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2.0 The Hypotheses Which Underlie Strategy


As we shall indicate, within this concluding section of the memorandum, humanity as a whole is presently confronted by the most profound crisis in the past six-hundred years of European civilization, the most extensive crisis in the known existence of the human species. The cause is the over-long toleration of a set of commonplace political beliefs which, in large part, are still generally accepted by the overwhelming majority among the population of the United States and western European nations. Thus, any policy which is put forth on the basis of its consistency with generally accepted public opinion of the U.S. population today, will be a disaster for that population itself. Since the United States is still the world's leading, if waning power, U.S. collapse would be a calamity for humanity as a whole.

It may be rightly seen as one of the leading causes for all crises of an existential quality which any society has ever faced, that, in history, as in Classical tragedy, no people has been willing to give up bad, generally accepted habits of belief, until the point is reached that the members of that society are shown that they have no alternative, but to choose between continuing the popular beliefs by which the society has done itself in, and the alternate possibility of continued survival.

Unfortunately, as Germany's 1934 election of Nazi Adolf Hitler as Chancellor and Reichsführer illustrates the point,[40] societies beset by existential crises do not always make the right choice of alternative beliefs. In fact, on this particular point, the history of cultures is chiefly a history of failures. It is, chiefly, the contributions of but a few cultures, among all of those which have ever existed, which has enabled mankind as a whole to rise from the potential population-level of a man-ape, never more than several millions individuals living on this planet, to the hundreds of millions realized during the time of European late-medieval society, and the billions made possible by the spread of modern European civilization today.

Once the fact of the present, downward spiral of planetary existential crisis is acknowledged, the important question is not whether or not significant features of existing popular beliefs will be demolished, but, rather, whether the choice of alternative beliefs will be a good, or a foolish one. From that observation, it should be but a step to the conclusion, that the most urgent question posed to us is: By what yardstick shall we know whether the choice of changed beliefs will be successful, or a disaster?

That is not a new question. It is the question which occupied a central place in the compositions of the greatest playwrights in known history, such as the tragedians Aeschylos, William Shakespeare, and Friedrich Schiller. Schiller's greatest work, both as historian and dramatist, was prompted by the horror which the European sympathizers of the American Revolution suffered in witnessing the bloody tyranny of London's agents Robespierre, Danton, and Marat.[41] As the candidate's wife, Schiller scholar Helga Zepp LaRouche, translates Schiller's observation on the French Revolution: "A great moment has found a little people." The greatest work of Schiller after that shows, as Jena University professor of history, and as tragedian: His late tragedies are direct successors of Shakespeare, and also of Aeschylos, in addressing the question: How are entire nations in crisis often doomed, like Hamlet's Denmark, by the refusal of should-be heroes to make the right choice of alternatives to those customary beliefs which are responsible for that nation's imminent ruin?

That question might be usefully restated: Are there not knowable principles of history, by aid of which we might be guided to make a correct choice of new beliefs to replace the folly of what we have believed recently?

The characteristic feature of the recent quarter-century of world history, has been the processes leading up, in the first instance, to the 1989-1991 collapse of a thermonuclear super-power of imperial dimensions, the Soviet Union and its Warsaw Pact extension. During the same quarter-century, the other great super-power alliance, that of the United States, was also headed for a similar collapse, a collapse now looming immediately before us. The failures of the Communist system, this candidate has addressed elsewhere. The question before the U.S. government, our political parties, and our citizenry, is: Wherein have we failed, too?

The characteristic feature of the present collapse of global civilization, is that this is a global economic catastrophe, a catastrophe which is directly traceable to a "cultural paradigm-shift" introduced on a mass-scale to European civilization, and beyond, at about the same time that U.S. President John F. Kennedy was assassinated, and British intelligence services were engaged in continued efforts to bring about the assassination of France's President Charles de Gaulle.[42]

Under the impact of this radical change in popular beliefs and governmental practice, the United States was transformed from a nation built upon commitment to fostering investment in scientific and technological progress, into a decadent, collapsing "post-industrial utopia." It is that thirty-year, pro-Malthusian, pro-Benthamite shift in "cultural paradigm," as it radiated into general practice globally, which is the immediate cause of the collapse of the world economy as a whole. However, the spread of the influence of the pro-Malthusian "cultural paradigm," by eliminating the previously powerful "Hamiltonian" tradition in the United States (in particular), permitted British intelligence operations, such as the neo-conservative Mont Pelerin Society, to spread the influence of the Adam Smith's anti-American ideology.[43]

This trend of the recent thirty years was reflected in a famous comment by Pope John Paul II, on the subject of the existence of "structures of sin" in both the non-Communist west and the Soviet system. Many American, and German conservatives attached to the liberalism of Adam Smith, including nominal Catholics, expressed anger against His Holiness on this point. As typified by the followers of House Speaker Newton Gingrich, the expression of the evil to which "structures of sin" referred, was a worse-than-indifference to the consequences of such willful moral crimes as transferring wealth out of funds allotted to Medicare and Medicaid, into a tax-grant bonanza to a pack of wealthy speculator parasites among Gingrich's admirers. The obvious principle of the post-World War II Nuremberg trials for crimes against humanity is, that if officials or professionals engage in practices which result in an actuarially foreseeable increase in death-rates, or kindred cruelties, that official or professional, for reason of acting to implement such a policy, is as guilty of crimes against humanity as surely as if he or she had murdered each victim, individually, with an axe.

The fact, that we might tolerate as "respectable political figures," persons who advocate such practices as looting the aged, and thus increasing the death-rate among them, to enrich a pack of parasitical speculators, shows something very rotten morally in generally accepted beliefs today. The fact that we tolerate the mass-murderous economic policies of "IMF conditionalities," is also a crime against humanity, also showing something very rotten in the moral character of those nations which tolerate such crimes in the name of the IMF. "Structures of sin" was neither a misplaced, nor an exaggerated charge.

For those and related reasons, those bad ideas which are responsible for the ongoing collapse of western civilization, like the Soviet communist system earlier, are chiefly either ideas about the principles of economic practice, or ideas which have an included clearly economic expression, at least if we employ the standard of the science of physical economy to define the applicable meaning of the term "economic." Thus, it is from the standpoint of physical economy, that we consider, in this concluding section of the memorandum: How do we know which changes in popular belief are valid alternative policies?

The ironical title of this second division of the memorandum contains an allusion to mathematical-physicist Bernhard Riemann's world-shaking, 1854 habilitation dissertation, On the Hypotheses Which Underlie Geometry.[44] This reference is prompted by the moral principle, that all policy-designs presented to, or by government, ought to be rendered "transparent" to any person with the professional competence to challenge those proposals and the ideas which underlie them. Whether or not the individual citizen has such competence, that citizen has the right to have the relevant disclosure available, that he or she might be able to have the matter investigated to proper satisfaction. For the convenience of those readers who may not, themselves, command relevant professional competence in these areas, this portion of the memorandum has been assigned the position of concluding division.


2.1 Economics and History

For the lay person, it is perhaps sufficient to report here two facts concerning Riemann's discovery. It should be noted, first, as a general observation, that that dissertation by Riemann was recognized by Albert Einstein and relevant other leading Twentieth-century professionals, as the specific origin of the physics conception called "General Relativity." Second, the specific relevance of that here, is the indispensable role Riemann's same contribution made to the furtherance of the present candidate's own fundamental discoveries in the science of physical economy, the candidate's principal professional competence.[45]

We proceed now, by summarizing a few essential points respecting the founding of physical economy as a branch of natural science by Gottfried Leibniz, and to the fundamental discoveries added to that body of science by this candidate, who was then a student of Leibniz's work.

As founded by Leibniz, during his published work from the 1671-1716 period of his life, physical economy puts to one side notions of price-mechanisms, in order to concentrate on the most essential aspect of those relations between society and nature upon which the human race depends for its continued existence. Emphasis is placed upon the variable relationship between the demographic characteristics of populations, and the society's consumption and production of the physical conditions for sustaining human life in a given quality of existence. In addition to the physical content of required market-baskets of personal and household consumption, and consumption by agriculture, mining, manufacturing, etc., physical economy also considers three rather strictly defined qualities of services as indispensable to fostering the health and productivity of the members of a society: education, scientific and technological progress as such, and health-care and sanitation. All of these demographic and market-basket magnitudes are measured in three principal scales of reference: per capita, of labor-force; per household; and per square kilometer of the relevant portion of the surface of the Earth employed.

The candidate's contributions to this branch of physical science are, summarily, twofold. First, to define from the standpoint of a mathematical outlook, the nature of the cause-effect relationship between science and increase of what U.S. Treasury Secretary Alexander Hamilton, like Gottfried Leibniz before him, defined as the productive powers of labor.[46] Second, the candidate understood, by 1952, the nature of the mathematical difficulties this discovery posed: the problem of what are termed singularities. That year, he tackled this difficulty, first, from the standpoint of mathematician Georg Cantor,[47] and, with greater satisfaction, from the standpoint of Riemann's cited dissertation.[48]

The combined result, of the original discovery and the subsequent application of Riemann's contribution to the problems of mathematical representation, became known, during the 1970s, by the descriptive name of LaRouche-Riemann Method. We outline the way in which required principles of strategy for a crisis of the present type, may be derived from this LaRouche-Riemann Method. This summary of the historical basis for strategic policy-shaping, is the basis for the content of this second division of the present memorandum as a whole.

From the standpoint of this method, the problem before us in modern times, is efficiently identified as the significance of the current crisis in light of the long, approximately 550-year cycle of history which the present crisis defines. That cycle may be described as Modern History. Modern History is defined against the backdrop of that which we know, from the standpoint of physical economy, as human existence in its historical and pre-historical totality.[49] Turn our attention to Figure 1, a chart in which the best generally accepted demographic data on combined past and present society is compiled, and to Figure 2, in which the curve of Europe's population-growth, from early times to the present, is summarized.

With reference to these two figures, the terms "history" and "economy" are now defined in the following way.

The first issue to be confronted, for the study of history, is that posed by Genesis 1:26-30. Are man and woman "made in the image of God"? For the working scientist, this question is restated as: Is there is a demonstrable, absolute distinction of the human individual, which sets man apart from, and above all other living species? For modern scientific knowledge, the answer to that question is readily found, by first restating the question in a slightly different form: is there some demonstrable behavior of the human species, attributable to the individual member of that species, which exists in no other species? Does this difference, should it be shown to exist, place man absolutely above all other species?

Simply, as we have already referenced this fact here, earlier, were the human species defined by the rules of animal ecology, the maximum population-level which might have been achieved by a man-ape sort of higher ape, under conditions existing on this planet during any part of the recent two millions years, would have been not more than several millions individuals. The increase of the human species' potential relative population-density[50] above the level of several millions individuals, represents a break with the rules of animal ecology, and places man apart from, and superior to all species whose reproductive potential conforms to the Malthusian or quasi-Malthusian rules of animal ecology.

