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Dialogue of Cultures
Footnotes to Parts 2 and 3
How Bertrand Russell
105. Plato, Parmenides, in Plato: Cratylus, Parmenides, Greater Hippias, Lesser Hippias, trans. by H.N. Fowler, Loeb Classical Library (Cambridge: Harvard University Press, 1926).
106. Therein lies the intent, by him and also among today"s typical mass-media personalities, to perpetrate sophistries, falsehoods euphemistically described as the mass-media"s "fourth estate" right to "spin," which is "spin" for "to lie recklessly in the most outrageous extreme."
107. Plato, Parmenides, op. cit., Steph. p. 156c-e. Plato's notion of "change" is that of Heraclitus before him. Georg Cantor's derivation of the notion of a "generating principle" of self-similar forms of change as defining a "type," is derived from Plato"s conception of change. Cantor emphasizes this explicit connection in his comparisons of Plato's Becoming to his own Transfinite, and Plato"s Good to his own Absolute.
108. On the Howards' role in the divorce of Henry VIII and Catherine of Aragon, see Betty Behrens, "A Note on Henry VIII"s Divorce Project of 1514," Bulletin of the Bolton Institute of Historical Research, Vol. II, 1934, pp. 163-4; and David Cherry, "Venice and England"s Break with Rome: A Cold Coup Shaping 500 Years of World Empire," unpublished, Leesburg, Virginia, 1992. For the Venetian role in Anne Boleyn"s seduction of Henry VIII, see Huth, Christina Nelson, "The Life and <i>Death of</i>Saint Thomas More," The New Federalist, Vol. 3, No. 14 &amp; 15, March 24 &amp; March 31, 1989.
109. The marker for the character of France"s Restoration monarchy is the expulsion of Gaspard Monge and his educational program, to replace the leadership of the world"s most advanced science, Monge and Lazare Carnot, with the neo-Newtonian scoundrels, Abbot Moigno"s LaPlace and Cauchy. Thus, French science survived in Germany under the patronage of Alexander von Humboldt and his brother Wilhelm. From 1827, through the First World War, the world leadership in science was in the Humboldts" Germany. British agent Louis Napoleon Buonaparte ("Napoleon III") was a British foreign-intelligence service agent who was brought to power in France, first as President and then Emperor, by Britain"s Lord Palmerston; Palmerston prot&eacute;g&eacute; "Napoleon the Little"s" policy was always to maintain France as a junior partner of the British Empire, even to the point of establishing a junior French colonial empire as a junior partner of the big British colonial empire. Ironically, Palmerston lost his position as Prime Minister, and was downgraded to Foreign Minister, as a result of bringing Napoleon III to power. Queen Victoria, who did not always understand the devious methods required to bring her to the British imperial throne, was upset that her minister would replace a monarch, even a French one, with a mere plebeian such as Napoleon Buonaparte"s nephew.
110. For analysis and bibliography on Sarpi, the Giovani, and England, see Webster G. Tarpley, "The Role of the Venetian Oligarchy in the Reformation, the Counter-Reformation, Enlightenment, and Thirty Years" War," The New Federalist,, Vol. VII, No. 14, April 12, 1993, pp. 6-7; and "The Venetian Conspiracy," Campaigner, Vol. 14, No. 6, Sept. 1981, pp. 23-46.
111. Francesco Zorzi (Giorgi), De Harmonia Mundi (1525). Zorzi, a friar from a famous and powerful Venetian noble family, wrote this book, which was based largely on the Kabbala, as an explicit attack on the De Docta Ignorantia of Nicolaus of Cusa. Zorzi became influential in Henry VIII"s court after writing a brief in support of poor-fish Henry"s desire to divorce his aging Hapsburg wife and thus clear the way for bedding the Howards" bait, the temptress Anne. Zorzi remained in England from 1531 until his death in 1540. Zorzi"s work is of particular significance for his introducing the pseudo-scientific dogma argued later as empiricism by Francis Bacon, and laying the doctrinal basis in the Kabbala for the Rosicrucian Freemasonic cults of Robert Fludd and Elias Ashmole, et al. See footnote 239.
112. See the following section.
113. On Mazarin, see Anne-Marie Cabrini, Mazarin: Aventure et Politique (Paris: Editeur A. Bonne, 1962).
114. On Colbert, see Lettres, instructions et m&eacute;moires de Colbert, 8 vols., ed. by Pierre Cl&eacute;ment, (Paris: 1861-82) (Nandeln: Kraus Reprint, 1979).
115. England and the later "triple alliance," conducted war against France from 1666-1668; then the Dutch war of 1672-1678, in which England was a secret ally of Netherlands; the Palatine War of 1689-1697; the "War of the Spanish Succession" (1701-1714); etc. See H. Graham Lowry, How The Nation Was Won: America"s Untold Story, Vol. I (Washington, D.C.: Exectuive Intelligence Review, 1987), pp. 59-233, on English events of 1701-1714 as seen from the English colonies in North America.
116. Edmund Fitzmaurice, op. cit. Shelburne assigned British East India Company employee Adam Smith to prepare the research outline for what became Edward Gibbon"s The Decline and Fall of the Roman Empire.
118. Anton Chaitkin, Treason in America: From Aaron Burr to Averell Harriman, 2nd ed. (New York: New Benjamin Franklin Publishing House, 1985). See also footnote 30.
119. The quasi-official 1982-83 back-channel discussion, between this author and the Soviet government, of what became known as the Strategic Defense Initiative, already stirred up some ominous foretaste of the explosion which was to erupt from Moscow and its friends in London and within the U.S. intelligence establishment from the time President Ronald Reagan delivered the March 23, 1983 announcement. During this entire period, but especially from about 1985 onwards, there were what appeared then as some very surprising sympathizers, from high-level Western intelligence quarters, of the Soviet system"s prolongation. Bronfman"s Anti-Defamation League and World Jewish Congress worked very closely with the Soviet KGB and East German agencies, for example, even beyond the last weeks of 1989. Prime Minister Thatcher and her Conor Cruise O"Brien and Nicholas Ridley expressed the policy of her government in denouncing West Germany as imminently a Fourth Reich, as part of her effort to prop up the Soviet system. The fear was geopolitical: that Germany might take the lead in integrating the East Bloc economies, more or less intact, into the West, thus strengthening, rather than destroying, the system of sovereign nation-states and technological progress. Thatcher and Bush were determined to have destruction of the economies of all of the former Soviet sector, using methods such as those of George Soros and proteages such as Harvard"s Professor Jeffrey Sachs, which is what they succeeded in doing. In this way, by destroying the agricultural and industrial economies of the East, the downhill slide of the economies of the West was accelerated.
120. European history dates from the emergence of the Greeks from the "dark age" of illiteracy, or, by rule of thumb, from the composition of the Iliad and Odyssey. In such a period of European history, the crucial issue is the menacing role of Babylon and Tyre (Canaan), as distinct from the friendlier relationship to the principal adversary of Babylon and Canaan, the Egypt known to Solon, or the Cyrenaica of the time of Plato and Alexander the Great. The pivotal events emerge at about 599 b.c.: , with the Babylonian suppression of the revolt of the Ionian city-states, and the coincidental constitutional reforms of Solon at Athens. On related premises, Friedrich Schiller"s famous lecture at Jena traces all modern European history from the conflict between the legal systems of Solon"s reforms at Athens, versus the oligarchical systems of Lycurgus" Spartan slave-society. The war between the Council of Florence and the oligarchists of Venice is a modern re-enactment of the conflict between Plato"s Academy and Babylon, between the legal systems of Solon and Lycurgus, and between Plato and the oligarchist Aristotle.
121. Laurence Hecht, "The Coming (or Present) Ice Age," 21st Science &amp; Technology, Vol. 6, No. 4, Winter 1993-1994.
122. Since we know, on physical-economic grounds, that the archaeologists" so-called "riparian" urbanizing cultures could not have sprung autochthonously from "hunting and gathering" inland, the retreat of the glaciation of the Northern Hemisphere, from about 18,000 b.c.: , into the Second Millennium b.c.: must have buried much of the record of pre-ancient history under very many fathoms of water and silt. On grounds of energy-throughput of nutrient at various levels of technology of cultures, the development of agriculture to the level represented by riparian cultures, such as Egypt, could not have occurred autochthonously except through the development of quasi-maritime coastal settlements based upon pursuit of the fish of the estuaries and seas. These would be precisely the types of archaeological sites presently buried under many fathoms of the accumulations which have occurred during the recent 20,000 years.
123. We are presently but a few thousand years from an astrophysically determined growth of glaciation. See Hecht, op. cit.
124. "Classical tragedy" should be read here in the sense of Aeschylus" Prometheus, and in terms of the principles of tragedy as set forth by Friedrich Schiller. For Schiller on tragedy, see "On the Use of Chorus in Tragedy," Fidelio, Vol. II, No. 1, Spring 1993, pp. 60-64. See also "Über den Grund des Vergnügens an tragischen Gegenstäden" ("On the Reasons We Take Pleasure in Tragic Subjects") and "Über die tragische Kunst" ("On Tragic Art") in Friedrich von Schiller, Sämtliche Werke in Sechs Bänden (Stuttgart: Phaidon Verlag, 1984), vol. 5, pp. 127-162. See also "On the Pathetic" and "On the Sublime," in Friedrich Schiller, Poet of Freedom, Vol. III, ed. by William F. Wertz, Jr. (Washington, D.C.: Schiller Institute, 1990). For Friedrich Schiller on the role of the punctum saliens in tragedy, see, e.g., the "Introduction" to his History of the Revolt of the United Netherlands Against Spanish Rule, in Friedrich Schiller, Poet of Freedom, Vol. III, ibid., pp. 177-191.
