Discussions, incl. FW Lawvere & M Wright

0:00 I have very good connections. They're part of those who say that they're actively working. And they're actually quite thick. You have to push it up. It's a very nice thing, this kind of thing. You've got to go on walks, don't you? I don't know. But you're actually a very good man, I think, because you've got a great strength. Not the way he's smoking, man. Well, yeah, but I think that's part of it. I think that's part of it. Like all these maths, he's just used to smoking. Look at you, who's talking? I know, I know, that's why. It's just to keep you busy while you're smoking. Thank you for your attention. There are a number of different types of mathematics in the world of physics, and I'm going to go through them one by one, and then I'm going to go through them one by one. And so then when she, when she took up with this, uh, Totski, I was, she, she, she, because we didn't have many friends, they were very, they were very, they were very, they were very solicitous, you see, I was, I was completely, uh, destroyed at that point, you know, so we had to teach each other.

2:30 No, I have to, you know, I have to do something. I'm excited. Since I was talking so much. I should have cigarettes, because this could be that sort of society. So they brought me a carton of cigarettes, and I was forced to find a cigarette. Smoke these, they're too bad. I said, no, no, no, no, no. Well, please, please take them. Just keep them here. Well, for a time, these were old chapbooks. I don't know. 1954. It's terrible, isn't it? Thank you for your attention. Thank you for your attention. It takes me a bit to think of some of the things that define this, the intensive part of this. There's one example that I'm not so sure about.

5:00 Not actually when you were talking about the little guru. Yeah. Yeah, well, you've done this first. Anyway, there's many different types of intensive parts. Exactly, exactly, exactly. So, this has two basic properties in terms of formulas. Once again, the new value of the formula. I'd actually like to go backwards, in order to show you the kinds of problems that I have to deal with. I mean, that's the problem of life. I'm a person who's composed. I don't have to go back. It's just my self-esteem. Self-esteem. In this case, r is omega, which is the propositional function, and it's simple to return that to the policy component, exceeding the propositional function, but that green value means that there's various products. The product is a mathematical model. It's simple, in this case, because it is less than or equal to 2, and that's the point of the law. You can carry them together and put them in the same component, but in this case, it's the time space. So if you can close that with that. I think this here is like, you know, this is, this is the sphere, so you have that, and some two of it. And just by associativity of composition, this concludes the fact that the product relates to things. And this concludes the fact that... There are a number of different types of products, such as preserved products, and we have read about them, but I don't know if there's a difference.

7:30 Well, the preserved edition also, there's a point in both intents and intents of the preserved edition. I think there's only intents and intents of this product, you know, and that's what makes it interesting. That is an example of a... Extensive faculty, we can take linear functions, so this is the sub-object of all of the five IPX, consisting of those, those marks are linear, and these are often written as 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21, 22, 23, 24, 25, 26, 27, 28, 29, 30, 31, 32, 33, 34, 35, 36, 37, 38, 38, 39, 40, 41, 42, 43, 44, 45, 46, 47, 49, 41, 42, 44, 45, 46, 47, 49, 41, 42, 45, 46, 47, 48, 49, 41, 42, 45, 47, 48, 49, 41, 42, 45, 47, 48, 49, 41, 42, 45, 47, 48, 49, 41, 42, 45, 48, 49, 41, 42, 45, 48, 49, 41, 42, 45 This is very just notation for the value of the media that we want to include. We want to know if there is any sense of value. So there is one kind of excellence in this kind of work. I didn't give that example because it's a subject. This is just a general pitch. You can use that in a paper. The reason I'm giving this example is because this poem is a theory. It looks very natural. It's a particular two-thousand-year-old translation of such-and-such a question. So you get a feeling about this kind of thing. So in extensive quantities, there is this particular definition associated with the integration process in a way that is associated with the material value of any information system. For example, volume, or length, affects as a line that length may be converted into a number of values of any function p for such a function. So that defines length as an extensive value. They said, so this has two parts, it's a sub-space because they have the condition of a group, and multiply, see how it's classified in a number of times.

