Developing a chorus of sound Mind
RIEMANN FOR ANTI-DUMMIES PART 37 THE DOMAIN OF POSSIBILITY Plato, speaking in the Laws through the voice of an Athenian stranger, holds it indispensable for leaders of society to possess elaborate knowledge of arithmetic, astronomy and the mensuration of lines, surfaces and solids. He also considers it a disgrace for any common man to lack … Continue reading Riemann for Anti-Dummies: Part 37 : The Domain of Possibility
Riemann For Anti-Dummies Part 36 TRANSCENDENTAL HARMONIES Discoveries indicating the existence of what Gauss would later call the complex domain began with Pythagoras and his followers in the 6th Century B.C, These discoveries, which include the ratios of musical intervals, the doubling of the line, square and cube, the five regular solids, and many others, … Continue reading Riemann for Anti-Dummies: Part 36 : Transcendental Harmonics
Riemann For Anti-Dummies Part 35 MIND AS POWER GENERATOR Rene Descartes (1596-1630) was, for all intents and purposes, a Bogomil. The geometry that bears his name, is brainwashing. Anyone exposed to it, unless cured, will suffer from cognitive deficiency. Symptoms include impotence and an inability to distinguish fantasy from reality. Gottfried Leibniz, writing to Molanus, … Continue reading Riemann for Anti-Dummies: Part 35 : Mind as a Power Generator
Riemann for Anti-Dummies Part 34 POWER AND CURVATURE In his 1854 habilitation lecture, Bernhard Riemann spoke of the twofold task involved in lifting more than 2,000 years of darkness that had settled on science: "From Euclid to Legendre, to name the most renowned of modern writers on geometry, this darkness has been lifted neither by … Continue reading Riemann for Anti-Dummies: Part 34 : Power and Curvature
Riemann for Anti-Dummies Part 33 HYPERBOLIC FUNCTIONS - A FUGUE ACROSS 25 CENTURIES When the Delians, circa 370 B.C., suffering the ravages of a plague, were directed by an oracle to increase the size of their temple's altar, Plato admonished them to disregard all magical interpretations of the oracle's demand and concentrate on solving the … Continue reading Riemann for Anti-Dummies: Part 33 : Hyperbolic Functions – A Fugue Across 25 Centuries
Riemann for Anti-Dummies Part 32 THE BEGINNINGS OF DIFFERENTIAL GEOMETRY Fifty-two years after Gauss' 1799 doctoral dissertation on the fundamental theorem of algebra, his student, Bernhard Riemann, submitted, to Gauss, an equally revolutionary doctoral dissertation that took Gauss' initial discovery into a new, higher, domain. Riemann's thesis, "Foundations for a general theory of functions of … Continue reading Riemann for Anti-Dummies: Part 32 : The Beginnings of Differential Geometry
Riemann for Anti-Dummies Part 31 THE CIRCLE'S ORBITAL PERIOD Most will find what follows very challenging, but anyone who makes the effort to work it through will be richly rewarded, as the insights gained have deep implications for survival of civilization.) If we look at the known cases of constructable polygons, the triangle, square and … Continue reading Riemann for Anti-Dummies: Part 31 : The Circle’s Orbital Period
Riemann For Anti-Dummies Part 30 THE POWERS OF ONE On the morning of March 30, 1796, Carl Friedrich Gauss discovered that the way people had been thinking for more than 2000 years was wrong. That was the day, when, after an intensive period of concentration, he saw on a deeper level than anyone before, the … Continue reading Riemann for Anti-Dummies: Part 30 : The Powers of One
Riemann for Anti-Dummies Part 29 THE CRIMES OF KLEIN When working through the conceptions underlying Gauss' 1799 proof of the fundamental theorem of algebra, or, Gauss' discovery of the principles behind the division of the circle (to take only two examples), one is immediately confronted with the fact that these discoveries arise from explicitly anti-deductive … Continue reading Riemann for Anti-Dummies: Part 29 : The Crimes of Klein
Riemann for Anti-Dummies Part 28 BRINGING THE INVISIBLE TO THE SURFACE When Carl Friedrich Gauss, writing to his former classmate Wolfgang Bolyai in 1798, criticized the state of contemporary mathematics for its "shallowness", he was speaking literally - and, not only about his time, but also of ours. Then, as now, it had become popular … Continue reading Riemann for Anti-Dummies: Part 28 : Bringing the Invisible to the Surface
Riemann for Anti-Dummies Part 27 GAUSS' DECLARATION OF INDEPENDENCE In September 1798, after three years of self-directed study, C.F. Gauss, then 21 years old, left Goettingen University without a diploma. He returned to his native city of Brunswick to begin the composition of his "Disquisitiones Arithmeticae." lacking any prospect of employment, he hoped to continue … Continue reading Riemann for Anti-Dummies: Part 27 : Gauss’ Declaration of Independence