125. Were the radical "environmentalists" to have their way, the population of this planet would soon collapse to that level, or, more likely, the human species would become extinct in the holocaust of disease brought about by such a biological shock.
126. See the author"s series of Fidelio articles on the principles of metaphor: "On the Subject of Metaphor," Vol. I, No. 2, Fall 1992; "Mozart"s 1782-1786 Revolution in Music," Vol. I, No. 4, Winter 1992; "On the Subject of God," Vol. II, No. 1, Spring 1993; "History As Science," Vol. II, No. 3, Fall 1993; "The Truth About Temporal Eternity," Vol. III, No. 2, Summer 1994.
127. See "The Truth About Temporal Eternity," ibid., for a treatment of the proof of this point. This definition of "idea" corresponds to Plato"s "idea" (eidos). In formal terms, any such scientific discovery, or equivalent form of idea, overturns at least one among the set of axioms and postulates upon which a pre-existing mathematical physics is premised. Thus, every such discovery of principle has an axiomatic-revolutionary effect, requiring an entirely new formal theorem-lattice to supersede the old. Thus, all of the actions subsumed by a new such discovery of principle are commonly members of a single type, as all placental mammals differ as a type from each and all marsupials. With apologies to biologists, it is admissible to understand Plato to signify by eidos "species," or, better mathematics, "type."
128. See "On LaRouche"s Discovery," Fidelio, Vol. III, No. 1, Spring 1994.
129. Johannes Kepler, De Nive Sexangula (On the Six-Cornered Snowflake), trans. by Colin Hardie (Oxford: Clarendon Press, 1966; reprinted by 21st Century Science &amp; Technology, 1991). The Latin title contains a relevant transliteral play upon the words "snowflake" and "nothing." Kepler, official court astronomer to the Emperor, is presenting one of the most important discoveries in science, illustrated by the case of the snowflake"s topology, as a "gift of nothing." As we proceed with the examination of Russell"s fallacy, the reader should come to recognize why Kepler is laughing so merrily. We hope the reader, once he sees the point of the joke, will join the old master in the merriment.
130. Kurt Godel, "Uber formal Unentscheidbare Saumlze der Principia mathematica und verwandter Systeme I" ("On formally undecidable propositions of Principia mathematica and related systems I," (1931) in Kurt Godel: Collected Works, Vol. I: Publications 1929-1936, ed. by Solomon Pfeferman et al. (New York: Oxford University Press, 1990), pp. 144-199.
131. See Gottfried Wilhelm Leibniz, Monadology, trans. by George Montgomery (LaSalle: Open Court Publishing Co., 1989).
132. To grasp the essentials of the relevant three works of Georg Cantor, these are to be examined from the standpoints of Plato, Leibniz, Dirichlet, Riemann, and Weierstrass. The most relevant Cantor works are: Grundlagen: &uuml;ber unendliche lineare Punktmannigfaltigkeiten (1882-1883); "Mitteilungen zur Lehre vom Transfiniten" (1886-1888); and Beitr&auml;ge zur Begr&uuml;ndung der transfiniten Mengenlehre (1897), in Georg Cantors Gesammelte Abhandlungen, ed. by Ernst Zermelo (Hildesheim: Georg Olms Verlag, 1962). See footnote 149.
133. In speaking of "Russell"s contributions," one must cast a wary glimpse out of the corner of one"s eye at the protesting figure of Russell"s senior in the Apostles, and ostensible co-author, Alfred North Whitehead. Without attempting to settle the dispute between the two of them here, it is necessary to state that to anyone who has studied Russell"s work, Whitehead"s accusations are plausible ones. Nonetheless, the point here is that we are considering those views for whose application Russell did assume responsibility in practice.
134. Uber die Hypothesesen, welche der Geometrie zu Grunde liegen (On the Hypotheses Which Underlie Geometry), in Collected Works of Bernhard Riemann, ed. by Heinrich Weber (New York: Dover Publications, 1953), pp. 272-287. For a passable English translation of the text, see the Henry S. White translation, "On The Hypotheses Which Lie at the Foundations of Geometry," in David Eugene Smith, A Source Book in Mathematics (New York: Dover Publications, 1959), pp. 411-425. Place the emphasis upon "III. Anwendung auf den Raum," in the Weber (pp. 283-286) ("III. Application to Space," pp. 422-425 of the Smith).
135. Smith, ibid., pp. 423-425. (Weber, pp. 284-286).
136. "Es fu:hrt dies himber in das Gebiet einer andern Wissenschaft, in das Gebiet der Physik, welches wohl die Natur der heutigen Veranlassung nicht zu betreten erlaubt." Weber, op. cit., p. 286.
137. See Bertrand Russell, An Essay on the Foundations of Geometry (1897) (New York: Dover Publications, 1956); A Critical Exposition of the Philosophy of Leibniz (1900) (London: Allen and Unwin, 1967); "On Some Difficulties in the Theory of Transfinite Numbers and Order Types," Proc. London Math. Soc. 4, 29-53, 1907; Principia Mathematica, op. cit. Russell"s attacks on Riemann et al. are discussed in Carol White, op. cit., chap. 6, esp. pp. 206-217.
138. John Von Neumann and Oscar Morgenstern, The Theory of Games and Economic Behavior, 3rd ed. (Princeton, N.J.: Princeton University Press, 1953). Also, see work referenced, p. 1, note 1: John Von Neumann, "Zur Theorie der Gesellschaftsspiele," Math. Ann. 100, 1928, pp. 295-320. Von Neumann made the public claim, prior to World War II, that economic processes could be reduced to solutions for systems of simultaneous linear inequalities. This led to his close collaboration with fellow-positivist and marginal utilitarian Oscar Morgenstern in producing the wartime first edition (1943) of this work. This work contributed a key part to the post-war emergence of ivory-tower "operations research" kookery of the sort associated with Tjalling Koopmans et al. of the Operations Research Society. The work of both contributing authors is pure Giammaria Ortes, and also pure Jeremy Bentham "hedonistic calculus." The mathematical absurdities of Von Neumann are another illustration of the equivalence of these kinds of mathematical ideas and the teachings of radical empiricism in the areas of social sciences and social policy.
139. Norbert Wiener, Cybernetics, or Control and Communication in the Animal and the Machine (New York: John Wiley, 1948); 2nd ed. (Cambridge, Mass: MIT Press, 1961). On LaRouche"s work to refute Wiener, see "On LaRouche"s Discovery," op. cit.
140. Unendlichkleinen. Weber, op. cit., p. 285.
141. Leibniz, op. cit.
142. P.G. Lejeune Dirichlet (1805-1859). A crucial figure in the Nineteenth-Century development of natural science. After the final overthrow and exile of Napoleon Buonaparte, Paris came under the domination of London and Metternich"s Vienna. In this circumstance, the "Venetian Party" inside France, such as the circles of the neo-Newtonians LaPlace and Cauchy, advanced to power, taking over the Ecole Polytechnique from Gaspard Monge, and ripping out the educational program which had made the Ecole the leading scientific institution of Europe. In this circumstance, French science found much-needed friends in Prussia and in the G&ouml;ttingen of Carl Friedrich Gauss. Similarly, Lazare Carnot, France"s famous "author of victory" and leading technologist of Europe, found refuge in the Prussian military academy at Berlin, and Magdeburg. The geniuses of French science relied upon their collaborator Alexander von Humboldt to assist them in saving French science from destruction. The famous Crelle"s Journal was representative of that new relationship. Thus, Dirichlet, while a most gifted student of the number-theorist and geometer A.M. Legendre et al. at the Paris Ecole Polytechnique, came under the patronage of Alexander von Humboldt, and emerged as among a gathering of mid-Nineteenth-Century German scientific geniuses in the Golden Age of Berlin University. Riemann became his student there. Later, at the death of Gauss in G&ouml;ttingen, Dirichlet was called to succeed him in that chair, and, upon his death in 1859 was succeeded by Riemann. One of the giants of number theory, famous for what Riemann described as "Dirichlet"s Principle"; a major player in the formal analysis of the continuum paradox.
143. Nicolaus of Cusa, op. cit.
144. Plato, Parmenides, loc. cit.
145. See footnote 126 above, for the titles and locations of the members of this series on the subject of metaphor.
146. See "On the Subject of Metaphor," op. cit.
147. Nicolaus of Cusa, "De circuli quadratura" (1450). For an English translation, see "On the Quadrature of the Circle," trans. by W.F. Wertz, Jr., Fidelio, Vol. III, No. 1, Spring 1994.
148. See "Metaphor," loc. cit.
149. Cantor, Beitr&auml;ge, op. cit., pp. 282-356. The available English-language reprint is Georg Cantor, Contributions to the Founding of the Theory of Transfinite Numbers, trans. by Philip E.B. Jourdain (New York: Dover Publications, 1955). A word of caution respecting the Introduction and end-notes in that translation, as supplied by Jourdain circa 1915. None of what Cauchy-apologist Jourdain represents as corrections of Cantor"s work, such as those allegedly by Russell, is to be considered competent comment upon Cantor today. See footnote 130: G&ouml;del demolished Russell"s criticisms of Cantor.
150. The Science of Physical Economy is a branch of physical science founded by Gottfried Leibniz, and developed chiefly by him over the interval 1672-1716. This was the original form of an economic science. Leibniz"s economic science exerted great influence during the Eighteenth Century and first two-thirds of the Nineteenth Century. For example, it appeared as a central feature within Alexander Hamilton"s "American System of political-economy," was the basis for the economics of France"s Ecole Polytechnique during 1794-1814 under Gaspard Monge, and was the policy of the Nineteenth-Century U.S. Whig Party and the Lincoln Republicans, in addition to the founder of the modern German economy, Friedrich List. However, under the influence of the Versailles Treaty and post-World War II financial system, knowledge of economic science vanished from the university campus, government, and industrial management. This branch of science was revived by the present author, based on new 1952 discoveries in this field.
