Question: Hi, Lyn. I've hated popular opinion my whole life, and I've always known it stunk. And it was from looking at the behavior of my parents, my parents' friends, looking at the effects of my teachers' dishonesty on young minds. And I think the reason I always knew popular opinion stunk, was because I knew truth through a method of observing social relations, and then, based on studying the geometry of social relations, hypothesizing about what's going on in certain individuals' minds. Or, in the mind of society in general. Or, by reflecting back on the geometry of certain social situations, and then, altering the geometry of that social situation in my mind, and then from that, hypothesizing about what's going on in certain of these individuals' minds, or the human mind generally.

And, I'm working on how Gauss determined the orbit of Ceres, and Guass's fundamental theorem, and I'm kind of having trouble with really getting at the meaning of this. For me, in constructing these geometries, the idea in my mind is like, "so what?" And I'm having some problems with it, because, I mean, I guess the way I look at this is: Isn't the purpose of us studying the Gauss, and working through these geometries, is to be able to apply this scientific method to society as a whole, to change the curvature of social relations between human beings. So, if you could talk about the relationship between--I have no background in math or science, either, so, if you could talk about the relationship between the math and science, the Gauss work that you've set forth as the curriculum for the Youth Movement, and then, how this applies to, specifically, to the method of looking at social relations.

LaRouche: Let's take it the other way around; let's reverse the question. And the answer becomes, again, reversed, which is where it lies. The problem is, how do you communicate a discovery of principle to other people, as a principle in physical science? How do you communicate that? What you have to try to do, is communicate your act of discovering the solution to another person, eh? Now, let's reverse it: How do they communicate that to you? And what is the problem--?

See, you may have a problem with this Ceres business, and so forth, and the fundamental theorem, in the fact that you have not defined a context with sufficient rigor, in order to pose to yourself the questions you should pose to yourself. The way to approach it--and I've been wrestling with this, from a pedagogical standpoint--I've been talking to Bruce and others about this problem of pedagogy, of making clear the construction, the principle of construction involved in the solution of the Delian problem. Because that's the crux of it. And to get the idea of the geometrical action.

Now, what your problem will probably be, as for most people, which is what I've been worried about in these attempts on pedagogy, is that the geometry: to see how the mind of Archytas actually had an insight into the two means. Because once you see that, the solution then becomes obvious. And therefore, that is the problem there. In the question of the Ceres orbit, Jonathan and Bruce went through this, I think, very well. And Jonathan had a very clear view of what the problem was of the mathematician--those who had not solved the problem, as contrasted to the way Gauss solved it. It's the same kind of thing. How did Gauss recognize, from these three sets of observations that he chose, what the orbit was?

Now there's a little element, which is not always emphasized in this connection--is to assume that Gauss found the solution de novo. He did not find the solution de novo. He found the solution by recognizing that this was a reflection of something Kepler had already discovered. See, Kepler had already defined the orbital characteristics of the missing planet between Mars and Jupiter. Gauss was aware of this work of Kepler. This was something his teacher, Kaestner, was very much involved in. Therefore, Gauss was able to have an insight, which is what's left out of the report by Jonathan and Bruce: Gauss already had an insight into the solution to this problem. Therefore, he was, by this insight, and by his knowledge of this problem from the standpoint of the treatment of the question of the complex domain, Gauss was able to recognize that what Kepler had said, as in this setting of this evidence, corresponded to a problem respecting the complex domain. And therefore, this involved the problem of elliptical functions, the way Kepler had relegated the question of elliptical functions to future generations, or future mathematicians. And Gauss was one of the future mathematicians, who responded to that problem of the elliptic functions.

Remember: A lot of Gauss's work, as a mathematician during that whole period, was on elliptic functions. And Gauss was the one who did a lot of work, together with a few others, on this question of elliptic functions, which is a very important phase in mathematics.

So, I think the problem you will have in this, is to look at this from that standpoint, and say: Have you, and have those with whom you discuss this, actually adequately defined the conceptual problem, into which Gauss had an insight. And my question is, which is always a question with this report that Bruce and Jonathan produced, that without taking into account Gauss's knowledge of what Kepler had done, in posing the orbit of the missing planet: Would Gauss have recognized, as quickly as he did (though, there was a tremendous amount of work in that; it was not that quickly, actually), but would he have recognized it immediately, in the sense that he did, what the solution was? I say, if you take the question of the elliptic functions, the work of Kepler, Gauss's knowledge of this work, Gauss's own work in defining the issue of Euler and Lagrange and so forth, this comes together, and suggests, implies, the way in which to approach the problem of the asteroid question, on Ceres.

So, I think, without that, perhaps, it's more difficult to find a--. If you're a mathematician; if you work it through as Jonathan did, you can come more quickly to a recognition. But you have to think about the person, or the student, who is not as versed in mathematics on this thing; does not have implicitly that knowledge lurking in the back of their mind, that perhaps that precondition for solving the problem, has to be brought into consideration beforehand.

On the other hand, as I said earlier on the other question, the question is clarity of insight into what Archytas' actual solution was, in terms of the geometric construction. And I just simply suggested to Jonathan to try to get animations which would help people to see more clearly the successive stages that Archytas went through in divining this solution. So the question here often is an adequate statement of the problem being lacking, i.e., a student who does not have the necessary background may not recognize the way in which to find the solution. And I've suggested in the first case, that a more adequate identification of the construction by Archytas is crucial; and in the second case, I think that one has to look at this thing from the standpoint of what Kepler had already written about the orbit of the missing planet, as something in the mind of Gauss, and also, the question of elliptic functions--the question that Gauss had already left, together with the idea of the differential calculus, had left to future generations.

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