NEW ACCOUNTING STANDARDS ARE IMPERATIVE
The Becoming Death
of Systems Analysis[1]
by Lyndon H. LaRouche, Jr.
March 2, 2000
On the day on which, existing money goes out of existence, as in Weimar Germany 1923, but this time more or less world-wide, what do the existing accountants do?
If we are to recover from the social effects of the currently onrushing disintegration of the present world financial and monetary systems, radically new methods of cost accounting will be required for private enterprises, as also for governmental and related kinds of institutions. The previously used, linear, "connect the dots" tactics, of both financial accounting and of systems analysis, must be abandoned, and replaced. A new standard must be adopted, for cost-accounting, budgetary, tariff, taxation policies, national-income estimations, and related practices.
The pivotal question of all competent cost accounting, is: What causes an increase in the net physical value of the productive powers of labor? For a moment, put aside calculations made in terms of nominal, that is to say financial, prices. Think solely in terms of physical contents of market-baskets of goods and services; measure inputs, as costs (inputs), and as outputs, in those physical terms. Instead of the common practice, of simply comparing ratios of prices of nominal inputs and outputs, seek to define the processes which determine a succession of changes in ratios of physical outputs to physical inputs. As measured in those terms, which increases, or decreases, in specific qualities of expenditure for infrastructure, production and distribution of product, and of which kinds of products, have neither beneficial, nor detrimental impact upon the functionally determined rate of net physical output, as the latter may be measured per capita of both total labor-force and population, and per square kilometer of a nation's, or region's surface-area?
Competent answers to those questions, lie outside the domain of a cost accounting based upon financial analysis, and outside the tyranny of those recently popular, pseudo-scientific hoaxes known as the "systems analysis" of the late John von Neumann and the statistical "information theory" of the late Professor Norbert Wiener. In the circumstances defined by the present crisis, we can no longer tolerate those faulty practices, which have been generally accepted standards of professional and related practice for much too long.
Formerly, this same issue, as expressed in physical terms, had been, for many decades, the most crucial, deeply underlying feature of a systemic conflict frequently erupting, between competent U.S. entrepreneurs and Wall Street's styles in financier management, a conflict reflected in the fierce battles which used to be fought, in happier and better times, between the industrial corporation's relatively competent production management, on the one side, and, on the other side, the usual Wall Street supercargo squatting in the finance department. Usually, the latter were so obsessed with the proverbial bottom line on this year's balance sheet, that they mustered little patience with discussion of the way in which the productivity of the enterprise was actually, physically generated.[2]
Many among what had once been formerly successful enterprises, including national economies, which later, eventually failed, had been led to that latter calamity by continuing the very policies which had ruined them, by such presumptions as the delusion, that pleasing shareholders' gains, as shown on "the bottom line," showed that the recent trends of policy-making in force should be continued. In such cases, the root of the ultimate disaster, is most simply identified as a fallacy of composition: the fallacy of assuming that what might appear to be true in reading of nominal cost-price ratios in the short term, or in the small, measures the physical result of present policies in the long term, and in the large. Too often, this fallacy of composition, this delusion, continued to reign, up to the point that the disaster struck, disaster caused by just such policy-trends. In short, a frequent cause of the bankruptcy which occurred in some such cases, was the cumulative impulse of decadent ownership and chief executive officers, to increase current short-term profits, by curtailing those investments, and curtailing payments of those elements of incurred cost, on which the long-term future of that enterprise had actually depended. Such were the self-doomed navigators, who charted a long journey on the presumption that estimates made for small areas, showed, in effect, that the Earth is flat. Among those fools, such delusions were often admired as expressions of "fiscal conservatism."[3]
Today, over the course of the recent quarter-century or so, the failure, by governments, many leading corporations, and public opinion, to grasp the nature of those issues, is the cause for the increasing loss of simple competence of today's managements, among an increasing ration of the leading aerospace and other manufacturing firms. This includes many among the world's automotive giants. A presently accelerating, already widespread collapse in both long-term and short-term product-safety factors, is an expression of this. A key factor in promoting the latter trends toward such increasing incompetence, among both corporate managements and governmental budget-management, has been the growing popularity of the fad known as "bench-marking," the substitution of computerized "mathematical modelling" and related "cost reducing" tactics, for the indispensable, science-driven, engineering-based approach to product design and production management.[4]
An hysterical, frankly pagan-religious quality of blind faith in the existence of an "information"-driven economic growth, and related sort of faith in the alleged miracles of "globalization," are expressions of such currently popular forms of economic dementia. The most extreme expression of that growing incompetence of the economic programs of both governments and shareholder interest, is the hyperbolic rate of increase, of the disassociation of nominal shareholder and market-index values from physical economic reality, as my now-widely circulated "triple curve" illustrates that point in the simplest possible, summary way.
