Question: When you discuss synthetic geometry, somewhere you state that there is some ontological principle, which is fundamental, and this is the self-evidence of circular action; so, what do you mean by self-evident?

LaRouche: Well, this essentially goes back to the idea of spherics of the pre-Pythagoreans, an idea which has continued from the Pythagoreans, and in modern times through the concept of the complex domain. One looks at the development of the concept of the complex domain, especially from Gauss on--[stops for translation to students]; so there's nothing very sophisticated, in a sense, from the standpoint of competent instruction in mathematical physics, on this issue, about what we mean by the function of circular action.

The idea of spherics, is the only way in which we can give a competent representation of the relationship between what we observe with the senses, and the physical principles, which are reflected as paradoxes in the flow of sense-experience.

So therefore, there's nothing particularly exotic about that. It simply was an ancient conception--for example, the problem we have today, with these kinds of ideas, is that the influence, in academic life and so forth, of the teaching of various derivatives of a notion of a Cartesian form of neo-Euclidean manifold. And, people try to say, you start from these a priori definitions, axioms, and postulates of Cartesian physical space-time, and you must interpret everything from that starting point.

When you realize that that's absurd, you realize that the correct standpoint, is that already understood by the Pythagoreans: That we're looking at the geometry of the heavens, at the starlit sky; we're looking as if at the internal surface of a great sphere. And, it's from the standpoint of looking at the action that we observe, in terms of spherics, so defined, that mankind has made all his important science--including geometry: That the ideas of geometry, which were transmitted by Euclid, were not developed by Euclidean methods. They were developed by pre-Euclidean methods.

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