Examine Figures 1 and 2 on that account. As Figure 1 signifies, the known record of human existence is not only a pattern of increase of our species' potential relative population-density; this trend correlates positively with an improvement in life-expectancies and related demographic characteristics of the population. Generally, the constraints which bound a definable increase of potential relative population-density, are, that the average productive powers of labor, as measured in required market-baskets of physical consumption (plus education, science, and health services), must tend to increase, and not decline, and, that the demographic characteristics of the population must either improve, or certainly not decline.

Moreover, since production entails a relative depletion of both natural resources and man-produced improvements in land-areas used, there must be a minimal margin of increased productivity (as measured in physical-economic market-basket terms) to offset this margin of potential "entropy." Thus, a minimal "world line" of rising productive powers of labor is a precondition for equilibrium in a constant potential population-density.

Moreover, turning to Figure 2, the combined picture supplied by the two figures, is of a general, statistically secular, historic (and pre-historic) rise in the human species' potential relative population-density. One need not elaborate here the argument, that this increase of potential population-density is the indispensable means by which mankind rose from relatively brutish savagery, to civilization. As we shall note, a short space ahead, this rise in potential is an indispensable characteristic of successful human existence. This picture forms the rough statistical basis for our reference to a notion of Universal History.

Now, focus upon the steep rise in the curve of population-growth since the middle of Europe's Fifteenth Century. The data alone suggest forcefully, that some rather fundamental change must have been introduced at that point in the internal history of Europe. That change marks a profound change in human history up to that point; for reasons to be given shortly, here, we refer here to the period of European civilization since the mid-Fifteenth Century, as Modern History. We extend the significance of the term "Modern History," to include the incorporation of non-European cultures, such as those of India, China, and Japan, into the patterns of growth of potential relative population-density characteristic of the history of modern European history in general.

For reasons to be supplied, the period since April 12, 1945 is designated as Current History. Similarly, the period of downturn which began about thirty years ago, is identified as the Period of Current Crisis. The spiral leading toward the presently onrushing collapse of the world's monetary and financial institutions, may be designated by a convenient term, such as "present crisis."

These are the terms within which the conceptions of strategy are to be formulated. These are not merely terms of statistics. There are, as we shall examine this briefly here, precise changes in the characteristic function shaping society's development, which distinguish one kind of history from the others.

Modern History

During the middle of Europe's Fourteenth Century, the banking system of Europe abruptly collapsed. The similarities to today's onrushing, world-wide monetary and financial collapse, are notable. This collapse coincided with the preceding and continuing spread of famine and epidemic disease, including the importation of the dreaded Black Death. There was a precipitous collapse in levels of population. However, there was also a positive development. The weakening of the Venice-dominated system of usurious Lombard banking, created the political opportunity into which anti-usury forces could intervene.

The happy outcome of that crisis was the Fifteenth-Century Renaissance--the so-called "Golden Renaissance"--centered around two events, the A.D. 1439-1440 sessions of the great ecumenical Council of Florence, and the subsequent establishment of the first modern nation-state, that of 1461-1483 France under King Louis XI. The success of France under Louis XI, prompted the emergence of the nation-state in the England of Henry VII, and role of Queen Isabella in launching the evangelization which established Hispanic America. It is from this point of inception, within the Golden Renaissance, that the ensuing, great improvement in population-potential, demographics, and productive powers of labor, was derived. From this came all the achievements of modern European civilization, including the great advance in intellectual life and civil liberties of the generality of the population. That is the crucial fact which defines the meaning of the term Modern History.

Until the emergence of Louis XI's France as the first modern nation-state, since the murkiest remotenesses of pre-history, never less than ninety-five percent of every culture, lived in a brutish state, as typified by serfdom, slavery, or worse. In ancient and medieval history, until Louis XI's France, people generally were the virtual property of a handful of powerful, oligarchical families, an oligarchy served by military and other lackeys, in maintaining the rule of the few over the many. In the Mediterranean littoral, one branch of the oligarchy, the feudal landed aristocracy, held both the land and its farmer population as chattel. Another part of the oligarchy, in the evil tradition of ancient Tyre, the newer phoenicians of Venice, ruled by means of usury in the forms of interest, tributes, monopolies in trade, and traffic in human slaves. Nations in the modern sense did not exist. The land and its population belonged to the feudal lord, and he to his feudal overlord. The highest ranking overlord was the emperor, and the nation was whatever and whoever belonged, as property, to the lord, overlord, and emperor.

With Louis XI's France, there emerged for the first time, a nation which belonged to its people as a whole. Power was shifted from the feudal lord, to a new type of monarch, based upon an urban intelligentsia, the latter constituting a kind of "national party," dedicated to the development of the nation, and its posterity, as a nation. In France, after Louis XI, Henri IV, Richelieu, Mazarin, Minister Colbert, Gaspard Monge, Lazare Carnot, the Marquis de Lafayette, Louis Pasteur, Gabriel Hanotaux, and Charles de Gaulle typify the continuation of a patriotic "national party," traced to the urban intelligentsia led by Louis XI.

There should be no mystery respecting the origin of this urban intelligentsia, the leading core of the national party of modern nation-states. This intelligentsia was developed by those religious orders, such as the Augustinians, Franciscans, and Brotherhood of the Common Life, which afforded a Classical form of secondary education to orphans and other boys from poor families. The new national urban intelligentsia, was a product of this kind of movement in education. Louis XI was the first head of state to establish the model of the Brotherhood of the Common Life as a form of state-supported secondary education, the kernel of the future development of state-supported universal education.

Thus, there should be nothing mysterious in the success of the Golden Renaissance's new form of sovreign nation-state republic. Such education of boys from the families of the poor, broke the back of the oligarchy's cruel monopoly over society, by breaking the class barrier. There are three keys to the vast superiority of the modern European nation-state over every other culture and form of society which has existed. First, the use of an increasingly universalized form of public education of the children of the poor, to produce from the children of the poor, those who had developed what the poet Shelley amiably described as the "power of receiving and imparting profound and impassioned conceptions respecting man and nature." Second, the commitment of the state to fostering investment in scientific and technological progress. Third, the commitment of the state, in going beyond the great project of Charlemagne, in fostering that necessary development of basic economic infrastructure, which is the precondition for growth of commerce, and of successful investment in scientific and technological progress.

During the period, 1763-1815, in which Venice, and its British and Dutch clones were destroying France, the young United States of America emerged, to assume gradually the leading place in the world which, during most of the 1461-1815 period, Louis XI's France had formerly held, in science and economy, among nations.

Modern European society was not uniformly good. It was a society seized by an internal conflict which continues to the present day. The national forces found resolutely hateful adversaries in the old feudal oligarchy, both in the landed aristocracy, and in those heirs of evil Tyre represented and led by the virtually imperial maritime, commercial, and financial power of Venice.

Over the subsequent centuries, the landed aristocracy was gradually destroyed, its remnant assimilated into the ranks of the financial oligarchy; in the course of World War I, with the destruction of the great feudal landed magnates of Austro-Hungary, Russia, and elsewhere, the power of landed aristocracy virtually vanished; only the international, Anglo-Dutch-dominated clones of the Venetian financier oligarchy, represented an efficiently powerful adversary to the modern sovreign nation-state.

The failure of the forces of the modern nation-state to continue their unity against Venice, allowed Venice to survive into the year A.D. 1510, and beyond. Later, during the course of the Eighteenth Century, Venice passed its mantle of leading oligarchical power to the new generations of international financier oligarchy power centered upon London and the Netherlands. With the crushing of France, by the 1815 Treaty of Vienna, the British monarchy, and the City of London, emerged as the dominant political force on this planet. From that point onward, the United States' constitutional tradition emerged rather rapidly, especially from 1865 onward, as the chief, most credible spokesman for the cause of the modern nation-state committed to fostering investment in scientific and technological progress for the benefit of present generations and their posterity. This was the role still performed implicitly, until April 12, 1945, the day of the untimely death of President Franklin Roosevelt.

The "Balance of Power"

From A.D. 1510, until beginnings of the British Empire about 1763, tiny Venice dominated Europe as it had earlier, from the Fourth Crusade until the collapse of the great Lombard debt-bubble during the middle of the Fourteenth Century. It ruled by the old Roman method of "divide and conquer," otherwise known today by such rubrics as "balance of power" and "geopolitics." Gasparo Contarini's Venice sponsored the establishment of protestantism, to divide northern Europe from southern, played Henry VIII's England against both Spain and France, played Spain and France against one another, and Austro-Hungary in various "balance of power" combinations. In 1582, Venice established a semi-permanent division within Europe. The majority faction in Venice, led by one Paolo Sarpi, chose to take over northern, Reformation Europe, with the Netherlands and England as the clones of Venice, while the remaining Venice faction based itself upon southern, Counter-Reformation Europe. In the first half of the Seventeenth Century, Venice organized the so-called "Thirty Years War" in central Europe. And, so on.

Do not be distracted by those "balance of power" conflicts in and of themselves. All of the nations who were entrapped into playing those games were "ships of fools." Do not be so fascinated with the details of these wars, that the subsuming issue is overlooked. The thing not to be overlooked is this: the real conflict of Modern History, is not the conflicts among nation-states as such. The real conflict is between the institution of the modern nation-state and the relics of the pre-Fifteenth-Century oligarchical institutions, such as feudal landlords and usurious financier nobilities.

The indispensable lesson of strategy, which the government of the United States must re-learn now, is that the relics of feudal oligarchism have been able to retain, and, lately, increase their political and financial power over this planet, solely because nation-states, such as the United States, behaved like fools, in allowing themselves to be trapped into feuds with other nation-states, rather than joining with other nation-states to eliminate the common enemy, the international financier oligarchy which is presently centered in London.

Examine the reluctance of many U.S. citizens to accept the simply, and conclusively demonstrated fact, that Sir Henry A. Kissinger KCMG has been, overtly, an agent of the British foreign service during his period of government service as National Security Adviser and Secretary of State for Presidents Richard Nixon and Gerald Ford, and, in fact, during about forty-five years to present date.[51] The issue is not whether Kissinger has been a "secret" agent of the British foreign-intelligence service, or not; Kissinger's agentry has never been secret; it has been overt. Since the publication of his book A World Restored,[52] Kissinger himself has repeatedly, openly bragged, that his role as a British agent within the U.S. intelligence services, was premised on the imperial tradition of Prime Minister Winston Churchill, in opposition to that of the intellectual traditions of the U.S. struggle for independence and U.S. Constitution. Kissinger's commitment to "balance of power" dogmas, throughout his career, to the present time, typifies this. This Kissinger issue typifies the characteristic conflict of Modern History, the conflict between the tradition of the Golden Renaissance, as typified by what U.S. Treasury Secretary Alexander Hamilton named "The American System of political-economy," against the feudalist heritage of that international financier oligarchy represented by the "bourgeois" Anglo-Dutch monarchies.