As the present world financial and monetary system is now careening toward its inevitable, early disintegration, the old issues between production management and the financial and accounting departments, now assume a qualitatively new importance. These considerations are now crucial, for defining the principles which must guide the urgently needed, global economic recovery, out from under the preceding thirty years of globalized overlordship, by a parasitical, floating-exchange-rate monetary system.
That presently doomed, globalized world financial system, the floating-exchange-rate system of the past three decades, can not be rescued. The Titanic is already doomed; among sane persons, the only tolerable policy is that of bringing the passengers and crew, freed of the grip of the doomed system, into safety. A sudden, relatively convulsive reorganization of the world's finances, monetary systems, and trade-relations, is the only hope to be foreseen among those nations which prefer that their nations survive the sinking of the doomed, present form of the International Monetary Fund's (IMF's), world-dominating, financial and monetary system.
The way in which the nations could actually be pulled safely out of the doomed system, should be obvious, from the lessons of experience, to any reasonably literate person above sixty years of age today.[5] To know which system is to be preferred, we have to compare the way in which Franklin Roosevelt led the U.S.A. out of Wilson's, Coolidge's, and Mellon's Great Depression, and compare the net relative successes of the pre-1966 Bretton Woods, with the catastrophe which has unfolded since August 1971.[6]
We must immediately return to the kind of monetary system which worked fairly well (for the U.S.A. and western Europe, at least) during the 1944-1966 interval, the old, protectionist, fixed-rate, Bretton Woods system. We must scrap all of those post-1971 changes in economic, financial, monetary, and trade policies, which have been introduced since the August 1971 beginnings of the now hopelessly, systemically bankrupt, present world monetary system.[7] This must include an immediate reversal and elimination of all agreements launched in support of so-called "globalization." That revival of the best features of the original Bretton Woods system, is not a matter of opinion; it is a matter of choosing survival over what would be nothing other than clinging hysterically to a hopelessly failed, and doomed system. Otherwise, a virtually planet-wide, now imminent new dark age for humanity, were inevitable for a generation or more to come.
All of the types of necessary emergency actions needed, again today, to put a bankrupt world system through an effective bankruptcy reorganization, were foreseen by President Franklin Roosevelt and key advisors, up to the point of his most untimely death. We must presently go beyond the measures which were actually carried out under the 1944-1964 phases of development of the old, pre-1971, economic-protectionist period of the Bretton Woods monetary system; but those pre-1964 precedents do provide a model for the first emergency actions to be taken. To those actions we must add, very quickly, other actions which had been intended by that President Roosevelt, but which were cancelled by the Truman administration almost immediately after Roosevelt's death.
To appreciate those 1944 designs of intentions for a post-war monetary system, one must take into account the points of similarity of the world then, and now. The similarity lies, essentially, in the fact that, at the time, we had to revive both the U.S. and European economies from the conditions accumulated under the exhausting conditions of the post-Versailles Great Depression and prolonged general war. The world economy today, especially that inclusive of both Europe and the Americas, is, systemically, in as ruined a state, or even worse today, if in a somewhat different form, and from somewhat different causes, than at the close of World War II. Despite the important differences between the Marshall Plan-led recovery of both the U.S. and western Europe, and today's circumstances, the framework of the needed emergency action establishing a new monetary order, is approximately the same.
