|This article appears in the January 14, 2000 issue of Executive Intelligence Review.
The Tinsel-Town Follies
by Lyndon H. LaRouche, Jr.
December 26, 1999
A formerly well-known figure of Los Angeles used to refer to the Hollywood of her time as "tinsel town." It was there, that the motion-picture screens were often filled by cheap, easily destructible movie sets. Now, the methods developed to produce those Hollywood sets, are spreading like mushrooms across that suburban landscape, where the "baby boomers" of today's middle-management world commute, from the suburbanite fantasy-world which they call home, to the highly leveraged fantasies of their work-a-day world.
As the little boy said, in "The Emperor's New Clothes," "But, he has nothing on!" Strip away those fantasies, and behold the result! We are living in a time when two of the dumbest, and most immoral notables to be found, George W. Bush, and Al Gore, have been considered, until now, as front-runners for President of the world's leading military power, the crisis-stricken U.S.A. In these times, the labor employed to construct the flimsy modern "Potemkin villages" of suburbia's homes and malls, is poorly paid and mostly unskilled, and the mortgage is as gigantic and long-lived, as the debt on those crumbling shacks will soon become unpayable.
More and more among the upper twenty-percentile of our family-income brackets, are living in such "Potemkin villages." Relatively speaking, that stratum among "baby boomers," and their like, are as wealthy as similarly demented predecessors had once been, who were suddenly ruined in the collapse of the Seventeenth-Century "tulip bubble," and the similar "South Sea Island" and "John Law" bubbles of the early Eighteenth Century. Think of the 1923 hyperinflation and bust in Weimar Germany. Think of the worst cases, those within the upper twenty-percent of the U.S.A.'s family-income brackets who are often living as "middle management" on the margin provided by a temporary hyperinflation in highly speculative stock options. Look at the mortgages, from $300,000 through $600,000 and up, on structures which appear to be composed of the same paper used to write the mortgages themselves. Think of those many from among today's "middle management" suburbanites, who, as in Germany's 1920s, may decide, in hyperinflationary desperation, to trade in their white shirts for brown.
Those who recall the U.S.A. from the 1929-1934 interval, will not smirk at the suffering about to come down upon such all too typical members of the upper twenty-percentile of our nation's family-income brackets. The duty of government is to help those presently fantasy-ridden suburbanites to find their way, as quickly as possible, back to a safe landing in the sanity of the real world, a happier, saner world, which must be made our nation's economic future. In brief, separate the victim from the lawful consequences of the madness which has lately gripped our nation, especially among the upper twenty-percentile of the family-income brackets. To do that, we must first recognize, and, hopefully, cure, the madness which brought today's suburbanites to that point of national disaster now looming before us all.
The Höuyhnhnms and the Yahoos
Once again, as in the case of those mass hysterias known as the "tulip craze" and the John-Law "bubbles," today's blind faith in what is called today "shareholder value," is a deadly kind of madness. In other words, it is a form of mass-insanity. To understand the kind of society in which this mass-insanity erupts, compare the England of the early Eighteenth Century, as the great humanist leader and satirist Jonathan Swift depicted it, in a piece designed for adult reading, Gulliver's Travels. I refer your attention to the chapter on the subject of what Swift identified as the case of the Höuyhnhnms and the Yahoos.
Compare the insanity of those höuyhnhnms with the terrible conditions of life imposed upon the yahoos. Take as today's parody of the höuyhnhnms, typical wealthier residents of Wall Street's southwestern Connecticut bedrooms, or the "hunt set" of present-day Virginia. Compare the terrible conditions imposed upon the yahoos, with the situation into which the lower eighty-percentile of today's U.S. family-income brackets are being degraded by currently ongoing trends in U.S. TV news and other fanciful entertainments. Think back to the Eighteenth Century, and compare present-day trends with the difference in cultural level between the U.S. citizens of that time, and the typical British subject of the same period. See thus the moral depravity of Britain under the House of Hanover, Walpole, and Pitt, as that state of affairs is typified by Swift's satire. Or, compare the state of affairs in Eighteenth-Century and early Nineteenth-Century Britain to the state of affairs under the höuyhnhnm tyranny of the Confederacy's slave-owning class. Think of the yahoo-like condition of the typical southern poor white, under the rule of what the slave-owning class termed, with a certain, bitter, ironical appropriateness, as its "peculiar institution."
To understand how people are transformed into yahoos, look at the number of jobs a typical family must work today, in a desperate attempt to match the real-life living standard of thirty years ago; compare the U.S. public and private elementary and secondary education of thirty years and more ago, with the already depraved, and rapidly worsening condition prevailing among virtually all of the public-school and private-education classrooms in the U.S.A. today. So it goes with both education and entertainment. So, under the Wall Street höuyhnhnms' preferences in managed health care, the principal function assigned to authorized medical practice, is, like imprisonment, to cull the herd of unwanted numbers of those consigned to the lower eighty-percent of family-income brackets.
A nation which has been caused to degenerate into a society divided between, chiefly, brutish tyrants, and yahoo-like creatures, both more inclined to rutting than to thinking, is a society which prefers rather stupid and immoral leading choices for President, more or less of the class of brutish Bush and thuggish Gore today. Real Presidents, like Swift's Lemuel Gulliver, who could actually think, are not wanted. Readily disposable, brutish dolts, who will do as Wall Street's financial aristocracy prescribes, are preferred, instead.
Once upon a time, the Classical scientist, high-technology farmer, and skilled machine-tool designer, were still the pride of our national economy. Such, then, was the American pride and ideal, in contrast to the decadence of the British upper classes, and the brutality imposed on the lower classes there. Indeed, already in our young republic, the U.S. adult population had a literacy-rate of about ninety percent, in contrast to approximately forty percent among British subjects. It was the programs, launched by President Lincoln and economist Henry C. Carey, which unleashed the great U.S. scientific and industrial boom of 1861-1876, the boom on which all the great economic progress of the world during the past century-and-a-half was modelled.
During the recent thirty to thirty-five years, the direction of economic conditions has changed radically, for the worse. We now import more and more of what we used to produce, and what we import comes more and more from actual or virtual slave-labor conditions abroad, such as the conditions which NAFTA has fostered in Mexico's maquiladoras strips. Cheap labor abroad now produces what more and more of our citizens can afford less and less to buy. A U.S. current accounts deficit now running, officially, between $300 and $400 billions a year, and still soaring, shows us to be a nation living on what we borrow, or loot, from weaker nations abroad. Indeed, we can no longer meet the technological standards of quality goods which the generation of the 1940s through early 1960s once took for granted. So, why educate a population from which we no longer require productive skills? Why pay to keep alive the senior citizens, or the extremely poor, which Wall Street insists we can no longer afford?
