Frontispiece of 14th century Latin translation of Euclid's Elements.
By
"Eaglebeak"
(An earlier version of these comments was posted on Factnet, Feb. 9, 2010.)
I received another email several weeks ago from a source who is interested in Lyn's Kulturkampf (that would be his Kampf against Kultur), providing me with a quote from Lyn and asking for a comment.
The quote--from a transcript of Lyn's remarks posted on the LaRouche Political Action Committee website, Sept. 17, 2009 under the title "Long Term Cultural Conflicts Are Being Played Out Today" (full text here)--is as follows:
"What you have to look at, is that population policy on the British side is very simple. And it has to do, not with simple issues that were debatable between the British and Leibniz, for example, but it goes back to an essential thing. It goes all the way back to Aristotle, and back to the adoption of Aristotle's folly by Euclid. So you have the Euclidean conception, which is the Aristotelean conception, as this was denounced as an Aristotelean conception. This idea was to prevent the technological and cultural development of populations, because if technological and scientific progress occurred, and were to influence sociology, then empires could not exist.
"And this whole thing, like the Aristotle operation, came after the death of Plato. It's always been understood that technological and scientific progress affects populations intellectually and otherwise, such that empires cannot exist....
"...The space program, for example, the killing of the space program, is actually the oligarchical principal [sic], which goes back to at least Aristotle and to Euclid. And those are the kinds of things that you've got to deal with."
Now, I don't know what anyone else's particular interest in this passage may be, but mine is this: does Lyn understand anything about Euclid?
I rummaged around the LaRouche Publications website, and found a telling passage from 2004 in which Lyn recollects his distant school days:
"[M]y initial and enduring personal hostility to Euclidean geometry erupted from within me on the first day of my high-school class in Plane Geometry. For me, the task of geometry was to uncover the principles which accounted for the increase of the functional strength contributed by an iron or steel beam, by eliminating certain weighty parts of a simply solid beam. It was apparent to me, from such experiences as frequent spectator visits to construction at Boston's Charles Town U.S. Navy Yard, there had to be [a] principled way in which the beam must be crafted geometrically, to optimize its function of support. The idea of a geometry apart from the geometry of physical processes as such, was for me a disgusting, foolish enterprise. Against this, I revolted in that instant, and could never accept a standard doctrine for geometry after that." (Emphasis added; read more here.)
You realize what we have here? We have a twofold confession:
1. Lyn couldn't "do" high school geometry (hence the hostility).
2. Lyn's concept of geometry is opposed to Plato's--because the geometry of Plato is precisely geometry apart from the geometry of physical processes.
Followers of Lyn steeped for years--marinated, really--in his view of Plato will need to question his grotesque mischaracterization of Plato as the "Philosopher of Becoming"; but once they do that, and re-read some Plato, they'll see what I mean.
Rummaging some more, I found the following statement from a 2006 presentation by Lyn to the LaRouche Youth Movement in Mexico. Again, the emphasis is mine.
"Now, the beginning is to attack Euclid as being a fraud. You can not derive a line from a point. You can not derive a surface from a line. You can not create a solid from a surface. Now, these are the elementary ironies, paradoxes, which are presented by Plato and by his predecessors among the Pythagoreans. You are subject to sophistry in schools, in which they teach you that these are definitions of axioms which you must accept. And they tell you you must use essentially linear algebraic methods. So you use linear algebraic methods, and you jump ahead assuming that you've proven something. You've proved nothing! Because what you did was, simply assume that Euclid was right. And Euclid was a fraud." (Full text here.)
Oh, dear. What an embarrassment. Can you find the place where Euclid derives a line from a point? Or a surface from a line?
I didn't think so.
Euclid does not "derive" his points, lines, surfaces, and solids. He defines them.
Thus, in the very beginning of Book I of Euclid's Elements, we have...definitions! Such as:
1. A point is that which has no part.
2. A line is breadthless length....
4. A straight line is a line which lies evenly with the points on itself.
5. A surface is that which has length and breadth only.
Philosophically, these are fascinating definitions--especially, perhaps, Definition 1. But any way you slice it, Dedekind schnitt or no, there's no generating of lines from points here, pal.
This is another one of those awkward moments where you realize: Lyn didn't read the book, he only saw the movie.
Lyn branches out from attacking Euclid to sneer at a whole raft of historic figures in science and mathematics whose work he's never studied and wouldn't be able to understand anyway because of his educational deficits. For instance, in the following statement from "Rescuing the World's Economy" (2009), Lyn not only denounces Euclid and Aristotle but also passes a characteristic snap judgment on the work of David Hilbert, one of the leading mathematicians of the late 19th and early 20th centuries:
"The follower of Aristotle, Euclid, chiefly copied into his own Elements the model solutions of earlier Classical Greek geometers, but added those infamous a-priori presumptions of his own making which echo Aristotle. The relevant issue of mathematical physics posed by this case, is expressed by the failure of the positivist David Hilbert's attempt to complete the process of solving the unproven assumptions of Nineteenth-century mathematics, most notably that of his sixth proposition, a proposition which goes directly to the point of Philo's attack on the theological argument of the Aristoteleans."
