EIR Science ON VERNADSKY’S SPACE More on the Calculus by Lyndon H. LaRouche, Jr. September 13, 2007 had been chosen by others, then assembled, with me, for be- ginning its mission of reliving of the actuality of the process Once again, for the second time, my receipt of the translation of Gauss’s discovery of that orbit. That was the occasion on of Academician V.I. Vernadsky’s On the States of Physical which I first challenged the LYM to discover the often over- Space, as a Festschrift for the occasion of my 85th birthday, looked difficulty which confronts any student of Gauss’s rela- prompts the following additional remarks. This second time, tively successful result in this matter. as part of a continuing discussion with the basement team on The problem, as I had emphasized this in earlier publica- a crucial feature of the content of my contribution to EIR, Vol. tions, is that, Gauss, after the 1800 death of Abraham Käst- 34, No. 39, I focus what I have recognized as much needed, ner, was working within that hostile environment for compe- deeper attention to a still deeper epistemological implication tent European science which had been created by a succession of the same subject-matter. of adverse political developments centered on the reaction- ary developments which had occurred in France, from July Despite all that which has been said on the subject of 14, 1789, through the Duke of Wellington’s appointment of physical space-time, between me and the LaRouche Youth France’s so-called Restoration monarchy and the related Vi- Movement (LYM) teams, one may still wonder: how well did enna Congress. These were, most notably, adverse conditions Carl F. Gauss know the orbit of the asteroid Ceres? The orbit, which were being shaped under the spread of Romanticism, as Gauss defined it correctly at that time, is known; but, the shaped by both the cultural impacts of the Napoleonic wars underlying principles of that universe in which Gauss’s think- and, later, under the regime of Prince Metternich and his like ing was actually located, remain poorly understood, even from the period of 1815 onwards.1 Much of Gauss’s life and among competent professionals, still today. work, was lived under those special, menacing political con- The issue so posed, might be regarded as “valid but eso- ditions of moral and related, widespread intellectual decay. teric;” it, nonetheless, must be considered as of crucial im- These were, conditions which were already widespread, as portance. an infection, within the science-environment of that time, Here, in this present location, I focus on the relevant im- and which have become far worse today. Within that lapse of plications of the matter of the calculus itself. I summarize time, prudence often impelled Gauss, then, out of an under- what I have said, during the interim, as said between me and standable sense of personal discretion, to hold back some some members of “the basement team.” Unavoidably, I shall among the most significant, controversial features underly- frequently restate what I had stated in the preceding reaction to the implications of the LYM’s contribution to the Fest- 1. The period from Napoleon Bonaparte’s installation as Emperor onwards schrift. What I add, as interpolations, here, on this occasion, was a time of a deep and widespread cultural decadence, called Romanticism. opens the field of discussion within a much larger and deeper Romanticism’s influence as a form of corruption infecting newborn genera- tions of prominent figures of science and artistic composition and its perfor- realm of exploration. mance, is typified by the influence of the corrupt Augustin Cauchy in physical As I have reported earlier (repeatedly), the time came, science, and Liszt and Richard Wagner in music. See Heinrich Heine on the when I was to meet with that LYM team of volunteers which subject of the Romantic School, for an example of the problem. 38 Science EIR October 12, 2007 Paolo Sarpi who adopted the medieval irrationalism of William of Ockham as the model for what has become the prev- alent, modern European Liberalism of both classroom and law-making today. The intent of Sarpi and his slime-ball style in-house lackey, Galileo, was to permit innovations, despite the rabidly pro-feudalist, Aristotelean conserva- tives, but to eliminate knowledge of ac- tual scientific principles, by substituting mere algebraic formulas for knowledge of principles. As the customary fraudulent, aca- demics’ attacks on Kepler and Leibniz attest, no actual physical principle, such as those of Cusa, Kepler, Fermat, or Leibniz, has been tolerated by these Liberals, to the present day. The silly fraud which the Newton faction, includ- EIRNS ing D’Alembert, Euler, Lagrange, and A LYM “basement” team, working outdoors on Gauss and the orbit of Ceres. Cauchy presented as a calculus, is typi- cal of the Liberal practice of substitut- ing sentimental, Sophists’ slop, in the ing many among his leading