However, so that what Roosevelt intended, is accurately understood, some words of caution must be inserted. In reviving the successful features of the pre-1959 form of the old Bretton Woods system today, we must take into account the chief flaws in the changes made in Roosevelt's policy, to which I had referred, above. Take into account the elements of Roosevelt's post-war policies which were summarily discarded, during the indecent, brief interval immediately following his most untimely death.
There were three such chief, categorical errors in post-Roosevelt U.S. policy of practice during the Truman years: First, the failure to shut down the Portuguese, Dutch, British, and French colonial systems and their relics, as Roosevelt had intended should occur immediately, on the ending of the war. Second, the militarily unnecessary, counterproductive, and otherwise foolish and cruel, dropping of two fission bombs on the helpless civilian populations of Japan's Hiroshima and Nagasaki. Third, the failure to launch a forced-draft rate of immediate and rapid conversion of our war-time industrial potential, without losing a step, as Roosevelt had intended.
Despite those terrible errors introduced under President Truman, the immediate need then, as Roosevelt had understood this, was to rebuild a shattered post-war world economy, not only the economy of war-torn western Europe, as the task defined by the leading post-war mission-orientation of the U.S. economy. Thus, those Roosevelt intentions which were put into effect, worked, as far as they were applied. Today, a similar outlook means, that we must implement Roosevelt's own intentions in full, as far as that is appropriate today. Leading developing nations from the so-called developing sector, must be leading partners with the U.S.A., Europe, Japan, and Russia, in establishing and administering the revived form of the newly revived, pre-1968-1972 form of the former, economic-protectionist Bretton Woods system, of cooperation among perfectly sovereign nation-state economies.
Today, such a new monetary system will provide the indispensable policy-framework of opportunity, for a long wave of global real economic growth, as measured in physical terms, per capita and per square kilometer. So far, so good. Then, having given ourselves such an opportunity to take the road to economic recovery, how shall we manage that journey? That situates the task of reformed cost accounting doctrine and practice, as set forth in the following summary of the crucial issues to be considered.
1. Monetary policy and cost accounting
To understand the way in which the needed new world monetary order must be administered, we must begin by defining certain axiomatic principles. For purposes of introducing the argument, I define the meaning of the term "axioms," if but briefly, as in first approximation, in the sense of the definitions, axioms, and postulates of a deductive form of Euclidean classroom geometry. My substitute for such a system of axioms, constitutes the principles of what has become known as the LaRouche-Riemann model of physical economy.
In a moment, I shall begin the account of how this discovery occurred, and show how and why the notions of cost accounting being presented here came into being. Yet, before I begin that account, a few words of caution must be presented to the reader.
The subject-matter presented here could not be delivered in a customary textbook-modelled style. The textbook style depends upon early agreement, between writer and reader, on an initial set of axiomatic assumptions. Thereafter, the customary type of report, proceeds from those variously stated and implied assumptions, never leaving them, deriving its conclusions from a series of facts, as the initially stated general assumptions determine the way in which those facts are adapted, to conform to the opening set of assumptions. In this case, the very nature of the subject-matter demands that the writer, in Socratic fashion, tear up sets of what had been the reader's own putatively customary axiomatic assumptions, one set after the other. This obliges both the writer and the reader to share the relevant successive experiences of tearing up customary assumptions which must be uprooted, and presenting the way in which those assumptions are replaced by the generation of the new, alternate, axiomatic and related assumptions, which comprehension of the subject-matter requires.
As I have just said, this task requires a Socratic approach; it also requires that the reader be supplied the means to live through, successively, the relevant discoveries on which comprehension of the final result depends. That is the course followed for this presentation of the subject-matter.
