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Dialogue of Cultures

How Bertrand Russell
Became An Evil Man
by Lyndon H. LaRouche, Jr.
July 28, 1994
Part 2

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This article is reprinted from the Fall, 1994 issue of FIDELIO Magazine. Footnotes to Part 2 and 3 are on a separate page. Click here for Footnotes to Part 2 and 3. (Window will stay open.)

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Part 2

Mind Over Mortality: A Lapsed-Time View

So, before proceeding further, we must now bring the rise and decline of Venice's "Brutish Empire" into focus, for the purpose of showing the coherence in all of these and related issues of the recent six centuries. The principled difficulty impeding the typical reader's comprehension of history is the cultivated habit of looking at the facts of history selectively, from the vantage-point of one's mortal, and ever-hesychastic umbilicus. It is chiefly that specific difficulty which we must overcome.

To the purpose of supplying a practical remedy for that impediment, let us employ a ruse of modern biology; let us apply the technique of lapsed-time photography to the six-plus centuries under review. By means of this experimental ruse, let us bring all of this span of history into the focus of the contemporary mortal individual's powers of perception, employing for that purpose the solution-method embedded in Plato's Parmenides.105 By reducing the facts of these centuries to that analog of a cinematographic representation, let us condense this history into the form of an experience by the mortal individual.

What the typical putatively educated individual believes about history is nonsense or worse, a kind of lie, in fact. It is nonsense according to the principle of fallacy of composition. It is a lie, because the individual's resort to such fallacy of composition is witting. He (or, she) is imposing a false philosophy upon the selection and interpretation of the evidence, and refuses, on the grounds of adhering to "our way of thinking," to entertain any criticism of the appropriateness of that philosophy itself.106 In that mode, those deeply embedded habits of both the street and classroom have taken on the quality of axiomatic mental and social behavior within the victim of such conditioning. It is important to provide that victim with a pedagogical prosthetic device, by means of which history is made accessible to him in terms of even his own limited powers of comprehension. "Lapsed-time photography" has an appropriateness which is more or less self-evident.

To assemble such a lapsed-time portrait of the origins, rise, and fall of Venice's imperial London, the configuration of more than six centuries of events is required: according to two principal types, under the governance of a third type, which latter is the interaction of the other two.

Instead of arraying the events and related facts in the foolish way the Eleatics and Sophists did, statistically, apply the lesson of Plato's Parmenides; adduce as the crucial facts of the series, the characteristic quality of change107 which defines the relationship among successive sets of events in the historic sequence. So, in the first series, we have changes which are generated by the principles of the Renaissance; in the second series, changes generated by the oligarchical principle of Venice and its accomplices; in the third series, the generating principle is the interaction between the first two series, this under the governance of the interaction between the first two generating principles. Thus is the analysis of historical processes rendered comprehensible, by examining them as processes composed through the interaction of types.

Consider some highlights of such a lapsed-time portrait of the key events themselves. A few key cases are sufficient to situate the case of Conti and Ortes:

Mid-14th Century: A chain-reaction of reversed leverage collapses the Venice-dominated semi-global financial system, throwing Europe into virtual chaos, and shattering temporarily much of the oligarchical power of Venice and its accomplices.
Mid-15th Century: The temporary reunification of the Eastern and Western rites of the Christian churches at the a.d.: 1439-1440 Council in Florence, sets into motion a revolution in political institutions, whose emergence threatens Venice's efforts to resume the levels of world-power it had enjoyed during the Thirteenth Century.
Late-15th Century: Venice launches a counter-offensive aimed at destroying the Renaissance. On the intellectual front, it mobilizes the Averroeist Aristotle of the Twelfth-through-Fourteenth Centuries gnostic cults. Otherwise, Venice's espionage and diplomacy recruits the Greeks of Mount Athos to betray Greece to the Ottoman conquest, and establishes an alliance against the Renaissance with the rulers of Moscow.
Early-16th Century: The Papacy allies with France and other powers of Europe, the League of Cambrai, in an alliance committed to destroying this usurious enemy of civilization, Venice. By 1508-1509, when the forces of the League are at the verge of crushing the adversary, Venice strikes back with its "fifth column" forces of corruption, to divide the allies of the League against one another. Venice then goes on the offensive, where its faction remains to the present day.
Early-16th Century: Venice uses its oligarchical assets in northern Germany to incite the schism led by Martin Luther. This schism is orchestrated by Venice's funding of the publication of Luther's works, by Venice's control over the finances of the Hapsburg Emperor Charles V, then also King of Spain, and by the "peace-maker" role of the anti-Renaissance Aristotelian, Venice's Gasparo Contarini.
1517-1582: Venice's intelligence services move in on a crucial ally of Spain and France, Tudor England. Venice assets in England, the Howards, deploy seductress Anne Boleyn to corrupt King Henry VIII.108 Henry's induced lust for the temptress renders him an obsessed fool under the control of Venice's manipulations. Relations of England to both Spain and France are not repaired after that until the period of the Napoleonic wars and their aftermath: after 1814, when the post-Vienna Congress France of the Restoration and Napoleon III becomes a de facto political catamite under London's imperial domination.109
1582 Onwards: Out of a factional affray within Venice's oligarchy, that faction, the so-called "Giovanni," led by one Paolo Sarpi, takes the leadership.110 Venice is committed to base its strategy upon developing the northern Protestant regions as its Nordic bastion against the anti-Venice forces of the regions, such as France and Spain, more closely tied to the Papacy. Actually, Venice is playing both sides in a "balance of power" game, as usual.
16th and Early-17th Centuries: Venice launches empiricism from among the followers of the Padua Aristotelian Pietro Pomponazzi, such as the notorious Francesco Zorzi ("Giorgi").111 After the Sarpi factional victory of 1582, the effort of Venice to destroy the scientific method of Plato, Nicolaus of Cusa, Leonardo da Vinci, et al. becomes more energetic, adopting figures such as Galileo, Francis Bacon, Robert Fludd, et al. as part of the deployment of empiricism to destroy the vitality of science from the inside.112
Early-17th Century: Venice orchestrates the launching of the so-called "Thirty Years War" of 1618-1648, destroying Germany and much of the rest of Central and Northern Europe, while finishing off the already broken power of Spain.
Pope Deploys Vatican Diplomat Mazarin to Become Candidate Successor to Richelieu in France:113 It was Venice's orchestration of perpetual conflicts between France and the Hapsburg interests which was bleeding Europe into a threatened "New Dark Age." The result is a somewhat stable peace, organized largely by Mazarin during the 1648-1652 interval. Mazarin's protégé, the most capable Colbert, becomes temporarily the power behind Louis XIV's throne (1662-1683).114
Beginning 1666, Venice organizes 130 years of almost continuous warfare and debilitating internal intrigues against its principal adversary, France,115 until the power of France is broken, and France goes virtually under British mandate in 1815.
Early-18th Century: London comes increasingly under the direction of Venice's intelligence controller Abbot Antonio Conti.
1763-1793: London organizes and then coordinates the French Revolution of 1789-1793. In 1763, Lord Shelburne employs Adam Smith to work on projects intended to bring about the destruction of France and the crushing of the aspirations for economic development and autonomy among the English colonies of North America.116 Shelburne, as Prime Minister of Britain, conducts secret peace-treaty negotiations with the newly independent American colonies and France; imposes Adam Smith's novel concoction, "free trade," as a condition of peace, intending thereby to bankrupt both the U.S. and France. In 1789, British intelligence assets such as the Duke of Orléans, Robespierre, Danton, and Marat, each and all directed by Shelburne's British foreign-intelligence service chief Jeremy Bentham, plunge France into the obscenities of the Jacobin coup d'état and rule.
Early-19th Century: After the defeat of and virtual British mandate over France, London prepares to destroy both the United States117 and its principal allies of the 1789-1815 wars against France. Against the U.S.A., it uses the opium-trading, treasonous "Hartford Convention" accomplices of Jeremy Bentham's British intelligence agent Aaron Burr. Against its former allies Spain, Russia, and Austro-Hungary, it deploys British intelligence's agent Napoleon III and the neo-Jacobin radical networks of British intelligence agent Giuseppe Mazzini.118
Close of 19th Century: London organizes for a coming Europe-wide general war, whose purpose is to finish off all European resistance to a "world-federalist" empire. The principal targets for mutual destruction in this war are Russia, Austro-Hungary, Germany, and the Ottoman Empire. The principal so-called "geo-political" motive for London's plans for such a general war is the collaboration, centered in proposed Eurasian railway development programs, between Russia's Minister Count Sergei Witte and France's Minister Gabriel Hanotaux. Should such projects mature, as Hanotaux and Witte intend, Britain's hopes of a world-empire were destroyed by the economic development of Eurasia which must result from carrying through Witte's policies.
Close of World War I: The utopian world-federalists, the hard core of the Venetian faction around Bertrand Russell and World War I British foreign intelligence chief H.G. Wells, takes over. London views the ruinous effects of the recent war as clearing the way for efforts to establish one-world government along Venetian utopian lines.
Following 1953: The death of Soviet General Secretary Josef Stalin clears the way for Moscow's capitulation to Bertrand Russell's demands for a nuclear condominium between the superpower blocs as a basis for developing the U.N.O. into a one-world dictatorship. The Anglo-American utopians move to unleash, beginning 1964-1966, an end to scientific progress ("post-industrial" paradise), aided by unleashing of the mind-destroying "rock-drug-sex counterculture" upon—first—the university youth-strata of North America and Europe.
Following 1989: The "collapse of the wall" is viewed in Prime Minister Thatcher's London as the end of the super-power controversy,119 clearing the way for the early transformation of the U.N.O. into a "one-world government" dictatorship, eliminating both the institution of the modern nation-state republic and scientific progress.