As Secretary of State John Quincy Adams expressed this, in condemning the proposal of Britain's Canning,[53] the foreign policy of the American Revolution is based upon the notion of a "community of principle" among those sovreign nation-states which share the tradition of our own 1763-1815 struggle for liberty against the British monarchy. On the opposite side, the dogmas of "balance of power" and "geopolitics" are the hallmarks of the wicked, oligarchical tradition of Venice and Venice's British imperial clone, the London-centered international financier oligarchy which continues to dominate the world's economic affairs, even still today.[54]

Current History and Current Crisis

Current world history began on April 12, 1945, the date of the death of President Franklin Roosevelt. The capitulation of the newly inaugurated President, Harry S Truman, to the wiles of London's spokesmen within his administration, Secretary of State Jimmy Byrnes, Secretary of War Stimson, and Stimson's devilish young accomplice, McGeorge Bundy, destroyed the kind of "American Century" for which post-war world Roosevelt had lain the intended foundations, and inaugurated the tumultuous and evil world-order intended by Roosevelt's war-time political adversary, Churchill.[55]

As we see today, the British Empire did not end with the close of World War II, as Roosevelt had intended, nor with the wave of nominal independence of former colonies, advertised by Prime Minister Harold Macmillan's "Winds of Change" address. Count the number of nations for which Queen Elizabeth II is head of state today.[56] Consider the role of London as the dominant force in the world's financial markets today. Consider the number of influential U.S. personalities and political-party factions which are allies of the British oligarchy against the President of the United States today.

President Roosevelt had been for a unified China. A post-Roosevelt London, with the complicity of a post-Roosevelt U.S. government, created two Chinas. Until Roosevelt's death, the United States had been committed to self-government of those former British, Dutch, French, etc. colonies which had been controlled by Axis powers during World War II. After Roosevelt's death, these nations were made once again subjects of their pre-war imperial masters. President Roosevelt's administration had restored John Quincy Adams' Monroe Doctrine for the Americas; under Kissinger's rule during the Nixon and Ford administrations, solemn treaties which had corrected Teddy Roosevelt's "Corrollary" were reversed, a condition underscored by the United States' disgraceful self-humiliation, in violation of the Monroe Doctrine and Treaty of Rio in Britain's Malvinas War of 1982.

Roosevelt had been the recipient of peace offers from the Emperor of Japan. Even had some among Japan's military commanders been shamefully resistant to their Emperor's command, by the time of Roosevelt's death, Japan's defeat was virtually complete, her imports-dependent economy effectively blockaded by U.S. naval and air power. Not a single U.S. soldier's life need be wasted in a superfluous invasion of the islands of Japan. Winston Churchill thought otherwise, and so did Churchill's agents of influence, Stimson and Byrnes. A needless nuclear bombing of Hiroshima and Nagasaki occurred, a needless bombing covered over with the official lie, that "one million American lives" had been saved, by this disgusting act in violation of all modern military-science tradition.[57]

The only purpose served by the dropping on Japan of the last two nuclear weapons then existing in the U.S. arsenal, was to launch what Britain's monstrously evil Bertrand Russell (the fanatically racist, nuclear "Madame Blavatsky" of British pacifism) had prescribed as the age of nuclear balance of power.[58] So, just as Truman's U.S.A. had violated all principles of justified warfare by carrying out Churchill's orders to drop the entire existing U.S. nuclear arsenal on Japan, Churchill and his Truman treated the war-exhausted Soviet Union similarly, with Churchill's launching of the "Iron Curtain" policy. Stalin reacted predictably, if more effectively than silly Churchill might have imagined. For the next fifty years, Current History has been defined by the actuality and aftermath of the pro-world-government, nuclear-weapons conflict--the "balance of power" conflict--prescribed by Bertrand Russell's statement in the September 1946 edition of The Bulletin of Atomic Scientists.[59]

The Current Crisis within Current History began in the immediate aftermath of the "Cuba Missiles Crisis" of 1962. Bertrand Russell appeared once more, as featured negotiator between Soviet General Secretary N.S. Khrushchev and the United States. Just as the terrifying spectacle of the August 1946 bombings of Hiroshima and Nagasaki, had created Russell's and Churchill's age of "nuclear balance of power," the world-terrifying shock of the 1962 "Cuba missiles crisis" set the stage for the adoption of Russell's pro-world-government doctrine of "Mutual and Assured Destruction," otherwise known as the MAD policies of systems-analysis freak Robert Strange McNamara and of Sir Henry A. Kissinger KCMG. That U.S. military engagement within Indo-China, which became known as "the Vietnam War," was the immediate fruit of two combined events: Bertrand Russell's successful "peace initiative" of 1962, and the November 1963 assassination of President John F. Kennedy.

The Kennedy assassination made possible the adoption of McGeorge Bundy's draft of an executive order revoking Kennedy's earlier order, which had prescribed orderly withdrawal of U.S. military forces from a Vietnam engagement. British intelligence's repeated attempts at the assassination of Kennedy's partner, France's President Charles de Gaulle, had the same general purpose. What became known as France's "Force de Frappe" nuclear policy was the principal issue of those assassination attempts, like Britain's and the Greenpeace organization's deadly threats against France's President Jacques Chirac today.[60]

The Period of Current Crisis is chiefly the cumulative effects of a profound change in economic policy, that introduction of the so-called "New Age" policy of "post-industrial utopianism," which was made feasible by the MAD, or so-called Détente agreements. It is the persistent application of this "New Age" policy to the shaping of economic policy, which is the direct, cumulative cause of the presently ongoing disintegration of the IMF-centered global monetary and financial system.

What was changed was, summarily, the following.

With some notable, if partial interruptions, the conflict between the United States and the British monarchy is rooted in the struggles of the Seventeenth-Century Massachusetts Bay Colony against the oppressive interventions under, first, the Restoration Stuarts, especially King James II, and, from 1688-1689 onward, the monstrously evil William of Orange and his British successors.[61] The Americans fought for the right to have native manufactures, and, in the case of the Massachusetts Bay Colony, the right to create a currency by means of which to promote full employment in productive enterprises. The Venetian Party in London sought to suppress manufactures in North America, and to apply to the colonies the same policy of "economy based solely upon primary-resources exporting" which Thatcher and Bush imposed as their new "Morgenthau Plan" for Russia (still in effect up to the present moment of writing).

In 1763, once France was no longer a power in North America, the British monarchy moved to crush the North America colonies. The colonies, under the leadership of Benjamin Franklin, prepared for the inevitable coming war with Britain. From that time, especially since the establishment of the U.S. Federal Constitution, until the aftermath of the assassination of President John F. Kennedy, the patriots of the United States had always maintained a policy of commitment to fostering public works in basic economic infrastructure, a currency independent of the London-centered Venetian Party's oligarchical control, and fostering investment in the increase of the standard of living and productive powers of labor, through investment in scientific and technological progress in the physical production of goods of agriculture, manufacturing, and other industry.

Even as anti-industrialist a Pre-Raphaelite fanatic, and avowedly pro-genocidal racist, as Bertrand Russell[62] could not eliminate investment in scientific and technological progress, as long as the risk of general war between the superpowers persisted. However, once the two superpowers had adopted the MADness of Russell, Szilard, McNamara, Bundy, and Kissinger, in the wake of the combined "Cuba Missiles Crisis" and assassination of President Kennedy, the effort to bring down "industrial society" was launched full-scale, from 1964 onwards. It is the downward-spiralling economic effects of that shift to "post-industrial utopianism," combined with lunatic extremes of a radically usurious "free trade" policy, which has brought the world's economy to the verge of threatened disintegration.

Thus, the post-1963 interval, 1964-1995, is defined as a distinct phase within Modern History, the Current Crisis.

Each of these aspects of Universal History, Modern History, Current History, and the present crisis, are set off from one another by an axiomatically distinct quality of physical-economic function. That distinction is shown most readily by application of the general principle underlying the LaRouche-Riemann Method.


2.2 Leibniz's Universal Characteristic Function

Those terms so situated, return to the conceptions implicit in Figures 1 and 2, above.

The subsuming issue in any review of U.S. strategy, is: How shall we define and locate the controlling "handles" through which the strategic situation might be changed, for better or for worse? Let that question be restated, as follows: How, from the standpoint of Universal History, might the disastrous course of Modern History's Current Crisis be reversed? By what standard of measurement might we recognize and monitor the choices available?

That question ought to recall a distinctive feature of the work of Gottfried Leibniz, Leibniz's references to the existence of a universal characteristic of processes. For convenience, we might say that this implies some universal function, and some central, most characteristic variable term of that function. This notion was developed by Leibniz as a corrollary of his founding of the science of physical economy, and could not be examined from any different standpoint. This notion equips us to render much more intelligible than otherwise, those notions of history which are the substance of competent strategic thinking and planning.

This Leibnizian notion is at the center of the fundamental discoveries by Bernhard Riemann, although Riemann's standpoint is limited to that of mathematical physics. The irony is, that the connection of Riemann's early 1850s discovery to Leibniz's universal characteristic, could be shown only after the discoveries, in the domain of physical economy, arising out of a 1948-1952 project of the present candidate.

Therefore, the immediately following pages of this section, are assigned two successive tasks. First, to identify the applicable features of the candidate's restatement of Leibniz's notion of a universal characteristic, and, then to show how that notion must be applied to the strategic problems immediately confronting the United States today.

The wrong-headed, if popular objection might be, is, as we stated earlier here, that some among the points within the immediately following pages here, are beyond the competency of most among today's generations of academically trained specialists. As we stated then, it is the candidate's view on this point, that government should develop no policy except as the design of that policy is rendered actually, or, at least, potentially, transparent to specialists with the necessary scientific or other relevant qualifications. The citizen has not only a right, but also an obligation, to know what it is that he or she must understand respecting policies he or she proposes to reject or support, and, should demand the sort of education wanted to equip himself or herself to understand such an important matter. The fact is, that any different policy than that we indicate here would fail catastrophically.

According to that latter policy, the following summary includes some relevant indications by aid of which a qualified professional might retrace crucial features of the candidate's original work of the 1948-1952 interval.

On LaRouche's Discovery

This candidate's fundamental discoveries in the field of physical economy, were developed in counterposition to the mechanistic fallacies of Norbert Wiener's "information theory" and John Von Neumann's "systems analysis," as the latter were then being popularized, during the late 1940s and early 1950s. The basis for the counterposition, was the manifest scientific illiteracy, respecting essential topics of epistemology, by Wiener, Von Neumann, and their like. The candidate's starting-point in this undertaking was, primarily, his adolescent and later grounding in work of Leibniz,[63] and his earlier defense of Leibniz's work against the argument of Immanuel Kant's Critiques.[64] The axiomatic epistemological blunder which underlies the work of Wiener and Von Neumann, was recognized then as a crude, radical-positivist echo of that same error which Kant, like the hoaxster Leonhard Euler before him, had directed against Leibniz's Monadology.[65]

The axiomatic blunder of modern "information theory" and "systems analysis" is fairly characterized as the substitution of the "virtual reality" of linearized mathematics for the real universe. Indeed, it is the popularization of a form of "pure mathematical" formalism with this embedded defect, which correlates with the high rates of insanity among professional mathematicians, notably those heavily weighted with the freight of the Bourbaki school: simply, they have drifted far too far afield, into a lunatic pseudo-universe of mathematical formalism. Nothing could be further from the truth, than to identify that sort of mathematical formalism as "scientific;" all fundamental scientific discoveries violate such misconceived mathematical formalism. The best formal statement of the proof of that argument, is Riemann's referenced 1854 habilitation dissertation.