Riemann for Anti-Dummies, Part 26 IDEAS CAST SHADOWS, TOO It can be a source of confusion for the naive, and a means of deception of the wicked, to restrict the meaning of Plato's metaphor of the cave, to those objects that originate outside of one's skin. As all great scientists have come to know, ideas … Continue reading Riemann for Anti-Dummies: Part 26 : Ideas Cast Shadows, Too
Riemann for Anti-Dummies Part 25 SCHILLER AND GAUSS In his "Aesthetic Estimation of Magnitude", Friedrich Schiller discusses a crucial ontological paradox that confronts science when it tries to exceed existing axiomatic assumptions: "The power of imagination, as the spontaneity of emotion, accomplishes a twofold business in conceptualizing magnitude. It first gathers every part of the … Continue reading Riemann for Anti-Dummies: Part 25 : Schiller and Gauss
Riemann for Anti-Dummies Part 24 LET THERE BE LIGHT As you heard Riemann proclaim in the opening remarks of his Habilitation lecture, without a "general concept of multiply-extended magnitudes in which spatial magnitudes are comprehended," you are left in the dark. You can not know the nature of the physical universe, the validity of an … Continue reading Riemann for Anti-Dummies: Part 24 : Let There Be Light
Riemann for Anti-Dummies Part 23 THE CIVIL RIGHTS OF COMPLEX NUMBERS As the unfolding of current history demonstrates, it is reality that determines policy, not the other way around. This should come as no surprise to a scientific thinker knowledgeable in the method of Plato, Cusa, Kepler, Leibniz, Fermat, Gauss, Riemann and LaRouche. It is, … Continue reading Riemann for Anti-Dummies: Part 23: The Civil Rights of Complex Numbers
Your Education Was Not Merely Incompetent If you felt a little disconcerted to sit in the same lecture hall with C.F. Gauss, listening to B. Riemann deliver his habilitation address, do not despair. Be happy. You are being afforded the opportunity to discover that your education was not merely incompetent, it was also malicious. Incompetent, … Continue reading Riemann for Anti-Dummies: Part 22: Your Education was Not Merely Incompetent
It is Principles, Not Numbers, That Count As we continue the investigations into the "hints" from Gauss, to which Riemann referred in his 1854 habilitation lecture, it is vitally important to maintain the perspective of a member of the audience in the lecture hall that June day when Riemann delivered his revolutionary address. Don't be … Continue reading Riemann for Anti-Dummies: Part 21 : It is Principles, Not Numbers that Count
Gauss' Attack on Deductive Thinking In his 1854 habilitation dissertation, Bernhard Riemann referred to two "hints" as preliminary to his development of an anti-Euclidean geometry--specifically Gauss' second treatise on bi-quadratic residues and Gauss' essay on the theory of curved surfaces. It is but one more testament to the ignorance of all so-called experts today, (not … Continue reading Riemann for Anti-Dummies: Part 20 : Gauss’ Attack on Deductive Thinking
The Know is Only a Special Case of the Unknown On June 10, 1854 Bernhard Riemann presented his now famous Habilitation Lecture, "On the Hypotheses that lie at the Foundation of Geometry", to the faculty of Gottingen University. To begin to comprehend Riemann's revolutionary address, imagine yourself in the audience, looking over the shoulder of … Continue reading Riemann for Anti-Dummies: Part 19 : The Known is Only a Special Case of the Unknown
Doing the Impossible "Nothing is fun but change," is an apt transformation of Heraclites' famous aphorism to convey the quality of mind required to grasp Leibniz' calculus and its extension developed by Kaestner, Gauss, and Riemann. Inversely, one who is gripped by a bullheaded resistance to its import, and the corollary, "Without fun there is … Continue reading Riemann for Anti-Dummies: Part 18 : Doing the Impossible
Science is not Concensus Over the course of this series we have built up a healthy collection of examples demonstrating what LaRouche so succinctly expressed at the Lebedev Institute: "What we call modern physical science, is based on taking what people believe is the organization of the universe, and proving it's wrong." This week we … Continue reading Riemann for Anti-Dummies: Part 17 : Science is not Consensus
What's in a Moment? We are now at the point in this series, where we can begin to dig directly into that rich vein of knowledge revealed by Bernhard Riemann' s development of complex functions. However, it is necessary, before embarking on that leg of this journey, that you first contemplate this short, but important, … Continue reading Riemann for Anti-Dummies: Part 16 : What’s in a Moment?