From the crucial decisions at the Council of Florence, until the present, is a span of 554 years. Since the bursting of the great Fourteenth-Century debt-bubble, which opened the way for the Renaissance to challenge Venice's oligarchism, is nearly 650 years. Although the institutions of statecraft created by the Renaissance were new, the underlying issues were not.

The evil of oligarchism is older than Babylon. In European history,120 the war between Venice and the Council of Florence is an echo of the war between the followers of Plato and those of the oligarchist Aristotle, or the uncompromisable conflict between the constitution of Solon's Athens and the oligarchic slave-system of Lycurgus' Sparta: that represents for us today a span of between 2,350 and 2,600 years.

Our immediate subject here, is that of recognizing the significance of the influence of an Ortes, more than two hundred years dead, not only upon Bertrand Russell et al., and on the relatively immediate fate of our world today, the United States included. Our subject is implicitly: How ought we to shape our practical response to current events? Our answer here, is that we must see current developments in light of roots which go back in a rather immediate way even hundreds of years, or even longer. To make that conception itself comprehensible in a practical way, we must leave the mechanistic fantasies of Cartesian space-time, and adopt instead a sense of real history, a sense of the "boundedness" of a period of time which stretches back thirty to a hundred and thirty generations.

The History of Chronology

Before resuming our examination of the 650-year process we have just illustrated with our series of highlights, let us attempt to define what a magnitude such as 650 to 2,600 years ought to signify to the way we may understand current events.

Roughly speaking, a glacial cycle is determined by astrophysical cycles at approximately 100,000 years, with intra-glacial warming periods of approximately 10,000 years.121 The existence of mankind on this planet is currently estimated, on the basis of evidence, to be not less than about two millions years. The most recent melting of the glaciation began less than 20,000 years ago, with the oceans levelling off at about their present levels during the middle of the Second Millennium b.c.: , about the time the ancestors of the Greeks were invading the Mediterranean region as "Peoples of the Sea" in their Viking-like craft, as described by then-contemporary Egyptian portraits.122 [see Box] The geography of most of Northern Hemisphere, the courses of major and other rivers, and the levels of the oceans and seas have been altered radically during the most recent 200,000 or even 100,000 years of glaciation.123

What a tiny fraction of human existence these recent 2,600 years of European history occupy—perhaps about 1%! Yet, the archaeological and other relevant objective demographic evidence is that the development of mankind's power to exist has been greater during the recent mere six centuries of post-Renaissance European history than during all human existence earlier—near to 0.2% of all human existence, at most. Thus, we know far more about man—respecting "human nature"—from the recent six centuries of the development and impact of European civilization than from all of the millions of years earlier. When we take into account the debt of European civilization's development to the impact of Jesus Christ's ministry upon the level of knowledge developed by Plato's Academy at Athens, the relative weight of the recent 2,500 years of European culture is truly awesome.

The key to that science of history which one must master to understand fully subjects inclusive of the Venetian case of Russell and the "Brutish Empire," is the distinction which sets mankind absolutely apart and above the beasts. Man is the only species which is manifestly capable of willfully increasing its power to exist—per capita and per square kilometer. This increase is premised upon discoveries, such as valid scientific discoveries of principles of nature, which, relative to any formal logical schema, have an axiomatic-revolutionary character.

The development of the human knowledge employed to this effect is the characteristic of human existence which does not exist within any animal species. Thus, the very existence of mankind, of particular societies, is never premised upon hedonistic traits such as those which characterize any animal species, or ordinary, simple interaction among the aggregate of lower life-forms within an environment. Human existence is characterized by the development of those ideas whose emergence, by the very nature of those ideas, impacts the power of mankind to exist, per capita and per square kilometer.

Thus, history can not be described in an actually rational form, except as it is viewed as the practical history of the axiomatic-revolutionary emergence and subsequent development and interaction of such ideas. The long sweeps of history, such as the conflict which has shaped the recent six centuries of European history, represent the unfolding and interaction of such ideas in their practice, and impact upon the development of precisely such ideas.

The concept of the punctum saliens, as identified by Schiller in his presentation of the principles of composition of tragedy,124 is also properly expressed as it has just been described here.

To understand historical processes, one must first apprehend a sweep of history in the terms outlined immediately above. One must then permit the types of ideas represented in that history to play out within one's mind as their stage. One must recognize that interplay within the actual history unfolding, in the sense of comparing the interplay of those types of ideas within one's own mind with the actual interplay manifest upon the stage of history.

One thus becomes, as a member of that audience, a participant in the history on stage, rather than a typical audience of "reckless bystanders," spectators commenting inanely upon the catastrophe they are witnessing. Such a participant in the audience of a Classical tragedy thus emerges from the performance a wiser and better person than entered the theater earlier. That is the principle of composition of Classical tragedy applied to the business of comprehending real history. That is the principle we are referencing by means of Socratic exposition here.

The moment we situate our personal identities within the domain of that view of the history of ideas, each of us is lifted out of the momentary span of our individual mortal existence. The moment we participate in the practical history of ideas as ideas, the span of six centuries on the Classical stage of real-life history becomes a drama in which we have a part, in which each of us has a relevant personal place. We assimilate, we act upon those ideas which are unfolding there. We able to assimilate those ideas, and to understand them as types. We are able to act upon those ideas, those types of ideas. Thus, efficiently, we are lifted out of the tiny confines of our mortal existence's time and place, into global history of ideas on the scale of centuries and longer.

That change in viewpoint affords us a far higher and vastly better prospect for comprehending the sweep of events in which our brief mortal existence is caught. It is from this vantage point that the formerly obscure becomes transparent, that the influence of Bertrand Russell today is efficiently situated in the influence of Conti's salon upon Eighteenth-Century Britain, and that Britain is situated efficiently within its true origins within the recent six centuries of Venice's efforts to eradicate the new institutional developments of the Golden Renaissance.

That situates us to examine more closely the efficient relationship among Conti, Ortes, William Fitzmaurice Petty (Lord Shelburne), and Russell. We examine next the crucial features of those changes which mark the transition of Bertrand Russell's precious David Hume, from a follower of Locke, into a follower, like Russell himself, of the Venetian Conti salon's Giammaria Ortes.

2. Russell: 'The Devil in the Detail'

Biology requires the investigator to rise above the methods of organic chemistry, and enter the higher domain of living processes. Similarly, to understand human behavior, one must leave behind "Brutish" methods of animal husbandry, to rise to the higher domain of that which sets all human behavior absolutely apart from and above all lower forms of life.