discoveries: where my native, form of merely descriptive language, for actual knowledge more militant disposition, for example, would not have per- of science. mitted me to do so. I have repeatedly warned those LYM members, and oth- Reading Gauss ers who have been assembled for sundry phases of this mis- That just-stated fact of the matter is illustrated by the ex- sion, that they must ask themselves: What were those hidden emplary case of Gauss’s reference to his own earlier discov- features to which I now allude, again, and why was Gauss ery of an anti-Euclidean mode in physical geometry.2 As I committed to suppressing certain among the relevant, under- have warned the LYM teams repeatedly, the Gauss living un- lying facts about his own discoveries? What is the difference der the political conditions menacing early Nineteenth Cen- between the method Gauss actually employed for his discov- tury science, often chose to present his discoveries without eries, and his method of presenting the proof of that which he taking the political risk of fully uncovering the actual method had achieved with such justified pride? Why is there such a by which he had achieved them; this is the case even some difference, why such a gap? among his most notable discoveries. This has been repeatedly, as presently, a subject of my As I have written, repeatedly, earlier, in such cases, as the continuing discussions with the LYM teams, a subject which LYM has met this problem frequently in its work, we may dis- must be shared more widely, as now. In this second response cover, at later points in Gauss’s work, that, often, his explana- to the LYM’s contribution to the Festschrift, I focus on the tion of the discovery, which, although an accurate description still deeper implication which must be considered if the cru- of the result itself, omitted accounting for certain crucial fea- cial error in most contemporary mathematics education is to tures of the means which he had actually employed for those be remedied. publicly reported achievements.3 The sometimes heated qual- The source of the problem lay not in Gauss himself, but in ity of the correspondence between Gauss and Jónas and Far- the corrupted, Liberalism-infected state of mind of most kas Bolyai, son and father (and others), on the subject of non- among the audience to which virtually all of among his dis- Euclidean geometry, merely exemplifies the kind of challenge coveries were presented for publication in those times. What is the crucial conception which must be introduced, to free 2. C.F. Gauss to C.L. Gerling, Feb. 14, 1832: in Kurt-R. Biermann, Carl science, finally, from that corrupting grip of Liberalism which Friedrich Gauss: Der “Fürst der Mathematiker” in Briefen und has pushed global civilization now, to the brink of a genera- Gesprächen (Munich: Verlag C.H. Beck, 1990), pp. 27, 137. tions-long, planetary new dark age today? 3. Typical is Gauss’s treatment of his argument against the empiricists in the It is to be emphasized on this account, that Anglo-Dutch matter of the Fundamental Theorem of Algebra, and the related matter of qua- Liberalism, as a philosophy, was an adopted ideology of the dratic reciprocity. See note, below. October 12, 2007 EIR Science 39 which those who would be serious students of Gauss, must, ‘Quadratic Reciprocity’ Again repeatedly, face and resolve in their own minds.4 This set of considerations obliges us to turn our attention That kind of challenge to today’s student, was not manifest to the most profound of the issues of the method required for in that problematic form, in the written reports of their own scientific progress in general. On this present occasion, I take work by such predecessors of Gauss such as Kepler and Leib- a broad step which is similar to what I have published on sim- niz. Kepler hides nothing in providing the student frank identi- ilar matters earlier, but is nonetheless a qualitative, and also fication of earlier assumptions he has discarded. It is also nota- necessary step beyond what I have presented in related mat- ble, that Gauss’s follower Bernhard Riemann, was to be much ters on which I have written earlier. franker than Gauss about the method of his own discovery, From the work of the ancient Pythagoreans and Plato, where Gauss had often been cautious on comparable points.5 through the crucial discoveries, as by Nicholas of Cusa, Leon- On that occasion, I cautioned the LYM team, that, there- ardo da Vinci, Kepler, and Leibniz, as capped, thus far, by that fore, before jumping, prematurely, to what might appear to be of Riemann, Einstein, and Vernadsky, all actually competent obvious conclusions, they must concentrate on digging deep- insight into crucial matters of science, as since the design of ly into the virtual map of the way in which Gauss’s mind actu- the great pyramid of Giza, is always to be rooted implicitly in ally worked on the Ceres project, and, also, in work on other the subject of astrophysics.