Toward the Determination of the Non-numeric Value of the Golden Section By Charles B. Stevens, 2/1/2013 Almost two decades ago Lyndon H. LaRouche specified that the non- numeric value for the Golden Section could be derived from the then recently rediscovered Carl Gauss Pentagramma Mirificum through the application of the Eudoxus Method of Exhaustion. The determination of this non-numeric valuation of the Golden Section is essential to both the immediate and near- term survivable of the human species on this Earth. Only in the last 50 years has the degree of threat to human survival from asteroid and comet impacts emerged as the data on past such events and observation of current actual planetary impacts and growing numbers of observed near-misses have grown exponentially. (This is not to mention more distant astronomical threats such as the recently detected Vela emissions.) Due to the work of such scientists as Eugene Merle Shoemaker and the spectacular impacts of Comet Shoemaker- Levy-9 on Jupiter, science leaders such as Dr. Edward Teller initiated efforts for mobilizing Planetary Defense and more recently the Russian proposed program for Strategic Defense of the Earth (SDE). And while all such efforts should be fostered and supported, they may prove to be not sufficiently effective to meet the actual threat. What is minimally required are major advances in our scientific comprehension of the dynamics of the Asteroid belt. Any such advance will depend on the determination and general recognition of the non-numeric valuation for the Golden Section. More immediately the United States and Europe are threatened with an immediate economic collapse fueled by super hyperinflation and the march toward global thermonuclear war. The inability to meet these dual threats to the immediate survival is strongly reinforced by the long-term degeneration of culture and education leading to an almost complete absence of creative thought generally. Concomitantly, the composition and practice of classical music and art has essentially evaporated. As history has shown, the renewed recognition and practice of Golden Section harmonics are essential for reversing this collapse and sparking a revival from this nadir for human civilization. Kepler's Asteroid Belt Johannes Kepler (1596) famously forecast the existence of the Asteroid Belt. But it was not until Carl Gauss provided the specification for asteroid orbits that, just about 200 years later, scientists were able to make telescopic direct observation of them. Kepler's forecast of the Asteroid Belt were based on the method by which he discovered his principle of Universal Gravity and the characteristic physical dynamics of planetary orbits. Kepler's work increased the accuracy of astronomical forecasts by several orders of magnitude. About 7 decades later, a practicing witch, who later became an accountant and chief torturer for the English Treasury, utilized the work of others to derive an inverse square law for representing the Kepler's Laws of Planetary Motion. Sir Isaac Newton's work did not significantly affect the accuracy of astronomic observations. (Gauss's work provide the leap in astronomic accuracies, again, by several orders of magnitude.) In the Leibniz-Clarke correspondence, Newton discusses the differences between his approach and that of Kepler. According to Newton, Kepler's approach was primarily focused on the formation and evolution of the Solar System as a unified process, while Newton was only concerned with “accounting” for what we currently observe. Newton assumed that the “lump” masses of the planets interact pairwise. Kepler derived his laws for planetary dynamics on the general Golden Section harmonics of the system as a whole and their evolution. For Kepler, particular aspects of the system were to be derived from the harmonics of the system as a whole. The work of Kepler can be explored in detail here: http://science.larouchepac.com/kepler/harmony/ Implicitly Kepler's notion of the Asteroid belt was that it acted as a sort of placenta of Solar System's birth. What we see today is the detritus of that placenta. Explicitly, the actual determination of the Asteroid Belt was an experimental verification of Kepler's method and concept of Universal Gravity, as opposed to multi-body chaos of Newton. To make any progress on fundamentally comprehending the dynamics of the Asteroid Belt we must revive Kepler's approach and no longer worship the abominable Newton concoction. A crucial feature of that revival of the Kepler approach is the necessity of recognizing the actual non-numeric value of the Golden Section. Eudoxus To carry out this determination and demonstration for the actual non- numeric valuation of the Golden Section it is essential that we address the second issue raised in the opening paragraphs. At a later point I will develop a number of precise exercises to demonstrate and explore “native” human creativity. But there still remains the problem that we do not emerge