Were man a beast, the total number of persons living on this planet would never have exceeded a level approximately equal to that of the chimpanzees or baboons.125 By medieval European times, the population of this planet had exceeded man's primitive population-potential by decimal orders of magnitude. Presently, we have surpassed that by more than an additional such order of magnitude. [see: Figure 1] Had we employed adequately the levels of scientific knowledge developed by the time of the first manned landing on the moon, the potential population of this planet today would be about twenty-five billions persons, with a standard of living about that of the U.S.A. 1967-1969 or higher. Plus, we would have already begun, not only the exploration of, but colonization of space.

The distinguishing characteristic of all known human existence, and thus the characteristic feature of any species' standard for successful human behavior, is a continuing succession of increases in potential population-density, for which the only comparison among lower forms of life is successful biological evolution to a higher species of life-form.

This characteristic behavior of the human species is the generation of a specific type of ideas. These are those ideas which correspond paradigmatically to valid discoveries of more powerful principles of scientific knowledge, whether in natural science or Classical art-forms.126 The existence of the human species to date has depended absolutely upon such changes in man's relationship to mankind and to nature as have been generated by those types of ideas.127 In that strict sense, and no differently, it is admissible to employ the short-hand expression: the difference between man and lower forms of life is that the existence of the human species is determined by ideas.

It is the governance of human practice by ideas, as we define that here, which is the ordering principle of history. This is the principle which orders each among the types of successive events in a well-constructed lapsed-time image of history over a span of decades, centuries, or millennia.

Let it be understood at the outset of this discussion, that valid discoveries of scientific principle are but a paradigmatic portion of what the term "mental-creative processes" must be understood to signify. With that restriction, it is admissible to focus upon the crucial epistemological features of mathematical physical thinking. That provisional inquiry provides the starting-point for a systematic comprehension of the curiously perverted mental processes of the late Bertrand Russell. This also addresses a much larger, more fundamental issue, the role of transmission of ideas over centuries in shaping the history of the recent six centuries of European and global civilization.

This is of special importance as a prerequisite for understanding the British radical empiricism introduced to Adam Smith, Bentham, and Malthus by Ortes, and the bastard French offshoot of that radicalism, the positivism which emerged over the course of the recent two centuries from the post-Restoration circles of Abbot Moigno's followers. This is indispensable for understanding the systematic evil permeating all of Russell's known work in every field.

As indicated above, this author did not take Russell seriously until the middle-to-late 1950's. That re-examination occurred as an indirect result of the author's own discoveries of 1952.128 Those discoveries made readily transparent the vicious incompetence of Russell's mathematics work, notably the sophistry upon which the entirety of the Russell-Whitehead Principia Mathematica is premised axiomatically.

For the benefit of those who might wish to argue that that examination proved no more than that Russell was a nasty sort of idiot savant in the natural sciences, let it be taken into account, that once the scope of Russell's mathematical and related philosophical writings is considered from the standpoint of Leibniz, Riemann, and Cantor, the systematic features of Russell's evil, and his connection to Ortes' "methods of Galileo and Newton" are clear beyond doubt.

To that end, situate Conti, Ortes, Russell, et al. within a six-centuries' history of science, a history which both parallels and intersects the lapsed-time portrait sampled in the preceding section.

Principia Mathematica

Perhaps Mephistopheles began his corruption of the damned soul routinely with a very tiny little sin. Without doubt, that is the way in which what might seem to many an almost undetectable sleight of hand, a so very tiny apparent blunder, unfolds to become the irredeemable evil of the notorious Principia Mathematica. For reasons to become clear, the author can hear Johannes Kepler laughing happily in the distance from where he dwells, somewhere above.129

Only a tiny error? Tiny, like a leak in a Netherlands dike, and, as we shall point out, approximately as devastating.

In 1931, a very gentle, self-effacing young mathematical genius, an Austrian by the name of Kurt Gödel, submitted a paper which implicitly obliterated all of the mathematical work of Bertrand Russell, and also debunked some very pompous, related absurdities of hesychasts such as John Von Neumann. Considering the content of his remarkable paper, the degree of personal modesty with which Gödel presented his argument, both orally and in his now-famous paper, is fairly described as "awesome."

That paper is entitled, in its English translation, as "On formally undecidable propositions of Principia Mathematica and related systems I."130 In principle, the kernel of Gödel's point is an echo of the devastating proof against the Eleatic school supplied by Plato's Parmenides approximately 2,400 years earlier; the conclusion presented was well known to Leibniz,131 and had been addressed by such Nineteenth-Century titans of science as Gauss, Dirichlet, Riemann (as we shall note), Weierstrass, and also Georg Cantor.132 In short, the mathematical-physical principles of the case were laid down fully more than a decade before Russell's hoax, and three decades prior to Gödel's 1931 paper. The historic significance of the Gödel of 1931 is not that he had refuted Russell's sophistry, but that he had refuted Russell and the radical positivist school as a whole, on their own formalist terms. The resonating effect of his paper was therefore devastating at that time and later.

For our purposes here, we must address the same issue addressed by Gödel from a more fundamental, and traditional mathematical-epistemological standpoint, a more elementary and direct approach, that of Plato, Cusa, Leibniz, and Riemann. In any case, as will be reported here below, the origin of all of Russell's abortive attempts at gaining fame in mathematics is rooted in the attacks upon Gottfried Leibniz by Abbot Antonio Conti and his salon. It is by situating Russell's hoaxes with respect to whom Conti, Ortes, and Russell after them, are attacking, Leibniz, that the motive underlying the issues posed becomes adequately clarified.

Russell's putative contributions to Principia Mathematica133 touch a most crucial area of Leibniz's continued influence upon Nineteenth- and Twentieth-Century physical science. That topic is conveniently identified as the "continuum paradox." The relevant succinct statement of that topic is highlighted by citing two relevant passages from the last section of Bernhard Riemann's famous 1854 Habilitationsschrift.134 Consider the issue as referenced by Riemann there: Russell's methodological frauds in the name of mathematics in the Principia will be shown to embody the crucial implications of the entirety of radical empiricism.

From the referenced White translation of that Riemann work, consider the following:

... there subsists an essential difference between mere relations of extension and those of measurement: in the former, where the possible cases form a discrete manifold the declarations of experience are indeed never quite sure, but they are not lacking in exactness; while in the latter, where possible cases form a continuum, every determination based on experience remains always inexact, be the probability that it is nearly correct ever so great. This antithesis becomes important when these empirical measurements are extended beyond the limits of observation into the immeasurably great and the immeasurably small. ... [W]hile in a discrete manifold the principle of metric relations is implicit in the notion of this manifold, it must come from somewhere else in the case of a continuous manifold. Either then the actual things forming the groundwork of a space must constitute a discrete manifold, or else the basis of metric relations must be sought for outside that actuality, in colligating forces [darauf wirkenden bindenden Kraeften] that operate upon it [emphasis added—LHL]135

A few lines later, appears Riemann's electrifying concluding sentence for the dissertation: "This leads into the territory of another science, into the domain of physics, which the nature of today's occasion [on the subject of mathematics] does not permit us to enter."136

Kepler, reflecting on his 1611 "Snowflake" booklet, would be very much pleased by that work of Riemann. To the careless observer, everything which is of fundamental importance in mathematics is disregarded as trivial, because it seems to him to be nothing in scale. We shall find Riemann's "immeasurably small" playing a crucial role in the work of Plato's Academy, about 2,450 years ago, as also up to the most recent work in exploring the "virtually null-dimensional" realities of modern nuclear physics.

Russell, for example, was familiar with this work by Riemann, and its relevance as counter to his own opinions.137 Yet, virtually no contemporary mathematician representing a positivist view like that of Russell, Von Neumann,138 or information-theorist Norbert Wiener139 has proven himself capable of understanding the crucial point made by Riemann in that passage.

From the standpoint of formal mathematics, the "continuum paradox" signifies that every effort using formal logic to perfect the continuity of a line, a surface, solid "space," or "space-time" fails. The failure is small, but its smallness does not lessen the fact that the failure is an efficiently devastating one in its effects. How small? "Immeasurably small," virtually null-dimensional.