10:00 This is a non-trivial condition with diffuse colors. So this is amazing. Now, the other thing I would like to address is the very last chapter of the book, but I don't have the opportunity to, so I'm going to find the sixteen times needed to even have a measure to measure the extent of time. What was the most massive part of it, as long as you think about it? I hope you enjoyed this video, and I'll see you in the next one. There are many reasons to see a typical quantum of y and x and y and y and x and y and y and x and y and y and y and y and y and y and y and y and y and y and y and y and y and y and y and y and y and y and y and y and y and y and y and y and y and y and y and y and y and y and y and y and y and y and y and y and y and y and y and y and y and y and y and y and y and y and y and y and y and y and y and y and y and y and y and y and y and y and y and y and y and y and y and y and y and y and y and y and y and y and y and y and y and y and y and y and y and y and y and y and y and y and y and y and y and y and y and y and y and y and y and y and y and y and y and y and y and y and y

12:30 The product of the mass, which is still a distribution, I mean it has a particular total value in e, the total value in the derivation of 1, and the total value in u, which is how we got the rock delta. You know, jumping ahead to 0, which is, well, jumping ahead to 0 is just as small as 0. AROC is the simplest possible thing, and you know it's excellent, but it's only complicated if you try to determine its intent, which you can never succeed to do until it arrives in its place. But it's the simplest kind of, it's the simplest kind of extension from the sense of its value at any point of x, or the value of x, which is its particular instance of quantity. It's simply the key to x, and the value of any key at that one point. And that's it. That's about it. It's not just possible to analyze it. It's possible. Its support is one point. In terms of logic, it's kind of a question of whether it's going to support you or not. It's going to support you at one point or another. It's like an individual, when you see an extensive bundle of elements, it's kind of an extended block. It's the size of a block. And the logic of that is that there is a plot. So who's actually refining that? So is the fact that it is to be filled with the support of each other at one point an instance of input? Of course. Of course, yeah. If anything, it's a restrictive function of the general landscape. It's not, except it's just not a function. It's just not a function. It's obviously kind of a function. In fact, if you could say a bit more about function as an instinctive, that's what I'd like to say. Is it a function? Yeah, that's what I'm saying. Taking as one type of extensive priming is precisely what is functional.

15:00 Okay. This is what you meant by functional. Yeah, yeah, thank you. The main is to say that function is a variable of function. That's our function. Okay. These are called linear constants because they satisfy each other's needs. I mean, another case of this is this monogamous semantics. The nouns might be points, but the pronouns could be extensive points. Generalized points, you see. Generalize it and go on this map. Extensive points are more general than points. The idea is that R are the actual sentences, the values of statements. Actually, in the space of nouns, this is the space of sentences, of credits, though. There's a credit for the P, the sine sine of X, the sine of C of X, the P of X. X has got to be a P of X, X P. You don't have the philosophy of that. No, no. But then, once you have the notion of a particular credit... Again, we go back and talk about, let's say, mineralizing them, and giving them the notion of neurons, predicated on making the sum of every one of the natural things. Conversely, so in particular, key nouns in science delivery are critical in some sense, but more generally, anything in science delivery is critical in some sense, so I would want to generalize on that, what precisely is generalization, except that normally they would satisfy this condition, it wouldn't be the most general thing like this, but they would satisfy this in some sense. If you took the conjunction of the product and the values from the outcome of the constant truth value with the variable of credit, you can then apply the pronoun to it, and it would be the same as just applying the pronoun to the credit of the person, and then you can join it with that truth value, the constant truth value, which amounts to this class value, the evaluation value.

17:30 So, to the point of defining extensive quantities as all women functions, which is not always exactly the correct definition, it means that this equation defines the new extensive quantity of components. The new extensive quantity just is a process of the science of which these are, so that is the extensive quantity of components. So now this projection formula is going to take me to the next part of the talk. So, continue now. Well, in fact, a very useful notation for the subsets of quantities is to think of mu as the generalized mass, the generalized element, mu as the interaction element, and delta as the expansion element. This is the space of what we use, the space of what we'll have to see. We'll have to reveal that this is a very special kind of view. Because that would be an ordinary view. But it's analyzed by other people. So to push forward what makes sense and positive along the map is just sort of compositions. That's the view.