With such changes for the worse, there goes a corresponding change in state of mind, a lowering of the quality of intellect, and of popular morality. The current rates of imprisonments and ritual executions, reflect, more simply and clearly than anything else, a galloping loss of elementary morality among that thirty percent of the adult population--especially the "Third Way's" suburban stratum--which dominates most of the recent Federal, state, and local elections. The resulting lowering of the intellectual and moral level of the population, over the recent thirty-odd years, defines a specific, relatively depraved, present state of mind, now rampant among the upper twenty-percentile of family-income brackets. It is in study of that so-induced, defective state of mind, especially among that stratum, that we will find the cure for the kind of madness which that stratum, by and large, has copied from the desperate fools of former times, those caught up in such earlier crazes as the "tulip" and "John Law"-style bubbles of the Seventeenth and Eighteenth Centuries.
Two opposing states of mind
To understand how that specific kind of speculative madness functions, one must do a bit of serious thinking about some very elementary scientific issues. Since our nation's ability to outlive the monstrous financial crisis now in progress, depends upon understanding those issues, no sane person could honestly object to being asked to do a bit of serious thinking about the following elementary questions.
Therefore, now focus upon two mutually exclusive views of what is called "Euclidean geometry." One view, the deductive method associated with both Aristotle and Galileo, for example, assumes that space is extended infinitely in three senses of direction (up, down, and sideways), and that this infinite extension is always in a straight line. Persons of that mistaken, but still currently popular view, usually insist, also, that time is also extended in straight lines. The opposite view, which is an ancient one, is based on discoveries associated with astronomy. Man discovered that there are regular changes in the angle at which constellations are to be observed. That latter view led to the judgment, that the laws of the universe are not determined according to straight-line pathways, but, rather, the type of curved pathways associated, approximately, with the regular angular changes in the observer's view of a point in the Zodiac.
So, in modern times, Galileo and his corrupted followers assumed, wrongly, that the universe was organized according to forces of repulsion and attraction acting along straight lines. These forces were assumed, mistakenly, to connect any two bodies at a distance from one another. Followers of the discoverer of universal gravitation, Johannes Kepler, did not agree with Galileo's view. Key scientists of modern times, such as Fermat, Huyghens, and Leibniz, proved that the pathway of radiation of light was not governed by the "shortest distance between two points," but, instead, by the pathway of least time between those points, a pathway which was a larger distance than the straight-line connection. This was the starting-point for Leibniz's original discovery of the calculus, and for Leibniz's related principle of universal least action.. These latter discoveries were carried further, chiefly, by the world's greatest modern mathematician, Carl Gauss, and by Gauss's follower, the physicist Bernhard Riemann.
Riemann laid down the principle, that the measurable form of action connecting two successive points in a physical process, can not be derived from a deductive mathematics, but must be established by a type of physical experiment which he defined as unique. In other words, rather than trying to connect the dots between two observed point-events by straight lines, one must discover, experimentally, the actual curvature which governs the shaping of the pathway by which that process generates the succession of points which it subsumes. The model for this notion is the Kepler-Gauss proof, of the anti-Euclidean way in which orbits, rather than action at a distance, determine the trajectories of planets.
In former times, in practice, every competent manager of production accepted that principle of science, in one way or another. If he did not fully understand the issue from the standpoint of a Gauss, Riemann, et al., he understood how to approach such matters in the practice of designing and testing products and processes of production. Thus, no competent production manager would ever launch a new design of product or production process, without first subjecting that design to the same kind of test which the scientist uses to determine the accuracy of what he or she believes to be a validatable universal physical principle. Only an incompetent would ever launch a new design-configuration solely on the authority of a deductive form of so-called mathematical model.
We should recall the awful loss of a space-shuttle and its crew, during the 1980s, precisely for reason of lack of such competence by those who, among other things, compelled NASA to substitute a new type of O-ring, thus replacing a tested design with an untested configuration, and putting the launch and its shuttle crew at risk in that way. I happened to be, at that time, in ongoing consultation with one of the world's leading experts in this area, who was gravely concerned by the risk involved in that reckless O-ring substitution; unfortunately, his wise advice was not heeded by the U.S. government's cost-paring official bunglers. The case of once-proud Daimler-Benz's embarrassment over the original design of its A-class model auto, typifies the follies of modern managements which have fallen prey to the practice of so-called "benchmarking," or similar kinds of so-called mathematical modelling.
Thus, in those former times--prior to the late 1970s--when leading industrial firms had more or less competent production-managements, there was a perpetual quarrel between these production managements, on the one side, and most of those in the accounting and financial departments, on the opposing side. All generally accepted accounting practice and financial theory, assumed that the cause-effect relations of production and product-design could be interpreted on the basis of that purely linear way of "connecting the dots" which is used in standard accounting practice. When the qualified production-managers and scientists began to be subordinated, more and more, to the linearized whims of the accounting and financial side of management, the U.S. economy gradually lost the relatively awesome competence which had carried it, so brilliantly, through and beyond the time of the World War II mobilization.
Ironically, during the period from Presidential pre-candidate Dwight Eisenhower's famous trip to Korea and the assassination of President John F. Kennedy, the chief factor weighing for competence in production management, was the pressure to keep ahead of the Soviet Union in militarily relevant technologies. At a time when the accounting mentalities of official Washington had moth-balled Huntsville's capability of launching an Earth satellite, it was the nagging beep of the Soviet Sputnik which revived U.S. space and related technology. As long as the scientists and skilled production managements were considered strategically indispensable, the accountants and financial wizards were compelled to accept the crucial role of the technologists, however reluctantly. It was the negotiation of détente, in the wake of the 1962 missile-crisis, which unleashed the process of gradually shutting down whole chunks of the U.S.'s former technological potential--especially from 1966-67 onward. When the scientists and production managers were no longer considered desperately important, the Wall Street gang of accountants and financial managements took over more or less absolutely. That was when everything about the U.S. economy began to go seriously wrong.
A parallel effect of détente was to be seen on the side of the Soviet economy. From about 1973 on, most notably, the Soviet economy relied more and more on exporting its raw materials, and relatively less on technological progress in the civilian-goods sector. This led, lawfully, to the 1989 collapse of the Warsaw Pact and its Comecon economic system.
