Originally formed in the context of the Year 2000 Presidential Election, the LaRouche Youth Movement has worked for nearly a decade on developing an understanding of the method of thinking employed by LaRouche in his economic forecasts and political activity. Returning to the primary sources of original geniuses, and in particular to the geometry and astronomy of ancient Greece, the LYM's continued work prompted LaRouche to offer guidance: he offered the Narrow Path, a trunk-line of the most important discoveries in physical science, required to develop a competent method for approaching other scientific problems and economic research. This narrow path, leading from the ancient Greeks (the Pythagoreans and Plato), through Johannes Kepler, Pierre de Fermat, G. W. Leibniz, Karl Gauss, to Bernhard Riemann, was designed to provide an insight into human creativity per se, rather than the mathematical reformulations found in textbooks and on internet encyclopedias. In an effort to spread these ideas broadly both among the political associates of LaRouche and society generally, a variety of pedagogical devices were created, including web-guides, books, magazines, and video presentations and guides. We present here what we hope will be an intriguing and helpful view into the train of human thought. As you work through the material presented here, feel free to email the basement ([email protected]) with any questions you may have. Enjoy!

Kepler, the first modern physical scientist, created the science of astrophysics. He freed science from the geometric-mathematical approach inherited from Aristotle and Ptolemy, and demonstrated that by incorporating the ironies between the harmonies of vision and hearing, the solar system, as a system, could be understood as governed by a universal principle of gravitation. The LYM presentations on the two major works of Kepler, his Astronomia Nova and Harmonice Mundi, were plagiarized in an act of epistemological warfare. LPAC produced a video, the Harvard Yard, to relate their understanding of Kepler and the circumstances around the plagiarism.

The Harvard Yard

New Astronomy
Harmonies of the World

Chronology of a Hoax: The Case of 'Kepler for Dummies'
March 2007 Dynamis - Contains articles on Parts I through III of the New Astronomy
January 2008 Dynamis - Articles on Part IV of the New Astronomy
Harmonic Dissonance - Presentation by Megan Beets on the Harmonies of the World, at the April 2009 basement conference on Dynamics.
'The LaRouche Show' Weekly Radio: Sept 9, 2009 - Jason Ross reports on his participation in the Prague conference on the 400th anniversary of the publication of Kepler's Astronomia Nova.

Fermat, the unique discoverer of the principle of least-time in his study of the propagation of light, dealt devastating (and quite funny) blows to the infectious agent known as Descartes. Although he did much work in the fields of what are now known as arithmetic (in the style of Gauss' Disquisitiones Arithmeticae), probability (in collaboration with Blaise Pascal), and the development of the differential calculus, his work on light's least-time propagation was most crucial in the development of the concept of a universal. The complete works and correspondence of Fermat on light have been translated as a book, and a website containing more translations has been created.

Dynamics II: Least Time and Credit • A thorough video report on Fermat's discovery.
Light: A History - Fermat's complete correspondence on light
Fermat website - translations of mathematical works
Feb 2009 Dynamis - contains Sarah Stuart's article that captures Fermat's sense of humor: 'Reflecting on History: Why You Should Know Pierre de Fermat'

Leibniz, the inventor of the physical infinitesimal calculus, the developer of the science of dynamics, and the creator of the science of physical economy, played a key role in Lyndon LaRouche's early intellectual development. A video on his concept of vis viva is available, as the opening shot in a series on dynamics. LaRouche's paper My Early Encounter with Leibniz: On Monadology discussed the impact of Leibniz on his thinking.

Other Suggestions:
Sufficient Harmony report by Sky Shields
My Early Encounter with Leibniz: On Monadology - an essay by Lyndon LaRouche
Leibniz papers: The Monadology and the Discourse on Metaphysics

Universally considered a genius and called the 'Prince of Mathematics' Gauss' actual thinking process is remarkably obscured, both by academia and by Gauss' own fear of the intellectual oppression of his day. Although his doctoral dissertation of 1799, written in a penetrating and polemical style, frankly expressed his search for true principles lying beyond mathematical formulations and empirical sense-perceptions, Gauss went underground as Napoleon took over Germany and the Congress of Vienna reaffirmed oligarchical rule in Europe. Following the work of the Kepler basement groups, a Gauss basement group was convened, to come to know Gauss' mind, with the specific focus of discovering how Gauss determined the orbit of the asteroid Ceres. The website the team created has quite a bit of content: on the history of Gauss, his work on higher arithmetic, bi-quadratic residues, and his discovery of the orbit of Ceres. Continuing work by the Gauss team on Gauss' application of the concept of the tensor is covered elsewhere, on the Tensor page.

The Mind of Gauss - The thorough website created by the Gauss team. Includes articles on history, arithmetic, astronomy, Ceres, and a large library of original translations of key works and correspondence of Gauss.
Gauss' 1799 Dissertation on the fundamental theorem of algebra: a crucial work for the early development of the LYM

The life of the revolutionary genius Bernhard Riemann was short (only 40 years), but his discoveries were profound. Putting aside a religious career to study mathematics, Riemann's habilitation dissertation, written in 1854 to become a professor, was later the inspiration for Lyndon LaRouche's development of what he has termed the LaRouche-Riemann method of economic analysis. This work, continuing the tradition of Kepler, Fermat, and Leibniz (vocally), and Gauss (implicitly), shatters any faith in a naive sense-perceptual view of the universe, sealing Euclid's coffin for good. With Riemann, a truthful geometry cannot be found in the department of mathematics, but in the department of physics. This new approach to geometry was adopted by Einstein and supported by Vernadsky.

Several videos on Riemann have been produced:
• I. The Habilitation Dissertation
• II(a). Potential and Metaphor
• II(b). Abelian Functions and Economics

Further development can be found on the Tensor page.

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