20:00 Regardless, from that viewpoint, it is clear now that this analysis is complete, so like it may be. Well, again, I told you this example about surgery, right? I didn't know that. So you don't have to do it yourself. So, consider time, space, and the surface of the Earth, and a path. One of your new travels. Uh-huh. And the surface of the Earth, and the path you visit there. So we've been in India and China for all this space time. Now, the natural extension of time is duration. Power is duration and extension of time because you have any function, any extension of time, time is very simple. Now, this extension of time is soldier. It is given that an extensive boundary on space, which has physical dimensions of time, is saying to me, in space, how long the time is going to be. Is this the time you're spending? That's the time you're spending, yeah. That's what's sort of giving me the notion of memory. Oh, so, so. I think that's what you're talking about. Oh, that's what you're talking about. So this illustrates also that you can have extensive boundaries on space that have physical dimensions of time. They arise from a specific dimension of time. Which results in a lot of confusion and doubt about the answers to these questions. So the actual definition of this in terms of mathematics is that we have to be able to integrate many kinds of C on the second space with respect to that V. So what does that define as V? Well, we already know we can substitute that into C. When you get a function of x, it's going to be able to describe the meaning of that function, which is going to be the value of x.

22:30 So you see that as really the same thing. The least value of x is c on the left of x. Take the property of c as being greater than 7, and that would be the square of x. This is the property of the square of x. This is the subject of the square of x. Thank you for your attention. The integration process requires many things to come together in the same space, but with respect to the using of it, there is another substitution in the combination of three words that I knew was going to come together in the same space. It's a very simple combination of the idea of substitution and the idea of function. Can you just give the example of those very simple logical concepts and relations that come after the system? I'd like you to just cite the notation of the subject. Yeah. Now, this notation of the subject. The next thing is to find there's a very last point, but there's also a general effect. And the amount of that, and that's what I'll discuss with you in the next section of this lecture. This is all within the context of this particular choice of mathematics and of quantum mechanics in the sense of how we're going to quantify all of it.

25:00 So, a generalized math is a new genius math, in the fact that it's a big gap. And then backwards, we have a number of times, this just generalizes this notation here, because if x is 1, and y is r, it will just be, for example, a line number. So, these things generalize mathematics in order to be composed, because if you have two generalized maps... That is the meaning of the definition of action math factors on the function of space, on the units, on the discipline of space-lives, and on the segment of the unit. And also it's really generalized math because if you have an action math, and in particular you have this induced math on the influence of quantities, R to F, you can only use that method. Yeah. In other words, this is not only in the units, but even when figured for the natural mass, by the factor of the natural mass, is there any product where it figures out the lambda, lambda, and in the unit of the unit, we can have a product that is a new product that one of the times is constant, one of the factors is constant. So this is the general nature of the...

27:30 So, the generalized math can be reviewed by a lambda conversion, so this is actually one of the problems. There are a number of different types of mathematics in the field of physics, such as quantum mechanics, quantum mechanics of the universe, quantum mechanics of the universe, quantum mechanics of the universe, quantum mechanics of the universe, quantum mechanics of the universe, quantum mechanics of the universe, quantum mechanics of the universe, quantum mechanics of the universe, quantum mechanics of the universe, quantum mechanics So, in other words, because of the zero out delta, the y, we have a generalized map. It might actually be an even one. The generalized map assigns here the point that x is the distribution of y. But it might happen to assign a critical point to a U-like distribution, to do just the point, which is just the point, too, to do the next one. So, let us explain in a better way to make sure we're getting to this point. Oh, yeah, so, in case I was doing a manual, when there's generalized maths, you might call it a U-like slide.