Kepler, be assured, is chuckling again.

Riemann's "immeasurably small"140 is an ironical choice of descriptive term. These apparent lapses in the continuum, which no formal logic can bridge, are mathematically "virtually null-dimensional"; they have no lower limit to their measurable degree of smallness, yet the presence of their discontinuity can not be eliminated. They are what we must call "true singularities." Not only is formal logic unable to rid mathematics of their most abundant presence, but they have an extremely significant role in physics, as we shall identify one example of that at the appropriate place below.

Russell and his admirers have no defense against this. The continuum paradox was not dreamed up by Riemann. It is the central feature of Leibniz's Monadology.141 It involves a phenomenon central to the mathematics work of Plato's Academy. It was central to the work of Kepler before Leibniz, and was a central concern of such followers of Carl F. Gauss as Riemann's teacher Lejeune Dirichlet,142 and Karl Weierstrass, among numerous others. In the history of science, rigorous treatment of this problem is as old as the treatment of both "incommensurables" and the "Platonic Solids" by the mathematicians Plato, Eudoxus, and Theaetetus at the Academy of Athens. Modern science was founded on the basis of recognizing a crucial further implication of this problem.

While we conduct this necessary, and brief excursion, the reader should not lose sight of our purpose here. The issue is not a formal issue of mathematics and mathematical physics. This is being addressed here only in the degree this important detail of mathematical-physical principle is key to understanding the implications of Conti, Ortes, and Russell, and the historical implications of radical empiricism in general. The background for this is summarized now.

The Principle of Metaphor in Science

Although the roots of modern science are found in Plato's Academy of Athens, modern science as such began with Nicolaus of Cusa's De Docta Ignorantia,143 published in the setting of the 1439-1440 Council of Florence. It was Plato's Academy which first supplied a rigorous treatment of the problem of the "immeasurably small." The central formal feature of Cusa's breakthrough in mathematical science was his application of the solution-principle of Plato's Parmenides144 to effect a correction in Archimedes' constructive efforts at quadrature of the circle. Cusa's work bears directly on the issue of the same "immeasurably small." This case bears directly upon the central fraud of Russell's work in mathematics, a fraud which is also central to all radical empiricism and its positivist derivatives.

All of the issues to be addressed in exposing the implications of Russell's mathematics are covered in the present author's "Metaphor" series referenced above. Thus, taking into account the limited purpose of addressing this matter here, it should be found sufficient that we consider with minimal delay the several successive conceptions which are indispensable here, and refer the critic of our argument here to those earlier locations where the sundry aspects are treated at some length.145

(a) The Four Types of Mathematical Ordering

To bring the issues within the scope of the reader whose mathematical education is somewhat less than professional, the relevant features of Archimedes' approach to quadrature and of Cusa's correction of Archimedes' error, are summarily as follows.

The term "quadrature of the circle" signifies an attempt to construct a practical estimate of the value of a number, π, which represents an estimated ratio of the length of the perimeter of a circle to that circle's diameter.

Insofar as records exist, the more rigorous proof of the existence of a class of magnitudes not congruent with rational numbers was developed by Plato's Academy, following the lines of prior work by Pythagoras et al. As the geometric proof of the famous Pythagorean theorem is exemplary of this conception, there exists a class of magnitudes in geometry which can not be rendered congruent with rational numbers: incommensurable magnitudes, such as the hypotenuse of a right triangle. However, by use of the principle of geometric proportions, we can place these incommensurables between two magnitudes which are congruent with rational number orderings, showing that the incommensurable is less than the one of this pair, but greater than the other.

This concept was embedded in a tactic employed by Plato's student and collaborator Eudoxus, the "Eudoxian method of exhaustion," which was used by him and other Greeks to perform an early form of integration, treating the incommensurable volume of a pyramid or cone, for example, as a subject.

Archimedes used this Classical Greek method of Plato's Academy for his theorems on quadrature.

Choose a circle. Simultaneously inscribe and circumscribe regular polygons of an equal number of sides. [see: Figure 2] Increase the number of sides, at a constant rate of doubling, to a very large number. Since the radius (to the point of tangency of the circumscribed, or the apices of the inscribed polygon) remains constant, calculate the variable length of the relevant side and area of each of the triangles of which each polygon is composed. Determine thus, the perimeter and area of each of the respective pair of polygons. Average the perimeters and areas. By this method, without further improvement, the arithmetic value of π may be measured to any desired decimal precision for such purposes as carpentry, plumbing, or ordinary engineering tasks.146

Can it be assumed, therefore, that the series of polygons 2n converges upon identity with the circular perimeter? "No," replied Cusa: the polygonal and circular perimeters are of different "species," of which the circular species is higher.147 If one chooses a length of side no greater than 10−33 centimeters, and a diameter of the circle greater than any specified estimate for the size of the universe, there will always be a gap between the polygons and the circle; on other grounds, too, there will be progressively less congruence between the polygonal and circular perimeters as the number of sides is increased.148

At that point in the construction, Cusa made the discovery which set into motion the development of modern science. He stated that this construction proved that the circular perimeter is of a higher species of existence than the polygonal. Earlier, Plato's Academy had shown that measurable magnitudes were divided between two species, rationals and incommensurables. So Archimedes had viewed the matter; it had remained at that level until Cusa. Now, Cusa had shown that the incommensurables were divided into two mutually exclusive species; the first we term today the "algebraic" magnitudes; since the work of Leibniz and Johann Bernoulli during the 1690's, the second, the higher species discovered by Cusa has been identified as either the "non-algebraic" or, more commonly today, the "transcendental" domain. Later, Georg Cantor added a fourth species of magnitudes, the higher "transfinites," or "Alephs."149

So, we have, in succession, in order of rising cardinality (increasing "power"), four species of magnitudes: rational, algebraic, transcendental, and the higher transfinite species. Each of these four mutually distinct species of magnitudes is separated from its successor, of the higher species, by a gap, such that the higher can not be accessed formally from the predecessor, although the lower can be accessed from the standpoint of the higher. This gap in the upward succession is termed a logical discontinuity, or a singularity.

Cantor's Alephs, the domain of the higher transfinite, has the included physical significance of corresponding to what Riemann references in the cited location as "the immeasurably small" (Unendlichkleinen). We might term this the domain of "the virtually null-dimensional." This notion of such discrete and also efficient existences (e.g., objects) which have "virtually null-dimensional" magnitudes, has a very precise, central significance in the branch of physical science called Physical Economy.150

It must be recognized as a principle of knowledge, that no student could ever come to know a previously developed axiomatic-revolutionary discovery of valid principle unless the student has, in effect, replicated the original mental act of discovery by reliving it. That principle is most aptly illustrated by applying the solution-principle which Plato embeds implicitly in his Parmenides to the study of the four successive levels (powers, cardinalities) of mathematics just listed here.

This must be understood to recognize the devilish effect of the radical empiricist method in destroying essential faculties of judgment in its credulous victim. The close examination of Cusa's discovery of what we term today the "transcendental" domain from the standpoint of Plato's Parmenides, is the most direct way of illustrating the principle of creative reason in mathematics discovery.

Cusa's treatment of Archimedes' attempted quadrature of the circle is among the best conceivable illustrations of Plato's Parmenides. We employ that connection pedagogically here.

One of the simplest ways to set up the increasingly precise estimation of the rational approximation of π, after Archimedes' theorems on quadrature, is the following. Again: begin with squares, one inscribed in the circle, the other circumscribed. Then make finer approximations in a succession determined by halving the angle between the points of tangency of polygon to circular perimeter. This defines a general case for paired polygons: 2n [n ≥ 2] sides. For each value of n

2, there is a corresponding estimate of a numerical approximation for |π |

The resulting, indefinitely extendable series of estimates, π : F(2n),

can be regarded in the light of the Parmenides as a "Many." What is the unity which subsumes all of these elements of the "Many" into a "One"? The answer, in modern language, is to treat the "Many" as a Cantor type. The answer is, thus, the change from 2(i) to 2(i+1). From the standpoint of geometric construction, the change is clear enough151 ; Cusa's recognition that circular action is a higher species of mathematical existence than algebraic magnitudes, flows directly from this.

