Question: Hi Lyn, I'm from Seattle. I have a question about the mathematics of Gauss. I've read a little bit of what you've written on him, as far as the teachings of Gauss and Riemann and Leibniz, contrasting those of Euler and Lagrange and Newton. I was wondering if you could contrast those for me, so that I can maybe understand why the one, Gauss' teachings are so much more important, than the others? And what so specifically had gone wrong with Newton, Euler, et al.

LaRouche: Well, first of all, the root of this thing, is empiricism. Empiricism was invented by Paolo Sarpi, the tyrant of Venice, from the latter part to the last two decades of the 16th Century and the first decades of the 17th Century. Paolo Sarpi, among others, had a great influence on, to some degree, France; but, especially on England, where his influence is most notorious, upon Francis Bacon and Thomas Hobbes.

Sarpi was most famous through a student of his, who was also a household lackey of his: Galileo Galilei, who was quite a faker in his own right. Who was the teacher of mathematics and so forth, to Thomas Hobbes.

Now, the purpose of this teaching, was that Paolo Sarpi explained it as being based on the doctrines of a fellow called William of Ockham. And so, it was the so-called Ockham's Razor, was stripping out from science and knowledge, all those things which pertained to principle. Eliminate all principles, and substitute, instead, a set of so-called "reductionist" axioms and postulates and definitions. And allow nothing.

All right, now the effect of this, was to reduce knowledge to a statistical interpretation of sense perception. Now, I had earlier, the second question that I received this morning, there, from Seattle, was on this question about curvature. Now, imagine that, here you have the spherical sensorium of the observation of the heavens, of the night sky. And, imagine that you can see nothing but those points, as such. You now run a statistical interpretation of those points, which you see displayed, as events, or singularities, on the sensorium of this oval, this sphere, in which you're contained. Then, you are in the realm of empiricism.

Whereas science is based on rejecting that. Remember, now, before all these crap artists came along, you had the case of Kepler, among others; you had Leonardo da Vinci, before Kepler; you had Nicholas of Cusa, before Leonardo; you had Brunelleschi in the same period as Cusa. So, science was already developed! You had the principle of least action, as discovered by Fermat, in his work. You had the work of Pascal.

Along, in the middle of this, comes Descartes, comes all these things--this Cartesian model, which was used by Newton. And, Newton was a plagiarist. Newton's work on astronomy was all fake. He plagiarized an English translation, essentially--an English publication, of Kepler's New Astronomy, with the assistance of some people who worked with him. And, then he faked the results. And that became known as the Newtonian system.

So, what the problem here is, that these guys were all involved in faking! What's the effect of the faking? If you have a society, in which some faking is not allowed, in which people are actually discovering universal principles, experimentally, proving them, then you have a society in which the individual member of society knows what it means to discover a principle, which lies outside naive sense impression; does not rely upon statistics, but relies upon the experimental ability to demonstrate the efficiency of the principle discovered. Then, you have a society, which is progressive.

Now, if you have a society, which is not so trained, then what do you have? You have a bunch of dumb sheep: who will do as they're told, follow orders, know nothing better, and just do it, like human cattle. The objective of this process, is to produce human cattle.

Now, in the case of Euler and Lagrange: Euler was not stupid, but he was a fanatic. Newton was probably not too intelligent, actually. He specialized in black magic. But, Euler was a very skilled, very intelligent mathematician, from a formal standpoint; from tricks with arithmetic--for example, his discovery for the mathematical model for the knights' moves in chess is famous. But, he was evil. It wasn't that he was stupid, he was evil. And he deliberately created a fakery on the question of the complex domain. Euler's student, his protégé, who succeeded, and then later went to become the protégé of Napoleon Bonparte, faked it also.

So, Gauss simply made a demonstration from the standpoint of simple proof, that this was fake--it's fake. And that's what Gauss proves; he proves that it's fake; that these guys are fakers. And, by doing so, demonstrates what I said in answer to the first question today, from Seattle: That we actually live, not in a sensorium, which is some kind of a big sphere--we're looking at the dots, the lights on the points of the sphere. But, rather, what we see of these events, as singularities, are actually tangential points, of intersection of a real process, with the imaginary process, which is the spherical system. And, by studying the curvature of patterns of certain events--Gauss used three, to demonstrate the orbit of Ceres--by taking a pattern of several of these events, and discovering the curvature, of the tangency, associated with the observation of those events, now discovers the real universe.

So, the complex domain, actually pertains to this concept of the universe of reality, which lies outside the simple sensorium. So therefore, you have what we call "the complex domain." And Gauss's essentially discovery was to prove, by these and related works, and by his work in astronomy, to prove the principle of the complex domain, on which all competent modern physical science is based. Anything contrary, is incompetent.

-30-