Thus, it was during the middle 1960s through early 1970s, that the Wall Street gang unleashed its cult of "post-industrial" utopianism. It was the Trilateral Commission which, from its famous Kyoto, Japan conference on, unleashed what has since been a continuing process of destruction of the entire policy-structure which had been used to get the U.S. out of the Great Depression, through World War II, and through the 1945-1964 period of post-war economic recovery. The U.S. agricultural system, based on parity principles, began to be destroyed. The system of Federal regulation on which prosperity had been built, was shattered. Under successive Federal Reserve Chairmen Paul Volcker and Alan Greenspan, the U.S. banking system, the pivot of growth of productivity, was systematically, and viciously corrupted.
Meanwhile, there was an ongoing effort to confuse and corrupt the minds of those who would come, generation by generation, to assume most of the top-most positions in management of both the public and private sectors of the economy. This subversion was typified by the pernicious influence of two devotees of a man who was perhaps the most evil man of the Twentieth Century, the father of nuclear terrorism, Britain's Bertrand Russell. Those devotees were MIT's Professor Norbert Wiener and John von Neumann. The crux of Neumann's role in destroying the competence of most of today's middle and top management, was his insertion of his quack-dogma called "systems analysis." This dovetailed with Wiener's fabrication of another quack doctrine, known variously as "cybernetics" and "information theory."
The relevance of both those quack-doctrines for the present crisis of the world economy, is that, to the extent that young professionals, and many other susceptibles, were brainwashed into adopting those two cults, the net effect of Wiener's and von Neumann's linearized mathematical constructs, was to assure the accountants and Wall Street-type financial experts, that there was nothing in physical science which should prevent economic policy from being based entirely upon guidance by the same linear way of "connecting the dots" used by ordinary accounting practice.
Al Gore climbs back up the trees
The entirety of human progress has been the fruit of a quality of the individual member of the human species, a quality which is lacking in any and every lower species. This quality is the power of cognition, otherwise known as the unique ability of the cultivated individual human mind to generate validatable original discoveries of universal physical principles. This is the quality of the individual human mind which defines man and woman as made equally in the image of the Creator of this universe, and which provides the human species a unique ability to exert increasing dominion over all other species of things within the universe.
The relevant problem of European civilization, from about the time of the Romans' murder of Archimedes, until Europe's Fifteenth-Century Golden Renaissance, has been that society lacked a political form consistent with the requirements of a being, man, made in the image of the Creator of the universe. Meanwhile, from the rise of pagan Rome, the wicked legacy of Babylon once again dominated the Mediterranean region. The Roman Empire and its feudal successors defined government as the property of a ruling "race," or class. This was the form of government which had been known to ancient Greece as "the oligarchical model," the same oligarchical model which the brutish Norman barons dictated to King John as that predator's pact known as England's Magna Carta. Under such oligarchical models, government and its laws were the personal property of a ruling oligarchy, often represented by the absolute authority delegated to an emperor.
Until the Fifteenth-Century Golden Renaissance, the tradition of the imperial (oligarchical) model ruled Europe and adjoining regions. Typical is the case of the long period of war, launched by imperial Venice, the wars of the so-called Guelph League, whose specific purpose was to prevent the rise of forms of government, in which the general welfare of all of the people was secured under a form of government whose authority and responsibility were based entirely on the obligation to promote the general welfare of all persons and their posterity. Approximately a hundred years of warfare brought a depopulated and ruined mid-Fourteenth-Century Europe to the condition of chaos, from which, finally, there emerged, during the Fifteenth-Century's Golden Renaissance, forms of government which were based upon both the literate development of the popular language, and a form of state constituted according to the principle of the general welfare. France under King Louis XI and England under Henry VII, were the first governments which avowed their dedication to that principle of law known as the general welfare. That notion of government and law, is what is properly known as republicanism, as opposed to oligarchical forms.
That said, please turn your attention to a chart [Figure 1] which both Al Gore and I have used to illustrate our respective, directly opposing conceptions of man, nature, and law: his is oligarchical, mine is republican. This account appeared in his Earth in the Balance, and my opposite view in "How Bertrand Russell Became an Evil Man." The two of us have drawn respectively opposite conclusions concerning man, God, nature, government, and law, from that same demographic evidence. The rate of improvement of the demographic conditions of mankind which emerged from Europe's Fifteenth-Century Renaissance, until the downward trend emerging since 1971-72, surpasses all known other cases from both history and prehistory. The cause for this improvement in the human condition, has been entirely the emergence of that modern conception of government based on the principle of the general welfare, or the so-called commonwealth principle, as introduced to North America's Massachusetts Bay Colony of such admirable intellects as the Winthrops and Mathers of the Seventeenth and early Eighteenth Centuries. I praise this progress; but Gore rabidly abhors it, and proposes to turn back the clock by whatever means possible.
Under France's King Louis XI (1461-1483), a new kind of state emerged from a unified France. During this interval, the national income of that territory doubled. Louis' success in France provided the model for the overthrow of the evil Richard III of England, and the establishment of a form of government like Louis XI's design, under England's Henry VII. The developments from the convening of the great ecumenical Council of Florence, through the establishment of governments based upon the principle of the general welfare in France and England, was the hour of birth of the modern nation-state, and also the moment of birth of both modern science and modern national economy, the hour of birth of what should be recognized as the practice of economics.
This spectacular improvement in the human condition depended predominantly upon three interdependent elements of policy of practice. First, the commitment of the state to regulate commerce in such ways as to promote the general welfare, and to provide, with similar intent, for the development of the basic economic infrastructure of all of the usable territory of the nation. Second, to foster rapid improvements in the productive powers of labor through promotion of scientific and related discoveries. Third, to foster the general health and education of the entirety of the population, to such included effects as fostering scientific and related forms of technological progress, while also fostering in the population a proper sense of the permanent place and value of the mortal individual personality in the eternal scheme of human existence.
To understand this development during that time, it is essential to recognize that Fifteenth-Century Italy was the center of the greatest rate of increase of knowledge of scientific and Classical-artistic principles since the rise of the Classical Greek culture of Plato and such followers as the great Eratosthenes. The founder of the method of modern experimental physical science, was the same Cardinal Nicholas of Cusa who had played a leading part in the pre-organizing of the Council of Florence, and who set forth, after A.D. 1453, the policy of global exploration followed by the Portuguese explorers and Columbus. Leonardo da Vinci was, together with Luca Pacioli, a leading follower of Cusa, and bearer of that influence of Cusa's discoveries and policies, which led to the achievements of such as Johannes Kepler and of all of the greatest scientific minds, such as Gilbert, Fermat, Pascal, Huyghens, and Leibniz, of Europe's Seventeenth Century.
