Question: [starts mid-sentence] ...mathematics was a way of communicating ideas. I mean it's a language, and the first of the three questions is: How do you actually see the mathematics, the way Gauss used it, in a poetic way, in a way of communicating ideas, as opposed to getting caught up in the particulars, which is generally in terms of the approach, what a lot of us are having trouble with?

Similar to that, on the question of music, because it's also very difficult, when you're talking about music, to define an approach to discover the ideas, as Furtwaengler did, as opposed to just becoming familiar with the notes, and relationships among notes, and all the particulars.

And then, my final, concluding question: Obviously, in our society, most of the things that people experience when growing up, has generally a tendency to either completely blunt the emotional development of the individual, or to develop the superficial type of emotions. And often, it takes what could be a very difficult crisis for any kind of real, deep emotions to be able to come forth, in the sense that a crisis, where -- it's like a storm that came, seems to just shake your foundation. My question is, the irony is that, when someone goes through that kind of a crisis; similarly, when someone is engaging in things that they find profound and exciting, very often, that same kind of emotion, can be called forth. Right? That is, where before it may have been defined by fear, anxiety, in this case, when working through something, it becomes a type of elation, but something that has an overwhelming quality to it.

And my question is, why is that the case, that what first was experienced by something in the terrible, would later, all of a sudden, appear once again, also in a very powerful form, and something you find beautiful and profound? And, can you actually sustain that and use that as a form of motivation, or impulse in the political and intellectual work, as a driving force?

LaRouche: That's the same question in three parts. It's the same question. Now, in the case of the first, the answer is obvious. The problem comes when you try to think algebraically, or arithmetically, about the Gauss problem. That's a mistake. Think about it. That's why I insisted upon using the Archytas. Think about it in terms of construction. The solution does not lie algebraically; it lies in construction. And there are a lot of problems involved in that, including the question of the tendency to think in terms of simple Euclidian plane geometry. That's another problem, eh?

All right, now: the same thing in music. The minute you find yourself trying to identify a composition in terms of the succession of notes, you're in trouble. Stop, and go back. Never try to memorize the notes. Find a--define the concept; define, first of all, a set of thematic concepts, and forget the notes for a moment. Think of the interval, think of the modalities that you're dealing with. What modality are you in? And what modalities are you going through? So now, you think of the composition as a process of development of modalities, in a simple way, then you go to your contrapuntal conception--the same thing. So the way you think--if you try to simplify, and say, I'm going to solve this problem arithmetically, and you're trying to understand a musical composition in terms of a succession of notes, you're missing the essential thing. You're missing the reality of the problem, because the solution is in construction.

See, the point is: What did Gauss do in the 1799 paper? What Gauss did, essentially, was to, number one, was simply to replicate the Classical solution, starting with the line and the doubling of the square--the Classical solution to the Delian problem--by construction! Not algebraically. By construction. Now, he then turned around and converted that, what that meant, algebraically, and said, wait a minute, this act of construction, which solves the problem, is an action outside the Cartesian manifold, or the Euclidian manifold. But you can define it in terms of spherical action, which is what the method of Pythagoras and Archytas was.

Now, if you define it in terms of spherical action, it comes out as rotation. Rotation where? Rotation of the action! Not rotation of the line; rotation of the action, as a power. So now the whole thing is comprehensible. The complex domain has no mystery for you at that point. Whereas, if you're trying to figure out the arithmetic solution, you get tied up with the kind of thing of being trapped into what many people are trapped into: is the Lagrange or Cauchy conception of this problem, eh?

And the music, the same thing: In music, you have to think of action. In music, everything is action. Now, what is the complex domain of musical composition? It involves modalities; it involves a change in modality. Without change, there's nothing. Without change, there's Rameau, eh? Rameau is the baby who was never changed; that's why his music stinks! [laughter] Rameau is the composer of curry sausage; you just slice it off, whenever you want to end it. There's no development! Really. And so the essence of music is a developmental process, and the developmental process can only be interpreted as a coherent process, in terms of counterpoint.

So therefore, you have to think about the contrapuntal development; you've got to find a unit of contrapuntal development--as the idea. That's why the Bach Preludes and Fugues are so significant for people, particularly, from the First Book, the C-minor, the C-minor fugue, contains in germ, many of the problems which you deal with, in many of Bach's works--that first C-minor fugue, in the First Book of the Preludes and Fugues. It contains a very simple problem. You get that problem, understand that, then you can work though the thing and see how Bach deals with the whole development of that composition.

And so, therefore, you're thinking in terms of that idea, not a succession of notes. People try to think of a succession of notes that produces an effect. Then they try to interpret the notes, and produce an effect based on the interpretation of the notes. It's crazy. What's the idea?

Now, look at the basic idea: What's he start with? How does it develop? You've got the germ. Now, what is the development process to which he subjects that treatment, and how does he come to a conclusion? That is what you want as the idea. Now, if you forgot every note in the works, but just knew where you were starting from--you could reconstruct from memory what Bach did. That's musical memory. Not memory of note-by-note memory; not eidetic memory, but getting the concept; having an idea what the development is, and what end it's leading to. Once you know that, now you can replicate it. You can recompose it in your own mind, because you have the germ elements and you understand Bach's method, and you come up with this stuff. And then you go with some other exercises, and get them the same way.

So, whenever you find yourself in a trap, of trying to fall back into an arithmetic, note-by-note understanding of a composition, say "No! I refuse to do that." What's the idea; what is the basic idea? What is the germ idea that Bach introduces. All important music has that thing, from the beginning: Boom! Your attention is caught. What's the development? What is the development?

For example, take the case of the Brahms 4th Symphony. Where does it come from? It comes from the Adagio Sostenuto of the Opus 106 Sonata of Beethoven, a development passage in that, which becomes the basis which Brahms adopts as the idea from which he generates the 4th Symphony, the entirety of it. And if you follow it through, and look at Beethoven's 7th Symphony, and look at what Brahms does, compared with his knowledge of what Beethoven did with the 7th Symphony, then you've got a very interesting thing, and the whole thing becomes comprehensible. It falls into place. So that's the point.

Now, on the question of emotion: The most powerful emotion, the most convincing one, is the sense of truth. Now it doesn't mean a sense of truth about the universe, entirely. But it means a very powerful sense of truth about something. And when you get an idea of truth per se, and this is the most powerful kind of experience you can have in the ordinary course of thinking. A sense of an insight into a principle of truth per se. It may not be original to anybody but you, I mean, other people may have discovered it beforehand, but you have rediscovered it; you have experienced the act of, suddenly: "AH!" You were taken by surprise by recognizing something. An idea. It's an idea which has generic characteristics to it, not just an idea: It's not just one--but, it has generic aspects. It changes the way you're thinking about a lot of things: "Ah! Same thing."

Your question, you see: The three parts are all the same. The first, the question of the Gauss, one thing: the question of principle. How do you think about the problem? Not what do you think about the problem. How do you think about it? Second, music: How do you think about the problem? Third: How do you think about problems, in general? What is the most important kinds of reactions you get to your own thinking about problems, where you think you've discovered something, or a solution has discovered you! That's what the interesting thing is, in what you're describing. The case in which you didn't discover the solution, but the way you experienced it, you feel the solution discovered you. [applause]

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