151. I.e., circular construction is the method required; one can reach circular action only by way of circular action. The problem arises the instant we commit the blunder of abandoning constructive (e.g., "synthetic") geometry for formalist algebra. In the latter case, there is no true solution for this problem possible. See the discussion of Felix Klein"s "Famous Problems" hoax, below.
152. E.g., what is later adopted as the "Cartesian" space-time of Galileo, Descartes, Newton, et al.
153. E.g., the principle of universal least action of Gottfried Leibniz and Johann Bernoulli. The root of the notion of a bounded space-time is the case of the Platonic Solids, a track which leads through the work of the followers of Cusa, Pacioli, and Leonardo da Vinci, into explorations into the hypergeometric realm from such starting-points as C.F. Gauss" study of Kepler"s work on the Pentagramma Mirificum. See Lyndon H. LaRouche, Jr., "An Economist"s View of Gauss" Pentagramma Mirificum," 21st Century Science & Technology, Vol. 7, No. 2, Summer 1994. See also C.F. Gauss Werke (Hildesheim: Georg Olms Verlag, 1986), vol. III, pp. 481-490; vol. VIII, pp. 106-117.
154. The author"s teen-age wrestling with Kant began with his Critique of Pure Reason, trans. by Norman Kemp Smith (New York: St. Martin"s Press, 1965). The remainder of the series is Prolegomena to a Future Metaphysic, trans. by Paul Carus (Indianapolis: Hackett Publishing Company, 1977); Critique of Practical Reason, trans. by Lewis White Beck (Indianapolis: Bobbs-Merrill Company, 1956); and Critique of Judgment, trans. by J.H. Bernard (New York: Hafner Press, 1951). This series as a whole has two principal features: (1) The denial of the possibility of intelligible knowledge of a principle of creative reason ("synthetic judgment a priori"), the attack upon Leibniz"s Monadology, Theodicy, Leibniz-Clarke Correspondence, etc.; and, (2) a defense of custom against the extremism introduced in England through the British radical empiricists, including Kant"s former mentor, David Hume. Formally, Kant appears to have been the founder of the Romantic school in art (Liszt, Berlioz, Richard Wagner, et al.), science, and statecraft generally (e.g., F.K. Savigny and the "intuitionist" school in mathematical physics). The essence of Kant is that he was a Venetian work-product of the Conti brand, and implicitly the evil existentialist which Schiller suspected, and Heine (Religion and Philosophy in Germany) knew him to be.
155. Eratosthenes, an Athenian geometrician, grammarian, and historian of Cyrenaic extraction (b. during the 126th Olympiad, d. 195 b.c.: : c.80 years), famous for, among other achievements, estimating both the size of the Earth"s sphere, and the distance of the moon and sun from the Earth: estimated the perimeter of the Earth passing through Alexandria and Rome at approximately 24,662 miles. Moved to Alexandria, where he became Chief Librarian of the famous library there. He is otherwise most famous in geometry for his work on the so-called "Delian" problem of doubling the cube, and in number-theory, for devising a "sieve" used to locate the succession of prime numbers. The work on this problem later by (most notably) Euler, Legendre, Gauss, Dirichlet, Riemann ["U;ber die Anzahl der Primzahlen unter einer gegebenen Gro:sse," (1859), in Weber, op. cit., pp. 145-153]. Cantor used this work, notably Eratosthenes" "sieve," as a tool for defining the number-theoretical equivalence of "power" and "cardinality."
156. In fact, it was the author"s prior discovery of the physical significance of this notion of "power" which led him to his 1952 studies in the work of Cantor and of Riemann. See text, this section, below.
157. As White translates Riemann"s Unendlichkleinen.
158. Take the relatively commonplace misuse of the notion of applicability of the Golden Section to living processes. The estimated value of the Golden Section, as an algebraic root of the calculated ratio of two skew lines, is, obviously an algebraic number. What then of the disgusting spectacle of attempts to project harmonic orderings of living processes as if the Golden Section were a simple Galileo coefficient of mechanical action, a limit of a Fibonacci Series? Why do so relatively many foolish people fall into what should be such an obvious folly? The folly is the failure to ask oneself the question: Whence (i.e., "generating principle") did Luca Pacioli (De Divine Proportione, 1497), Leonardo da Vinci, and Kepler derive their notion of the ontological significance of the Golden Section? From the attempted partition of the interior of a spherical shell, leading to the proof that only five regular solids can be constructed so. That construction is illustrated by the Kepler-Gauss treatments of the Pentagramma Mirificum (see Lyndon H. LaRouche, Jr., "An Economist"s View of Gauss" Pentagramma Mirificum," (loc. cit.); this leads into the domain of hypergeometric functions as elaborated by Gauss and Riemann. See, C.F. Gauss Werke, loc. cit. This is a line of investigation which begins with our friend Kepler, and leads into the most fundamental questions of the mathematics of a generalized quantum field theory today. The significance which Plato, Pacioli, Leonardo, and Kepler find in the Platonic Solids harmonics is by no means a matter of an algebraic ratio.
159. Not Felix Klein"s fraudulent 1882! See below on Klein et al. Although Cusa"s formal proof of this was presented in his a.d.: 1450-53 "De Circuli Quadratura," loc. cit., the discovery is already reflected in the 1440 De Docta Ignorantia.
160. The discussion of these principles of hypothesis is found in the referenced "The Truth About Temporal Eternity," op. cit.
161. See "Metaphor" series, loc. cit.
162. Or, should one say, in the strictest sense, "termerity"?
163. See Lyndon H. LaRouche, Jr., In Defense of Common Sense (Washington, D.C.: Schiller Institute, 1989); also in LaRouche, The Science of Christian Economy and Other Prison Writings (Washington, D.C.: Schiller Institute, 1991).
164. For example, for an introduction to outlining such a set of inequalities, see Lyndon H. LaRouche, Jr., So, You Wish To Learn All About Economics? (New York: New Benjamin Franklin House, 1984).
165. See G.W. Leibniz, "Society and Economy" (1671), Fidelio, Vol. I, No. 3, Fall 1992.
166. On differing types of hypothesis, compare the discussion of this matter in "The Truth About Temporal Eternity," loc. cit., sec. IV, pp. 15-19.
167. Note that the relevant ideas within Hamilton"s "Manufactures" respecting "increase of the productive powers of labor" are derived from Leibniz"s design for the Industrial Revolution, done at the French Acad&eacute;mie des Sciences and elsewhere before and shortly after the beginning of the Eighteenth Century. This includes, notably here, work on the principles governing the relationship between development of heat-powered machines and rise of per-capita productivity. These were mediated into the American colonies from various channels, most emphatically Franklin"s direct intersection, especially between 1763 and 1787, with active continuations of the Europe-wide scientific and political networks formerly established by Leibniz. As a comparison of the John Locke draft of the constitution of the Carolinas, and the Preamble of the Constitution of the Confederate States of America, with the Preamble to the U.S. Federal Constitution of 1787-1789 shows, the American Revolution and founding of the U.S. Federal Republic were outgrowths of the victory of the ideas of natural law promulgated by Leibniz over the empiricism of John Locke. These political influences from Europe were intermeshed with those ideas of science, technology, and political-economy which figures such as Franklin conveyed from Leibniz"s heritage in Europe into North America.
168. The use of the term "productivity" here should not be confused with the monetarist"s use of the term "productivity" as synonymous with "rate of usury": i.e., the ratio of monetary profit to money wages. Statistically, "productivity" is defined as follows. As measured in physical units of market-basket consumption, the consumption-level must rise per capita, per household, and per square kilometer. (Compare Leibniz on the subject of real wages and productivity, in "Society and Economy," op. cit.) In these terms, that consumption must increase in correlation with an increase of the "free-energy ratio" as we have described that immediately above. The satisfaction of that constraint reflects an increase of physical productivity.
169. This was the "model," applied circa 1950-1951, which impelled the author to plunge into Cantor"s 1897 contributions.
170. I.e., investments in improved technology in a capital-intensive, energy-intensive mode. See U.S. Treasury Secretary Alexander Hamilton, "Report to the U.S. Congress on the Subject of Manufactures" (1791), in Nancy B. Spannaus and Christopher White, The Political Economy of the American Revolution (New York: Campaigner Publications, 1977), pp. 375-442, passim.
171. Thus, the present writer was electrified to re-read Riemann"s Hypotheses paper, following an intensive study of Cantor"s Beitr&auml;ge, in 1952.
172. I.e., the work of Academician Vladimir I. Vernadsky should be seen as an integral part of the further development of the science of physical economy today.
173. Bernhard Riemann "@auber die Fortpflanzung ebener Luftwellen von endlicher Schwingungsweite" (1860), in Weber, op. cit., pp. 157-175. For an English translation, seeOA "On the Propagation of Plane Air Waves of Finite Amplitude," trans. by Uwe Parpart and Steven Bardwell, International Journal of Fusion Energy, Vol. 2, No. 3, pp. 1-23. The publication of that translation was an outgrowth of conflicts (over geometric versus algebraic methods) with some leading physicists, which arose as by-products of those of the author"s 1952 discoveries in physical economy reflected here. In the midst of a quarrel with Lawrence Livermore Laboratories, and others, over matters including inertial-confinement fusion, in 1978, this writer asked two collaborators to secure from open Soviet scientific literature proof that Soviet H-bomb designs had depended upon Riemannian notions of isentropic compression. The search was a success; the translation of this Riemann paper, and certain designs tested by the Osaka Laser Engineering Laboratory, were included results of those controversy-ridden researches. This is noted here, because it is relevant to a major point to be made on Russell"s role in science below. See also, related work-products of such relevant followers of the Riemann hydrodynamics tradition as Ludwig Prandtl and Adolf Busemann. Note also, as of prime relevance for related matters of the internal history of science, that the pre-1945 German accomplishments of world-leadership in aerospace depended significantly on the leading role of Italy"s hydrodynamicists working in the field. Into the 1930"s, for example, Italy"s scientific and related engineering prowess in airframe design was the best in the world. The key to this was the fact that the leading tradition of Italian physics from the mid-Nineteenth Century on, was located in the Italian collaborators of Riemann, around Enrico Betti. The first supersonic wind-tunnel in the world, for example, was built by these Italian scientists during the mid-1930"s.