The result is the recognition that the set of interdependent formal axioms and postulates of so-called "Euclidean" geometry must be superseded by adopting circular action as such in place of the so-called "Euclidean" axiomatic definitions of point and line, that we must abandon the notion of unbounded space-time,152 and that we must accept Nicolaus of Cusa's, Pacioli's, Leonardo da Vinci's, and Kepler's notion of a bounded physical space-time.153

(b) The Method of Mathematical Discovery

Once we have established ourselves in Cusa's domain of the transcendental, all of the arithmetic and algebraic realms, respectively, are accessible to us as a special, subsumed case of the transcendental. One can always reach the lower, the more primitive from the higher; the problem is, one can not reach the higher by a deductive analysis of the lower. How, then, does one reach the higher for the first time?

That question is the focus for all of the culminating work of Immanuel Kant's life, his famous Critiques.154 From the standpoint of a thoroughly Aristotelian formalist such as Kant, Plato's proposal that one discover a single unifying principle for the "Many" addressed in the Parmenides would be to go outside the deductive-inductive mode of formal logic, and to arrive at the answer by means of a "leap." That is the formal basis for Kant's obsessive vendetta against the work of Leibniz. That locates the crucial point at issue between Mosaic and Christian tradition, on the one side, and the Aristotelians, such as Pomponazzi and Kant, on the opposite side. This is otherwise known in the Classical literature as the issue of hypothesis; we shall come to that below.

Before addressing this matter of the apparent "leap," let us grant, since it is demonstrated to have occurred so often in history, that the "leap of discovery" bringing mankind to use of valid new principles does occur, and that successful students do relive many such leaps as an integral part of their educational experience. Acknowledging for the moment, the fact that this does occur, how do we represent the fact of this occurrence in physical science? Use the mathematical examples just referenced to show the answer to that question.

Pause for a moment to consider the following thought. Permit us to introduce at this point of the discussion what might appear to some an arbitrary definition. Let the reader understand, that from this point on in this text, we are using the terms "power" and "cardinality" interchangeably. On the one side, we are introducing this ascribed equivalence in the sense Georg Cantor, for example, employs the "sieve" of Eratosthenes to provide the student an intelligible notion of the equivalence of "power" and "cardinality" in number theory.155 As will be indicated below, the present author's discoveries in physical economy show that this notion of "power" has a most important physical significance, in addition to a number-theoretical one.156 With that in view, this special emphasis upon the use of Cantor's notion of "power" is underscored at this present instant.

In ascending "power" (cardinality), today we know four species (types) of mathematical functions: A = rational numbers; B = algebraic functions; C = non-algebraic, or transcendental functions; D = higher transfinite functions, beyond the transcendental. Access to the higher, successor species of function from a relatively lower is blocked by a formally impassable gap, a discontinuity, a singularity—although there is no difficulty in passing from higher to lower. This gap is "immeasurably small,"157 yet formally impassable. Consider: what knowledge can be extracted from these several facts of the history of mathematics?

At the implied insistence of Kepler, perhaps it is indispensable pedagogically that the crucial mathematical feature of Cusa's discovery of the transcendental domain, the ontological reality of the existence of the immeasurably small, be stressed again at this immediate juncture.

The commonplace fallacy of such persons as Isaac Newton, Samuel Clarke, Felix Klein, and Russell's besotted admirers among mathematicians, is to abandon the standpoint of Classical constructive-geometric rigor in thinking, in favor of a flight into the domain of arithmetic-algebraic fantasies: to assume that the apparent convergence of infinite series upon a boundary value signifies ultimate congruence with that boundary. In short, that there are no true discontinuities, no true singularities.

As we have illustrated the conception, by using a side of a regular circumscribed polygon no larger than 10@ms33 centimeters for a circle larger than any assigned size of the universe, it is impossible to conceive any point at which the persisting existence of an unbridgeable gap between polygonal and circular perimeters might dissolve from definiteness into fuzziness. The existence of the gap is not merely persistent, but absolute.

By constructive-geometrical rigor, we are emphasizing at this moment the notion that equivalence is dependent upon congruence by virtue of "hereditary" implications of a method of construction. That equivalence and congruence so defined must be shown in that way. Something is a part of the series of events of which it is generated as a part. For example, by this definition, the value of the hypotenuse of a 3,4,5 triangle is not the rational number "5," but the irrational (algebraic) number "5.000...000... "; a number is the way in which it is generated, by the function which it performs, rather than what it appears to be as viewed in isolation from the context in which it occurs.158

Cusa's discovery of the transcendental domain, not later than a.d.: 1440,159 was prompted by recognizing that this ineradicable gap between the perimeter of the "infinite" polygonal series and the circle is a difference in (what we term here) "power," or cardinality, placing the circular action in a higher species, unreachable by the polygonal series of algebraic numbers.

Each of the three higher species of magnitudes—incommensurables generally, transcendental, and Alephs—were discovered by a mental act comparable to the implicit solution-principle for the ontological paradox which Plato poses by his Parmenides. The apparent "leap of discovery" in each such case corresponds to the "gap" of singularity which separates the lower species from formal access to the higher.

Let us apply to that ordered series of species (of mathematical function) the same Parmenides solution-principle which Cusa applied to Archimedes' quadrature theorem. Let the succession A, B, C, D be the "Many." What is the "One"?

In Plato's theory of knowledge, each of the "leaps" corresponding to a singularity is a phenomenon of mental life designated as an hypothesis. Thus, for this case, we have hypothesis AB (the leap from A to B), hypothesis BC, and hypothesis CD. The question implicitly posed by comparing this situation to that of the Parmenides is whether or not there is a common principle of change which generates B from A, C from B, and D from C? If so, then that intelligible form of a principle of change represents what we know as an higher hypothesis. If, in science and Classical art-forms, there are several valid choices of higher hypothesis, the question, whether these are commonly subject to some higher, subsuming principle connotes hypothesizing the higher hypothesis.160

That quality of knowledge which corresponds to the solution for such a gap, i.e., hypothesis, is the proper definition of the term "metaphor."161

Kant, the least irrational of the historically prominent Seventeenth- and Eighteenth-Century opponents of Leibniz, professes to see something intrinsically unintelligible in the very idea of human creativity. On the premise of that false assumption, Kant rejects the Platonic principle of discovery (hypothesis) used by Leibniz. It is against the background of that Kantian formulation of the issue that Russell's mathematical follies—and those of all the modern positivists, such as such Russell followers Karl Korsch, Rudolf Carnap, and Von Neumann, as well as Norbert Wiener—are strictly identified and understood for what they are.

Essentially, these radical empiricists deny that human creativity actually exists. One might wonder, whence apostles of such an irrational dogma fetch the temerity162 to describe themselves as scientists?

(c) The Demographic Evidence

This creativity, which the empiricists, and the Aristotelians generally insist does not exist, is expressed most plainly in its essential function as the characteristic of the continued successful existence of society. It is, thus, nothing less than the successful existence of the society itself, which these misguided fellows overlook.

The British empiricists, and Aristotelians generally, place great emphasis upon sense-perception, but slyly evade those relevant sense-perceptions which would shatter their foolish philosophical prejudices. For an inhabitant of modern history, the evidence of the recent six centuries' changes in the population-density, productivity, and consumption of society is overwhelming evidence against most of what is either explicitly taught or implicitly assumed as philosophy and scientific method in universities today.

The "hard factual basis" for examining the effects of creativity, or its absence, upon the possibility of society's successfully continued existence,163 is called the science of physical economy.

It is shocking, and unfortunately commonplace, to encounter a professional scientist who blunders ahead in life, in blind ignorance of the existence of the physical-economic process which exists more despite today's financial markets, than by aid of them. If scientific ideas are sound, must they not imply a potential for increase of man's power, per capita and per square kilometer, over the universe? Is that relationship not a measurable one?

Those considerations are introduced at this point of the report, as precondition for locating the physical significance of the "immeasurably small" in a matter of no less importance than the successfully continued existence of mankind.

