totem, you've got the ordinary power set there. You can go and find all of the propositions, all of the propositional functions, as opposed to the other end, so it's an interesting sub-function of the co-variant power, defined by parallel restrictions, this is the most obvious thing, so there exists, if I can, a major theoretic, it's an almost all, almost all, right?

5:00 Again, to check some of those innovations, but yeah, or even up to, but the programming, I think there's probably not much that can be done in that area. They don't even consider, they talk about the power set when it's not the power set, not the representable for all sub-objects in the category, it's just another parameter. So what I'm saying is, well, it's quite natural to have many such parameters, if not just one, and their achievement was to find something that it could do short of parametrizing all the power sets, because it parametrized all the power sets that broke out of the framework, not something that it could do without breaking out of the framework, which was close enough to being a power set. But there are many such structures which in some sense should be taken. At the same time, one of the new arbitrariness of the Singleton called the lead. I mean, in its core, it wasn't arbitrarily. I mean, from hindsight, Singleton did a couple of findings. It's arbitrary in the sense that you could have given a lot of others, not Singleton, but Lee, Crosby, and Lewis. Is this an effectual effect in any way with the fact that the Singleton in the way? Many notions of extensive modernity actually, you know, moan that, so they have this... Moan it says, yes, just once.

7:30 ...to Laurence Schwartz, because these equations are not generalized functions. This is a fundamental mistake in terminology and conceptualization, which I think about by many people. For example, Calderon and Courant, and they all point out that, well, you know, we don't mind generalizing, but these things don't behave like functions. We can't substitute. Exactly that. We cannot substitute. That means what? They're not a complementary function. No, I mean, the distributions have to be considered sort of alongside and operating on the functions, but the variance is opposite. In fact, if you have this operating on, it means that the distribution is from the module over the function. If you choose a particular distribution, you can consider all the possible multiples of it by functions. That's the thing which gives more distributions. So that's the embedding of the functions into distributions, the sense in which it's sort of generalized, which of course, they have in mind to use the big measure for that if you're in space, but often the big measure is not relevant, you couldn't say, you know, relativity or continuum campus, it's not an invariant, and so there really is no recurring embedding. The final conceptual error was to confuse a lot of people. Even though I didn't do anything wrong mathematically, I just lead people down the wrong path again and again. This is attempting to be pointed out, rectified by the work of Hawking and Reyes on the weight equation. The weight equation from the beginning is supposed to be an extensive one, but it's not an intensive one. It's really a very, very nice distribution, like the Dirac distribution. To recognize it as such, it's the most simple thing. It corresponds to the function that's evaluated to the point.

10:00 It's only when you try to force it to have a density which is expected to be very limited or something that you start getting into conflict. So I always call this, you know, the Xerox map and all sorts of different contexts where you have these, some of the corresponding reasons for the existence of quantum physics is the Xerox map. From the domain space... You can get into the space of all the distributions on there because you have this natural transformation which is concentrated on the given part. The main space has a distribution that only says yes to yes. The approximation of one functional by another kind of functionals. Where the kind of functionals are just linear combinations of these deltas. Particular quantities in fact. Assuming that the extensive quantities form a linear space. You can then take linear combinations of all of these, and that means a three-month integral equation, which is very often taken care of with you. I absolutely agree with that, and get your master away. By saying, I think, that Pogues, as an extensive, may have been, for the sake of Mr. Hayes, also taken over by Maxwell.

12:30 That was in the 1970s. Mathematics, philosophy, mathematics, because they work, because of this thing that Russell Sherman made about it. I mean, it's the vast five lines of geometry, for sure. Distinguish things you integrate over. I'm making purely a chemical point. If you say that this is all simply due to the covariance, the contrarian, the contrariality of the maps, and things that are ultimately respective to names, If you introduce the idea to them, how much has been missed outside of the common confident anyway, they just tend to switch off. It happens to be locations. But I just find it so interesting that they keep the shutter coming down, the mind switching off, intensive, extensive. Hegel, Maxwell, I mean this must be an antiquarian interest. Hegel said they're indistinguishable in philosophy. That's the best way. There is impractical hostility to ignorance. Not to the ignorance, of course, because it's our own ignorance which we at first want to attack, diminish, and eliminate from.