30:00 In other words, you're assigned to the point of subsets that is the point. Now, the proof of that is that the crucial point is not the point of subsets, but the point of subsets. The point of subsets, if I consider an intensive problem, sorry, an extensive problem in the domain, the intensive problem in the domain, then I can teach. By a particular composite, the notation of species of the earth is associated with the modified history of the universe. But actually, it's stronger than that, because it's talking about multiplication by a variable, by a density. Multiplied by a variable density, not just by a constant. So, what it means is that if there's an effort needed... And I can multiply that by g, and there's a multiplication of this by intensive times extensive in the same space and another extensive in the same space, like that. Or, I could substitute this, you know, point c. Or I can substitute f e to get c first, which would give me an intensive function of m x. Now that's probably the best suggestion of m x, rather than the modified function of m itself. So I can do that. All of these terms may be used to describe a person's life, or to describe a person's life, or to describe a person's life, or to describe a person's life, or to describe a person's

32:30 I have to get the same value, which is all the same value. I have to get the same value. So the same value, I'm going to be able to respect it. The same time is left to me. I mean, by definition of multiplication, I take the linear product, the same value of C, and I get it back, which is what's left to me. For the weapons from FU, I substitute them to C times, to bring them back to F5 and get them back to U. And now I use the pushing factor to substitute them to U of F. So this is C power F times C F. And there it is. Notice this. CYF is the product of CYF, which means CY as of the year. This is the proof. It is the law of CYF. That translates into the same values as the equal. That's the difference. You know, the same values as the other. So there's a proof of this one. It's funny. Thank you for your attention.

35:00 When you have a person ask you what, it's always going to be in the middle of the list. Generalized math is when it's values are not points, it's distributions. Which point in the domain needs to have a distribution? Maybe a probability, right? I know I start here and I end up with the same probabilities and I get the same distribution, but you don't think you can bring me into being function? Yes, those are basically kernels. In other words, it's a generalized mass from the... Which one is the linear vector here? The role of mathematics is that we use that in mathematics in order to generalize mathematics in mathematics, and that's what I do, and that's what I'm trying to do at the moment. And just as you were saying, you were saying when you found it, you just went back to that. F-upper-star-c. That really just means c-f, so f-upper-star-c is f-upper-star-t-n-n-n-n-n-n-n-n-n-n-n-n-n-n-n-n-n-n-n-n-n-n-n-n-n-n-n-n-n-n-n-n-n-n-n-n-n-n-n-n-n-n-n-n-n-n-n-n-n-n-n-n-n-n-n-n-n-n-n-n-n-n-n-n-n-n-n-n-n-n-n-n-n-n-n-n-n-n-n-n-n-n-n-n-n-n-n-n-n-n-n-n-n-n

37:30 This is one thing I learned from Ivan here. At every base of God, there's a distance. So I don't, I try to speak for them, you know, once I've talked to them a little bit. Oh, you don't want to talk about mathematics? Yeah, you know, it's okay. Yeah. Yeah, I think that's probably a good thing, I guess. Well, keep going, baby. The difficult sort of thing is this is just a sociology. That's great. I hope you enjoyed this video. If you have any questions, please feel free to ask them in the comments. Thank you for watching. The key acting model comes from C, which means that it has tons of different procedures. And the other one, Q, which seems interesting, 2x, 2x. So now, I'll just write back the Q, 2x. And it's 2x, 2x, 2x. 2x times 2x, 2x.

40:00 All of the above are used in the course of the course of the course of the course of the course of This is proof of mathematics. This is proof of mathematics. This is proof of mathematics. This is proof of mathematics. This is proof of mathematics. Now, this is the operator field, I to Q, you know that, right? This is the world of seas. Both the deep blue and the solid. This is the rest of the blue and the green. I mean, in this particular country, not a problem. I mean, this is another key. So, this is the company. So, that's where it's done. If you take this classification, p is 1, p of x is 1, p of x is x, so p of x is 1, p of r of x is 1, p of x is x, p of x is x. Of course, one could say about Heisenberg. Heisenberg is a special place of life, you know. There are two special places of life.

42:30 I think this is a useful point, because he is an exotic person, you know. Now you may say, this is not the end of Heisenberg's relations, but there are two other areas which I have commentated on. So, they're linked together in a way that reduces the concentration of this. Then you can organize each of these into a type of space along the line. In such a way that they respond to the problem in a way that they don't respond to the problem in a logical way. I really think that the most general example of Tyson-Briggs theory is that point, in that sense. Now, this is the differential point. We want to express it in a negative way. I mean, the operators of science have already seen it, and they've come to see it as well, so... So, this is a case of a substitution, so it goes down.