That word of caution stated, I proceed now, by first stating the significance of that term, "LaRouche-Riemann model of physical economy," then showing how that "model" provides an indispensable kind of guidance toward the needed new forms of generalized cost-accounting practices. I begin that now, by introducing the principled conceptions upon which that LaRouche-Riemann model was founded.
My original discoveries in the science of physical economy, which I made during 1948-1952, were prompted by my study and rejection of Norbert Wiener's "information theory." I was prompted to undertake that study, by my recognition of the fact, that Wiener's axiomatic assumption was readily refuted by even the ordinary industrial experience of day-to-day increase in the productive powers of labor, gains generated through scientific and technological progress, in industry. My resulting original discoveries, led me, in late 1952, to recognize a certain special degree of coincidence between those discoveries, and the kinds of anti-Euclidean geometry defined by Professor Bernhard Riemann in such locations as his 1854 habilitation dissertation.[8]
My own original discoveries in physical economy, had followed the same track I had employed, a decade earlier, in a youthful defense of Leibniz's method against the reductionist method and conclusions of Immanuel Kant's series of Critiques. My 1948-1952 attack on Wiener's hoax, had proceeded from my recognition of the fact that Wiener had merely echoed the same fraud as Kant before him, if in a more radically positivist, and vulgar way. Late during 1952, after recognizing that my own original discoveries, could be best restated in a Riemannian form, I redefined the Leibnizian science of physical economy accordingly.
A summary of the relevant features of my attack on Wiener's cultish notion of statistical "information," shows the relevance of that discovery to cost-accounting methods. In the later refinement of that discovery, during 1952, I recognized the appropriateness of applying Riemann's wonderful work to enhance the application of my own discoveries in the field of economics.[9]
As I have already noted, above, already in 1948, from the outset, I was encouraged to make the attack on statistical information theory, by my recognition of a crucial vulnerability in Wiener's fabrication of his hoax; I saw the readiness with which even the elementary economics of industrial production, refuted Wiener absolutely. The point was, that society's ability to increase mankind's power over nature, both per capita and per square kilometer of surface-area, was a reflection of those cognitive powers of the individual human mind which set mankind absolutely apart from, and above the learning capacities of all lower species, the higher apes included among the categorically sub-human types. From the standpoint of production, this unique power of the individual member of the human species, is expressed, most simply, by the individual mind's capacity to generate validatable discoveries of universal physical principles.
This qualitative gain in mankind's per-capita power over nature, is the source of humanity's power to willfully increase its potential relative population-density, as no other living species can. These discoveries can not be generated by mere learning, nor by any use of deduction. They can be generated solely by means of that non-deductive, cognitive process, which exists only within the sovereign mental capacities of the human individual, that as a sovereign individual. This is the source of what we recognize as the impact of corresponding, qualitative leaps in the quality of technological progress in agriculture and manufacturing. Typical expressions of this, are revolutionary changes in choice of employed physical principle, in the design of products, and in the processes of production as such.
The function of the human individual's cognition to this effect, is most simply expressed in the form of an axiomatic change in belief, as such a change is typified, in first approximation, by a validated, externally imposed change in the set of definitions, axioms, and postulates of a deductive form of classroom Euclidean geometry, as in a so-called non-Euclidean geometry.
2. Cognition, science, and productivity
As we now turn to the body of this report, I shall first state, once again, as I have in various earlier published locations, the essential distinction between mere learning, and its transmission, of which the higher apes, are capable, and the processes of cognition, a capability unique to the human species.