The essential argument to be supplied here could be followed by a graduate of any good program of secondary education. The points to be made have sophisticated implications; but, the underlying argument is elementary.

That argument is constructed as follows. We begin with mathematics, and then situate the most elementary notions of physics in those terms of reference. After that, we situate the problem addressed by Riemann against that background. After that, we show why the candidate's turning to Riemann's discovery was indispensable for defining the problem of measurement created by the candidate's earlier discoveries in physical economy. After that, we show how the LaRouche-Riemann Method resituates Leibniz's universal characteristic. The root of conventional, formal classroom mathematics, is what the naive imagination portrays as elementary space-time. The naive imagination presumes, that space is defined axiomatically by three senses of direction: backward-forward, up-down, side-to-side; it presumes, axiomatically, that extension in all three senses of direction is perfectly continuous (unbroken by discontinuities), and without limit. It assumes that time has only one sense of extension, backward-forward, and that this extension is without limit, and perfectly continuous. This defines a simple Euclidean, or Cartesian space-time. This is also termed a quadruply-extended space-time manifold.[66]

The attempt to construct a physics which is consistent with such a quadruply-extended space-time, begins by locating bodies within the imagination's presumably empty space-time, initially representing those bodies and their motion in terms of the axioms of extension of simple space-time. This proves insufficient; new dimensions are added in the effort to account for the aspect of motion which can not be sufficiently explained in terms of simple space-time axioms. Mass is introduced as one such added dimensionality. Kepler's use of the optical "inverse-square" principle, is a modification of simple space-time introduced to similar effect. Charge is introduced. After Ole Rømer's demonstration of a constant rate of retarded propagation of light, and Christiaan Huyghens' and Jean Bernouilli's applications of this to the principles of reflection and refraction of light, a "constant speed of light" had to be added as a dimensionality, in such terms of reference; similarly, the principles of "least action" and "least time," introduced by the collaboration of Leibniz and Bernouilli, had to be incorporated. And, so on. Thus, in the effort to construct a mathematics which is consistent with the evidence of physics, we are obliged to exceed the four dimensions of the imagination's simple space-time by a physical space-time of "n" dimensions, by an n-fold physical space-time manifold.

The principle upon which all mathematical physics depends, is that stated by Plato and elaborated by his followers, through both Archimedes and Eratosthenes. One of the simplest illustrations of the relevant principle, is Eratosthenes' fair estimate of the size of the Earth's meridian, approximately twenty-two centuries ago. The relevant question is: How was it possible for Eratosthenes to estimate the curvature of the Earth with such accuracy, twenty-two centuries before any man had seen the curvature of the Earth? In this case, one may easily recognize, that it was an inconsistency in the sense-perception of the shadow cast by the noonday Sun's radiation, which was crucial. Indeed, the very existence of astrophysics and microphysics, which each and all depend upon measurable certainty respecting phenomena beyond the reach of the senses, and also biophysics, depends absolutely upon the kinds of ideas which are based upon demonstrating the absurdity of common sense. In science, the term "idea" is restricted to conceptions which are of this quality. That is the meaning of "Platonic ideas," for example. All competent mathematical physics is based upon the method of Platonic ideas.

In terms of physics, in each case of the discovery of such a Platonic idea, there is a corresponding measurement by means of which the efficiency of such an idea is demonstrable. The estimated measurement of the curvature of the Earth by Eratosthenes (within about fifty miles of the actual polar diameter of our planet) is an example of this principle of physics. In other words, as our physical space-time manifold is expanded, from n to n+1 dimensions, the yard-stick we must use changes, just as Eratosthenes' yardstick for measuring distances on the surface of the Earth was changed. A convenient general term for describing such impact of validated ideas upon measurement, is curvature of physical space-time.

When we are working with the conceptual domain of an n-dimensional physical-space-time manifold, it is our desire to render our work communicable, by representing our physical space-time manifold in terms of its projected image, as an n-dimensional manifold, upon a quadruply-extended space-time manifold. The quality of "curvature" so exhibited by that representation, is not a property of the space-time manifold, but is a measure of the deformation introduced by the use of the space-time manifold as a kind of mirror of reality: like the shadows on the wall of Plato's cave.

The preceding summary points, bring us to the crucial argument to be made. In each instance a validated discovery alters our construction of the n-fold physical space-time manifold which mathematical physics employs, we have introduced an absolute mathematical discontinuity into formal mathematics. Herein lies the key to Leibniz, and to the absurdity of the contrary argument made by venetian Abbot Antonio Conti's Dr. Samuel Clarke and the Conti salon's lackey Leonhard Euler.[67]

Any deductive system has the form of what is termed a theorem-lattice. Such a system is premised upon the deductive principle, that no proposition can be adopted as a theorem of a system, unless it is not inconsistent with an underlying, interdependent set of axioms and postulates. Such a set of axioms and postulates represents what Riemann, like Plato, identifies as an hypothesis. Any validated change in the set of axioms and postulates underlying a theorem-lattice, produces a new theorem-lattice, none of whose theorems are consistent with the old theorem-lattice. This inconsistency, introduced by the addition of a (validated) change in the underlying hypothesis, has the deductive form of an absolute mathematical discontinuity.

That is what Euler et al. denied hysterically. That is the key to Riemann's discovery, and to the discoveries by this candidate.

Return attention, once more, to Figures 1 and 2.

Both figures represent, in net effect, a succession of increases in mankind's potential relative population-density. The relevant measurements are each and all made in terms of three parameters: 1) per capita, of available labor-force, 2) per household, and 3) per square kilometer of relevant land-area. Consumption and production are measured in terms of physical components of household and production market-baskets, plus education, health-care, and science and technology[68] as the only services included in the market-basket.[69] A constant rate of potential relative population-density is subject to the following, included constraints: the life-expectancy and other demographic characteristics of the total population and its households must be equal to or better than during the comparable preceding epoch, and the consumption and per-capita output must be not less than during the preceding epoch, even after allowing for increased capital-intensity costs per capita.

The historical increases in potential relative population-density, represent a series of changes in human behavior. These changes can be assorted among "ecological-like" ranges of potential relative population-density, such that each range corresponds to approximate representation by a theorem-lattice. Each such formal theorem-lattice of that series of representations, corresponds to a range of technology. Each such theorem-lattice is separated from its successful successor by a formal discontinuity, a change in technological principle corresponding to an alteration within the attributable underlying set of axioms and postulates. Each of these changes corresponds to the discovery of an axiomatic principle, a Platonic idea, like that of the Eratosthenes' discovery referenced here. Each such discovery, once validated by appropriate, corroborating measurement, has the mathematical implication of a increase of the physical space-time manifold of technological practice, from n to n+1 dimensions. The mathematical function corresponding to a succession of such changes of the (n+1)/n form defines a pathway of successive increases of the potential relative population-density of society.

This function has two leading aspects. One aspect is the increase of mankind's power over nature: per capita of labor-force, per household, and per square kilometer of the relevant land-area of the Earth's surface. The other aspect is the succession of cumulative qualitative increases in human knowledge, each increase marked by an axiomatic-revolutionary discovery of a principle expressed as a Platonic idea. Riemann's habilitation dissertation contributed an indispensable part to the candidate's ability to address what were initially, otherwise awesome, mathematical implications of this connection between the individual's discovery of an axiomatic quality of principle and a consequent increase in the potential relative population-density of society.

In this relationship, (n+1)/n typifies an increase of the density of discontinuities for any chosen interval of action of the process by means of which potential relative population-density is increased.

Ideas As Metaphors

The essential nature of all scientific discoveries, is that they have no previously existent referent either in the images of sense-perception, or in the existing vocabulary. They have the same form of existence as the musical ideas which "lie between the notes" of a Classical composition, or the poetic idea which is invoked by the concluding couplet of a Classical poem, for which no symbolic meaning exists.[70] They are true metaphors; all important ideas are generated as true metaphors, for which no prior, literal definition or symbolic meaning exists.

The typical reader would understand this point more readily, had both the U.S. education system and popular culture not degenerated as thoroughly and rapidly as they have during the recent quarter-century. In a Classical humanist education, as opposed to the textbook-oriented variety of classroom, the lesson plans are based predominantly upon the student's reliving the axiomatic-revolutionary discoveries in science and art.

To render fully transparent the crucial principles we are describing here, the reader must be able to recreate, within the sovreign precincts of his or her individual's mental processes, a notion of the principle of creative reason, otherwise known as the generation of Platonic ideas. Since his initial, 1952, elaboration of the discovered principle underlying the LaRouche-Riemann Method, the candidate has used as his pedagogical method, the comparison of the role of metaphor in science, music, drama, and poetry.

The best choice of comparison for understanding scientific creativity, is the Classical method of composition employed by J.S. Bach's principal successors, Haydn, Mozart, Beethoven, Schubert, Brahms, et al. For pedagogical purposes, the most direct presentation of the case is provided by reference to the new form of thorough-composition employed for musical settings of Classical poetry, the new form of song-composition introduced by Mozart's setting of the Goethe poem Das Veilchen.[71] However, since only a small minority among even today's professional musicians understand these principles of Classical composition, the illustration supplied here is limited to the case of Classical modes of composition of strophic poetry. This poetry involves the exact-same principle of metaphor as Classical musical composition, but is more easily accessible to the typical reader.

Stated compactly, the relevant facts are summarized as follows.

A Classical strophic poem, such as one by Johann Goethe, for German,[72] or P.B. Shelley or John Keats, for English,[73] is represented by a series of stanzas, in which the contrast among the concluding couplets of each is the most crucial feature of the poem as a whole. We remind the reader there exists an unfortunate tradition, supplied to modern education by empiricists such as Thomas Hobbes: the attempt to outlaw both the subjunctive and metaphor from English-language usage. This is a popular enterprise among today's professionally trained illiterates of the Modern Language Association, as reflected in The New York Times Manual of Style. In order to avoid hated metaphor, the modern empiricist introduces the Romantic hocus-pocus of "symbolic meaning," as a substitute for metaphor. Whatever the reader has been instructed, on behalf of the doctrine of literary symbolism, the reader should dump into the waste receptacle, that one might focus upon metaphor.

Consider the significance of the term "metaphor" as such, and then consider that two-tiered hierarchical structure of metaphor, which is the invariable characteristic of the simplest, competent example of a Classical strophic poem. Embedded within what might appear, at first glance, as a simple proposition, there lurks one of the most sophisticated and excitingly beautiful constructions in all human composition, a true manifestation of that same quality of individual creativity otherwise attributable to the valid discovery of a revolutionary principle of the physical universe.