174. To "bound" the characteristic of this discussion in progress here, one should call attention to the implications of another major work establishing the young Riemann"s habilitation in German science, his 1854 "&Uuml;ber die Darstellbarkeit einer Function durch eine trigonometrische Reihe," in Weber, op. cit., pp. 227-265. This can be read usefully as a mathematical survey of the development since the crucial 1697 work on the light-based principle of universal action by Bernoulli and Leibniz. It is admittedly specialist"s work, but no one addressing the internal history of science should overlook Riemann"s account in this paper.
175. Gauss" successful demonstration that the asteroid orbits conformed to Kepler"s astrophysical case for the necessary former existence of a since-exploded planet in this specific orbit, between those of Mars and Jupiter, demonstrated crucially that all of the proposed alternatives to Kepler"s method, such as those of Galileo and Newton, had been shown to be erroneous by this evidence. See Gauss Werke, vols. VI-VII, passim. Kepler"s uniquely vindicated method for astrophysics, as reflected in the 1611 Snowflake booklet, is the relevant platform from which to launch a comprehension of this problem of reciprocity between a bounded universe, on the one side, and the matters of harmonic ordering (quantum field theory) and the continuum paradox on the other.
176. Executive Intelligence Review News Service, Inc. (EIRNS), 333@c4 Pennsylvania Ave., S.E., Washington, D.C. 20003. The newsweekly Executive Intelligence Review was founded in 1974. It was developed in conjunction with an international news service, which converted into a commercial vehicle those specialized news-intelligence functions which produced the work-product featured in EIR and other publications using this service. The publication"s authority was derived initially from this writer"s exceptional success in forecasting, during the 1960"s, the virtual inevitability and probable policy-sequelae of the 1967-1972 succession of crises leading into the breakdown of the original Bretton Woods monetary system. During December 1978, this present writer designed a computer-based quarterly forecasting system, using chiefly U.S. Value-Added data, which began publishing its regular quarterly forecasts in EIR magazine during the interval January 1980-October 1983; those latter forecasts were the only reliable forecasts issued publicly by any agency during that time. At the end of 1983, this writer advised EIR to discontinue the forecast, because of the wildly erratic fraud which the U.S. government and Federal Reserve System were employing for what might be termed charitably "cosmetic purposes." He recommended that a new forecasting base be constructed on the basis of physical data, rather than Value-Added ones. The publication of the 1986 textbook, So, You Wish to Learn All About Economics?, was a by-product of elaborating the specifications for constructing the data-base for the new forecasting system to supersede use of official (increasingly fraudulent and arbitrarily cooked) Value-Added data. What is described summarily here, are part of the current specifications for implementation of that EDP application.
177. Astronomical charts for various localities of the planet at various times past are extremely handy for the routine kitchen-work of the economic historian. (It is the quickest way to be certain that Claudius Ptolemy was essentially a hoaxster.) Who does not work with ancient and medieval economic history will overlook some of the most important differences which distinguish the present from the past.
178. "If one wished to be fancy," as the saying goes, one would use the astronomical model included among the graphics as the calendar and clock for all other studies included in the work. As we shift toward more and more space-exploration and colonization, even in the advanced-planning phases, we should begin to think in such sidereal terms.
179. No secondary pupil in any part of the world should graduate without knowing the highlights of Gauss" scientific biography, including his development of statistical methods for observations in the successive domains of astronomy, geodesy, and Earth-magnetism. By comparing Gauss" standard for this work with the previous highest standard, that of France"s Ecole Militaire and of the Ecole Polytechnique under Monge, Legendre, et al., the student acquires a sense of the difference between reality and observation which he or she will carry to great benefit throughout life, in whatever occupation, or simple functions of a citizen they are subsequently situated. In no place, does this challenge present itself more plainly than in the effort to allot available statistical data-arrays to the grid-cells of a scheme of the sort being outlined here.
180. On August 13, 1946, Public Law 725 went into effect, titled, "Hospital Survey and Construction Act," otherwise known as the "Hill-Burton Act" after its two chief sponsors, Senators Lister Hill (D-Al) and Harold Burton (R-Ohio). Hill-Burton authorized grants to the states for surveying the adequacy of their hospitals and public health centers, and for planning construction of additional facilities. The law, which was extended many times over through the early 1960"s, through Congressional amendments, can be found in the public laws volume for the 79th Congress, 2nd session, Chapter 958. Lengthy excerpts appear in the Executive Intelligence Review article, "Why U.S. health care must return to the Hill-Burton standard," by Donald MacNay, Marcia Merry, and the EIR Economics staff, Executive Intelligence Review, Vol. 21, No. 30, July 29, 1994, pp. 6-13. The 1970"s marked the end of Hill-Burton-standard health-care facilities throughout the U.S., and the beginning of the marked decline in facilities, staff, and treatment programs per thousands of population. In 1974 in New York City, for example, under the austerity measures adopted by the Municipal Assistance Corporation ("Big MAC") run by Lazard Fr&eacute;res banker Felix Rohatyn, community hospitals were penalized by New York State, which withheld reimbursement for indigent cases, if the hospitals" bed-use level fell below a new government-mandated level of 75-85%. This drove many hospitals into bankruptcy. In addition, "Big MAC"-style decrees eliminated thousands of specialty-care beds for the mentally ill; the patients were turned out into the streets.
181. Before the effects of the later 1960"s "paradigm-shift" to a "post-industrial" matrix.
182. Physicians, nurses, other specialists, etc., hospital beds, outpatient facilities, public health services, etc., with respect to efficient access to and by population served per 100,000 persons. Compare this combined capacity of the governmental and "voluntary" elements of personnel and facilities with the forecast of relevant disease, trauma, etc. and derived estimates of care requirements for the coming short-term (one year), medium-term (five years), and long-term (ten to twenty-five years). Return to the physician-patient relationship of past medical-ethics fame, instead of the recent trend of malpractice by government and insurance companies, which ignores the needs of the patient, and substitutes the assignment of the physician to deliver aliquot services on schedule to the type of legalized disease prescribed for authorized ministrations.
183. Cf. Morris Levitt, "Linearity and Entropy: Ludwig Boltzmann and the Second Law of Thermodynamics," Fusion Energy Foundation Newsletter, September 1976, pp. 3-18.
184. Loc. cit.
185. Loc. cit.
186. The Nazi Gleichschaltung is fairly translated as equivalent to today"s "political correctness."
187. Even the language which these ideologues apply to themselves is unabashedly Orwellian Doublespeak.
188. All of these modernist varieties of economist are intrinsically fascists. Fascism is no more than an attempted throw-back to Caesarism under modern circumstances. The model Roman economist is thus Illyria resident Diocletian, the man who split the Roman Empire into two parts and passed the remains to his heir Constantine. It was the "Malthusian," or often so-called "socialist" decrees of Diocletian, which are the specific precedent for all Twentieth-Century fascism. Notably, the effect of these decrees was to accelerate the rate of collapse of the Empire as a whole, leaving the more civilized, less depopulated sector, the Greek-speaking region, to rot away over the ensuing centuries, in an overall constantly descending spiral of decadence and attrition. There are many precedents for fascism in modern European history, notably the British system of colonial rule, and all the other petty and more virulent tyrannies which esteemed the Roman Empire as their model. The comparison to the characteristic, regressive economic features of Diocletian"s decree is the reference to be made in examining liberal and post-liberal varieties of economic dogma today.
Part III Footnotes
190. The Roman killing of Archimedes in 212 b.c.: , and the more rapid encroachments of decadence within the eastern Hellenic culture during the following century, set off the referenced, preceding two centuries of rise of Hellenism (to gain and hold its power in the region) as exceptional in quality.
191. Gaspard Monge, founder of the Ecole Polytechnique of 1794-1814, and his one-time student and collaborator Lazare Carnot, were products of the pre-Revolution Oratorian Order in France, a teaching institution which intersected the Colbert-founded Académie des Sciences (where Huyghens and Leibniz once collaborated) and the military school. Thus, although Aristotelian fanatics (e.g., Venetian factions) more or less effectively destroyed the Brotherhood of the Common Life during the course of the Sixteenth Century, its influence persisted in other ways. See W.F. Wertz, "On The Brotherhood of the Common Life," op. cit.
192. The introduction of the mind-destroying "new math," at the close of the 1950"s and early 1960"s, brings into a more extreme form a longer-term tendency toward crippling talented minds during their adolescence by means of placing priority upon algebraic methods in establishing the mental habits of mathematical thinking, and also of scientific thinking generally.
193. The Thirteen Books of Euclid"s Elements, trans. by Thomas L. Heath (1925) (New York: Dover Publications, 1956).
194. Adrien Marie Legendre, Eléments de géométrie (1794) (Paris: Firmin Didot fréres, 1857); Engl. trans. by David Brewster as Elements of Geometry and Trigonometry (New York: Gallagher and White, 1830). This was the work written by Legendre to define the program of education in geometry used by the newly founded Ecole Polytechnique of Monge.