After that, I shall examine the needed principles of cost accounting in two successive, preliminary steps. First, I examine this in terms of the phase-spatial characteristics of increases in productivity, as these are driven by new applications of universal physical principles; after that, the scope of the presentation is broadened, to take into account the powerful role played by application of ideas in the form of Classical-artistic principles of composition. In the first stage, our focus is upon the functional characteristics of universal physical principles in determining the individual's functional relationship to nature, as per capita and per square kilometer. In the second stage, the emphasis shifts to the determining role of universal principles expressed in such forms as principles of Classical-artistic composition, in governing the social relations through which the individual's relationship to nature is determined. In the latter stage, we take into account the functional, physical-economic role of the costs necessarily incurred in developing the individual mind, and also social relations, to the degree needed to foster both scientific productivity and its efficient, physical-economic application by society.
In summary of the immediate, first series of points to be developed:
The essential, categorical distinction, separating human societies from animal ecologies, is the increase of society's power over nature, per capita and per square kilometer, through cooperation in the fostering and application of discovered universal physical and related principles. The ability to discover and cooperate, in terms defined by such discoveries, is an indispensable source of all willful improvements in the potential relative population-density, and conditions of life of the human species. The generation and sharing of such universal discoveries of principle, is the fruit of a quality unique to human individuals, the power of cognition, as distinct from, and opposed to mere learning, or to mere "sharing of information."
Thus, this faculty and practice of cognition by individuals, defines the absolute separation of the human species from all lower forms of life. Here lies, thus, the only rational definition of human nature. Here, in individual cognition, lie all the supposed secrets of humans' behavior, as individuals, as agents of cooperation, and as entire societies. The only rational definition and analysis of political economy, is, therefore, the study of the functional characteristics of those social processes, by means of which the fostering of cognitive propagation and sharing of universal principles, prompts long-term increases in the potential relative population-density of mankind. All conceptions pertaining to these matters, must find their axiomatic roots in the characteristics of such cognitive processes.
Therefore, we now derive the principles of cost accounting, in accord with that. We begin with emphasis upon the generation and nature of universal physical principles.
What is cognition?
The discoveries of what are later experimentally validated as universal physical principles, are prompted by the demonstration of those qualities of paradoxes, the which are not susceptible of formal solution by means of the deductive and other methods of the philosophical reductionists. Such paradoxes are typified by the ontological paradox of Plato's Parmenides dialogue; the impossibility of solving such by deductive methods, is typified by the case of that historical Parmenides, whose method Plato referenced in that dialogue. A successful solution is generated when something occurs, the which is sometimes described as an ignited flash of insight, to produce a validatable hypothesis in that person's mind.
The acceptance of that hypothesis by other persons within society, requires that two special conditions be satisfied. First, the same experience of insight must be replicated, independently, within the sovereign cognitive precincts of at least one other individual's mind. Second, that hypothesis, so generated, must be shown to be an existent, efficient principle, by means of experimental demonstration of the efficiency of its willful application to the physical domain as a whole. The latter such experiments belong to the class which Riemann defined as unique: it is not sufficient to show experimentally that the prescribed effect might be produced; it must also be demonstrated that that hypothetical universal principle coheres, in a multiply connected way, with all validated other universal physical principles.[10]
The crucial point is, that the only way in which we can generate a functionally efficient notion of such a cognitive idea existing in another mind, is the three-step method of sharing such an experience (paradox, hypothesis, validation), as I have just identified this summarily. In such a case, we know three essential things. First, we know, independently of our cognitive processes, the paradox which prompted the generation of a discovery of principle, as the only feasible solution to that paradox. Thirdly, we know the manifest experimental proof of the proposed solution. Thus, by sharing the first and third of those steps, we are able to correlate the specific act of cognition, the second step, in the other mind, with that recallable experience of cognition we experience in our own.
Finally, by comparing that specific, recallable experience, with a similar but different experience of the same functional type, respecting a different paradox, hypothesis, and proof of principle, we are able to begin to discriminate consciously and willfully among the cognitive experiences specific to each such hypothesis. This ability, so prompted, permits us to recognize each such repeatable cognitive act as a distinct idea within the mind, and to give it a recognizable name, which then identifies that act; that generates the class of what are called Platonic ideas. The way in which hypotheses are generated, by Socratic method, in Plato's dialogues, is a now age-old exercise in training the mind to build up a repertoire of nested such Platonic ideas. After Plato, this became the age-old Classical method of cognitive education in globally extended European civilization.