I assume that when Lyn refers to the "sixth proposition," he means Hilbert's Sixth Problem, and not Euclid's Sixth Proposition (or Fifth Postulate)--but with Lyn you never really know. At any rate, here's Hilbert's Sixth Problem:
"Mathematical Treatment of the Axioms of Physics. The investigations on the foundations of geometry suggest the problem: To treat in the same manner, by means of axioms, those physical sciences in which already today mathematics plays an important part; in the first rank are the theory of probabilities and mechanics."
I believe Hilbert was suggesting probability and mechanics as two areas for fruitful work.
For Lyn to refer to Hilbert's "failure" to "solve" the "unproven assumptions" of 19th-century mathematics is sophomoric at best. Hilbert enunciated his 23 problems in mathematics in 1900--at the time, all were unsolved. It may be that some--and here the Sixth Problem leaps to mind--are in fact insoluble, so that Hilbert's "failure" is hardly his fault. What Hilbert was doing was offering problems for his colleagues (and himself) to explore.
But Lyn will not be stayed by any such considerations.
As is well known, the very word "axiom" is enough to set Lyn off. Although his followers are taught to prattle about "changing one's axioms," the fact is that to Lyn the notion of an axiom is, er, anathema.
"Axiom," of course, comes from the Greek axioma--something worthy, or worthy to be held; from axioun, to think or consider worthy, from axios, worth, worthy--wait a minute--I think I see the problem!
Lyn was frightened by an Axios many years ago,[FN 1] and it's been all downhill from there.
At the sight of any axiomatic framework, the fit is on him again. The idea of a vast architecture of theorems derived from a small number of axioms causes tremendous anxiety in Lyn.
This is because he does not wish to be fettered by any laws of thought, as it were.
His individual sovereign creativity cries out, whenever confronted with a structure.
Hence the hostility, the animus, the venom. He cannot bear to be just another human being, bound by space and time, by rules and by mortality. Let alone by God.
None of that for Lyn. No sir.
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Comments
from Lyndon LaRouche Watch
February 20, 2013
Eaglebeak is right that LaRouche appears not to have read Euclid's Elements but only watched the movie. And while sitting in the theater with his box of popcorn, he must have tuned out the dramatic scene that reveals the difference between Euclid's definitions and Euclid's five postulates or axioms. Hence we get his pronouncement that "these are definitions of axioms" [huh?] which "they" (the sophists in "schools") say you "must accept."
It would appear that LaRouche has definitions, axioms, deductions, derivations and one plus one equals two all jumbled up in his head and can't distinguish between them--just as he can't distinguish in his conspiracy theories between British MI-6 agents and high-school geometry teachers.
Regardless of what LaRouche claims, Euclid's axioms are not taught today as ultimate truths but simply as the basis for doing two- and three-dimensional geometry in the everyday world around us. And if such geometry were a "fraud" (or to be more precise, if an Alien Space Bat would suddenly, as a prank, change the nature of reality in our corner of the galaxy to conform to LaRouche's peculiar geometric conceptions), we would surely be in a pickle. All of the world's bridges and high-rises would collapse as would just about everything made according to engineering designs and blueprints. And all the land deeds filed in U.S. county courthouses and all the contracts based thereon would become void, triggering a vastly greater real estate crash than the one in 2007 that LaRouche would have us believe he predicted.
As to the very real limitations of Euclidean geometry, they are not some dark secret that members of the LaRouche Youth Movement can only learn from LaRouche himself. The Wikipedia article on Euclidean geometry states up front:
"For more than two thousand years, the adjective 'Euclidean' was unnecessary because no other sort of geometry had been conceived. Euclid's axioms seemed so intuitively obvious (with the possible exception of the parallel postulate) that any theorem proved from them was deemed true in an absolute, often metaphysical, sense. Today, however, many other self-consistent non-Euclidean geometries are known, the first ones having been discovered in the early 19th century. An implication of Einstein's theory of general relativity is that physical space itself is not Euclidean, and Euclidean space is a good approximation for it only where the gravitational field is weak."
Whatever high school geometry textbook LaRouche was refusing to read back in the late 1930s probably did not mention non-Euclidean geometry, but today we find an outline of the subject even in New York State Regent's exam cram sheets (the example here is from the Oswego City School District's Prep Center). And non-Euclidean geometry is taught in universities throughout the world, as it should be: it's a mainstay of theoretical physics and higher mathematics.
LaRouche's view of geometry as an ideological battleground since ancient times between two warring elites--a conception that he set forth in the Sept. 2009 tirade cited by Eaglebeak--is absurd on the face of it. Euclidean geometry and the non-Euclidean geometries deal with different levels or aspects of reality (e.g., the Riemannian system focuses on curved spaces) and are intended for different purposes. The people who use non-Euclidean geometry in theoretical physics would turn readily to Euclid if, for instance, they had to survey where to put a fence.
