The emergence of the notion of vector fiber space, Part 1

1:50:00 We don't know what's going on, but we know that there is a common thinker, there is a common thinker, there is a common thinker, there is a common thinker, there is a common thinker, there is a common thinker, there is a common thinker, there is a common thinker, there is a common thinker, there is a common thinker, there is a common thinker, there is a common thinker, there is a common thinker,

1:52:30 After that, we find at SEDAR this idea, we find at Koenig this idea. My friend, Cartan, didn't write anything like that because he was working. So it's really a little bit of a balance, but at his place, we all cite SEDAR. So Cartan, certainly before working with Sherton, did not write SEDAR. And I don't think Cartan ever cites SEDAR. And if I hadn't read Sherton, I would never have heard of SEDAR. Maybe he's someone who historically has no posterity at all. There are quite a few examples of this idea, but it has never been implemented. But this idea is being taken up by others later on. So, what are the ideas of this seminar? It is to interpret these systems of components, the ways of transformation, as extensible vendors. They have a certain passion, to be able to produce intrinsically, to be able to produce more geometrically, to be able to generate more geometrically, because they are extensible vendors. This is a very intense interpretation, we see it in the 1920s, we see it in Hammond-Weil, who are sitting, who are rectoring in a very unusual way.

1:55:00 And you see, because it creates, the ideas of Sennbert and Schumann that you have exposed, they arouse a kind of reason for waiting. We wonder if the big artillery of Grazmannian ideas can give something in this... When we say that, the artist is called Victor Yann Le Grune, so we have to find some very interesting explanations like that. We didn't find everything in the article, but the article was a bit of a question, in fact, in relation to this notion of waiting. By the way, when I wrote the book, it's not at all for this extension of the word. There is a link to the fact that this notion of waiting was not at all taken as an important idea at the time. That's not why Schaudel calls it Heisenberg. Heisenberg gives the idea that covariance derivation is a type of object, so it doesn't depend on the DSD. So there could be other covariance derivation systems than the one formed from Christoffel's coefficients, which are the derivatives, but which belong to the DSD. So it's an essential idea for them, because they are people who work on the generalization of the connections. There are teams that have derived other connections than the linear connection. There are also non-Riemannian varieties of economics. That's what Rael is working on, and that's why Schottl is doing this research. It's not at all based on vectorial terms. Is Rael... Well, it's in the Mathematica at home, because we thought that Rael had... When you say Rael invested in vectorial, it's a vectorial that creates... I mean, you know what, it's in... It's a vectorial that is limited in relation to...

1:57:30 The construction of Brassman, which is still very adherent to the geometry of ordinary geometry. What it does is the vector foundation of the Euclidean geometry. We are talking about the Euclidean geometry, but in a different language. But electronically it is important because it is not at all the framework of elementary geometry reading at the time. So, we must not forget that this is a very important element, I think, in the history of vector theory. Yes, certainly. But is there, in your work, this idea of interpreting it as an extensive grandeur? Because what we would expect is to know, precisely, if we interpret it in a Grasmanian framework, what operations can be built on it? Yes, it is to pass passengers with selected subjects, since it is not the role of vector theory. The case of Trastanien is not so much linked to the emergence of the vectorial model. If you look at the algebra of the ball, the vectors are defined from the bases. Vectors are not extensible elements. Vectors are the things that can be generated by a linear number from two, when you ask a question. So it's not the mathematical definition of the vector space as a set of operations of the core. It's really almost what we find in the waves, that is to say, it's the idea of the symbols that we combine, and we have bases on each other, but not so much, because there is a translation that starts from the notion, then it is translated into a vector term, then it goes from the vector term, and then it goes from the vector term, and then it goes from the vector term, and then it goes from the vector term, and then it goes from the vector term. That is, the idea of a vector is a...

2:00:00 While we have the impression that, according to Faudral, he considers the tensor as a generalization, the vector is a particular case of the tensor. Exactly. So, the fact that the vector is a particular case of the tensor, which is actually a retrofit vector. If we consider the algebraic space, the space of the tensor associated with Penrose is also the space of the vector. Of course, the vector space that you see is actually the space in the middle of this differential variety. It's important not to make objects that depend on different barriers. That's what they have in the line of sight. So, when we have 100 lines of sight, they are not the same as the other ones. They are not the same as the other ones. So, we are not at the end of the question. The question is whether it is geometry, because I have translations, what happens when I finish the translation. And what I do with translations, when I differentiate the coordinates, I come to an infinitely close point. If I have a translation, I have to learn how to read it. What was the first contact between Cartan and Wagner? Well, I don't know exactly. When we see Cartan in 1922 making the first notes of the Contre-d'Hume Academy of Sciences on the analysis of general relativity and the first generalizations of the collection, he is immediately referring to Wagner. He knows the generalization of the Michivita collection by the similitudes of Wagner. And what about the work of Cartan on the spinner?

2:02:30 It depends on what we call the spinner. There is the work of the end of the 20th century.