195. Jacob Steiner"s Gesammelte Werke, 2 vols., ed. by Karl Weierstrass (1882) (Bronx, New York: Chelsea, 1971). Steiner is the "father" of a refined form of constructive geometry known as "synthetic geometry." Bernhard Riemann, who studied Steiner"s program in systematic constructive (i.e., "synthetic") geometry under Steiner himself, emphasized to Enrico Betti that education in science should be premised upon a mastery of Steiner"s work.
196. The cases of Gauss, Bolyai, and Lobachevski are adequately represented in either Gauss" writings, or references to this connection. For a general guide to the C.F. Gauss Werke, op. cit., see W.H. Buehler, Gauss, A Biographical Study (New York: Springer, 1981). On Gauss" relations to Bolyai and his work on Lobachevski, see also Carl Friedrich Gauss, Der "Fürst der Mathematiker" in Briefen und Gesprächen, ed. by Kurt-R. Biermann (Munich: Verlag C.H. Beck, 1990 [(@cW) Urania Verlag, Leipzig]), with Introduction (Einfuehrung) by Professor Biermann. On Bolyai, see Einfuehrung (Introduction), p. 12 (Wolfgang, father) and p. 27 (John, son), and Nicolai I. Lobachevski; see also Letters to Christian L. Gerling #96, #137, and to Wolfgang (Farkas) #99. On Lobachevski, see also Letter #137. On both Bolyai and Lobachevski, see also C.F. Gauss Werke, op. cit. "Briefwechsel mit Gerling," Letters #337, #338, pp. 666-668.
197. Op. cit.
198. See, e.g., The Notebooks of Leonardo da Vinci, 2 vols., ed. by Jean Paul Richter (1883) (New York: Dover Publications, 1970). Vol. I contains all of Leonardo"s entries on the principles of perspective, light and mathematics, light and shade, and all topic areas related to drawing and painting proper. Vol. II contains all applications of these principles to nature and the sciences (astronomy, anatomy, geography, etc.) and the constructive arts (architecture, design, mechanical and military appliances, music, etc.).
199. E.g., The Six-Cornered Snowflake, op. cit.
200. The apparent exceptions to the rule, on closer examination, merely prove the rule as cited.
201. This cited example is one of the most crucial to be presented to the student in a mandatory introduction to mathematical physics on the secondary level. The student would begin from the Cusa proof of the transcendental character of @gp, and proceed through Roberval"s and Huyghens" treatment of the cycloid. Convenient references are: (Roberval) Evelyn Walker, A Study of the "Traite des indivisibles," (New York: Teachers College, 1932) (available in libraries), with relevant excerpts provided by D.J. Struik, ed., A Source Book in Mathematics, 1200-1800 (Princeton, N.J.: Princeton University Press, 1986). (Huyghens) Christiaan Huygens, The Pendulum Clock, or Geometrical Demonstrations Concerning the Motion of Pendula as Applied to Clocks, trans. by Richard J. Blackwell (Ames: Iowa State University Press, 1986); Treatise on Light (1690), trans. by Sylvanus P. Thompson (New York: Dover Publications, 1962). Also in Struik is a translated excerpt from Johann Bernoulli"s announcement of his solution to the brachystochrone problem, under the obvious Latin title of "Curvatura radii in diaphanis nonuninformibus," Acta Eruditorum, May 1697. The implication is, that the crucial functional appearance of the cycloid in the two cases—the pendulum clock and the refraction of light under conditions of retarded potential for propagation, as shown by Ole R@tomer and assessed by Huyghens—requires a change from the space-time of Galileo and Descartes to that of Cusa, Fermat, et al., the non-algebraic or transcendental domain.
202. Cf. LaRouche, "The Truth About Temporal Eternity," loc. cit.
203. The reader is reminded, that the German translation for this form of "political correctness" is Gleichschaltung.
204. Zorzi (Giorgi), loc. cit.
205. Bacon asserts in the New Organon: "There are and can be only two ways of searching into and discovering truth. The one flies from the senses and particulars to the most general axioms ... . [T]his is now in fashion. The other derives axioms from the senses and particulars, rising by a gradual and unbroken ascent, so that it arrives at the most general axioms last of all. This is the true way, but as yet untried." Aphorism XIX, in The New Organon and Related Writings, ed. by Fulton H. Anderson (Indianapolis: Bobbs-Merrill Company, 1960), p. 43.
206. Sir Isaac Newton"s Mathematical Principles of Natural Philosophy and His System of the World, revised trans. by Florian Cajori (Berkeley: University of California Press, 1960), General Scholium, p. 547.
207. Kant, loc. cit., passim.
208. Among "New Age" varieties of psychologists and sociologists, Sigmund Freud popularized the term "cathexis" for this. The U.N.O."s mind-destroying "educational reform" sometimes promoted under the rubric of "Outcome-Based Education," is based upon virtually banning all cognitive thought. Out of racists such as the Harvard University circles of Jensen and Shockley comes the dogma that certain "races" are not naturally inclined to cognitive thought, but only to conditioning of their associative-emotional behavior. The New Ager cult-lunacy of "right brain, left brain" originates in the same pseudo-scientific gobbledygook as these referenced U.N.O. and Harvard developments.
209. If itself tending increasingly to the exceptional.
210. It is sufficient to note, as a word of caution, that without that mooring in an orientation toward measurement, examining formal theorem-lattices merely from the standpoint of Aristotelian logic can lead into insanity. This is a notorious problem among specialists in mathematics from a logical positivist or related standpoint: they do not go mad despite being "good mathematicians"; they go mad because they are all too devoutly trained in that variety of "mathematical thinking"; the more academic honors they accrete, the greater the danger, the rarer the survivor of that lately increasing mental disorder: "Kronecker"s Disease."
211. This is perhaps the place to note, specifically, that the same method is key to Classical fine arts. The failure of many otherwise gifted and learned musicians to grasp the rudiments of Beethoven"s method of composition, as employed in most exemplary fashion in his late quartets, can be represented as the same form of mental disorder which impedes comprehension of Georg Cantor"s work on the transfinite, or Riemann"s famous Hypothesen dissertation. The ontological key to the connection can be discovered only from the humanist standpoint addressed here: the principle of change represented by the intervals. One must think always of tones in their place in the C=256 musical continuum, but we must also be conscious, thereafter, that it is the interval "lying between the notes" which is the ontologically primary event (change) upon which heard music is premised. For example, after Haydn"s revolutionary Opus 33, No. 3 quartet, the subsequent event with the greatest impact upon music- up to and into Beethoven"s compositions from Opus 102 onward- is Mozart"s discovery, through van Swieten"s regular Sunday salon, of the six-part Ricercare from J.S. Bach"s Musical Offering. The proliferation of Mozart"s compositions, and then of Beethoven and other successors, based directly upon Mozart"s combining of Haydn"s discovery with Bach"s, is the central event of all Classical forms of musical composition from 1783 through Brahms" "Four Serious Songs." From Mozart"s discovery, and Beethoven"s own, frequent, pre-Opus 102 elaboration of it, into such works as his Opus 111 treatment of this, his usually misapprehended Missa Solemnis, and his last quartets, everything depends upon the freshly acquired comprehension of "composing and performing "between the notes" as primary, which first emerges clearly in Bach, and in a more advanced way in post-1781 Mozart. From this vantage-point, musical and mathematical creativity are reflections of a common mental substance.
212. See Georg Cantors Gesammelte Abhandlungen, op. cit., pp. 204-209 ("Anmerkungen des verfassers zu Nr. 5," of Über unendliche lineare Punktmannigfaltigkeiten). Cantor"s view on this matter is to be judged by the information that he equates his use of "Transfinite" to Plato"s "Becoming."
213. Some Aristotelian, or quasi-Aristotelian hard-heads will insist that "This sounds like Deism to me." So, Pietro Pomponazzi professed that he had no soul, and so atheist Paolo Sarpi, a sponsor of Galileo"s method and the sponsor of Francis Bacon"s "Zorzian" British empiricism, professed the non-existence of God. Since the idea of the existence of God is not possible within a consistent Aristotelian argument, the Aristotelian can provide a place for the existence of God only outside all logic. This was a crucial, included feature of Philo"s valid argument against the folly of Aristotelianism. The Aristotelian"s "God" is not the God of Moses and Christ, but, rather of the Delphic pagan apotheosis of Jekyll-Hyde, Apollo-Dionysus. (Since Aristotle was an agent of the Cult of Apollo, this connection might not surprise us.) Thus, Dionysus Nietzsche deriding Apollo (Aristotelian formalist) Kant for being a "mandarin from Königsberg," is Mr. Hyde ridiculing Dr. Jekyll. The satanic Nazi, Martin Heidegger of the ultra-leftist school of Horkheimer, Adorno, and Arendt, is therefore a consistent Tübingen University Aristotelian when he makes room for the release of his infantile, Dionysiac inneren Schweinhunds from between the cracks of the Aristotelian formalist"s latticework of logicism.
214. Get the picture! Visualize the situation. This high priest, Moses, walks freely into Pharaoh"s presence (Exodus 7). On the first visit, Aaron throws a snake into the presence of mighty Pharaoh. The next day, they return to Pharaoh"s presence, retrieve the snake, and threaten to turn the waters of Egypt into blood. Next visit (Exodus 8), a pestilence of frogs. Next visit lice ... flies ... boils ... more pestilence ... thunder, hail, and fire ... locusts ... . Imagine some priest had prophesied one-one-hundredth as much as any one of these (say a couple of days of acne) to the recently self-proclaimed U.S. Pharaoh George Bush: does one not know what would have happened suddenly to every parishioner of that church! Pharaoh could have told you: Moses was powerful.