Some among the fuller implications of the same point are identified in my policy-statement on education. Here, I focus upon the specific matter of physical science. Although those universal principles associated with Classical artistic composition, are also essential for scientific and other cooperation within society, I focus attention here on the matter of the average person's power, per capita, and per square kilometer of the Earth's surface, in and over the physical universe. My focus is the act of discovery and validation of universal physical principles, the same focus presented in Riemann's referenced 1854 habilitation dissertation.
Although higher apes, for example, can learn improved techniques through experience and learning, neither mere experience nor learning could ever produce a validated discovery of a universal physical principle, or ever did. Such validatable discoveries of universal principles, are a unique and sovereign capability of the cultivated individual human mind. The learning of mere information, is not knowledge.
Such discoveries are typically prompted by irrefutable experimental, or equivalent proof, that existing knowledge contains a systemic error of axiomatic assumption, usually a measurable form of error, and a most stubbornly persisting one. The suitably cultivated individual mind then generates an hypothetical, new principle, which has the effect of seeming to transform existing knowledge in such a way that the new state of knowledge is freed from the error in question. If a suitably designed experimental observation shows that that hypothetically proposed new axiom is true for all possible cases, the discovered hypothesis is then considered as validated. This newly validated universal physical principle then joins an accumulation of such axiomatic universal physical principles.
What Riemann's 1854 habilitation dissertation did, on this account, was, first of all, to outlaw all so-called self-evident assumptions of mathematics, such as those of schoolbook Euclidean geometry, from physical science. The kind of geometry acceptable to competent physical science, then became a geometry in which no axiom was allowed which was not an experimentally validatable universal physical principle of the type I have just indicated. Although Carl Gauss had already, privately, adopted an anti-Euclidean geometry, he had long refrained from publishing his discovery for very weighty political reasons. Thus, under slightly more favorable political conditions, Gauss's student, Riemann, in 1854, carried Gauss's earlier work to the proper conclusion we meet in Riemann's cited dissertation.
My own work in advancing the science of physical economy adopted Riemann's work as providing the basis for defining the way in which modern economy succeeds in increasing the physical-productive powers of labor, both per capita and per square kilometer. From that standpoint, the meaning of the evidence reflected in the chart cited by both me and Gore, among others, should become clear. The key to this is the nature of those experiments which establish an hypothesis as a universal physical principle.
Any experiment which actually validates a universal physical principle, contains within the design of that experiment a definite, new element of design, an element which bridges the gap between the notion of that principle as such, and the application of that principle in the form of an element of design of constructable new types of designs of products and productive processes. The successful application of that experimental design to different media of action, results in a new specific technology. The experimental validation of proposed new combinations of such technologies, thus leads to a corresponding generalization of the relevant universal principle for productive and other practice.
Such are the essentials of the internal history of the progress of modern science and technology. Such are the means by which the physical-productive powers of labor are increased.
Thus, the idea that economy is bounded by some fixed array of types and quantities of so-called "natural resources," as the anti-people Malthusians, such as Al Gore, argue, is a childish absurdity, a popularized, and, in fact, devilish delusion. Similarly, the fanatical insistence of a Wiener and von Neumann, that economy can be reduced to a matter of linearized definitions of "information," and solutions to simultaneous linear inequalities, is to be regarded as a fruit of superstition and witchcraft, not science.
What `non-linear' really means
To understand why linear accounting methods are not competent guides to making economic policy, we must define a few additional terms. This will require some concentration among laymen, but the point to be made is of indispensable importance for the future of the citizen and his or her posterity.
From the standpoint of the mathematical physics of Gauss and Riemann, the physical universe, considered as a whole, is what is called variously a "multiply-connected manifold," or "hypergeometry." The two terms, used in that context, mean the same thing. By "multiply-connected manifold," Riemann signifies, in his habilitation dissertation, a universe in which there are no axioms, excepting those universal physical principles which have been experimentally validated in a unique way. These principles take the place of the dimensions of a so-called Euclidean geometry. Each principle has its own characteristic curvature, and the interaction among such principles also implies a specific curvature. Each such curvature is determined by appropriate qualities of physical experiment. An interconnected set of some selected such principles, we refer to as a "phase-space."
For example, as Kepler and Gauss showed this, successively, for astrophysics, the measurable orbit of any planet, comet, and so forth, within the Solar system, involves measurements which go beyond the scope of any calculation of the type we associate with the teachings of Galileo, Newton, et al. For example, the original discovery of a principle of universal gravitation, was made by Kepler, on the basis of his assessing a complication in the measurement of the orbit of the planet Mars. This led further, to the recognition that the characteristic feature of orbits in the Solar system is non-constant curvature. The subsequent proofs, by Fermat, Huyghens, Leibniz, et al., that universal action follows a pathway of least time, rather than "shortest" linear distance, led to Leibniz's original discovery of the calculus, and to the proofs developed successively by Gauss and Riemann.
All of this proved coherent with the principle, that it is the orbit of the planet which determines its trajectory, rather than "action at a distance." For the physicist, this signifies that that orbit reflects a multiply-connected, relativistic manifold of the Gauss-Riemann type. This manifold includes, as implied axiomatic features, both presently known, and presently unknown universal physical principles. Phenomena of this type, are to be recognized as "non-linear" processes. These are otherwise to be known as processes characterized by regular, but non-constant physical-space-time curvature, as Nicholas of Cusa, Leonardo da Vinci, Kepler, Leibniz, Gauss, and Riemann viewed this matter.
Unfortunately, in today's commonplace academic misuse of the term "non-linear," the definitions for use of the term "non-linear" usually signify calculations made from the standpoint of a currently standard, linearized formal mathematics. The use of the term "non-linear" in connection with the work of such disciples of Bertrand Russell as both John von Neumann and Norbert Wiener, is typical of that kind of misuse of the term. The phenomena addressed by such quacks may be, indeed, actually "non-linear" in their own right, or not, but the use of the term "non-linear" by such fellows, signifies the observation of a real or merely conjectured phenomenon from the standpoint of a linear-deductive, formal mathematics, not the standpoint of physical science as the Gauss-Riemann method defines it.
Admittedly, in engineering, we usually rely upon mathematical formulations which have, speaking formally, a linear basis. We do this as a convenience, to simplify the calculations. However, the use of such approximations is allowable only when no new physical principle, or new combination of technologies is involved. Whenever the matter addressed involves paradoxes suggestive of some new physical principle, or new combinations of established technologies, we must put formalist calculations to one side, until the relevant experimental test of principles has been made.
