3 de junio de 2007

<body><div id="article"><tr><td height="23" valign="middle" width="184"></td><td valign="middle" width="185"></td></tr><h1>THE TRAGEDY OF LEONHARD EULER</h1><h4>by Lyndon H. LaRouche Jr.</h4><h4>June 3, 2007</h4><p>Today the Fachschaft Physik der Uni-Dortmund 2007 is opening a festival commemorating the birth of the celebrated Leonhard Euler three hundred years ago.</p><p>Euler, who rose to justly acclaimed fame under the influence of Gottfried Leibniz and the guidance of Jean Bernoulli, had been celebrated as an accomplished representative of the work of Leibniz and Bernoulli, until he changed his allegiances in science rather radically, to the anti-Leibniz camp, as this is typified in the clearest and most flagrant fashion, by his wretched 1763 Letters To a German Princess.</p><p>In the matter of this about-face, it is neither useful for necessary to debate each Euler work one at a time. There is an absolutely crucial and fundamental issue of science at stake. Every other topic which might be dragged in as a kind of academic foliage, is essentially irrelevant to both the fact and implications of Euler's apostasy, most notably that which put him in embittered opposition to Gottingen's Abraham Kaestner, and Gotthold Lessing and Moses Mendelssohn at Berlin.</p><p>The issue is that treated with bold precision by Carl F. Gauss in his own 1799 doctoral dissertation, the same issue for which the famous student of both Gauss and Lejeune Dirichlet, Bernhard Riemann, was celebrated by such as Albert Einstein later: the most important of the issues of scientific method in all known science to the present day, the issue of the ontological actuality of the infinitesimal which remains the principal issue of modern European science, from Nicholas of Cusa's discovery of the systemic error in Archimedes' mistaken effort to treat the circle as an expression of quadrature, and with Kepler's celebrated treatment of higher order of the methodological fallacy of the quadrature of the circle, in his definition of the principle of motivated action in the generation of the planetary elliptical orbit.</p><p>In fact, the entirety of the mainstream of actual progress from the work in Sphaerics by the Pythagoreans, and the combined work of the Pythagoreans and the circles of Socrates and Plato, is the conception of the infinitesimal as an ontologically efficient actuality, rather than, as Euler attempts, as do de Moivre, D'Alembert, Lagrange, et al. to treat the concept of the infinitesimal as merely a fantastic formality, rather than the ontological actuality recognize by Cusa, Kepler, Leibniz, Bernoulli, et al., the actuality of the catenary principle of the Leibniz-Bernouilli universal principle of physical least action, that of the Leibnizian complex domain and the actually physical hypergeometries of Bernhard Riemann.</p><h4>The Issue Is Humanity</h4><p>The essential issue implicit in Euler's descent into mere mathematician's formalism, instead of physics, is not a mere issue of formalities. The issue, as since Aeschylus' Prometheus Bound, is whether or not the high priesthood reigning over the opinions which society is permitted to believe, shall be a pretext for denying society the right to access to practical knowledge of the use of various ordinary, and also higher forms of "fire."</p><p>In physical science, as opposed to mere mathematical formalism, the central issue of these discoveries, of the use of "fire," or related kinds of scientific principles and technologies, is the nature of knowledge of an efficient form of universal physical principle. The crucial issue in the teaching and application of physical science for the promotion of the general welfare of society, is the issue of whether or not a physical principle of mathematical work is merely an enticing formality, or, as Kepler defines the universal principle, of motivation of the planetary orbital pathway as a physical motive, as Gauss saw the motive of planetary action expressed in such forms as the asteroid orbits of Ceres and Pallas.</p><p>The central achievement of Bernhard Riemann has been that of the revolutionary advancement in methods of scientific practice which came boldly to the surface with Riemann's 1854 habilitation dissertation, and the development of the physical conceptions in hypergeometry which came along the same pathway cleared by that dissertation. That is the pathway opened by Cusa's exposure of the error of Archimedes' quadrature of the circle, by Kepler's discovery of the physical science of elliptical functions and the calculus, by Fermat's opening the gates on the physical concept of least action, by Leibniz's and Jean Bernoulli's development of the concept of a universal principle of physical least action, by Gauss's insights into the nature of physical motivation, and the discoveries of Riemann.</p><p>It should be recalled by anyone claiming competence in physical science, that the Kepler-Leibniz infinitesimal is not the mere formality which de Moivre, D'Alembert, Euler, Lagrange, et al., proposed. It is expressed as a constant rate of change of the direction of the motivated orbital pathway. It was this conception of the infinitesimal, which was already implicit in Archytas' construction of the doubling of the cube, already clear in Nicholas of Cusa's rejection of the use of mere quadrature for the circle, and Kepler's taking the attack on the fallacy of the "equant."</p><p>The world of today, is gripped by the onrushing force of what threatens to become, soon, the gravest, planet-wide crisis in all modern history. The remedies for this are available, provided we abandon the ivory-tower mathematical fantasies of information theory which had mostly replaced emphasis in employment, on a return to physical-scientific progress in agriculture, industry, and basic economic infrastructure. The efforts of Euler's turn into awful ideologies such as those expressed by his 1763 Letter to a German Princess, is not the sort of thing we should promote under the specific kinds of breakdown of the production process which Europe and North America are suffering today.</p></div></body>