Every metaphor of Classical strophic poetry is rooted in the same principle as Eratosthenes' estimate of the curvature of the Earth along a meridian running through ancient Ptolemaic Egypt's Aswan and Alexandria. The idea, that curvature, is to be found in none of the individual facts assembled in the observations made, nor is the idea of that curvature located within the attribution of any possible symbolic significance for any of those reported observations. Just so, the metaphor in a Classical poem is not embedded in any dictionary's or thesaurus's reflections upon the literal definition, or symbolic attributions of any of the terms.

In a competent sort of education, on each important topic, the student is guided to recreate the internal mental experience of an original discovery: thus, to know, rather than merely to learn.[74]

Each such replication of a relatively valid, axiomatic quality of original discovery represents the generation of a true metaphor, and also a mathematical discontinuity in the relevant preceding form of a mathematical-physics theorem-lattice. The sum-total of valid human knowledge of applicable principle, represents, thus, an accumulation of such discontinuities, a series of the (n+1)/n form. It is this process of accumulation of knowledge, which is the correlative of realized increases of society's potential relative population-density.[75]

As is typified by the astrophysical science reflected within ancient Vedic hymns, datable from the interval between 6,000 and 4,000 B.C., the earliest transmitted forms of human scientific knowledge

were incorporated in, and transmitted by means of Classical forms of strophic poetry, within which, prior to the development of formal mathematics, the relationship between poetic metaphor and discovery of principle of knowledge is most immediate.[76] All great poetry of European civilization, and the great dramas, such as the tragedies of Shakespeare and Schiller, demonstrate the same principle for Modern History.

The principle of Metaphor dictates that no important new idea could ever be acquired by formal-logical manipulations of extant literal meanings of terms, or by symbolic referents, sensory or otherwise.

As the Eratosthenes example, given above, illustrates that point: Reference the validation of original, replicatable creative-mental acts by some appropriate form of measurement. The metaphor which was Eratosthenes' discovery of the Earth's curvature, and his corroboration of the existence of a reality corresponding to that metaphorical idea, by astrophysical measurement, is a faithful model for all true metaphor, in poetry, music, or otherwise situated. The fact that this idea could not be represented deductively from any extant dictionary meanings of names, nor metaphysically, as by means of epiphenomenal symbology, is the quality which defined "curvature" as a Platonic idea, a true metaphor, in that location. All metaphor, that of poetry, and as the meaning of all Classical musical compositions, is purely metaphorical, not symbolic.[77]

The points which are required here, for rendering the idea of creative reason transparent to the thoughtful reader, can be made by referring the reader to a general model containing the crucial highlight of a Classical strophic poem. Let our abstract general model defined for this purpose be a Classical poem of four stanzas, A, B, C, D, for which case the relevant metaphors, those defining the poem as a totality, are situated with respect to the concluding couplet of each stanza: a, b, c, d. Identify the metaphor associated with each stanza's final couplet as of the same form of metaphorical idea as "curvature" in the referenced Eratosthenes case. Then, treat the series a, b, c, d as a "Many" in the sense of Plato's Parmenides dialogue; the meaning of the poem as a whole, is of the form and ontological significance of the "One" in that Parmenides dialogue.[78] What is the single idea, the Platonic idea, the metaphor, which is the controlling meaning of the poem as an entirety? In other words, what is the unique meaning of that poem; in other words, what is the newly discovered idea, the metaphor, which never before existed anywhere, until that truly original strophic poem (or Classical song) was composed?[79]

This principle of composition of Classical strophic poetry is also the crucial principle of Classical musical composition in general, most notably the song-setting of a poem. The simplest illustration of the way in which the mind locates and applies the principle of metaphor, in composing a Classical strophic poem of the type described here, is found in the case of a musical performer performing from memory.[80] Any thoughtful reader can reconstruct the idea associated with that experience; that reconstruction is key to rendering transparent the idea of "idea" itself.

The indispensable task here, for understanding the most fundamental principle of economic science, and of history, is the fundamental distinction between an idea, and what is otherwise fairly identified as a mere opinion. Until one has mastered that exercize, one does not yet know both the proper formal and ontological meaning of "idea," as distinct from mere "opinion." The way in which memory functions in the reading of the simplest Classical form of strophic poem, contains implicitly all of the elements required for rendering transparent this meaning of the term "idea."

The first step for understanding a Classical poem, is to have memorized it. Once one has developed a sense of a single meaning for the poem as an entirety, rather than a succession of parts, one may think of rendering the spoken (sung) poem in such a manner that, as the final couplet of the last strophe has been enunciated, the listener should recognize that no additional strophes should have been written. In that delivery of the memorized poem, as in the performance of a Classical form of musical composition, the speaker is "singing between the notes."[81] The phrasing of the recitation as an entirety, is accomplished in such a manner, that the recitation is heard within the mind as a continuing process of development, a process of development which is resolved, to assume the form of a Platonic idea, by utterance of the concluding couplet of the composition as a whole.

By performing this exercize, and perhaps by aid of hearing some of the best singers of poetry or music, the reader should recognize, readily, that two, opposing processes of memory dominate such a performance of a Classical poem (or musical composition). On the one side, there is the remembered idea of the poem as a whole, a fixed conception of the poem as an entirety, a Platonic "One," which rings in the singer's mind from a moment before the poem begins, and remains, virtually unchanged, until the momentary silence which marks the end of that recitation. On the other side, there is the unfolding of the poem's metaphorical development, within each strophe, and beyond the enunciation of the concluding strophe's last couplet. The latter typifies the quality of idea associated with Plato's use of the term "Becoming;" the former, fixed conception, corresponds, as an approximation, to what Plato's Parmenides identifies as a "One." The "One" is memory of the completed poem, as if from the future into the present moment of mid-performance: it is the idea which embraces in itself the alpha and omega of that idea's existence in all place, and all time. The "Becoming" is the progress of the recitation through "Many" successive phases of continuing development, proceeding from the past and present, toward the future.

Between the two, opposing senses of idea of the poem, there is a controlling "tension." The "One" must shape the utterance of each of the "Many" to such effect, that the process of "Becoming," during the succession of the "Many," up to each present moment, is a progression of the development of an idea, as a metaphor, leading to nothing but the "fixed" conception, the "One." So, future shapes a past which is, at each moment, a progression from the past to the future. It is the tension between the two, opposing ideas, which supplies any form of artistic composition--poetry, music, tragedy, or the Classical painting of a Leonardo da Vinci, Raphael, or Rembrandt--its essential quality as art. This is that which supplies to a masterful performance of the Adagio movement of a great composer's Classical sonata, string quartet, or symphony, its compelling sense of "energy."[82]

All ideas have this form and ontological content. Memory, as its function is depicted as just described here, is the function upon which the generation and continued regeneration of ideas depends. The paradox of the "idiot savant," with memory, but with a tenuous grasp of ideas, illustrates the point.

It is this isochronic interaction between the opposing time-sense of "One" with "Becoming," which defines a Platonic idea functionally, topologically, as a discrete idea. All true metaphor is located in that form of isochronic relationship: first, immediately, between the whole utterance and the part of that utterance being considered, and the whole-world historical setting in which the utterance is heard. There can be no legitimate attempt to find a local symbolic significance linking a part of the utterance, as if epiphenomenally, to some explicitly attributable, ostensibly alluded, discrete referent.[83]

In this respect, all Classical artistic ideas and fundamental scientific ideas have the same underlying formal and ontological characteristics.

All such metaphors are, formally and ontologically, intrinsically not-entropic.

The candidate's discovery posed the question: By what yardstick shall we measure the ordering of all possible yard-sticks? Riemann's 1854 habilitation dissertation supplied the needed clue.

Prior to Wiener's "information theory" hocus-pocus, the term "negative entropy" was commonly employed, as a metaphor, to signify whatever quality must necessarily account for the functional distinction between living and non-living forms of otherwise ostensibly identical organic compounds. In the same vein, the distinction between the human cognitive processes and the behavior of lower living species, is comparable to the distinction between living and non-living processes in general: the human cognitive processes function within the domain of living processes in general, as living processes function within the domain of non-living processes. Wiener and his followers insisted on assigning to the neologism "negentropy" the sense of reversed statistical entropy. The popularization of "information theory" and associated "virtual reality," crowded out recognition of the original biologist's significance for "negative entropy."

If we employ a different term, using the metaphor "not-entropy," rather than tainted "negative entropy" or "negentropy," "not-entropy" signifies a process which functions in congruence with the Riemannian series we have referenced here, a series typified by the term (n+1)/n. There is a immediately implied correspondence among the notion of a series typified by that term, and the notion of an implicitly enumerable density of discontinuities for any arbitrarily selected interval of action. That term, correlated with such a density of discontinuities, is the metric which corresponds to a function expressing continuing increase of potential relative population-density. All notions of this form express what we ought to signify by the term "non-entropy."

This notion of "not-entropy" is then congruent with the notion of Universal History. Within that universal setting, the impulse supplied to Modern History by the Council of Florence and Louis XI's France, is distinguished by a higher rate of potential, by order of magnitude, per capita, per household, and per square kilometer, for the series (n+1)/n, than any previously existing form of culture within Universal History. The dualism of Modern History--the conflict between the not-entropic impulse supplied by the Renaissance, on the one side, and the contrary, entropic impulse supplied by the oligarchical principle, on the opposing side--is expressed functionally within those same terms of reference.

The point just made should be restated, that the comparison of the two statements might afford a clearer idea. The vast superiority of the modern European culture associated with the Golden Renaissance and Louis XI's France, is expressed mathematically by the notion of higher cardinality. In history, and in competent strategic planning, we count, not in numbers, but in cardinalities.

The Substance of Reason[84]

Correlation is not causation: formal logic, by its own axiomatic presumptions, is incapable of representing causation. Mathematics can be more or less truthful, according to the intent, and relative competence, of the user. No formal mathematics could contain within itself a measure of truth, or could be a language of truth. Alas, the contrary opinion is widespread, among the ranks of U.S. strategic analysts, for example. That contrary opinion has often proven fatal to entire nations, such as the former Soviet Union. Such potentially fatal, axiomatic flaws, as they are embedded axiomatically within "United States Security for the Americas," fall within that pathetic classification.

We have just identified the way in which the effects of not-entropy must be measured, as progression to states of higher cardinality: greater density of discontinuities per interval of action chosen. Discontinuities are not numbers in the ordinary sense; although we can measure effectiveness of the relative population-density of a culture in terms of inequalities, the causal factor responsible for the effect of not-entropic action, is represented nowhere within the measurements employed.[85] As has been indicated, in the view of metaphor, immediately preceding, the discontinuity within the formality of mathematical physics, is a mark of the place where a metaphor occurs; unfortunately, many would-be scientists, and very many others, have broken their philosophical necks, when they have mistaken the mark itself for the metaphor. That mark is, in reality, merely the place-setting card for the metaphor; it is the chair where the metaphor sits, not that which sits upon that chair.

To assist the reader at this point, we supply a definition. Definitions, of course, prove nothing in themselves; their usefulness is only pedagogical; their usefulness lies entirely in their role as implied questions, as propositions to be examined in a socratic manner. This point in our text, is a very good choice of place to employ such a definition.