Thus, the rate of man's increase of the productive powers of labor, is limited by the ratio of scientific and related experimental activity to standard engineering and related types of activity. Typical of the investment practice which yields the highest rates of growth of physical productivity, per capita and per square kilometer, is the so-called science-driven "crash program" effort, such as the U.S. Manhattan Project and the German-American aerospace effort launched under President John F. Kennedy. Such latter, highly successful policies, are in direct contrast with the trends toward miserable results, today, when science and machine-tool design are being replaced by reliance on inherently unstable "mathematical modelling." The increasing rate of failures in today's U.S. space program, is an example of this. So is the absurdity inherent in the so-called "ballistic missile defense" dogmas popular in today's U.S. Congress.
Putting aside important, and relevant other cultural considerations, the potential rate of increase of man's power in and over the universe, is determined by the cumulative growth and mastery of new, universal physical principles. This growth is best viewed from the standpoint of the concept of the Gauss-Riemann manifold. The possible rate of such growth depends upon the development of the cognitive powers of the mind of the individual.
Progress in generating valid new principles, does not occur as a result of learning mathematical models; it occurs solely through the cultivation of the individual mind, through the individual's reliving of the experience of validated original acts of discovery of such principles before him. In other words, the drill-and-grill method of transmitting "information" through mere learning, to prepare students to pass prescribed formal examinations, might produce an improved version of Texas Governor George W. Bush, but it would never produce a mind actually capable of thinking. The student must relive the original act of discovery of each relevant universal physical principle, and must be conditioned by the habit of working out appropriate sorts of unique physical experiments and other observations, as the way of validating hypotheses generated.
This requires the kind of society in which each young person is educated in the way coherent with that practice of knowing. That means, in turn, a family and cultural environment coherent with the production of such qualities of graduates of education. It means a society whose investment policies cohere with that kind of emphasis upon fostering crash-program-like rates of improvement in the physical-productive powers of labor. It is historical cases which approximate that approach to fostering scientific and related physical-economic productivity, which assist greatly in defining an effective approach to such goals.
This defines, from an elementary scientific standpoint, the way in which the best production managements of the U.S. economy's past, gave us the highest rates of improvement in productivity and quality of products.
If we then examine the apparent costs and expenses of households, communities, production, and distribution, from this standpoint, we are soon confronted with the fact, that customary accounting and financial-management methods are incompetent means for showing how viable forms of modern economies actually work.
Compare all of the ingredients of the activity of a population upon which the produced physical-economic output of that population depends. This includes the cost of maintaining the family households which represent the physical-productivity of that population. It includes all forms of physical consumption required to maintain that population in its present level of productivity. It includes maintaining the long-term equipotential of all the basic economic infrastructural improvements. It includes the physical costs of offsetting the depletion of the natural resources consumed.
That equipotential, so defined, represents some relative rate of net increase of the physical-productivity rates of that population. (This could be positive, zero, or negative.) The question is: what is the current allocation of resources needed to improve those rates of physical productivity for that society as a whole? The answer to that question will have no necessary relationship to the current financial accounting in use.
All of the necessary elements of physical consumption correspond to elements defined in terms of a Riemannian type of manifold.
For example, a change in educational policies of practice, from classroom and textbook methods of learning, to emphasis upon cognitive methods for generating the students' replication of the experience of validatable original discoveries of (for example) universal physical principle, will cause a marked improvement in the potential rate of increase of physical productivity in the population so educated, relative to a mere learning-based curriculum. It is the physical-functional character of the so-called "inputs" to the bills of production and consumption, not the "competitive cost" of those ingredients, which defines the net outcome in terms of physical productivity.
In the last analysis, the nominal cost of the elements of the bills of consumption and production, is measurable in accounting terms. However, there is no functional linear form of relationship between those costs and the output or rate of change of output. The functional relations involved are of the type of a Riemannian manifold.
To reduce the problem so posed to a more readily comprehensible form, let us continue to focus on the example of educational methods used in classrooms. Consider the difference between a relatively giant multiversity's populous classroom, in which learning in preparation for examinations predominates, in contrast to a smaller class-size for which the emphasis is on cognition, rather than learning. This latter class will cost more, in physical terms, than the class based on a learning perspective, and the teacher will require qualitatively superior training, and much higher ratios of pre-class preparation-time than the inferior, learning program. Also the student will require more access to means and time for constructive experimental, or kindred validation, than in the learning-oriented, cheaper version. Teacher education is much more demanding for cognitive, than for the poorer, mass-produced sort of mere learning-information regime. However, in choosing between the two policies, cheaper is worse, and less profitable to the economy as a whole.
The results of the cognition-oriented education are a graduate of far greater potential physical-productivity than a graduate from a learning-information-oriented background. How much? That is not a matter of some predetermined mathematical model, but of experimental approaches, including the experience of the teacher in learning better methods for prompting cognitive activity among the students.
Consider the impact of increase in time of commuting, upon the physical productivity of the population as a whole. Obviously, the increases in commuting-time incurred by shift to suburban, from urban residence, to suburban work-places for urban populations, and so on, are wasteful in many ways and degrees. Increasing the number of hours of work of adult members of family households, piles up potentially bad, even disastrous effects. For example: ask, how many primary and secondary pupils had at-home adult members of the family, during the period of the school-day and evening? The change, from the situation in the 1930s, 1940s, and 1950s, to the present day, has been disastrous in its effects on the cognitive powers of the population as a whole, and upon the per-capita rates of net physical productivity of that population.
There was never a competent way to manage production from the standpoints of linearized rules of thumb. One had to understand the production process and production-design itself, and make decisions in ways which echo the way of thinking of a scientist, whose way of thinking has been cultivated in the school of discovery and experimental validation of universal principles, and the way in which technologies reflecting those principles could, and should not be combined.
Real-life economic relations are to be understood in terms of the human species mastery of the physical universe. This relationship is expressed in terms of man's increase of the potential relative population-density of the human species, relative to nature at large. This relationship is located primarily in those valid discoveries of universal physical principle, by means of which mankind increases its power to exist in and over the universe we inhabit. Those relations belong to the domain of a Gauss-Riemann multiply-connected manifold. The functional expression of this relationship is located within both the domain of individual cognitive processes, by means of which valid universal principles are discovered, and in the social processes by means of which the cognitive powers of the individual members of society are brought into the form of mission-oriented cooperation, by means of which discovered universal principles are transformed into a social form of generalized human practice.