For any reasonably intelligent person who has a working experience with the management of modern manufacturing or modern agriculture, including skilled industrial operatives, no further special training is needed to guide one's hand in marking out a set of linear inequalities which fairly describe the prerequisites and effects of improvement, in terms of per capita, per household, and per square kilometer, in the productive powers of labor.164 Once that had been done, one would do two obvious things: (1) Examine the changes in productivity and composition of the social division of labor since the founding of our Federal republic in 1789, and (2) Examine this economic history of changes from the standpoint of the forecast of such changes supplied by U.S. Treasury Secretary Alexander Hamilton in his December 1791 Report to the U.S. Congress "On the Subject of Manufactures."

Mankind exists by producing. Our households consume to exist, to be productive, and to develop the institution of the household and of the persons within it; our farms, factories, and essential infrastructure consume to continue to exist, to develop, and to be productive or otherwise useful.

If we wish to compare the two processes, consumption and production (or other necessary forms of output), we must define the labor-force as a common parameter of the households and of the sundry forms of both the productive and other necessary sorts of analogous enterprises. We treat the household as a whole as a culturally determined function of the reproduction of the members of the labor-force. We measure these functions of consumption and production in the place where they occur (principally), by relevant kind of land-use classifications for each such activity.

We have thus defined the general requirements for allotting statistics, according to total land area, and land-use portions, and in terms of values stated per capita, per household, and per square kilometer. We must incorporate "market baskets" as a way of expressing the relationship between the supply of necessaries and their consumption.

To shorten the account, in keeping with the purpose for which these matters must be mentioned at this juncture, our next step is the labor of refining the notion of "necessary consumption." Consumption for production by agriculture and manufacturing, for example, is readily understood by anyone familiar with the industrial-engineering preparation and use of bills of materials and process sheets. Since objective requirements of production processes are readily approximated, at least as a matter of principle, the problem area of that ongoing inquiry is soon narrowed to the matter of functionally necessary consumption of physical goods by households.165

In this direction of inquiry, the variable area on which attention must be focussed is soon narrowed to consumption of physical goods plus necessary levels of certain categories which are best identified as "infrastructure." We employ "infrastructure" to signify something which is not directly consumed by households or goods-producing enterprises in separable units, but whose presence or absence, diminution or increase, affects the productive powers of labor in a variable way. These include what we may term "hard infrastructure," such as water management, general land-improvement and sanitation, general transportation, general supply of power, general urban and related infrastructure. These also include certain rather well-defined areas of "soft infrastructure," such as general requirements of education, health-care, scientific development by both households and productive and related enterprises. This combination of physical goods and infrastructure embodies the variable determinants of potential levels of net productivity of society as a whole.

Thus, for example, the quality of constructive leisure, education, health, technological advancement, and general physical consumption by the household, has a functional bearing upon the relative potential productivity of average members of households with those consumption and related characteristics.

Successfully continued survival may be expressed as a functional conception: potential relative population-density. This notion combines, statistically, notions of per capita, per household, per square kilometer, for land-use, for consumption of physical goods, for hard and soft infrastructure. This bears upon life-expectancies, health-expectancies, school-leaving age, adequate public libraries, and so on. This is packed together thus as what is usefully termed "general demography."

Sitting up, after a spate of working through such historical studies of the recent two centuries of the U.S. economy, one has a sense of something very special about the recent six centuries of western European civilization. Look at the changes in the social division of labor! It is as Alexander Hamilton described it in his "On the Subject of Manufactures"!

As recently as the first decennial U.S. Census of 1790, the U.S. population was more than 90% rural; yet, relative to medieval Europe, this represented already a very advanced degree of urbanization. Relative to medieval Europe, most of human existence, then and earlier, had been truly wretched. For countless millennia, prior to the Golden Renaissance, much more than ninety percent of the population toiled with the soil, to provide itself a precarious hold upon a meager existence.

If we assume today, that over 60% of our total labor-force should be employed in either manufacturing or infrastructure, with less than 2% rural component required by modern technology, the majority of the employment in manufacturing should be in the capital goods sector, and a growing portion of that in the machine-tool sector, with between 5% and 10% of the total labor-force employed in either scientific development or related pursuits—the latter in order to keep the rate of flow of new technologies adequate to human needs generally.

These changes in the social division of labor are functionally related to the increases in potential population-density. That is to emphasize the rapid reduction of the average amount of land-area which is required to sustain the average person in a demographic well-being better than his or her parents and grandparents.

How has this occurred? Through the mutually reenforcing relationship between pure scientific progress and the investment of that scientific progress, as improved technology, employed in a capital-intensive, energy-intensive mode in increase of the productive powers of labor per household, per capita, and per square kilometer.

How did this function prior to the mid-1960's shift to a "post-industrial," "countercultural" cultural paradigm? How was it that one U.S. penny invested in President John F. Kennedy's aerospace "crash program" of the 1960's returned a fairly estimated fourteen cents to the U.S. economy? One would think every scientific thinker with a conscience would have posed and answered such a question.

The cycle begins in "pure science." To demonstrate a discovery, a proof-of-principle experiment is required. This latter is expressed in the construction of some sort of apparatus. Once a satisfactory experiment has been conducted and suitably refined, the refined form of the experimental design becomes the basis for adding a new, improved machine-tool principle to the repertoire of capital-goods designs available, and of product and process designs, too. The flow of improved machine-tools and related benefits, as investment, into production, combined with the flow of newly developed knowledge, results in a spreading increase in productivity of labor per capita, per square kilometer.

Put that type of scientific discovery, from which this benefit is ultimately derived, under an appropriate kind of microscope of the imagination.

The possibility of a formal mathematical physics rests, in first approximation (at least), upon achieving an approximate deductive consistency in the mathematical representation of the perceived physical relations which are chosen to be abstracted from the real process considered. In that degree, such a formal physics describes a consistent, open-ended theorem-lattice, such that all possible theorems which might exist within that lattice (within the bounds of consistency) are mutually consistent with one another and, above all, with each and all of the relevant set of underlying, axiomatic assumptions—stated, or implied.

To the degree we signify such a mathematical physics, we are implicitly obliged to recognize a qualitative distinction between the one kind of discovery, which is the generation of an added theorem to be incorporated in that lattice, and a discovery which forces the replacement of that entire lattice by a new one. Looking at the second type of case from the standpoint of the formalist, the new theorem is of a type which implicitly overturns one or more of the axiomatic assumptions underlying the previously accepted theorem-lattice. In other words, the discovery has an "axiomatic-revolutionary" character.

The following crucial observations on discoveries of the second type are now to be identified and then examined.

1. The discovery of each of the three higher species of mathematics is exemplary of a discovery of the second, or "axiomatic-revolutionary" type.

2. All such discoveries are of the type represented by the solution-principle of Plato's Parmenides.

3. Each axiomatic-revolutionary discovery, just because it is axiomatic, is unreachable deductively from the relevant theorem-lattice which it overturns. It is thus defined by an absolute discontinuity of this formal type. This discontinuity, or singularity, is effectively virtually null-dimensional.

4. All valid such axiomatic-revolutionary discoveries therefore form a series of a type or types.166

5. The axiomatic-revolutionary character of the discovery has the dimensionality of axiomatic change.

6. The nature of the axiomatic transformation effected is reducible to a type of such change.

7. Thus, the discontinuity marking such discoveries of the second type is virtually null-dimensional, but not empty. It has the qualities of change and power; it has the quality of causality.

What is the size and weight, the mass and velocity, of the thought which represents such a second type of discovery? Is the result not that which we associate with the impact of an increase in power? Is there some connection between the type of thought which prompts us to equate "power" and "cardinality," and "power" of the type we associate with man's increased power over nature per capita and per square kilometer?

Before suggesting the answers to those questions, consider the same demographic facts just outlined from a slightly different vantage-point.

(d) What Should 'Negentropy' Signify, If Anything?

Once it is discerned which produced elements of consumption are necessarily variables or simply preconditions for a certain level of productivity with a certain level of technology, express this as required input to the demographic process. Term this the relative "energy of the system." Compare this with the rate of output of those same types of components. The difference in magnitude between the two (per capita, per household, and per square kilometer) may be viewed as the relative "free energy" of the process. The ratio of the two, "free energy" to "energy of the system" yields a "free-energy" ratio.