All the outstanding intellects of the Fifteenth Century Golden Renaissance, the associates or students of Nicholas of Cusa, typify minds exhibiting in their practice, the specific methodologies associated with that method and its associated policies for education of the young. A similar method of discovery of distinct cognitive ideas, is typical of the most enduring contributions of universal and related principle from sources outside extended European civilization. Nonetheless, it is the European experience, and its unique contributions to the development of modern science, technology, and political economy, which is the focal point of reference for this present report.
An hypothesis which has been discovered, shared, and validated in that way, as I have indicated here, represents a known universal physical principle of our universe. That use of known, as used in that exemplary setting, is, as I shall show, the most crucial issue posed by the fallacies of what are still treated today as commonly accepted, and often potentially fatal errors, errors which are also contained among most currently taught and practiced principles of political-economy and cost accounting.
The most common expression of the fallacy I have implicitly attacked in that way, is the following.
It is common, naive practice, still today, to limit the functional definition of fact, to either mere sense-perceptions, or to the implied superstitions of those putative authorities who are treated as set apart from ordinary witnesses, set apart in the fashion of those putative mystics who, as in Jonathan Swift's allegorical Laputa, are legally classed as experts. In this way, the term knowledge is usually misused, to suggest that, for all ordinary mortals, truth is limited to the domain of the philosophical materialist's simple sense-perception, or to "information" as the hoaxster Norbert Wiener, among other charlatans, has defined statistical "information theory." The two, variously bestial and mystical varieties of superstitious dogmas, implicitly exclude the possibility of the existence of truthful forms of knowledge of the real universe, as Immanuel Kant asserted this denial, categorically, in his Critiques.[11]
In what place, then, do validatable universal physical principles exist? How are they to be perceived? How do we reconcile the reductionist's notion of relative truthfulness with the fact, that any validatable hypothesis, nullifies the truthfulness of previously extant, expert opinion, in that degree? Since universal principles can not become known directly through sense-perception, nor known through the quality of expertise whose truthfulness they negate, by what mental faculty are they to be known?
The answer, of course, is: through the faculty of cognition, that faculty of insight found only beyond the bounds of sense-perception, found only within the sovereign precincts of the individual human mind. They are found as I have described the situation, in which the discovery and validation of a universal physical principle is established, through the social relationship between the cognitive processes of two or more individual minds, minds sharing the replication of that same cognitive experience of both discovery and empirical validation. Since cognition can not be observed by means of sense-perception, as operations of a strictly formal logic might be displayed in a textbook or on a classroom blackboard, we may "see" the cognitive act in the mind of another individual person, or persons, solely by the social act of replication and validation of fruitful forms of insight, those acts which have the form common to successful acts of replication of discoveries of empirically validatable, universal physical principles: principles which are empirically validatable as universal.
As a matter of contrast: In education, we often experience the case of a student who may achieve a nearly perfect score in the grading of his written or oral examination, and in his grades generally, but who, under different social circumstances, shows that he has learned much, but knows nothing of one or more of the matters on which he has been examined. To gain his excellent grades and other awards, he may have either crammed for his examinations, or gobbled up learning with exceptional facility. In that process, he has merely learned to pass examinations, not to master the original form of practice of that subject-matter. He does not actually know the subject-matter for which he has been drilled, and wrongly certified, by examination, as knowledgeable.