For example, in applying these general principles to the problems of assessing the performance of individual enterprises, I required that the accounting system of a firm (for example) make a functional distinction between financial and real accounts. Simply, every entry in the accounting system should have a different coding for the purpose of examining the real-life significance of the activity associated with the financial transaction. In other words, two charts of accounts were required. One met the financial accounting requirements; the other real economic activities. Wherever an entry in one of these two accounts corresponded to an entry in the other, the two entries were coded in such a way that they might be cross-related. Thus, the firm (for example) would have the strict financial accounting it required for legal and related purposes, but would not commit the folly of assuming that the linear schemes implied by financial-accounting methods, corresponded to the non-linear economic realities of the real world.
In summary, the use of standard statistical accounting and related ratios, as tools of analysis and forecasting, is, today, more often as disastrous in its effects, as it may be sometimes useful in other ways. In today's practice by governmental and influential private enterprises, the effect tends to be, more and more, disastrous. Turn now, to discover why that trend has been the case.
The doctrine of `shareholder value'
A half-century ago, more than sixty percent of the employed U.S. labor-force adopted physical production and quality of products and professional services as the standard of real-life performance for judging the progress or failure of management of our economy. This sense of real economic values, had been strengthened considerably in that population by the experience of the 1930s Depression, of World War II, and significant recovery from the disastrous--unnecessary--and deep post-war recession of the late 1940s.
That philosophical outlook, as it emerged during the Franklin Roosevelt years, was, relatively speaking, the high-water mark of popular sanity among the generality of the U.S. population during this past century to date. President Kennedy was moving in the direction of reviving that Roosevelt legacy. His launching of the Manned Moon Landing mission, was an outstanding effort in that direction; but, its benefit was cut short by Kennedy's assassination and what followed during the remainder of that decade.
Gradually, most notably during the late 1950s emergence of a phenomenon then often referred to as the mythos of "White Collar" and "The Organization Man," there was a marked shift in values among the emerging population of "suburbanites." The fuller implications of this shift would become apparent during the middle to late 1960s. The 1962 Cuba Missiles Crisis, the assassinations of President Kennedy, Martin Luther King, and then Robert Kennedy, combined with the deep impact of the war in Southeast Asia, brought the potential effects of the 1950s shift to the surface in such forms as the "rock-drug-sex counterculture" of the middle through late 1960s.
During 1964-1972, a deep cultural pessimism struck the generation of "baby boomers," producing in these U.S. layers a kind of existentialist counter-culture which had not been seen since the 1920s run-up to the Hitler regime. Existentialist influences such as those of Nietzsche, Nazi philosopher Martin Heidegger, Theodor Adorno, Hannah Arendt, and Heidegger followers Jean-Paul Sartre and Frantz Fanon, became characteristic trends in philosophical outlooks of the academic philosophy and sociology departments of the 'sixties and 'seventies, up to the present time.
A deep immorality gripped much of the "baby boomer" generation, spilling over into so-called "Generation X" today. Such fruits of shock-induced cultural pessimism are, unfortunately, not uncommon fluctuations in the history of European civilization generally. It was this which made possible today's epidemic cult of "shareholder value." Similar historical developments provide background for the eruption of the "Turkish tulip-bulb" madness of the Seventeenth Century, and the "John Law" bubbles of England and France during the early Eighteenth Century. We saw a similar development, then in a relatively shorter time-frame, in the "Pyramid Club" frenzy in the U.S.A. at the close of the 1940s.
On this account, there is no deeply principled difference between Nazi philosopher Martin Heidegger and his putatively leftist admirer Hannah Arendt. Existentialists of the nominal "left" and "right" varieties, differ only as do spotted and striped varieties of the same animal species. In her published writings, Arendt stressed the species-connection in her praise of the influence of Immanuel Kant upon existentialists such as Karl Jaspers, Heidegger, and herself. There is no difference in species-characteristics between Nazi Heidegger and his follower Sartre, or Sartre's clone Fanon. Two common species-traits are outstanding. As Arendt stressed, and as Heinrich Heine foresaw, existentialists follow Kant, as Hitler's Nazis did, in Kant's denial of the existence of knowable truth; they follow Nietzsche and Heidegger in the notion of man thrown, in violence, into a society which is axiomatically alien to him.
In contrast to the existentialists' self-definition, as being a feral beast, civilized Europeans find the meaning of their brief mortal lives within society, in what their lives may contribute to the benefit of future generations, and thus to mankind as a whole. The optimistic, civilized personality promotes and defends, even fiercely, as during the Roosevelt Depression and war years, his or her attempt to ensure that the good things given to the present shall endure to benefit the future. The civilized personality is thus dominated by a concern to determine what actions he or she might best take to foster such durable benefits for future generations. The civilized, moral personality, in direct opposition to the existentialist, finds his or her own meaning of life within the simultaneity of an eternity so defined.
The pessimist, the existentialist beast-man, is a feral creature focussed upon his or her choice of pleasure-seeking at the expense of society. Hence, "shareholder value." Or, as the defender of the Confederacy/Agrarian standpoint defends the tradition of the "peculiar institution," "shareholder value" and "slave-owner value" are interchangeable mind-sets.
One of the most notable of the ways in which existentialist and similar asocial behavior impairs the intellectual faculties, is the appearance of a quasi-schizophrenic view of the attributed meaning of words and grammatical forms. Such quasi-schizophrenics tend to regard words and grammar as "the mirror of reality."
One among the kinds of phenomena generated by such pathological states of mind, is a more or less extreme form of deductive argument, such as the usages of the modern logical positivists. For example, in the field of law, a radically positivist version of the philosophy of John Locke and David Hume, tends toward the most vicious form of fascist society, ultimately as bad or worse than the influence of Carl Schmitt and Roland Freisler in defining the peculiar doctrines of law of Nazi Germany. Trends in those directions of legal philosophy have been recently prominent in the practice of the U.S. Federal Court, for example. The mind of the person who holds to the currently popular definition of "shareholder value," exhibits an extreme type of this proto-fascist trend toward fascistic-like, quasi-schizophrenic tendencies. The most celebrated dogmas of Norbert Wiener and John von Neumann, "information theory" and "systems analysis," typify such tendencies. Von Neumann's doctrine of the "brain," expressed as the psychotic philosophy of "artificial intelligence" of MIT's late Walter Pitts, Professor Marvin Minsky, et al., is typical of the proto-fascist pathology we are considering here.