215. Cf. "The Truth About Temporal Eternity," loc. cit., passim.
216. It is sometimes argued, not without grounds, that the motivation is supplied by a sense of one"s mortality. The author would object to that as of no more significance than a predicate of the actual motive, the latter a motive which is visibly embedded in the response, a response which reveals an active axiom permeating what it means to have distinctively human powers of consciousness. It is not the questioner who defines the answer, but the character of he who responds.
217. The principle of the Good applies only to the case of Classical composition and its historical antecedents. "Romanticism," like the philosophical empiricism from which it sprang, is based on a rejection of this principle of truthfulness in composition and performance. Modernism is radically empiricist on this account.
218. Some highlights of the author"s own musical experience may be helpful in fostering recognition of the more general point being illustrated. During the post-war 1940"s, the author took the factional position, on purely musical-content grounds, rather than other documentation, that Mozart"s K.475 Fantasy had been intended to be prefixed to Mozart"s K.457 piano sonata. This led immediately to recognition of the many compositions by Mozart and Beethoven based upon the same "germ" as the combined K. 475/457. Why was the author so excited by this, so driven to discover some higher principle involved? Later, he recognized that Beethoven"s method of thorough composition had something to do with the same principle developed by Georg Cantor in mathematics. One of the most exciting moments in his life came more recently, when a friend pointed out the significance of the first movement of Haydn"s Opus 33, No. 3. This information put the roots of Beethoven"s method of composition in his last quartets into focus. (See "Mozart"s 1782-1786 Revolution in Music," op. cit.) What is the driving force behind such researches, whence the motive? In these matters it is in the very nature of Classical musical composition, the relationship between the performance of the music today and the composing of that work a century or more ago.
219. The analysis of the astronomical picture to be adduced from these Vedic sources was virtually completed during the lifetime of Gauss. These were the sources referenced by Bal Gangadhar Tilak in his The Orion; Or, Researches into the Antiquity of the Vedas (1893), 5th ed. (Poona: Shri J.S. Tilak, Tilak Bros., 1972). See also, his The Arctic Home in the Vedas, Being Also a New Key to the Interpretation of Many Vedic Texts and Legends (1903) (Poona: Tilak Bros., 1956).
222. The French scientist Edouard Biot and the Dutch philologist Gustav Schlegel, proved from evidence in the Confucian classics that astronomical science was already highly developed in the Third Millennium b.c.: ; and Schlegel"s research led him to hypothesize that significant mapping of the heavens existed at the extremely early date of the Sixteenth Millennium b.c.: Joseph Needham"s attack on these datings [Science and Civilization in China (London: Cambridge University Press, 1954), Vol. III] is transparently scurrilously incompetent in method, and therefore not to be considered seriously; see Michael Billington, "The Taoist Perversion of Twentieth Century Science," Fidelio, this issue, pp. 00-00.
223. For a convenient English text on Wilhelm von Humboldt and the orbit into which Boeckh"s work fitted, see Paul R. Sweet, Wilhelm von Humboldt, A Biography, 2 vols. (Columbus: Ohio State University Press, 1980).
224. The use of the literal name of one object to name a different object, is but a special case of this, the exception which reveals the rule. For one object to bear the name for another, if this substitution is meaningful, rather than only arbitrary playfulness, signifies an effort to show that the two different objects are predicates of a common mental object, as distinct from a sensual one.
225. During the author"s recent visit to Weimar, a copy of Goethe"s Mailied was seen affixed by the curators to a wall of the museum which had been the poet"s residence there. Nothing illustrates the principle of metaphor in poetry more simply, more intelligibly than the role of the concluding couplet of the most popular and typical short Goethe poem. The present author adopted this use of "metaphor" for all representations of mental objects (as distinct from mere sense-perceptions) circa 1947, as his own interpretation of the argument put forth in William Empson, Seven Types of Ambiguity (New York: New Directions, 1947).
226. Music is an integral aspect of all language. Music is derived from the singing of Classical poetry according to the natural principles of vocalization. The existence of five ordinary, and, in the extreme, six distinct, natural species of singing/speaking voice, each defined by its own distinct, characteristic array of bel canto mode register-shifts, defines natural polyphony, and the well-tempered system as discovered by J.S. Bach, through his work on countrapuntal ensembles" singing voices of people and their artificial instruments. Music is derived from the singing of Classical epic and other poetry, using the vocalization of the spoken terms as the implicit musical scoring.
227. LaRouche, So, You Wish to Learn, op. cit., pp. 23-39.
228. Those who passed through the author"s one-semester course of the 1966-1973 interval will perhaps smirk at this reminiscence. Certain pedagogical ruses, when apparently successful in one semester"s course, tend to be carried over to the next, and to the next, and ... .
229. Ortes, Riflessioni, op. cit.
230. Napoleon came out of his campaigning in Italy like Caesar returned from Gaul. In Julius Caesar"s footsteps, he went to Egypt, and then sought to become Caesar. However, meanwhile, according to the suggestions of Ortes, Shelburne"s Gibbon had been assigned already to write a handbook of guidance to those engaged in establishing London as the capital of the Third-Rome empire. As to the interesting scientific role of the Ecole Polytechnique in Napoleon"s Egypt campaign, that is another topic, another heritage, for which one must turn to study of the global strategic policies of Gottfried Leibniz.
231. Lyndon H. LaRouche, Jr., "The coming disintegration of financial markets," Executive Intelligence Review, Vol. 21, No. 26, June 24, 1994.
232. The United Nations aided the design of Outcome-Based Education (O.B.E.) via the work of Robert Muller, a former deputy secretary who is now Chancellor of the University of Peace, an institution related to both the U.N.O. and the U.N.O.-connected Lucis Trust (formerly Lucifer Trust). For this and an overview of O.B.E., see "Will You Allow Your Child to be Spiritually Molested," op. cit.
233. Aristotle was trained at the center of the teaching of sophistry in Athens at that time, the School of Rhetoric of Isocrates. This School was a leading philosophical and political adversary of the Academy of Athens. Aristotle was deployed from the School of Rhetoric to infiltrate Plato"s Academy. Aristotle"s writings, not only his infamously oligarchical Ethics and Politics, but also his so-called scientific works, are a thoroughly anti-Socratic expression of the same sophistry promoted by the Delphi agents of that time, such as the School of Rhetoric.
234. As noted in the author"s "History As Science," op. cit., the monetary theorist John Maynard Keynes was entrusted with the assessment of a chest of Isaac Newton"s private scientific papers. Keynes, opening the chest, was shocked to find the scribblings of a superstitious lunatic, a Newton whom he described, in his report, as "the last of the magicians, the last of the Babylonians and Sumerians ... wholly devoid of scientific value"; see "Newton the Man," in Newton Tercentenary Celebrations (Cambridge: Cambridge University Press, 1947), pp. 27-34.
235. Op. cit.
236. See Norbert Wiener, Cybernetics, op. cit.; John Von Neumann, The Computer and the Brain (Stillmann Lectures) (New Haven: Yale University Press, 1958); Alan Turing, Mechanical Intelligence, (New York: Elsevier North-Holland, 1992); Marvin Minsky, Artificial Intelligence (Eugene: University of Oregon, 1973); Noam Chomsky, Cartesian Linguistics: A Chapter in the History of Rationalist Thought (New York: Harper and Row, 1966); and Kenneth Colby, Artificial Paranoia: A Computer Simulation of Paranoid Processes (New York: Pergamon Press, 1975. See footnote 248.
237. The issue behind the British orchestration of the Malvinas War against Argentina, in 1982, was London"s effort to push through a new NATO doctrine called "out-of-area deployment," signifying the use of NATO military forces outside the delimited areas of operations designated by existing NATO treaty-agreements. London, eyeing the oil-rich regions of Argentina"s Atlantic shelf, chose Argentina as the target for a precedent-setting operation. The "bait and switch" was set up through Lord Peter Carrington, one of Mrs. Thatcher"s highest-ranking controllers of that time, and her Foreign Minister "Palmerston" of the moment. Secretary of State Alexander Haig, a former protégé of London"s Henry Kissinger, was used to assist this operation. London "let it be known" to the ruling Argentina junta, that London might turn a blind eye to Buenos Aires simply taking the contested Malvinas islands; both direct British channels and Haig were used to foster this. Once Argentina took the British bait, Britain was able to secure full support of the U.S. government for a colonial war of subjugation, and the subsequent "taming" process, against the Republic of Argentina. Thatcher and Bush repeated the exact-same "sandbagging" technique to set up the 1990-1991 "out-of-area deployment" against, and prolonged colonial occupation of, Iraq.
238. See Jasper Hopkins, Nicholas of Cusa"s Debate With John Wenck, A Translation and an Appraisal of De Ignota Literatura and Apologia Doctae Ignorantiae, 2nd ed. (Minneapolis: Arthur J. Banning Press, 1984). Hopkins" work is invaluable as a scholarly treatment of this topical area, but the reader should be cautioned that this is by no means a blanket endorsement of Hopkins" commentary here: the skater must be alert for some not entirely surprising philosophical thin ice here and there on crucial conceptions of Cusa"s Platonic method.
239. Zorzi, op. cit. From Francis Yates" translation: "Those who retreat from the direct knowledge of the universe will retreat into the Docta Ignorantia" [Francis A. Yates, The Occult Philosophy in the Elizabethan Age (London: Routledge and Kegan Paul, 1979)]. This statement foreshadows the same argument in Francis Bacon, who denounces the deviation from sense-perceptions into consideration of mental phenomena, such as metaphor, as objects: How could anyone seek to sustain insistence upon the myth that Bacon actually wrote Shakespeare"s works after comparing Shakespeare"s work with Bacon"s attacks on metaphor! It should not be imagined that Kabbalism originates in Judaism; it does not. Moreover, the English Kabbalists of the Sixteenth and Seventeenth Centuries were a stoutly anti-semitic crew centered, from no later than mid-century, at Cambridge and Oxford universities, and also, in Elizabethan times, in Walsingham"s intelligence service.