into the world as blank sheets. By the age of reason we have had embedded in our personal psychologies the personalities and key experiences of thousands of generations or more. How can we even begin to organize this vast array in any rational manner? One approach is to proceed through a program in which one relives the creation of great discoveries, like that of Kepler and Bach. I will proceed by first laying out Lyndon LaRouche's specifications of his concept of the Golden Section. We will then address the one almost universal block to creative thinking: Euclid. And, in general, we will proceed by developing the anti-Euclidean method of Carl Friedrich Gauss and Lyndon H. LaRouche. This process will be informed through the application of the Eudoxus Method of Exhaustion. Even among many of his closest collaborators it is believed that LaRouche made an error in 1994 when he suggested the application of the Eudoxus Method of Exhaustion to the Gauss Pentagramma Mirificum to derive and demonstrate the non-numeric value of the Golden Section. First of all, none of Eudoxus's original work remains extant. Second, all extant sources report that the Eudoxus Method is identical to that of Archimedes. And in 1994 LaRouche and others had completed a series of papers demonstrating that Nicholas of Cusa had refuted the Archimedes Method of Exhaustion and its application to the Measurement of the Circle. Obviously, Lyndon LaRouche thought there was a basis for distinguishing Eudoxus from Archimedes. It is only recently that I have developed the means of addressing this question. I will take the specifications for the Golden Section from a September 9, 1986 LaRouche paper titled “Truth is Beauty, And Beauty is Truth: Understanding the Science of Music.” LaRouche Specifications The design of the Athens Acropolis is one of the true wonders of ancient civilization. Contrary to some textbook myth-making, the Acropolis's design was not a hodge-podge of successive additions at different points in time. The final structure was the fulfillment of a comprehensive, original design, to the effect, that from Erectheum, through Parthenon, and Nike Apteros by the gate, the whole is a coherent design, based on the elaboration of a single principle. The principle of design, is a constructable series of divisions of the circle. These divisions correspond to the harmonic composition of the human form. Underlying that ordering, is a very special geometric construction, the Golden Section. All great classical Greek plastic art and music were based on that same ordering principle: the harmonic orderings determined implicitly by the Golden Section.... Plato's dialogues are the first still-surviving source in European literature, for the proof that whatever is beautiful according to these principles is also truth, and that whatever is truthful is also beautiful. Plato's dialogues define the proposition, that physical science is the study of the universe in terms of the same Golden-Section harmonics.... Modern physical science was founded by Cardinal Nicolaus of Cusa. Formally, Cusa's founding of modern science appeared first in the 1440 publication of his De Docta Ignorantia (“Of Learned Ignorance”), and in those of his sermons which address the same matters. In this, Cusa picks up the central topic of Plato's Parmenides dialogue (most emphatically), the knowable and efficient interconnection between the macrocosm (the universe, etc) and the microcosm (the human individual, etc.). In De Docta Ignorantia, Cusa's treatment of this connection is posed in terms of the efficient interconnection between the Maximum (the macrocosm) and the Minimum (the microcosm). This writing has many implications for the most fundamental issues of physical science, but two of those features are most noteworthy at this immediate point....First, Cusa presents his argument in the terms of what modern science terms a “synthetic,” or “purely constructive” geometry. A synthetic geometry is one, which prohibits all axioms and any use of an axiomatic-deductive method of argument; the only allowed argument is one based on construction from a starting-point of nothing but circular action... (End of first selection) We shall proceed along the lines suggested above on the Athens Acropolis And that shall provide our model, though, instead of describing that particular construction we shall set fourth a series of hypothesized first constructions for the first calendar with its embedded “star map.” As suggested by Tilak, this star map was realized tens of thousands of years ago. It furthermore provided the basis for global navigation over the world's oceans. See http://www.docstoc.com/docs/88064602/Scientific-Implications-of-Vedic- Calendars-from-the-Standpoint-of-Kepler-and-Circles-of-Gauss And while the realization of that workable star map took thousands of years, nevertheless, I believe it is the product of a single harmonically coherent conception and not the episodic gathering of simple observations.