The depths of the present strategic crisis, in which Obama’s actions drive a process that makes a US/NATO confrontation with Russia becomes more possible by the day, cannot be understood without posing the question: how have people, generally, allowed this situation to develop?
To answer this question, Lyndon LaRouche has emphasized the deterioration in thinking and morality seen around the turn of the last century: from the ouster of Bismarck in 1890 and the imposition of mathematics instead of science by David Hilbert and Bertrand Russell in 1900 and beyond. The cultural and scientific decay brought about has been covered in several issues of EIR (1, 2, 3, 4), and a number of LPACTV shows (example).
In this post, I will take up Bertrand Russell’s pre-1900 attack on the outlook of the great Bernhard Riemann, whose work supported scientific breakthroughs for the next fifty years and catalyzed LaRouche’s economic breakthroughs, and hint at how Russell’s errors can highlight essential changes in thought today.
In 1895, Bertrand Russell, the most evil man of the twentieth century, submitted a dissertation, “An Essay on the Foundations of Geometry” for his fellowship at Trinity College, Cambridge. In his shockingly incompetent dissertation, Russell declares his opposition to the central thesis of Bernhard Riemann’s 1854 habilitation dissertation, that the basis of geometry lies in physics, and that among all possible three-dimensional spaces, true physical space is to be discovered by experiment.
Instead, Russell cleaves to precisely the Euclidean outlook that he purports to supersede, and demands that nature obey his geometric, a priori fancies.
This quotation from §65 is particularly telling:
Riemann has failed to observe, what I have endeavoured to prove in the next chapter, that, unless space had a strictly constant measure of curvature, Geometry would become impossible; also that the absence of constant measure of curvature involves absolute position, which is an absurdity. Hence he is led to the conclusion that all geometrical axioms are empirical, and may not hold in the infinitesimal, where observation is impossible. Thus he [Riemann] says:
“Now the empirical conceptions, on which spatial measurements are based, the conceptions of the rigid body and the light-ray, appear to lose their validity in the infinitesimal: it is therefore quite conceivable that the relations of spatial magnitudes in the infinitesimal do not correspond to the presumptions of Geometry, and this would, in fact, have to be assumed, as soon as it would enable us to explain the phenomena more simply.”
From this conclusion I must entirely dissent. In very large spaces, there might be a departure from Euclid; for they depend upon the axiom of parallels, which is not contained in the axiom of Free Mobility; but in the infinitesimal, departures from Euclid could only be due to the absence of Free Mobility, which, as I hope my third chapter will show, is once for all impossible.
Russell is saying that a non-constantly curved space is impossible (which forbids Albert Einstein’s theories of relativity), and that no departure from Euclid is allowed in the infinitesimally small (which forbids Max Planck and Einstein’s work on the quantum).
To pull apart Russell’s massive errors, a review of Riemann’s groundbreaking work is in order. For this, see this video:
The two dissents given in this quotation from Russell are that varying curvature would introduce absolute position, which Russell considers an absurdity, and that any curvature in the infinitesimal would be impossible, by violating free mobility. These two complaints are considered after a short review of Riemann.
Riemann gives three possibilities for the curvature of space:
- zero curvature—flatness
- constant curvature, in which objects would not change by being moved
- general curvature, in which every location in space could have a different measure of curvature, which would be determined not by geometric precepts, but by the physical forces.
While Russell acknowledges the possibility of the second of Riemann’s three cases, he categorically rejects the third, saying “from this conclusion I must entirely dissent,” citing the absurdity of absolute position.
Absolute position is an error, but Russell is applying a mathematical sense of absolute position, in which position has a universal meaning, based on something like a fixed, universal coordinate system for space, rather than the physical concept of spatial relations differing in different locations based on physical principles.
Historically, the error of absolute position in an absolute space was famously (and devastatingly) demonstrated by Gottfried Leibniz in his correspondence with Samuel Clarke, the prominent Newtonian. In discussing natural philosophy and theology, Clarke advances, as a proof of God’s great power, that at the moment of Creation, God decided where, among the vastness of space, to place the heavens and the Earth. Had He created everything elsewhere in space, while maintaining the same relationships among created things, no one would know the difference. This demonstrated, according to Clarke, the great power of God, unrestrained by reason, to do things simply because He felt like it. Leibniz counters that God is not only infinitely powerful, but also infinitely wise, and it would be undignified for such a Creator to do anything without a reason. Space cannot exist prior to, and independent of, things in space, for otherwise God would be led to a choice without a reason. Thus Leibniz concluded that there was no absolute space, and therefore no absolute motion or absolute rest: motions were all relative (although causes were not).
It is upon the lack of absolute position in this sense that Russell bases his case. In doing so, he either does not understand, or chooses to ignore, the difference between absolute space itself and universal characteristics of space. Absolute space does not exist. Yet, it does not follow that regions of space cannot possess different characteristics.
Jump ahead to Einstein’s 1905 special theory of relativity and to his 1915 general theory of relativity. Space and time are no longer separable aspects of reality or scientific thought: a combined four-dimensional space-time is curved by gravitation, and skewed by the motion of an observer making observations about it. The non-constant curvature does distinguish regions “in space” from each other, but does not create the “absolute position” that Russell decried; the differing characteristics of different positions arise not from space itself, but from physical processes occurring in space—gravitational acceleration and light propagation. Russell, in 1895, forbade the discoveries of Einstein in 1905 and 1915.
Now consider the second of Russell’s dissents: that spatial relations in the infinitesimal may not correspond to presuppositions of geometry, and that physical discovery may lead to precisely that conclusion, a notion from which Russell felt he “must entirely dissent.”
Leap forward again, to Planck’s 1900 quantum hypothesis, and Einstein’s 1905 solidification of the quantum in his work on the photoelectric effect. Here we see quite clearly those two conceptions singled out by Riemann, the “rigid body” and the “light-ray”, changing their meanings in the infinitesimal. The geometry of the very small developed by physical hypotheses, as Riemann foresaw, and as Russell forbade.
Russell’s mathematical, rather than physical mind-set, and his attack on the possibility of truly revolutionary discovery as a characteristic of the human mind, took more direct form in the next century, even as the creative work of Max Planck and Albert Einstein overthrew Russell’s outlook.
This direct assault on the mind came after David Hilbert’s 1900 speech at the International Congress of Mathematicians, in which he posed the axiomatization of arithmetic and of physics (which, if possible, would mean that no fundamentally new discovery could ever be made). Hilbert’s challenge was taken up by Russell, who produced his Principles of Mathematics in the early 1900s, setting out an approach of making mathematics a branch of logic, in which nothing fundamentally new could be created. Planck, in 1900, and Einstein, in 1905, fundamentally overthrew the basic concepts of space, time, energy, and matter. Yet, Russell continued to toil on his Principia Mathematica, attempting to show how all of mathematics could be derived from logic, rather than from discovery. After this three-volume work was released over 1910-1913, Einstein shook up the world again with his 1915 general theory of relativity.
While true geniuses advanced knowledge through discovery, Russell worked, academically, on proving that discovery was impossible, and, politically, on eliminating it as an active part of cultural life.
This evil, racist, hideous man was not a supporter of peace, a great philosopher, or a lover of learning. As a thinker, underneath his puffery, he is cultivated ignorance.
There is much more to say about the full story of 1900. Consider this a preview.
Acknowledgement: Thanks to David Shavin for leads and discussion on Russell’s 1895 paper.