In any healthy economy, that "free-energy" ratio is rising, per capita, per household, and per square kilometer. However, as inspection of physical-economic history over the recent six centuries shows, the maintenance of this needed "free-energy" ratio depends upon increase of the relative "energy of the system" per capita and per square kilometer:167 without an increase in the capital- and energy-intensity of the economic process as a whole, as well as at technologically advanced points of production, the net physical productivity of labor can not be improved, or even sustained.168

This is not only an ostensibly anomalous picture of any healthy state of a modern economy; it is crucially paradoxical. No ordinary thermodynamic representation of this is possible.

The cause of this anomalous correlative of successful economic growth is clearly defined, by isolation. Speaking paradigmatically, this cause is investment in scientific-technological progress.169

In making the statistical estimates which correspond to this case, we must discount the fact that the economies of so-called metropolitan countries have been heavily subsidized, during recent decades, by relatively very large net flows of capital out of the developing nations economy into London, etc. Without those subsidies of the "formerly industrialized nations" by the so-called "Third World" nations, the industrialized nations of the northern tier would have collapsed more than a decade ago.

The spectacle of post-1963 Britain collapsing into a "post-industrial rubbish-heap," while the London financial center ostensibly prospers from those profits of pure swindle called "invisible earnings" from foreign sources, typifies the need for discounting the statistics to reflect the net physical-economic growth generated through improvements in the national economy's own performance at home, and also net contributions to improvements in the global economy taken as a whole.

To resume the discussion of the thermodynamically anomalous picture of sustained growth: in brief, any economy which collapses into a state of "zero technological growth" will collapse from cumulative technological attrition (unless it postpones this collapse by looting other economies). It is infusions of what Hamilton named "artificial labor,"170 which are the source of the apparent "not-entropic" character of any successful physical-economic process, that is the source of the increased "power" over nature, per capita and per square kilometer.

There is only one place in mathematics in which this kind of power-function is found. Consider, for example, Cantor's series, Aleph-1, Aleph-2, Aleph-3, ... . Each term is of higher power than its predecessor, yet the entire series is of a strict type. Indeed, strictly speaking, the successive Alephs, from Aleph 1 upwards, should not be treated as simply successively higher types (species), but rather as the domain in which cardinality supersedes ordinary notions of denumerability in the function of ordering-principle. They form a series (a type) whose characteristic change is increase of power.

What ought we to signify by such observations? We must move beyond the territory of mathematics, into the domain of physics.171 To recognize that there is interdependency of the thermodynamically anomalous phenomena of sustained growth of modern economies with the "causal factor" of scientific discovery measured as a virtually null-dimensional singularity, is the key to economic science, and also the key to the history of physical science in general.

Look first at the biogeochemistry172 of the economic process. The planet Earth is a bounded system. The entire universe is a bounded system, too. Therefore, throw away, as useless for any practical application, the Cartesian manifold as employed by Galileo and Newton, et al. Look at the bounded processes whose development and character are essentially internal to the planet Earth; see this through the eyes of the Kepler-Gauss use of the subject of Pentagramma Mirificum as a way of furthering what Plato began with his understanding of the implications of the so-called Platonic Solids. Begin with our planet, and see our planetary civilization's changing relationship to the universe at large, in terms of the interaction of those two layers of bounded processes.

Look at the Earth, as if from nearby space. Look at what Vernadsky defined as the noosphere, which, today, is the relatively shallow covering of this planet inhabited by regular human activity. This stratum extends downward from the planet's land and water surface through mining; the balloon, the dirigible, and the application of Leonardo da Vinci's and Bernhard Riemann's anti-Helmholtz hydrodynamics to powered flight173 have extended man's reach upward. We have moved from the heights of balloons to the geostationary orbit around Earth which is our future base for an interplanetary travel freight and passenger terminal. Technology in sight will permit us to bring mankind's personal reach into space to within the limits of the asteroid belt, to limited Mars colonization by a "science city" base for astrophysical and related researches.

Already, the boundedness of the universe was shown not only by Plato's recognition of the implications of a delimited possibility for partitioning the interior surface of a spherical shell, but by Leonardo da Vinci's recognition that the radiation of light was bounded by limits upon a potential rate of retarded propagation, as this was measured by Christiaan Huyghens' student Ole Rømer in 1677, and used successively by Huyghens, Johannn Bernoulli, and Leibniz to establish the foundations for a modern physics of a complex variable.174 I am certain I hear Kepler acknowledging that this is consistent with his standpoint. As he would agree, most emphatically, there is a reciprocity between the boundedness of the universe in the large and the continuum paradox encountered in the "immeasurably small." If one wishes to master economic science, these matters must be mastered; if we wish the human species to survive the sundry looming threats variously nearly or distantly visible before us today, we must master that quality of economic science.175

Accordingly, the statistical application of economic science begins with the examination of the historical development of this relatively thin spherical shell, which Vernadsky locates as the noosphere. To help to overcome the fear and confusion which modern education fosters respecting anything to do with scientific work and conceptions, we must seek to bring home to the reader a sense of the reality of the subject-matter within which this unavoidable anomaly appears.

To afford the reader a sense of the concreteness, the reality of the work of applied physical economy, some of the features of statistical applications are now described briefly.

The core of the special problem in this case, is that economic processes are, on the one side, readily measurable, but, on the other side, those measurements themselves produce results which are not consistent with today's generally accepted notions of statistical or other mathematical functions. That is the anomaly. That is the source of the feeling of eeriness which the typical science graduate suffers when confronted with the simple showing of this anomaly.

Therefore, it should be most helpful to such readers, emotionally and otherwise, to situate the anomalous phenomena in their concrete setting. Then, the characteristics of economic science lose much of their strangeness, and the special problem of "negentropy" is more readily comprehended.

Review summarily the policy for applied physical economy specified by the Executive Intelligence Review News Service, Inc.176 Presume that the reader had a modern personal computer of relatively large capacity and power. Presume also, that, given this facility, and some talent in using such devices, that reader were to wish to set himself or herself up "doing applied physical economy."

Start with the graphics; it is crucial that the work begin with the graphics.

Start with an animatable Earth-ball, whose average surface of reference is the relevant, very thin ellipsoid shell situated slightly above sea-level. This should permit one to view Earth's physical geography as it appeared circa not later than 18,000 b.c.: , with projections of likely geography up to, at a minimum, a.d. 2200. It would be useful to have also one of the relatively low-cost and reasonably accurate animatable astronomical maps, to enable one to look at the night sky on any assigned date from any part of the planet back some eight-thousand years, or something approximating that.177 In addition to astronomy, correlate weather and other global phenomena with this Earth-ball model.

Correlate this Earth-ball with a collection of two sets of regional and local electronic maps. Use the positions of latitude and longitude on the Earth-ball to make this correlation. Two master sets of regional and local maps are required: physical geography, and political geography. These must be correlated with a cell-grid system, common to the physical and geographical maps, whose grid correlates geodetically with latitude and longitude. On the mapping of physical geography, the customary features of physical geography are located functionally. Man and his activities otherwise are located on the political mapping. The two mappings are overlapped in terms of land-use parameters.

The political mappings are, from the top down, continents, regions, nations, regions within nations, states (analogous to U.S. Federal states), U.S. counties, or analogous, and urban areas. The economic mappings are superimposed upon the correlation of physical and political geography.

Consider urban areas, for example. An urban area's land-use is apportioned among residential, industrial, commercial, parklands, and other municipal functions. One requires a grid which is sufficiently fine-grained to apply relevant statistics which are land-use-type related to the topical analysis of the land-area of this municipality. It would be convenient, as much as possible, to be able to assign entire cells to one of these land-use categories, or to such manageable approximations as "50% residential, 15% commercial, ... ."

People and persons and households, appear in this mapping in principally two ways: in residence, as members of households (chiefly), or as place of employment. When those persons are in neither of the two principal types of land-use location, but "in between," they are in transportation, visiting parks, city hall, or perhaps strolling about the city's sidewalks. It is sufficient, at first pass, to think of a percentile of the month's total hours spent in the residential area of the households, so many of those total hours in land-use area of employment, leaving a residual percentile for the "in-betweens."