240. A significant player in the circles of Conti and Ortes. Born in Venice 1712, died in Pisa, 1764. In 1726, he began studies in Bologna under the circles of Ortes" patron, the leading apologist for Galileo, Abbot Guido Grandi. Achieved fame in 1729, with his adulation of Conti"s protege Isaac Newton: "Saggio sopra la durata dei reigni dei re di Roma." Appears in Paris in 1735 as an acquaintance of Voltaire and of the Maupertuis from whom Ortes adopted features of his own hedonistic calculus. Visits England, meeting with Conti"s network of Newton-faddists there.
241. Giammaria Ortes, born in Venice, 1713, entering the Camaldolensian monastery of Murano as a novice in 1727. Died 1790. During 1734-1738, a student, at Pisa, of Camaldolesian professor of physics Abbot Guido Grandi. Praised as an economist in Karl Marx"s Capital, Vol. I, chap. XXV, sec. 4; Marx lays emphasis upon Ortes" second general work on economics, the 1777 Della economia nazionale libri sei, published after the 1776 Wealth of Nations of Ortes" student Adam Smith. Author of the 1790 Riflessioni (op. cit.) upon which the currently proposed U.N.O. Cairo Population Conference draft is based (as distinct from Thomas Malthus" more famous 1798 parody of Ortes" work).
242. The reader should be reminded, that, also with the existentialists of Nietzsche"s Vienna following, the gentle Delphic art of Aristotelian formalism corresponds to the Apollonian side of the pagan Jekyll-Hyde cult of Apollo-Dionysus, Apollo-Osiris, Apollo-Python Apollo-Satan. Even the late Bruno Walter, whom one might have taken for a genial and honest man, effused the babbling nonsense of this crew of Nietzscheans and Wagnerians, publicly, on a New York City radio broadcast, stating the unmusical proposition, that whereas Brahms "was an Apollonian," Beethoven "was a Dionysian." There have been, unfortunately, those conductors who have contrived to perform Beethoven as if his works had been composed by either Nietzsche"s Silenus, or, worse, Stockhausen! Beethoven was, in his own way, a devoutly Christian adversary of the pagan deities, a Promethean bringing the fire of creative genius to mankind in defiance of all of the pagan gods of Olympos.
243. E.g., "The Coronation of Poppea."
244. Galileo Galilei, Dialogues Concerning Two New Sciences (1638), trans. by Henry Crew and Alfonso de Salvio (New York: Dover Publications, n.d.). Exemplary of the empiricist method of Sarpi"s protégés, is the case of Galileo"s and Newton"s shared fraudulent claims to have discovered universal gravitation. For a demonstration of the way in which this Galileo-Newton hoax was constructed, see Lyndon H. LaRouche, Jr., The Science of Christian Economy, chap. VII, notes 7-9, in The Science of Christian Economy and Other Prison Writings, op. cit., pp. 471-473.
245. Op. cit.
246. Robert Fludd, Harmonia Mundi (1527). See Johannes Kepler, Harmonice Mundi, Book VI, for the reply to Fludd"s attack; Johannes Kepler, Harmonice Mundi (1619) German trans. by Max Caspar as Weltharmonik (Munich/Vienna: R. Oldenbourg Verlag, 1982).
247. Galileo, op. cit.
248. This ruse later served as the assumption employed for defense of the idea of a mechanical "artificial intelligence (AI)," beginning the 1930"s work of formalists such as Alan Turing (e.g., "Turing machines"). Since, as Gödel (1931) showed the implicit impossibility of simulating the human mind mechanically, the defenders of AI retorted with a proposal to ignore all aspects of human mentation which could not be reduced to "algorithms" of which they approved. Thus, out of the combined work of AI zealot Marvin Minsky and Russell follower Noam Chomsky at M.I.T., came researcher Kenneth Colby"s computer model, which neatly simulates cognition-free, associative-emotional types of psychotic behavior! See footnote 236.
249. For which the Ashmolean Museum is named, of course.
250. The putative origins of the cult are in the early-Seventeeth-Century Palatinate, where, ostensibly, the myth of "Christian Rosencreuz" was either spawned, or first found notable support. It is a medley of gnostic cults, all relying upon the methods of symbolic magic, and heavily saturated with heirlooms of the Bogomil and other cults proliferating in the Burgundian and Pyrenees regions. Adolf Hitler, like others associated with the Nordic Vril society, was a patron of this cult.
251. b. 1677, d. 1749.
252. The sub-circle around Abbot Guido Grandi negotiated the rehabilitation of Galileo, which occurred in 1757.
253. See footnote 30, "Lord Palmerston"s human zoo." In any case, Karl Marx had been warned of the fact that his organization, the Mazzinians, were controlled by Lord Palmerston"s Bentham-founded British former intelligence service, through Heinrich Heine"s famous exposure of the case of Ludwig Bo:rne ["Ludwig Bo:rne, Eine Denkscrift" (1840), in Heinrich Heine, Sa:mtlich Schriften in Zwo:lf Ba:nden, ed. by Klaus Briegleb (Munich: Carl Hanser Verlag, 1976), vol. 4]. Marx refused to accept the evidence, of course, since it would have obliged him to face the somewhat disconcerting fact that he, too, was nothing more than an agent of Britain"s Lord Palmerston!
254. See footnote 49.
255. Giovanni Botero (1544-1617). Although he studied Aristotelianism with the notorious follower of Pomponazzi, Bellarmino, the Jesuit order showed an aversion to Botero, and refused to accept him as one of their own. Although a Venetian agent closely tied to Paolo Sarpi, he was officially an agent of the House of Savoy throughout his adult life. The significance of Botero in introducing Malthusianism into Seventeenth-Century England is emphasized in Joseph A. Schumpeter"s A History of Economic Analysis (New York: Oxford University Press, 1955).
256. Karl Marx, Theories of Surplus Value, I: Addenda, [3.] Petty, Sir Dudley North, Locke (Moscow: Foreign Language Publishing House, n.d.). See also Schumpeter, ibid.
257. An Essay on the History of Civil Society (1767) (Edinburgh: Edinburgh University Press, 1966).
258. Tarpley and Chaitkin, op. cit., passim.
259. Schumpeter, op. cit.
260. Luca Pacioli, De Divina Proportione (1497) (Vienna: 1896; Milano: Silvana Editoriale, 1982, facsimile of 1497). Leonardo"s work on the application of Plato"s Solids, and the derivation of Kepler"s work (op. cit.) from this established the general principles of biological growth as general knowledge throughout literate circles of post-Renaissance Europe.
261. See footnote 47.
262. Benjamin Franklin, "Observations Concerning The Increase of Mankind, Peopling of Countries &c," (1751). See H. Graham Lowry, op. cit., p. 460, 463.
263. Loc. cit.
264. It is admissible, and convenient to speak of a Europe-wide "Venetian oligarchy." Over the centuries since the Council of Florence, especially since the collapse of the League of Cambrai, Venice"s nobility had assimilated more and more of Europe"s aristocratic and other oligarchical forces into its faction. By the time Venice fell from the status of a government, most of the royal and aristocratic houses of Europe, and the financial nobilities, were being assimilated into a Europe-wide social stratum basing itself everywhere on the Venetian model, and ruled more and more by Venetian ideas. Insofar as exceptions existed to this process of assimilation, the result was a division, across national boundaries, between a hardened Venetian oligarchical faction, and its opposition. The League of Armed Neutrality, which brought Britain to its knees on the issue of U.S. independence, is typical of this sort of division, as well Czar Alexander II"s similar action to defend the 1862-1863 United States against a planned intervention by joint British and French imperial forces.
265. Admittedly, it was the Cult of Mithra with which Octavian had struck the deal leading to the defeat of Antony and Cleopatra, and thus to imperial power, on the Isle of Capri. It was Tiberius" Cult of Mithra which murdered Christ (with help of a "Quisling" jury), and which committed mass-murder of Christians under Roman emperors from Nero through Diocletian. Nonetheless, the forces which murdered Christ and the Christians in this way were the same forces behind that Democratic Party of Athens which murdered Socrates, ostensibly in a "neo-conservative" fit of "political correctness." Key is the fact that the controlling force behind the rise of Rome was the same Cult of Apollo which had orchestrated the affairs of Classical Greece and Hellenism afterward.
266. E.g., Sigmund Freud, Leonardo da Vinci: A Study in Psychosexuality (New York: Random House, 1910). Or should one say Sig. Fraud? Freud had been a practicing homosexual, ostensibly ending the affair several years prior to publication of that book; there is no evidence that Leonardo was homosexual, and all the psychosexual indicators are to the contrary. Key to Freud"s book: Leonardo was creative, unlike the Freud who was innovative in a different sense.
267. Felix Klein, Famous Problems of Elementary Geometry, in Famous Problems and Other Monographs, trans. by Wooster Woodruff Beman and David Eugene Smith (New York: Chelsea, 1962), pt. II, "Transcendental Numbers and the Quadrature of the Circle," pp. 49-92.
268. Klein insisted upon the most simplistic, wrong reading of "Pythagorean" form under the second, middle section of Riemann"s paper.
269. Hegel died in 1831, during an epidemic, still doing his utmost to prevent the introduction of Nineteenth-Century science to the University of Berlin.