The Solar System's Harmonic Twist Significant insight can be obtained, for those wishing to master the art of changing one's own axioms, by re-living Kepler's transformation of his own thinking, from his initial hypothesis connecting the planetary orbits to the five Platonic solids, to the supersession of that hypothesis, under his concept of "World Harmony." … Continue reading Riemann for Anti-Dummies: Part 15 : The Solar System’s Harmonic Twist
The Dissonance that Smiled By all accounts, Descartes, Newton, Euler, and Kant all shared one common trait: they were grouchy old farts. As such, these poor souls fled from the dissonance and tension by which the universe presents its development to the mind of man. Like their Venetian brethren, who only desired forms of music … Continue reading Riemann for Anti-Dummies: Part 14 : The Dissonance that Smiled
The Finer Art of Science How often have you heard, after briefing someone on the strategic situation and LaRouche's unique role in leading mankind out of this crisis, the retort, "I just don't think one man can have the answer." Such a response, not only indicates a narrow, petty, and small minded way of thinking, … Continue reading Riemann for Anti-Dummies: Part 13 : The Finer Art of Science
Gauss' Division of the Circle The pursuit of a discovery of a universal principle always requires the pursuer to follow the Socratic method of negation, or, as Cusa called it, "Learned Ignorance". This is the method by which Kepler ascended from the tangle of observed motions of the planets on the inside of an imaginary … Continue reading Riemann for Anti-Dummies: Part 12 : Gauss’s Division of the Circle
Transcending Euclid It is crucial for anti-dummies to always bear in mind the groundwork for all modern science, that Nicholas of Cusa teaches us in "On Learned Ignorance": "Wherefore it follows that, except for God, all positable things differ. Therefore, one motion cannot be equal to another; nor can one motion be the measure of … Continue reading Riemann for Anti-Dummies: Part 11 : Transcending Euclid
Justice for the Catenary On the very eve of his unjust incarceration, Lyndon LaRouche issued a short, but substantial, memo on the catenary function, that was vigorously maligned by a few, and, unfortunately, largely ignored or not understood by many. The principles identified there, are critical at this stage of this pedagogical review of the … Continue reading Riemann for Anti-Dummies: Part 10 : Justice for the Catenary
Bernouilli's Brachistichrone: An Exemplary Case of the "Science of the Moments of Becoming" In response to Kepler's call for the development of a mathematics appropriate to non-uniform motion, Leibniz invented a new form of geometry of position, that he called, the "infinitesimal calculus". While a horror may well up in the minds of some at … Continue reading Riemann for Anti-Dummies: Part 9 : Bernouilli’s Brachistochrone
The Significance of Precise ambiguity in Science It is evident from all great examples of classical art, that the only way to precisely communicate an idea, is through ambiguities, in between which, one mind can say to another, "I know exactly what you mean." It is also evidence, that cognition is an embedded principle of … Continue reading Riemann for Anti-Dummies: Part 8 : The Significance of Precise Ambiguity in Science
Towards a Hylozoic Calculus It always comes as a shock to the mathematically schooled, that Leibniz' infinitesimal calculus is not, essentially, a mathematical procedure. It is just as shocking to the unschooled, but mathematically intimidated, that it were impossible to grasp the deeper implications of Leibniz' discovery, without digging into its mathematical expression. These two, … Continue reading Riemann for Anti-Dummies: Part 7 : Towards a Hylozoic Calculus
Happiness as a physical principle In the Dedication to the "Fourth Book of the Heroic Deeds and Sayings of the Noble Pantegruel", Francois Rabelais refers to a discovery of Greek father of medicine, Hippocrates. "The question over which we sweat, dispute, and rack our brains, is not whether the physician's visage depresses the patient, if … Continue reading Riemann for Anti-Dummies: Part 6
No person is qualified for political leadership today, or for that matter, even competent to vote, unless they know the significance of what has been called, "The Kepler Problem". So important is this paradox, and so widespread is its fame, that every significant discovery in physical science since, can trace its origins to it, and … Continue reading Riemann for Anti-Dummies: Part 5
when Kepler demonstrated the non-linear characteristic of the solar system, and consequentially, the entire physical universe, he set in motion a revolution in thinking, that to this day, is either hated or misunderstood, by scientists and laymen alike. Witness the discussion with a Baby Boomer mathematician who works for NASA, that took place at a … Continue reading Riemann for Anti-Dummies: Part 4
ON KEPLER No mortal yet as climbed so high, As Kepler climbed and died in need, unfed: He only knew to please the Minds And so, the bodies left him without bread. --Abraham Gotthelf Kaestner In "On Copernicanism and the Relativity of Motion," G. W. Leibniz presents a proposition that might provoke you. "To summarize … Continue reading Riemann for Anti-Dummies: Part 3 : On Kepler
Don't tell me how the universe is constructed," protested an early 17th-Century ancestor of today's Baby Boomer, "I just need to know when Mars will be in Leo, when Saturn will be in opposition to the Sun, and when Jupiter will align with the Moon. Armies are massing, and on good information, I've been told, … Continue reading Riemann for Anti-Dummies: Part 2
Indicative of the cognitive deficiency of the Baby Boomers and subsequent generations, is the proliferation of "How To" books, under the appellation, "`X' for Dummies." Such tomes originated, as did many of the more destructive trends in the late 20th Century, in the computer-based information/entertainment business. Desiring ever-increasing values in stock prices, the high priests … Continue reading Riemann for Anti-Dummies: Part 1
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