The content of any valid discontinuity is a metaphor. The term "valid discontinuity" is elementary; it is the place at which what someone might have assumed, rationally, to have been a relatively best mathematical-physics lattice, fails to accept a physically valid proposition as a consistent theorem. It is the point at which reality crushes formalistic logic. Rather than saying "metaphor," let us be more precise about this matter. Let us say, any valid discontinuity marks the place at which the production of an appropriate metaphor must be introduced. This begs the issue: How is a valid metaphor produced? It is the production of a valid metaphor, which is the efficient content--the substance--of the occurrence of that discontinuity.

Let us define, for the same pedagogical purpose, and to the same effect, the production of a metaphor, by comparing the issues posed by the ontological paradox of Plato's Parmenides with the relationship, between a good Classical strophic poem's forward succession of stanzas and the single, unchanging, retrospective idea of the poem as a whole. We have already indicated, here, that no valid idea can be generated simply by sense-perception, or by symbolic or other arbitrary speculation: all the accumulation of ideas which were ever added to the accumulated store of human knowledge, were developed as metaphors. The method by which the human mind fulfills this task, is of the observable form which we have considered in reviewing the role of metaphor in a Classical strophic poem, or in the Classical song-setting of such a poem by a Mozart, Beethoven, Schubert, Schumann, or Brahms.

For example. A child is observed to grow, as a living creature, through a process of metabolism which depends upon the consumption of dead matter. The metamorphosis of the human egg-cell into child, is already a miracle, speaking in formal-logical terms of reference. Obviously, both series of "Many" changes is the work of some unifying principle, "One" principle. This "One" we call, in broadest terms, life, or, more narrowly, human life. The idea of life or human life exists only as a metaphor.

To set the stage for the argument which follows that definition, use an example from music which continues explicitly the case we presented for Classical strophic poetry, above. The following musical example is either within the competence of the reader, or of a musically trained friend or acquaintance who could assist in demonstrating the argument, at a keyboard, for example. The purpose of the example is to demonstrate the gulf which separates the discontinuity as a place-marking on a seating-plan (e.g., mathematical physics), from the ontological quality of that which sits in that place, in real life.

The occurrence of terms such as canto and its relatives, in pre-Renaissance and Renaissance Italian Classical poetry, reflects the relevant real-life connections between Classical poetry and Classical musical composition. All the crucial features of Classical music, including the well-tempered scale pivotted upon Middle C equal to 256 cycles per second, are products of the naturally-determined features of voice-registration in singing-voice polyphony.[86]

The characteristics of Classical musical composition, as defined by Wolfgang Mozart's reworking of J.S. Bach's A Musical Offering,[87] can be best expressed by a method of composition whose formalities are subsumed by the term "motivic thorough-composition." The entire composition is implicitly derived from a germinal pair of intervals. The introduction of this rigor, as elaborated by Mozart in response to the opening movement of Josef Haydn's Opus 33, No. 3 string quartet, obliges the composer to limit the subject of the entire composition to a principle of development. This principle of development is to be compared with the four-strophe model for Classical poetry which we supplied above; the principle of development so introduced is of the same form as the role of "change" in solving the ontological paradox examined by Plato's Parmenides.

Once a musician masters the rudiments of motivic thorough-composition[88] as employed by Haydn, Mozart, Beethoven, Brahms, et al., a straight-forward analysis of virtually all Classical compositions follows. The practice of this discipline should greatly improve the interpretative quality of performance of any musician. It would also improve, significantly, that musician's efforts at original composition. However, by itself, that accomplishment would not ensure that that musician emerged as a successful composer. The crucial point here, is that the understanding and application of this method produces performances which are recognizably more coherent than otherwise.[89]

No formal analytical method could ever represent the processes by means of which a metaphor is either generated, or recognized. A metaphor is a work-product of what Immanuel Kant sought to mystify as "synthetic judgment a priori," Kant's term for creativity in either God or man.[90]

On that account, the entirety of Kant's Critiques might be described by a member of the post-1968 generation as a "Class A freak-out," a recognizable echo of the explosion of irrationalist hysteria which permeates Aristotle's Metaphysics. On this account, Kant insists, that (since creativity can not be comprehended by an Aristotelean such as he is, it can not be comprehended analytically) creativity probably does not exist. He concedes, that, perhaps, the events which we would attribute to creation exist; but, he insists that these events are produced by a process beyond the reach of human understanding.

Kant was correct in asserting (in effect), that Aristotle could never understand creativity: that creativity could not be represented by analytical methods. It is true, that mathematics could never analyze a principle of nature as such. The characteristic fraud underlying Aristotelean method in its entirety, and also Kant's Critiques, is the hysterical claim that the human mind's consciously, recognizably rational capabilities are confined within the formalistic, school-book methods of a deductive theorem-lattice, such as mathematical analysis.

The power of generating and recognizing metaphor as something more than a mere discontinuity, is found in only two places: within the developed, sovreign creative powers of the mind of the individual person, and embedded as the adducible lawfulness of the existence of our universe as a whole. Although creativity can not be explicitly communicated within a medium which is subject to formal analysis, it is efficiently communicated, nonetheless, by such means as the Classical-humanist form of secondary education, as typified by the Humboldt reforms of gymnasium education for Germany. That is to say, society is capable of willfully replicating the development of the creative processes of adolescents (for example), to such effect that the resulting successes of education are efficiently demonstrable and comprehensible.[91] In a similar fashion, the metaphors generated by irony, as in poetry, can communicate, in an intelligible mode, ideas which can not be represented by the language employed as the carrier-medium which irony modulates.

From this latter standpoint, human creativity has the form, as we have said above, of being an analog for the distinction between living and non-living processes. The cognitive processes of the individual developed mind, are to be contrasted to the behavior of the lower species, as all living processes are to be contrasted to all non-living ones. Digital computers are among the non-living existences incapable of replicating human cognition. Only human individuals can replicate cognition: neither digital computers, the mythical Golem called Bourbaki, nor mathematical formalists, can do so. That form of cognition which typifies what must be seated at the place marked by the relevant discontinuity, that form of cognition typifies the quality of function which must be inserted into the analytical schema at each point such a discontinuity appears.

What must be supplied to the place in a formal theorem-lattice which is marked by the discontinuity, is the production of a valid and appropriate metaphor. On the scale of macro-physics,[92] there are only two kinds of phenomena which present effects attributable to the production of a metaphor: living processes, and the creative aspect of the human cognitive processes.

Ask: What is the size and weight of the thought which distinguishes a perception from a valid metaphor? We are in the domain of a discontinuity, in which measure in arithmetic terms must be superseded by reliance upon the notions of inequality associated with higher expressions of relative cardinality.[93]

That is not the only difficulty presented. There is no symbolic process outside the sovreign precincts of the individual person's creative-mental processes, which can represent explicitly the activity of those creative-mental processes by means of which even a good pun is generated.[94] The difficulty is, that those processes can be represented only by themselves; there is no medium of communication possible, which could represent explicitly the process by which an idea is generated. The greatest achievement possible, through the use of a medium of communication, is to aid one mind in provoking another to replicate the same process of thought by which the first mind generated a Platonic idea; however, the medium employed for that result, could never, in itself, represent the idea whose generation was provoked by aid of the use of that medium of communication.

As we said: On the scale of macro-physics, there are only two ways in which demonstrably not-entropic effects are efficiently produced. One is the action of living processes to generate living processes from materials assembled from non-living ones. The other is the creative cognitive processes of the individual human mind. Neither of these efficient agencies can be represented by a formal logic, except in the form of the discontinuities which mark the place at which the existence of life or a human individual's cognitive powers, are the cause of relevant continued action.

This not-entropic quality, which no formal mathematical physics can represent, is called "Reason" by Johannes Kepler, and is identified as the phenomenon of "necessary and sufficient reason" by Gottfried Leibniz.

The candidate's initial argument against Wiener's "information theory" dogma, back during 1948, had two leading aspects. The first aspect was, that the principle of Reason has the apparent form of the principle of life acting upon the principle of life. As noted above, human reason's efficient effect, in terms of increased potential relative population-density, has the apparent form of being related to living processes generally, as living processes are related to the non-living ones. In other words, as not-entropy of the second order. The second aspect accepted, conditionally, Wiener's attempt to supersede the Clausius-Grassmann, caloric notion of thermodynamics, by a notion of organization: that the passage from a relatively lower state, to a higher one, is not to be represented primarily by a density of caloric heat, but, rather, heat-potential must be examined as a by-product of level of organization. The contribution of Cantor's and Riemann's work to the candidate's grasp of the second of these two aspects, is that, in mathematics, "level of organization" has the obvious mathematical form of relative cardinality[95] in a system of counting transfinitely.

Against this background, one must consider a special implication of mankind's successful increase of potential relative population-density. Not only does mankind survive in this way, in contrast to the lower species, such as higher apes; the universe submits obediently to the power of creative reason which mankind wields in this way--as Genesis 1's "dominion" of man over nature. Hence, the notion of laws of the universe must be referenced to that which the universe manifestly obeys. It obeys Reason, as man's not-entropic, willful increase of potential relative population-density manifests that power of creative reason setting the individual person apart from, and above all other sub-eternal species of individual existence. We know the law of the universe only as we observe the universe submitting to mankind's willful increase of potential relative population-density.

Thus, this notion of not-entropy, as expressed in terms of manifest increase of potential relative population-density, is the proper form of Leibniz's universal characteristic. The efficiency of this principle, thus expresses the substance of reason. It is those processes by which Platonic ideas are generated, which reflect this universal characteristic, this substance of Reason.

Apply the ontological paradox of Plato's Parmenides to this case. We have reminiscence of all such known manifestations of reason, chiefly through reliving, within the sovreign precincts of each our own creative mental processes, a series of individual reenactments of valid, original discoveries of principle. This array constitutes a "Many," in the sense of Parmenides. This array corresponds to the series of metaphors associated with the couplets a, b, c, and d of the strophic model discussed above. What, then, is the "One" which corresponds to this "Many"?

The reminiscence of that series, as a reminiscence of the metaphor which corresponds to the culminating development of a strophic poem, or song-setting of such a poem, is a "One," an indivisible Platonic idea. This idea, applied without any change in itself during that entire interval, is applied retrospectively to a reexperiencing of the cumulative process of development marked by a, b, c, and d. The latter, cumulative process, has the form of "Becoming" in Plato's writing; the first, the retrospective single idea of the completed Becoming, has the form of the "Good" in Plato's writing.[96]

All creative reason (all production of valid ideas) is of the isochronic topological form we have indicated for Classical poetry, music, and the solution of the Parmenides ontological paradox. The key to Reason, to all valid ideas, is the application of the power embedded in the reminiscence of an experienced "Many": to generate a notion of that "Many" as subsumed by some indivisible, constant generating-principle, some constantly subsuming, unchanging principle of change. That application of reminiscence to the reexperiencing of the relevant Many, is the production of Metaphor, is the musical beauty which lies between the notes. This is creative reasoning; this is the substance of Reason. This not-entropic principle, is the universal characteristic of history.