The form of the issue here, is the same as we have considered in identifying purely deductive thinking in physical science, as pathological behavior. In looking at the existentialist phenomenon from this vantage-point, we are focussing upon the factor of emotion--e.g., implicitly sexual, sado-masochistic expressions of greed, rapacity, and hatred--in such pathological expressions of deductive thought. The fanatically deductive personality is incapable of actually loving; he can only rape, or be raped--into whichever of those two conditions he finds himself, or herself "thrown."
Focus for a moment on the nature of the verb. Contrast the verb, as seen and used in a purely deductive, pathological mode by Immanuel Kant, Thomas Hobbes, John Locke, David Hume, or Adam Smith (for example), with the use of the verb by a mind which is functioning in a cognitive mode. Again, by "cognitive," I signify the state of mind of the person reliving the experience of an original discovery of some universal principle.
The radically deductive state of mind, such as the empiricist, materialist, or Cartesian, sees the "dots" we associate with sense-impressions. He connects those dots deductively; this means, that he, or she interpolates straight lines between those dots. This is exactly what the empiricist Leonhard Euler did in writing his fraudulent attack upon Leibniz. This is what Euler's student Lagrange did, in introducing the same perverted principle to the teaching of a theory of functions in Napoleonic France.
Contrast Euler's deductive view with the cognitive standpoint in science, Classical artistic composition, and education. In the cognitive view, every use of language to identify an idea, bases that statement on the verb. In each latter case, the verb so employed, identifies a form of transformation of the condition of some phase-space. The verb thus corresponds to an action of someone or something upon a state of reality indicated as pre-existing, to produce a transformed state of the referenced reality. Simple deduction is not permitted.
Each verb so used corresponds to a non-linear transformation in the indicated phase-space. In other words, a transformation of a definite--non-linear--curvature, in the Riemannian sense of the use of the term "phase-space."
For example, at an earlier point here I have referred to Hans Christian Andersen's "The Emperor's New Clothes," and, similarly, to Jonathan Swift's Gulliver's Travels. Contrast the literate and quasi-schizophrenic reactions we must expect among readers of my allusions to those writings.
With respect to the first of those writings, imagine the current electoral campaigns of George W. Bush and Al Gore marching proudly down mass-media street, festooned in nothing but their only imagined, mythical glories. So, the naked Emperor disports himself before the awed populace, which has duped itself into imagining it sees the wonderful, if non-existing garments with which the crooked tailors have festooned the gulled Emperor. Suddenly, a little boy's voice pipes up: "But, he has nothing on!" The spell is broken; the Emperor and his lackeys cover his nakedness with their shame. George Bush and Al Gore flee, in all their shameful nakedness, from the arena, hopefully to the showers.
The little boy of Andersen's account is a truly Classical-poetic creation, like the last strophe of one of Goethe's most successful short poems. The boy is Andersen's elegant choice of an agent of metaphor for that tale, the catalyst which leads the cognitive powers of the mind to free themselves from the paradox which the earlier portions of the story have presented. Echoing from the hearing of that tale, there is a voice, heard from somewhere, a voice whose presence can not be denied, saying: "So, a little child might lead them."
Swift's Gulliver's Travels illustrates the same principle of artistic composition, but in a more profound way. In this case, the reader will probably not recognize the paradox of Swift's series of satires until he, or she becomes familiar with the tragic state of affairs in post-Queen Anne Britain, a Britain populated then chiefly by tyrannical höuyhnhnms and brutalized yahoos. Then, the likeness of that Britain to the legacy of the Confederacy and the Nashville Agrarians, or the post-1971 U.S.A.'s growing decadence, becomes clear in a cognitive mode of thinking about such metaphors. The effect of comprehension is of the same characteristics as that of the voice of the little boy in the Andersen fable.
In the literate use of words, the function of speech is to evoke a cognitive experience in the hearers. Words and phrases in relatively common use, such as direct references, or allusions to literary works, have the function of calling recollection of a past cognitive experience to the mind of both speaker and hearer alike. For sane persons, the meaning of words does not lie within a deductive reading of some glossary, but, rather, within the experiencing or re-experiencing of a cognitive experience.
Among sane people, the cognitive allusions employed by speakers are shaped by shared experiences rooted chiefly in Classical scientific or artistic compositions, or, in folk-art, such as the American Negro Spiritual, which has the same quality of social function. Literacy lies, thus, in the sharing of the kinds of meaning which reside originally within the sovereign privacy of the cognitive powers of the individual mind. It is the sharing of such private cognitive experiences, by induced replication, which is the basis for all Classical art, competent scientific teaching, and healthy social relations among the members of society. This is in direct opposition to everything which deductive formalism and existentialism of all forms represent.
In general, the power to comprehend such references, or to think in that way generally, requires a cultivated mind, a mind cultivated in the tradition of Classical thinking about matters of science and artistic composition. Nonetheless, whether poorly cultivated or not, the sane mind always regards the use of words and the functions of grammatical forms in the way which I have just illustrated.
From that standpoint, the psychopathology exhibited by the cult of shareholder value, is more readily understood.
A financial profit-margin on an investment in production is real, only to the degree that it corresponds to a margin of net physical-economic growth. Such a profit may be regard as earned under two circumstances. First, that the margin of increase of physical output over physical-economic costs, is the fruit of the combined efforts of the entrepreneur and the operatives and staff associated with the work of that firm. Second, that someone not employed by that firm has provided the means of supply for the physical-economic capital stocks on which the firm's performance has significantly depended.
It is a different matter if someone buys up stockholder's or other creditor's control over an enterprise for the purpose of looting that firm, or the firm's physical-economic environment. Such purely parasitical practices are the commonplaces of the post-1982, junk-bond-afflicted U.S. economy.
Earlier, as U.S. leading economist Henry C. Carey showed, the U.S. economy did not gain wealth from chattel slavery, but directly the contrary. The use of slavery for production of Britain's cotton and related enterprises, enriched the slave-holders--and the British economy--at the expense of the U.S. economy as a whole. Once freed from the direct and indirect burdens of slavery, the U.S. economy of 1861-1876 boomed, to become the leading national economy of the world, and the most advanced in technology. It was the sabotage of that economic growth by the combined forces of Wall Street and the former slave-holder faction of the southern states, which wrecked that recovery-process, producing the series of great financial and economic crises leading up to World War I.