270. Savigny, to whom Karl Marx owed his instruction in law at Berlin, is the forerunner of Carl Schmitt, whose radically positivist dogma provided the basis for law under Hitler"s Reich. Real history tends to be like that; Heinrich Heine understood the principle of the matter when he wrote of the Rothschild control over the future revolutionaries of 1848, and later of the evil embedded in Kant.
271. Loc. cit.
272. See Bierman, op. cit., pp. 25-26.
273. It was under the direction of Kelvin, and with mathematical assistance from Grassmann, that Clausius cooked up the "second law of thermodynamics" by aid of an elementary blunder of misreading of the work of Sadi Carnot. Helmholtz was a robust and frequent hoaxster, devoid of scientific conscience, and completely a British agent.
274. Charles Babbage and John Herschel, The Principle of Pure Deism, in Opposition to the Dotage of the University (1811), an attack on the uselessness of Newton"s "fluxions," demanding the adoption of a real calculus, that of Leibniz, instead.
275. Professor Hermann Helmholtz, The Sensations of Tone (1863), trans. and appendices by Alexander J. Ellis (New York: Dover Publications, 1954). Under British "influence," Helmholtz attempted to impose Conti"s methods of Galileo and Newton upon music. Among the notable frauds in his work: (1) he proposed to eradicate the foundations of Classical music, the Florentine method of bel canto voice-training, substituting an unpleasant Nineteenth-Century British novelty, the "blank voice"; (2) he sought to outlaw the entire Classical tradition of musical tuning, that of J.S. Bach et al., and to replace it by a false, mechanistic model derived by Conti"s methods of Galileo and Newton; (3) he concocted a false theory of hearing to conform to his dogmas on music. (See Riemann, Werke, op. cit., pp. 338-350; see note by the original publisher on page 338: Riemann was correct scientifically; Helmholtz"s "politically correct" concoction on this subject, not.) In addition, still taught in defective university and conservatory classrooms today, is the argument of Ellis included in the appendices to Helmholtz"s work. In the case of those organs identified by Ellis on which Bach actually performed, only by adjustment and keyboard transposition could the organs have been tuned to ranges which Bach"s singers could have tolerated, a fact which Ellis knew, and which every competent instructor in a contemporary conservatory then or now has known: fraud! See A Manual on the Rudiments of Tuning and Registration, ed. by John Sigerson and Kathy Wolfe (Washington, D.C.: Schiller Institute, 1992), passim, for documentation of the ranges and registration of the human singing voice. The only reason that Helmholtz"s fraudulent opinions, and modern elevated pitch, are tolerated, is the pervasiveness of Nazi-like Gleichschaltung: "political correctness." Conti again.
276. See Cantor, Gesammelte Abhundlungen, op. cit., pp. 205-207, especially notes 1) and 2), the references to Plato and Cusa. (Cantor"s view of Giordano Bruno as a follower of Cusa is mistaken as to Bruno; it must be recognized that on this point Cantor is relying upon the secondary source.) Access to the issues arising between Cantor and Klein over the period of their sometimes close professional relationship is noted by Herbert Meschkowski and Winfried Nilson in their Georg Cantor Briefe (Berlin: Springer-Verlag, 1991). See Letters and editors" notes on pp. 63-64, and in the editors" references to the controversy with Klein in notes on pp. 109-110. Although Klein was a signator to the 1916 Göttingen honors for Cantor, he had joined the ranks of Cantor"s scientific adversaries long before 1895.
277. E.g., Euler, 1761. See Lyndon H. LaRouche, Jr., "Euler"s Fallacies on the Subjects of Infinite Divisibility and Monads," in The Science of Christian Economy, op. cit., pp. 407-425. This was also the central issue of Kant"s attacks upon Leibniz in the Critiques.
278. See G.W. Leibniz, "History and Origin of the Differential Calculus," in The Early Mathematical Manuscripts of Leibniz, trans. by J.M. Child (Lasalle: Open Court Publishing Co., 1920), pp. 22-58. See also, Gottfried Wilhelm Leibniz Philosophical Papers and Letters, ed. by Leroy E. Loemker (Chicago: University of Chicago Press, 1956), pp. 1095-1169.
279. LaRouche, The Science of Christian Economy, loc. cit.
280. Remember, in reading Klein, we are not dealing with some half-educated modern university graduate; Klein had a grounding in a serious Classical education, and was well-versed in the history of mathematics. The omissions we identify here could only have been witting fallacies of composition. One will see that there is a clear pattern to these.
281. Klein"s lecture may be compared with David Eugene Smith, "The history and transcendence of @gp," in Monographs on Topics of Modern Mathematics Relevant to the Elementary Field, ed. by David E. Smith (1911) (New York: Dover Publications, 1955).
282. LaRouche, The Science of Christian Economy, loc. cit.
283. See a note by Heinrich Weber, citing one of Clausius" blundering attacks upon Riemann, in Riemann, Werke, op. cit., p. 293. This is typical of the attacks upon the work of Gauss, of Heinrich"s brother Wilhelm, and Riemann coming from Britain, through Clausius, Helmholtz, et al. under the influence of Thomson (Kelvin) et al. from the 1850"s onward. James Clerk Maxwell, like Rayleigh, one of the leaders of the British attack on Gauss, Weber, and Riemann, made clear that he and his colleagues were rewriting electrodynamics in order to rid the subject of mathematical conceptions rooted in "geometries other than our own." Rayleigh went so far as to insist, that were Riemann correct in showing the possibility for powered transonic and supersonic flight of projectiles, then all of British mechanistic physics would collapse; therefore, he argued, Riemann had to be wrong. Under the initial direction of his senior in the Cambridge Apostles" cult, Bertrand Russell got into this British business of Riemann-hating in the 1890"s, with his tour of lectures in geometry.
284. Cf. Riemann, Werke, op. cit., p. 273: "... in which the difficulties lie more in the conceptualizing ... and I could make use of no preparatory work but several very brief indications given on this by Privy Councillor Gauss, in his second treatise on biquadratic residues ... and some philosophical investigations of Herbart." According to the Weber Werke (N.B., Appendices, pp. 507-558—one should ignore Hans Lewy"s tendentious introduction to the Dover reprint edition), Riemann"s revolutionary breakthrough came during a period of intense work, during a period preceding the crucial date of discovery, March 1, 1853, through his June 10, 1854 presentation of the hypothesis dissertation. It was his initial breakthrough of the earlier of those dates which plunged him into intensive library researches. Notably, it is the mid-1840"s Göttingen lectures of a former student at Friedrich Schiller"s Jena, the anti-Kantian Herbart, which continues through 1853 and beyond, to supply Riemann"s point of departure for his revolution in physics. He is fully aware of this nature of his work in the 1854 dissertation, as the reference to March 1, 1853 otherwise indicates. One should not exaggerate Einstein"s insight into Riemann"s work; briefly, there are indications that Einstein, although he broke with Machian positivism, was not able to comprehend the ontological implications of the crucial discoveries of his friend Gödel, or of Leibniz, Riemann, Cantor, et al. (The portion of the Riemann paper to which Einstein refers implicitly is section II, as summarized in sub-section 5.)
285. Riemann, Werke, op. cit., p. 272.
286. Russell admittedly played around with pretending to understand such matters. Notably, he played the role of Britain"s assigned control of Albert Einstein for a while, gaining at least one expression of glowering resentment from Einstein for this, and Marburg gnostic Ernst Cassirer"s opportunity, in his book Substance and Function, to poke great fun at Russell"s virtual philosophical illiteracy. This is in addition to the fact, that Russell"s access to Einstein had some other unpleasant, radioactive and related consequences.
287. From Gauss" Werke, op. cit., "Theoria residuorum biquadraticorum II" (1832), II, pp. 95-148 (Latin), pp. 170-178 (Gauss" German-language commentary on the Latin work); "Anzeigen: Disquisitiones generales circa superficies curvas" (in German) (1827), IV, pp. 341-347.
288. Riemann, Werke, op. cit. For Riemann on Herbart, see pp. 509-525; for editor"s comment on this, see pp. 507-508.
289. The term physical space-time is used here in the sense of Riemann"s definition of higher geometry-like relations above the mathematical domain.
290. The now customary reference to Riemann"s alleged debt to Cauchy typifies the phenomenon. (What of plagiarist Cauchy"s fraud respecting his own debt to Abel?) Riemann himself emphasized a debt to an Isaac Newton with whom he disagreed: See, for example, the page note on p. 534 of the Werke, citing "the third letter to Bentley." See in the context of pp. 524-525 (on "causality") as a whole the last lines on p. 525, beginning with "Das Wort Hypothese (the word hypothesis)," through to the bottom of the page, "... so würde er diese Geschwindigkeit beständig behalten."
291. LaRouche, loc. cit.
292. See Riemann"s treatment of what he terms Geistesmassen, in Werke, op. cit., pp. 509-525. This same matter is treated at length in the author"s "Metaphor" series, loc. cit.
293. Riemann, Werke, op. cit., p. 507.
294. The term "generating principle" is employed here strictly in Georg Cantor"s sense of the notion.
295. In first approximation, the relationship between the relative species-distinctness of the One versus the Many is formally analogous to the distinctions made by Kurt Gödel"s famous proof (e.g., 1931, op. cit.).
296. The formal definition of "relatively valid," as employed in this location, implies the test of the relative cardinality of the state of knowledge achieved through the discovery.
297. N.B., "The Truth About Temporal Eternity," loc. cit.
298. See B.F. Skinner, The Behavior of Organisms; An Experimental Analysis (New York: Appleton-Century-Crofts, 1966); also Science and Human Behavior (New York: Free Press, 1967).
299. For which the author is indebted principally to Leibniz"s discovery of that science, and to Riemann"s discovery, with a crucial subsidiary debt to Cantor.
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