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FOOTNOTES

40. There is no mistake in our use of the year 1934 here. Hitler was brought to power, initially, during 1933. The British, who controlled Weimar Germany's Social-Democratic Party and trade-union leadership, used that social-democratic leadership, together with Anglo-American agent Hjalmar Schacht and his liberals, to bring about the fall of the government of Chancellor Kurt von Schleicher. This created the preconditions under which Schacht, on orders from Britain's Montagu Norman, and with financial backing delivered by President George Bush's father, Prescott Bush, was enabled to bring Hitler to power as Chancellor. Following that 1933 coup d'état, Hitler was consolidated in power through the aid of an overwhelming majority of the popular referendum. Hence, Hitler's Nazis, which were headed for virtual oblivion in the 1932 election-trends, were somewhat freely chosen by foolish Germans in 1934, but not 1933.[return to text]

41. There is no exaggeration in this reference to London's control over Jacobin leadership. The direction was supplied by the head of the British foreign service (since 1782), Jeremy Bentham. Bentham personally housed and trained Danton and Marat in London, prior to dispatching them to Paris to conduct the Terror under Bentham's personal direction.[return to text]

42. The Montreal, Canada-based organization, Permanent Industrial Expositions, a.k.a. "Permindex," was expelled from Switzerland, on grounds of its involvement in the attempted assassination of France's President Charles de Gaulle. This assassination-bureau was, like today's Hollinger Corporation, an off-shoot of Canada-based, Beaverbrook-Stevenson, World War II British intelligence. The head of Permindex was a British intelligence agent, Major (ret.) Louis Mortimer Bloomfield; Bloomfield was, from about 1938 into 1963, a London-assigned personnel consultant to the U.S. Justice Department's clone of Britain's MI-5, the Division Five section of J. Edgar Hoover's FBI. According to the relevant sources, had the existing photographs of David Ferrie, together with Clay Shaw, been shown in court during the relevant trial of Shaw, Shaw, Bloomfield's head of New Orleans Permindex, would have been convicted of complicity in a conspiracy to assassinate President John F. Kennedy.[return to text]

43. As Dr. Armin Mohler documented in his The Conservative Revolution in Germany, the Nazi party was but one of scores of so-called "conservative" movements proliferating in Europe during the 1920s and 1930s. The Mont Pelerin Society of British asset Friedrich von Hayek and Professor Milton Friedman, et al., served as a post-war gathering-place for many of those movements which, during the 1920s, and sometimes also 1930s, had variously competed with, or allied with the Nazis. There is nothing inconsistent between Adam Smith's, von Hayek's, and Milton Friedman's hyperventilated misuse of the term "freedom," and core fascist ideology in general.[return to text]

44. Bernhard Riemann, "über die Hypothesen, welche der Geometrie zu Grunde liegen," Bernhard Riemann's gesammelte mathematische Werke (New York, N.Y.: Dover Publications [reprint], 1953), pp. 272-287.[return to text]

45. On the subject of the candidate's work in physical economy, note the references given in note 37, above: the introductory textbook, So, You Wish to Learn All About Economics?, the book-length treatise, The Science of Christian Economy, and two recently published articles of relevance from EIR intelligence news-weekly; "Why most Nobel Prize economists are quacks," (July 28, 1995), and "Non-Newtonian mathematics for economists," (Aug. 11, 1995).[return to text]

46. Alexander Hamilton, Report to the U.S. Congress on the Subject of Manufactures, December 1791, passim.[return to text]

47. The 1952 reading was of a (pre-1952) Dover reprint edition of the English translation: Contributions to the Founding of the Theory of Transfinite Numbers, by the British mathematician Philip E.B. Jourdain. There is a 1955 Dover reprint edition extant. The German original is found in Beiträge zur Begründung der transfiniten Mengenlehre, in Georg Cantor gesammelte Abhandlungen mathematischen und philosophischen Inhalts, Ernst Zermelo, ed. (Berlin: Julius Springer, 1980), pp. 282-356.[return to text]

48. See LaRouche, op. cit.[return to text]

49. Here, the distinction made between "historical" and "pre-historical" is, broadly speaking, the conventional academic one.[return to text]

50. See Lyndon H. LaRouche, Jr., So, You Wish to Learn All About Economics? loc. cit. The term "potential population-density" is descriptive. "Relative" signifies the variability of this potential with respect to relevant quality of land-area considered, a relative value which varies with the degree of "natural" or man-caused depletion, or enhancement of this relative quality.[return to text]

51. See Special Report: "Sir Henry's lifelong service to the British monarchy," EIR, Sept. 22, 1995.[return to text]

52. Henry A. Kissinger, A World Restored: Metternich, Castlereagh and the Problems of Peace 1812-1822 (Boston: Houghton Mifflin, 1973).[return to text]

53. that the United States "become a cock-boat in the wake of a British man-of-war" in the waters of the American hemisphere. See Lyndon H. LaRouche, Jr., The Case of Walter Lippmann (1977).[return to text]

54. "The big commodities hoarding crunch of 1995," EIR, Sept. 15, 1995.[return to text]

55. e.g., Elliot Roosevelt, As He Saw It (New York: Duell, Sloan, and Pearce, 1946). See, also, Lyndon H. LaRouche, Jr., et al. "The Coming Fall of the House of Windsor," EIR, Oct. 28, 1994, and "Britain's Pacific warfare against the United States," EIR, May 12, 1995.[return to text]

56. The following listing summarizes the state of affairs (excluding Antarctica): [view listing] [return to text]

57. See Niccolò Machiavelli, Commentary on the Ten Books of Livy (New York: Viking Penguin, 1984). Machiavelli comments on Livius' detailing of the argument that disaster must tend to result from launching unnecessary assaults against an adversary who has been already defeated and cornered. The attack may provoke the defeated adversary into a savage counter-attack, to no one's advantage, thus ruining the previously won peace. That doctrine, that one does not needlessly attack a hopelessly defeated enemy, had been taught in every competent curriculum provided to modern military officers. The point is illustrated by the emerging effects of the actions of the foolish Prime Minister Margaret Thatcher, with the support of the halcyonic President Bush, in imposing upon a politically defeated Soviet power the murderous "Reform" policy whose rapacious, continuing effects have created the enraged state of affairs inside Russia today. No government competent in strategic planning would ever impose such a lunatic policy as this "Reform" upon a defeated former adversary; the folly of continuing such a policy was nearly suicidal during the 1945-1989 nuclear balance-of-power age; it could be as bad or worse now.[return to text]

58. See Lyndon H. LaRouche, Jr., "How Bertrand Russell became an evil man," Fidelio, Fall 1994. The Emperor of Japan, using his diplomatic channels in Europe, had been negotiating peace through the Secretariat of State of the Vatican in Rome. Monsignor Montini, later Pope Paul VI, and then special representative for Pope Pius XII, was the channel through which the Emperor's offers were conveyed, via the U.S. Office of Strategic Services (OSS). In order to prepare for the nuclear bombing of Japan, following the death of Roosevelt, London dispatched two American OSS agents, the inveterate scoundrels Allen Dulles and James Jesus Angleton, into Italy, for the purpose of working to discredit the Vatican channel. It was this London-controlled channel within OSS which Churchill et al. used to discredit the Emperor's acceptance of the peace terms actually employed under General Douglas MacArthur.[return to text]

59. LaRouche, op. cit.[return to text]

60. See Feature: "British assassins' bureau targets Chirac and Clinton, EIR, Sept. 8, 1995.[return to text]

61. The British enemy of both the English colonies in North America and the later United States, was the faction within Britain known as "the Venetian Party." King James I, like his Francis Bacon, was already a tool of Venice's Paolo Sarpi at the time of the A.D. 1603 accession. Oliver Cromwell was a blood relative of the Venice-Genoa Pallavicini family, and also a tool of the Venetian Party. The Restoration Stuarts, as typified by the London Royal Society, the notorious "Cabal" ministry, and James II, were also tools of the Morosini family's contemporary imperial Venice of the Peloponnesus wars. However, Venice oligarchy's control over Britain was not consolidated until 1712-1714, with the defeat of the anti-Marlborough faction associated with Jonathan Swift and accession of George Ludwig of Hannover as the first British monarch. Until 1712-1714, there were still powerful currents of resistance against the Venetian Party from within the British Isles, within England itself, as in Scotland and Ireland. When the Restoration Stuart reign was challenged afresh by this internal resistance, the tyrant William of Orange invaded England, and drowned the Ireland resistance in the notorious fashion recorded. It was not until the death (possibly by poisoning) of Queen Anne, and accession of Georg Ludwig as George I, that the Venetian Party of Winston Churchill's notorious ancestor, the First Duke of Marlborough, consolidated its power. See H. Graham Lowry, How The Nation Was Won: America's Untold Story, Vol. I (Washington, D.C.: Executive Intelligence Review, 1987).[return to text]

62. See Bertrand Russell, The Problem of China (New York: The Century Co., 1922). See also, his The Prospects of Industrial Civilization (London: George Allen & Unwin, 1923); already, before Adolf Hitler, Russell argued: "The Asiatic races will be longer, and the negroes still longer, before their birth rate falls sufficiently to make their numbers stable without help of war and pestilence.... Until that happens ... the less prolific races will have to defend themselves against the more prolific by methods which are disgusting even if they are necessary," p. 273.[return to text]

63. The Leibniz works studied by the candidate during his early through middle adolescence, featured the Theodicée, the Monadology, and The Leibniz-Clarke Correspondence. A convenient location for those and related writings is Gottfried Wilhelm Leibniz Philosophical Papers and Letters, trans. and ed. by Leroy E. Loemker (Chicago: University Press, 1956), Vols. I and II.[return to text]

64. The candidate's adolescent readings of Kant were the Critique of Pure Reason and Prolegomena to Any Future Metaphysics.[return to text]

65. There will be some incompetent, but nonetheless boisterous objections from among professionals on this point. To forewarn such would-be critics against embarrassing themselves publicly, the following facts are noted here. Leonhard Euler was a most gifted, and productive mathematician, who prostituted himself for about twenty-five years in service of King Frederick II ("the Great") at the Berlin Academy. Euler is notorious for two leading frauds in which he participated during that period of service. The first was his complicity in the "least action" hoax for which Pierre-Louis Maupertuis left the Berlin Academy in disgrace. The second is the attack upon Leibniz's Monadology featured within Euler's Letters to a German Princess. [See Lyndon H. LaRouche, Jr., The Science of Christian Economy (Washington, D.C.: Schiller Institute, 1991); Appendix XI: "Euler's Fallacies on the Subjects of Infinite Divisibility and Leibniz's Monads," pp. 407-425.] This was written by Euler as a parody of, and direct refutation of Leibniz's Theodicée. The center-piece of this Euler production is a crude, and absurd argument against the existence of mathematical discontinuities, and a defense of Dr. Samuel Clarke's argument on this matter, within The Leibniz-Clarke Correspondence. This fraudulent claim, to have eliminated the existence of discontinuities in mathematical physics, was the basis for the anti-Leibniz, anti-Gauss, anti-Riemann faction in Nineteenth-century mathematics (e.g., Lagrange, Laplace, Cauchy), and the root of the fanatical extremism of the Bourbaki school. Mathematically, the crudities of Wiener's and Von Neumann's work in "information theory" and "systems analysis" are hereditary reflections of Euler's influence. The definitive refutations of Euler's hoax, respecting discontinuities, were supplied by Riemann, Weierstrass, and Georg Cantor. Kurt Gödel's devastating exposure of the axiomatic fallacy of Bertrand Russell's and Alfred North Whitehead's Principia Mathematica, and of Von Neumann's work of the 1920s, replicated relevant features of the work of Weierstrass and Cantor.[return to text]