Also, we must take into account the fact that people may reside in one locality, outside a city, while being employed regularly in that city.

Also, remaining for the moment with the urban case, we must superimpose basic economic infrastructure upon the whole complex of various land-uses. We should provide for noting capacity and utilization of water, sanitation services, power, educational services, medical services, scientific services, and so on by land-use types.

Land-use types are composed generally of "waste land," "reserve land," land utilized by transportation and closely related warehousing, land used for generation and distribution of power, "rural productive, other" "urban productive, other," and residential, etc. portions of the "rural productive" and "urban productive" areas. "Land-use types" overlap "land types" which themselves often overlap one another mutually: desert, tundra, mountain, forest, pasture, riparian, coastal, and marsh and swamp subsidiaries.

All of these and related structures of the economic study are in the form of graphics, with no demographic data yet "plugged in." We are thus prepared, conditionally, to situate such data in its appropriate time and place. The condition is, that for each decade of economic history of the planet or of the region being considered, the land and land-use types assignable to grid-locations vary, as the star-map varies by place and time.178 For U.S. statistics, the decennial census is a useful choice of periodicity for shifting from one land-use model to the next, treating interim developments as applications to modification of the land-use model established for the beginning of the decade.

Now, assign the data, learning from C.F. Gauss the principles for alloting observations to assigned places and times in physical reality.179

Above all: Any effort to generate a statistical forecasting model of the sort in commonplace professional practice today, is to be strictly prohibited. Insofar as the consequence of an action is mediated through a human agency's response to that action, all assumptions of behaviorist sociological and other dogmas recently or currently in vogue are incompetence per se, even absurdity per se.

The function of economic-statistical observation is not to assume how people will behave, but to show the effects of the way in which they did behave. Plug in the data-arrays accordingly.

Since health-care policy is among the leading topics of policy-discussion in the U.S.A. today, examine briefly now some of the applications of that to the kind of "modelling" just described.

The former post-war Federal standard for health-care was provided by the wonderfully neat, pungent and forceful Hill-Burton legislation, which the United States ought not to have abandoned, as it did under the influence of such mid-1970's follies as Felix Rohatyn's disastrous financial-looting operation for New York City, "Big Mac."180 The point is, if Joe Doaks or his wife falls down in the street, or is taken sick at home, or their son is stricken in the schoolyard, that person shall be treated promptly and adequately, and the financial implications of the events attended to after adequate care has begun and its continuation assured. During the post-war 1940's and 1950's, in the days of the post-war U.S. National (Economic) Security doctrine, when the U.S. population was still moral, as under the Administration of President John F. Kennedy and President Johnson's Civil Rights legislation, the right to life and health of every person was implicitly the standard of political behavior.181

Situate the impact of Hill-Burton goals in the graphics scheme of economic-data mapping described. To the extent Hill-Burton is representable in terms of the infrastructural logistics of delivery of health care reasonably proximate to when and where it is needed, what is the distribution of capacity for care?182 This typifies the logistical aspect of the "soft infrastructure" concept for health, education, and science services to households and productive functions alike.

Those kinds of studies, today technologically within the reach of small research organizations, represent an elaboration of the approach employed by this writer back during 1948-1951, in connection with his ongoing commitment to refuting Norbert Wiener's radically positivist Golem, the attempted application of statistical "information theory" to human behavior. The conceptual problem which the author addressed then, is the commonplace problem to be confronted in the course of any competent sort of economic analysis today. The issue today, as during the 1948-1952 period of the author's original discoveries in this field, is to put aside for the moment any prejudices respecting mathematical physics learned from the classroom, and simply to measure the comparison of successful and failed economic policies of practice as those distinctions occur in nature, whether taught thermodynamics likes that result, or not.

Entropy, as this is defined by Clausius, Kelvin, Boltzmann, et al., has a well-defined ontological character, an essentially mechanical character. Wiener et al. perpetrated the kind of fraud which implicitly justifies David Hilbert's expulsion of Wiener, as incompetent, from a Göttingen seminar. Wiener et al. employ a low-probability factor within Boltzmann's mechanical derivation of his H-theorem, the low probability that, in that case, apparent entropy might be reversed temporarily and locally.183 Wiener et al., make the wildly extravagant ontological assumption, that because neither living processes nor intelligent human behavior are characteristically "entropic," their characteristic "not-entropy" is to be neatly explained statistically as a temporary and local reversal of universal mechanical entropy, Wiener's abusive reading of his neologism, "negentropy!" Wild positivist John Von Neumann, fleeing from the avenging furies of Gödel's 1931 proof,184 performed an even cruder, but otherwise Wiener-like hoax in the name of economics.185

Through the influence of radical positivists such as Russell, Wiener, Von Neumann, and many others, the world of democracy has come under the ideological reign of madmen. In place of rule by old forms of flesh-and-blood individual despots and Babylonian, or Roman or Mongol or British military forces, we have entered into the Dantean Hell in which Walter Lippmann's utopia of induced public opinion reigns, induced by mass media, induced by democratic guises for Nazi Gleichschaltung,186 a more lunatic tyrant than a Nero, Dracula, Henry VIII, or Ivan "The Terrible" in the flesh.

In that spirit, in place of economic policies premised upon successful forms of economy, policy-shaping is ruled by the Von Neumanns, the von Hayeks, the Milton Friedmans, the "Chaos theorists," and even the Phil Gramms, who measure success not by the old-fashioned, objective performance of economies, but what is called the more "conservative" modernist standards of conformity with some recent radical-empiricist lunacy which has been awarded academic or Nobel Prize credentials.187 These dogmas, if put into practice, show a common, perverse quality of self-fulfilling prophecy.

It is fair to say of Thatcherism, one of this recent rash of extremist "isms," that she promised to purify the British economy of any economic practice not consistent with her dogma. In that particular aspiration, she succeeded; the British economy obediently died. Seeing the followers of Smith, von Hayek, Von Neumann, Friedman, and Sachs, one might think of an auto-mechanic who assures his client, "I am going to bring your automobile up to my standards, even if it kills you." Such is the way in which the U.S.A. and world economy is viewed by the "free traders" in London, Washington, or the Wall Street Journal; such is the way in which the economies of the "Third World" nations, sub-Saharan Africa most notably, are viewed by the followers of Bertrand Russell, the Malthusian fanatics currently controlling the policies of the U.N.O.188

Apart from such fanatics as those, their cases but illustrate more luridly the vicious incompetence of the reigning liberal189 theoretical economists before them. All efforts to impose a linear model of performance upon economy must tend to have the practical impact of a self-fulfilling prophecy. Any economic process which is subjected to a form of policy-making which is itself based upon a "linear model" will be "linearized" by efficient enforcement of those policies; in that case, the economy will, in the relatively milder cases, undergo cycles of entropic collapse, or a more devastating collapse like that gripping the entire world presently.

Academics who fail to grasp this connection, will insist on babbling a post-mortem diagnosis on the state of a collapsed economy of this sort, "You see, the economy's behavior is linear, and also demonstrates once again a principle of universal entropy."

Both Von Neumann's and Wiener's dogmas are characteristically linear; therefore, the effect of adopting their dogmas as policy can be nothing but disastrous. This illuminates the fact, that Wiener's definition of "negentropy" is simply reversed "entropy," and is strictly linear in consequence of this. In contrast, the "not-entropic" processes of living beings and of human intelligence are not linear. Either one uses "negentropy" to signify the latter, non-linear characteristic, in which case "negentropy" has nothing to do with "information theory," or "negentropy" has the dictionary meaning supplied by Wiener, in which latter case it is a nonsense-word.

During the interval he progressed into making his original discoveries in economic science, this writer was confronted with the choice: accept the evidence of measurement, or accept the established dogma of present-day physics-teaching. The author chose to stand by the evidence of measurement, and leave the dogma to those ivory towers where dwell those hesychasts who seek refuge for their fantasies in a dwelling-place as far removed as possible from cruel reality. After all, everything we have come to discover as truth was gained for mankind by adhering to that same principle; a well-defined anomaly, based on good measurement, has always been the signpost leading the way to scientific progress.

Part II Footnotes

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