15:00 But ignorance on the part of physicists, ignorance on the part of mathematicians. We have to simultaneously help to bring out enlightenment in the program. Heating a house is based on the thermodynamics which heating engineers learned in the language of energy, enthalpy, and so forth, but all those are in the framework of intensive and extensive. So they're very, very solid. And then, if you want to tell them what it has to do with the heat hazard, because it exists in mass and volume. If you divide one by the other in some sense, what is the sense? Well, you get density. Density is an intensive one. This is what one should start with. Intensive quantities are ratios of extents. I should tell a whole story about what a ratio really means, which most people have never been able to do. It's a calculation or something like that. One extensive point and then you get another extensive point of it. So in thermodynamics you have pressure, which is intensive, which could be, for example, a ratio, depending on which possibly relation is spread, but in some contexts it's energy divided by volume, where energy is extensive, and you can work. You don't have the energy of a point, you have the energy in this room and the energy in the next room taken together makes a bigger energy and dividing it. The energy divided by volume might be a pressure, but pressure is also intensive. Your quantities are more or less similar to quantities, some of which are of an extensive character, some of which are of an intensive character, some of which are clearly of a character, of ratios, and then you can start.

17:30 There is a funturality because whenever we talk about these quantities there is a domain of variation. The intensive ones vary in one kind of way, the extensive ones in another kind of way. Within that, the object, the part is a map from a smaller plane. But when I observe something, I'm applying a function to this domain space. So when I start learning about transforming, These quantities, as they are existing, sit on the state space of the gas in the box or whatever it might be. Along either observable function or point positions apart, I will see that they have this co-variance and co-variance. That's it. Extensive and intensive magnitude, the notion was sort of named. It goes back to scholastic, you know, I mean, we do have a sort of scholastic development, but I think as it emerged, I mean, everybody knew, even in sort of basic physics in sort of high school, that you have quantities that are like density and the temperature and so on. Well, I think the way you sort of saw it was that they... They are defined as if you like it twice. They don't add because there's no way of adding them up. It doesn't mean anything to take two temperatures and try to stick them together. And then on the other hand one has X set quantities like math, which are of course properties of regions. Now, the connection between the two is affected by the, you know, the differential mythical calculus, and everybody knew in some sense that, and that's what you pick up when you learn sort of basic physics, even perhaps though, I think the mystery about it was part of the fact that the actual numbers, the pure numbers, real numbers, are the same in both cases. I mean, they're just added numbers. In other words, when you convert the distinctions between intents and extents, you end up with a temperature of 80 degrees, let's say, and a mass of 80 grams, which is really quite, these are two numbers the same, but the actual quantities they represent in that case are sort of really different. And that's, I think, why...

20:00 But the point is you could take two times. That's right. You could take two times. That's right. That's right. But I think that was part of the... Those distinctions are things you sort of pick up. And they're very natural. You can do one of those automatically in sort of basic physics, mechanics, and so on. And then later on, these distinctions get sort of locked. There's some kind of a bias in favor of intensive properties, at least in actual mathematical history, so that one continually tries to replace the extensive by the intensive, by some device or other, and this can This can distort the conceptual world. When I think of specific philosophers and where they lose it, the philosophers in mathematics where they lose it, one way to concentrate it, they think you can integrate a function over an interval. They don't know what a form is. They just take the standard measure for granted, or they don't think it's entering into the problem. You take the interval of a function. But you can convince them that you can't take the interval of a function. You take the interval of a form. And forms vary differently than functions. You could show them that if they happen to be interested in it.