66. This is the author's preferred restatement of the opening argument from Riemann's habilitation dissertation.[return to text]

67. During the Eighteenth Century, Isaac Newton, Dr. Samuel Clarke, and Frederick II's Berlin Academy, were each and all instruments of an international salon created by Venice's leading intelligence operative, Abbot Antonio Conti. It was Conti who directed the campaign against Leibniz. See, "Why most Nobel Prize economists are quacks," and "Non-Newtonian mathematics for economists," loc. cit.[return to text]

68. Classical art-forms are subsumed under either education or science and technology, as most applicable.[return to text]

69. An allowance is made for other selling and administration expenditures of both the public and private sectors of societies, but the quantity of the service supplied is not otherwise measured in detail.[return to text]

70. See Lyndon H. LaRouche, Jr., "Musical Memory and thorough-composition," EIR Sept. 1, 1995, pp. 50-63.[return to text]

71. See LaRouche, Sigerson, Wolfe, et al., A Manual on the Rudiments of Tuning and Registration, Book I, John Sigerson and Kathy Wolfe, eds. (Washington, D.C.: Schiller Institute, 1992). Note, especially, Chapter 11, "Artistic Beauty: Schiller versus Goethe," pp. 199-228, especially pp. 203-208, on Mozart's setting of Das Veilchen.[return to text]

72. The simplest example from Goethe, is his popular Mailied. This references remarks on this subject which Helga Zepp LaRouche supplied, in response to a question, during the Sept. 2-4, 1995 conference of the International Caucus of Labor Committees in Vienna, Virginia.[return to text]

73. Adequate examples are Shelley's Ode to the West Wind and Keats' Ode on a Grecian Urn.[return to text]

74. Perhaps, this still occurs in a dwindling number of classrooms. No student ever mastered a subject without reliving, within the impenetrably sovreign limits of his or her own mind, the mental experience of recreating the mental act of discovery experienced earlier within the sovreign mental processes of the original discoverer. [return to text]

75. This is key to the intrinsic incompetence of Norbert Wiener's "information theory" dogma, and also to both Von Neumann's "system analysis" and the "Third Wave" fantasies of Alvin Toffler, Newt Gingrich, et al. Since each singularity of an (n+1)/n Riemannian series conveys "more information" than is contained with the entirety of the band-pass of signals of a n-fold manifold, the very notion that any idea could be assessed statistically by aid of Boltzmann's H-theorem, is sheer quackery. This is key to the general limitation of all "virtual reality" systems; the one thing no "virtual reality" system can ever represent functionally, is reality. The essence of "virtual reality," like Bourbaki, is that it assumes the non-existence of singularities (e.g., mathematical discontinuities), whereas all knowledge of the real universe is based upon the human mind's peculiar capacity to resolve the singularities typified by a Riemannian series of ascending cardinalities of the type indicated, the ability to generate and comprehend true metaphor.[return to text]

76. See Bal Gangadhar Tilak, Orion or Researches into the Antiquity of the Vedas (1893), and The Arctic Home in the Vedas (1903) (Poona, India: Tilak Bros.).[return to text]

77. The emphasis upon symbolic interpretation expresses most directly the axiomatic distinction between the Classical mode of composition, Haydn, Mozart, Beethoven, Schubert, Mendelssohn, Schumann, and Brahms, and the Romantic mode of Berlioz, Liszt, Wagner, et al. The so-called "Moderns" follow the Romantics on this point of axiomatic distinction.[return to text]

78. The Parmenides dialogue serves functionally as a statement of the formal and ontological paradox which is examined and resolved within the other, logically following, last dialogues of Plato.[return to text]

79. The term "composer" should be read here as being employed in the sense the equivalent term is used by Plato in, for example, the Timaeus dialogue.[return to text]

80. See LaRouche, "Musical Memory...," loc. cit.[return to text]

81. Ibid.[return to text]

82. Among the best examples of this, is the conducting of Wilhelm Furtwängler; his conducting "between the notes" represents precisely the approach described here. For the same reason, typified by first violinist Norbert Brainin's emphasis upon the Haydn-Mozart-Beethoven principle of Motivführung (motivic thorough-composition), the Amadeus Quartet's recorded (DGG) performance of the Beethoven Opus 59, "Rasumovsky" quartets, is remarkable for exemplary demonstration of this principle of "energy."[return to text]

83. Since the mind generates distinct ideas in this way, the presently customary practice, of attempting to infer the idea of motion from the starting-point of fixed objects, is intrinsically absurd. Rather, since fixed ideas are generated in the isochronic process identified here, our beliefs respecting what we identify as apparently "fixed objects," are given to us through the generation of singularities within our conceptual imagery of change. These are the singularities whose existence is reflected by the presence of those marks which formal mathematics denotes as discontinuities. So spake famously Heraclitus, and Plato (e.g., Parmenides) after him.[return to text]

84. The crisis-gripped U.S. election-year 1996 is also the 400th anniversary of the first publication of Johannes Kepler's Mysterium Cosmographicum, the founding work of modern astrophysics and also of mathematical physics in general. [The second edition, the original text supplemented with added notes by Kepler, is the work best referenced for an overview of all of the successive phases of Kepler's further development, after 1596.] In place of the mechanistic notion of causality, introduced by Paolo Sarpi and his followers at the beginning of the Seventeenth Century, Kepler rejected such mechanistic notions of cause, in favor of Reason, as Kepler follower Leibniz insisted upon necessary and sufficient reason, in contrast to mechanistic-algebraic notions of "causality."[return to text]

85. As we go ever-deeper into the realm of the transfinitely small, it is through the application of the notion of inequalities to relative cardinalities, that the principle of measurement is preserved beyond the remotest possibility of any mere arithmetic.[return to text]

86. See A Manual on the Rudiments of Tuning and Registration, above, passim. Note also, that the supposed documentation on tuning by Alexander J. Ellis, editor of Hermann Helmholtz's On The Sensations of Tone [2nd edition, (New York: Dover Publications, Inc., 1954); Appendices, pp. 430-556], is fraudulent. The proof that the case for elevated, or variable elevation of pitch (such as Nazi Propaganda Minister Josef Goebbels' decreed international standard of "Concert A"=440) is fraudulent, is readily demonstrated by examining the scores of polyphony composed by Bach for use in relevant locations of organs treated by Ellis. No human chorus could have sung at the organ tunings Ellis suggests; J.S. Bach, as Michael Praetorius before him instructs, not only adjusted the pitches of the organ pipes, but transposed at the keyboard, to the effect of agreement with the requirements of the vocal polyphony. The characteristics of the Florentine model of bel canto singing voice, are the natural, biologically constrained characteristics of the human singing and speaking voice. The singing of poetry is the origin of polyphony, and thus of music.[return to text]

87. See Lyndon H. LaRouche, Jr., "Mozart's 1782-1786 Revolution in Music," Fidelio, Winter 1992, note 62, pp. 28-29.[return to text]

88. Also known as Motivführung. See Lyndon H. LaRouche Jr., op. cit.: "Musical Memory and thorough-composition."[return to text]

89. Thus, the clear superiority of conductor Wilhelm Furtwängler's work over that of his savagely jealous would-be rival Arturo Toscanini. Similarly, Sergei Rachmaninoff, like Toscanini's famous in-law, Vladimir Horowitz, had a prodigious concert-stage technique for his time; but, both were incurable Romantics. Neither Toscanini, nor the Romantic performers exhibited comprehension of the generative principle of "playing between the notes," which Classical compositions require. A once-popular anecdote about a mythical fundamentalist preacher, told of markings which his survivors found in their zealous exploration of his worn Bible. Notably, "text unclear; shout like Hell!" There are musicians, who, similar to that mythical preacher, will perform a passage they do not comprehend musically, by resorting to mere physical technique, for "setting off fireworks."[return to text]

90. The formal key to refutation of Kant's argument (in the Critique of Pure Reason, for example), is his use of the term "a priori." Reference the representation of an idea as the product of "One" and "Becoming," in the discussion of a model of strophic poetry, above.[return to text]

91. The cognitive collapse within that portion of the population of Germany affected by the so-called Brandt reforms of secondary education, should be featured evidence on this account. The difference between those who matriculated from a gymnasium prior to the so-called "Brandt reforms of education," and those educated in the same gymnasia after the reform, is the best example of the effect of the "New Age" reforms introduced as the "new math" and as the general 1963 program of international educational reforms proposed, with tragic success, by the Paris office of the OECD: not because the post-reform education in Germany is worse than in neighboring nations, or in the U.S.A., but because the resurrection of the Humboldt principles in post-Hitler Germany's gymnasia was the world's best secondary-education program of the entire post-war period. Thus, the contrast is more marked than in other countries, such as the United States, where public education is even far worse than in today's Germany, or in the pre-1989 Soviet Union.[return to text]

92. All physical science is usefully divided among four functionally distinct domains. Three of these are domains in which the senses as such are hopelessly inadequate as means for examining directly the relevant phenomena: the very large: astrophysics; the very small: microphysics; and biophysics as a study of the characteristics which distinguish living processes functionally from those which are not living. Betwixt astrophysics and microphysics, is the domain of sense-experience, macro-physics.[return to text]

93. As in Georg Cantor's notion of the series of Alephs existing beyond Aleph-null.[return to text]

94. During the 1948-1952 period of his initial discoveries, the candidate relied upon the celebrated William Empson's Seven Types of Ambiguity for the foil against which to test his own usage of the term "metaphor." Plainly, the candidate goes beyond Empson on several major points, but, to this day, he continues to warn students and others against retreating below the commendable intellectual standard set by the celebrated Empson. A "good pun" is one which (usually) keeps its perspective well above the waist-line, and which satisfies all of the criteria stipulated by Empson. Such a pun represents the highest form of humor, a fact which demonstrates something missing in the mental life of those who insist upon a contrary view.[return to text]

95. Increased density of mathematical discontinuities per arbitrarily chosen interval of action.[return to text]

96. In Platonic theology, as in Plato, God is the highest "Good" of this form, the efficient Idea, which is the Alpha and Omega of all existence, the Efficient Intelligence acting always, at once, in each and all place and time. There are other, lesser existences, which have the form of the Good, but which are not this Good. All great art, all true science, thus participates in God (capax Dei); all great music, all great art, all true science, has, thus, a sacred, a religious quality, inasmuch as its primary motive is love of truth, and love of that creative reason, within the individual person, which is in the image of God.[return to text]