Since 1971-1972, the U.S. financial economy has lived on cannibalizing both previously accumulated capital investments in productive and related facilities, and using the military and related political power of the U.S. and Wall Street's British Commonwealth ally to loot most of the rest of the world. The fact that the U.S.A. can no longer afford the infrastructural maintenance and social-welfare programs it once could, reflects chiefly the fact that this economy has become poorer. The explosion of U.S. public debt, launched by the Trilateral Commission policies of the Carter Administration, and accelerated by the Trilateral Commission policies of the 1980s and beyond, has multiplied the kind of national debt which did not exist until Carter became President. Outsourcing, as replacement for looted-out U.S. agro-industrial productive capital, is part of the process of looting both the U.S. and source nations simultaneously. The fact that the "yen carry-trade" bubble, a bubble ripe for popping, has been carrying the U.S. economy for years, and close examination of other factors behind the sky-rocketting U.S. current account deficit, repudiate the delusion of a marvellously growing and prospering U.S. economy.
If the internal U.S. economy is actually collapsing, per capita, in net physical-economic terms, as it has been doing for so long, how then do the upper twenty-percentile of our nation's income-brackets imagine themselves to live so prosperously? In general, the answer is, that that stratum, and some others, have been living on a marginal income derived from their combined direct and indirect participation in stock-market and related financial speculation. The ability to maintain that illusory prosperity, depends upon mechanisms of so-called financial leverage. This leverage depends, in turn, on the greatest monetary and financial pump-priming in world history. Until now, especially since late 1997, and, ever more wildly since Fall 1998, that financial pump-priming supplies the entire margin which has kept the world-wide financial bubble from popping.
Now, that very pump-priming itself, is generating the kind of hyperinflationary threat within real-estate and other commodity markets, which threatens to set off, world-wide, a hyperinflationary blow-out, like that which struck Germany in 1923.
The delusion of the person duped by the cult of shareholder value, is the quasi-schizophrenic assumption, that ownership of a real, or even a merely imagined future income-stream, entitles the owner to sell that ownership at a financially capitalized price many times the size of that income-stream itself. That ratio corresponds to what is termed "financial leverage," or, more often today, what the past hour's trading suggests the current ratio of financial leverage for such types of nominal assets might be.
Persons deluded into believing that that pyramiding of purely speculative financial leverage, might be continued more or less indefinitely, are to be considered virtually insane. For such cases, the aggravating problem is, that that is exactly what is conveyed as current doctrine by the devotees of John von Neumann's hoax called "systems analysis."
So, the pack of lunatics caught up in the tulip bubble, and the early Eighteenth Century's "John Law"-style bubbles were generally wiped out financially, and that very suddenly, and, for them, unexpectedly so. So, it will be soon, with the suburban tinsel-town follies of today.
It will be up to us to clean up the mess that creates.
 See Hans Christian Andersen, "The Emperor's New Clothes," Hans Christian Andersen Fairy Tales, translated by R.P. Keigwin (Odense, Denmark: Flensted, 1950).
 Usually, when today's mass media speak of "morality," they put a stink of hypocrisy in the air. They swallow elephants of evil in matters of their support for financial speculation and other mass-murderous offenses against the welfare of our own and other nations, and strain pornographically at the gnats at which they might hope to peek, in private bedrooms.
 See H. Graham Lowry, How The Nation Was Won: America's Untold Story, Vol. I (Washington, D.C.: Executive Intelligence Review, 1987).
 Bernhard Riemann, "On the Hypotheses Which Underlie Geometry" [Über die Hypothesen, welche der Geometrie zu Grunde liegen] Bernhard Riemanns Gesammelte Mathematische Werke, H. Weber, ed. (New York: Dover Publications reprint edition, 1953).
 Ibid., p. 286: "Es führt dies hinüber in das Gebiet einer andern Wissenschaft, in das Gebiet der Physik, welches wohl die Natur der heutigen Veranlassung nicht zu betreten erlaubt." (This takes us into the domain of another science, that of physics, which the subject of today's proceedings [mathematics--LaRouche] does not permit us to enter.)
 See Lyndon H. LaRouche, Jr., "The Coming Scientific Revolution," EIR, April 30, 1999; Jonathan Tennenbaum, Rüdiger Rumpf, and Ralf Schauerhammer, "The Fallacy of `Benchmarking,' " EIR, June 11, 1999.
 See Lyndon H. LaRouche, Jr., Oct. 12, 1988 Berlin address forecasting the imminent collapse of the Comecon system, and the early emergence of Berlin as the capital of a reunified Germany. See Lyndon H. LaRouche, Jr., Presidential candidate's broadcast, "The Winter of Our Discontent," Oct. 31, 1988. The full transcript appeared in EIR, Nov. 4, 1994.
 Friedrich Freiherr von der Heydte, Die Geburtsstunde des souveränen Staates (Regensburg: Druck und Verlag Josef Habbel, 1952).
 These were the so-called Guelph-Ghibelline wars, centered in the period from approximately A.D. 1239 through England's repudiation of its usurious foreign debts, in A.D. 1340.
 Al Gore, Jr., Earth in the Balance: Ecology and the Human Spirit (New York: Houghton Mifflin, 1992).
 This point of difference between me and Gore is doubtless beyond the comprehension of loutish Texas Governor George W. Bush.
 Eratosthenes, a Cyrenaican educated at the Platonic Academy of Athens, was the great scientific mind of the Third Century B.C., and the first known scientist to measure the length of the great circle on the Earth's surface. His discoveries were a source for Cusa collaborator Paolo Toscanelli's design of the map which guided Christopher Columbus to rediscover the Americas.
 De la Divina Proportione, 1498.
 A classical example of this is provided by Fresnel's exposure of the falseness of Isaac Newton's doctrine of the radiation of light, and by the proof, developed by Gauss, Bernhard Riemann, and Wilhelm Weber, of a principle unknown to J. Clerk Maxwell, the so-called "angular force" of Ampère. Fresnel and Ampère were collaborators, whose principled discoveries in light and electromagnetism were of one piece.
 See Gauss on the general principles of curved surfaces.
 See Kurt Gödel, "On Formally Undecidable Propositions of Principia Mathematica and Related Systems" (1931), Kurt Gödel Collected Works, Vol. I (New York: Oxford University Press, 1986) pp.144-195. This proof against Bertrand Russell by Gödel drove Russell devotee von Neumann wild, leading von Neumann through his theory of games, into the related proposal of 1938, his insistence that all economic processes could be reduced to the form of solutions to simultaneous linear inequalities.
 "Letters to a German Princess" (1761). Every important axiomatic form of corruption in Nineteenth-Century mathematics and physical science, including Cauchy, Clausius, Grassman, Helmholtz, et al., based itself upon the precedent of this argument by Euler.