Thus, that graduate, in decision-making and other discussions among his professional peers, often responds, as if ritually, to problematic situations, by means of either arbitrary regurgitations of formulations he has learned to repeat, like an ideologue repeating the political-party line on this or that; he shows, thus, little or no sense of the inappropriateness of that regurgitation to the relatively anomalous challenge at hand. Or, in other manifestations of this type, that person, as a student, may have relied on playful private exercises in which original discoveries of principle were replicated in a cognitive way; however, as that same gifted student had been induced to conform to reductionist methods of argument, as the price of success in securing a terminal degree, or, out of a wont to conform for sake of career opportunities, or in a similar way, the earlier intellectual promise faded; increasing conformity leads, thus, to an increasing number and variety of non-cognitive dead patches, appearing in more and more of the topical areas of thinking exhibited by such persons.[12]
Today, unfortunately, this saddening state of affairs is often demonstrated in industrial-design, and related practice, for the cases of those design engineers whose practice relies upon so-called mathematical modelling, rather than upon the quality of engineering practice associated with crafting successful proof-of-principle kinds of experimental designs. This deadening of the cognitive powers of the mind, is to be seen respecting their lack of regard both for universal physical principles, and, for the multiple-connectedness of combining two or more of the technologies derived from such principles.[13] The same precaution must be observed in respect to the practices of financial analysis and cost accounting.
Thus, in a competent program of education, efficiently dedicated to the goals of scientific literacy, the emphasis is always upon inducing the student to replicate the relevant cognitive experience of generating and validating universal principles of an implicitly axiomatic quality. This is not accomplished by mere learning, or by substituting simpler experiments in which no axiomatic quality of universal physical principle, is put explicitly at issue for the student's cognitive processes. The most significantly beneficial results, are usually effected, and that quite lawfully, in the instance in which the student is made aware of the fact that he, or she is replicating the original discovery as a personalized, historical event. It is important that the students also conceptualize the validation of the historical act, rather than conjecturing an abstract, ahistorical sort of proof-in-general. Typical of appropriate questions are: "How did Eratosthenes actually measure the length of the great circle of the Earth's perimeter, and the length of the great-circle arc from Alexandria, Egypt to Rome, Italy?" "How did Fermat define the principle of shortest time, in opposition to the notion of shortest path?"
In such an historically specific and personalized, cognitive approach to the education of students in the rediscovery of universal physical principles, the student is impelled to replicate the original acts of discovery and validations of the universal physical principle, the which are posed to the student in the form of an ontological paradox. The student is thus induced to replicate the cognitive act of that original, historically situated discoverer, thus to live inside that cognitive moment of the discoverer's mind, and to experience that moment as his own cognitive experience, to that degree. All education should be premised on emphasizing such re-enacted discovery of such principles.
Such were the fruits of the work of truly great teachers, as distinguished from those showing, customarily, relative competence in merely describing the relevant subject-matter. These considerations are among the crucial distinctions which qualified cost accountants must take into account, in estimating the necessary costs of fostering the production of creative scientific and related productivity among the generality of future adults of today's society. The issue of cost of both education and related conditions of family-household life, must be situated in terms of that variable quality of resulting cognitive development, or lack of development, in the graduates, as in the policy-shaping of government and private enterprises.
Higher cognition
However, although we were obliged, here, initially, to present cognition in terms of single acts of discovery of individual hypotheses which represent validatable universal principles, the general notion of cognition is found in a higher place, in the notion of higher hypothesis.
This distinction is adequately illustrated by the case of a generalized insistence upon the cognitive method of generating, and validating hypotheses of an axiomatic quality, as in classroom and related education. That case is best illustrated, by adopting the view that a child's and adolescent's schooling in matters of science and mathematics, must adopt as its general goal, the rejection of the inductive method, for that of fostering of the Riemannian world-outlook of anti-Euclidean geometry, in the maturing student population. Something approximating this was always manifest in the most creative members of student populations; on that account, early adolescent, or even pre-adolescent, confrontation with Euclidean classroom geometry, as opposed to inculcating blind faith in such dogma, was a crucial feature of the education of the secondary pupils.[14]
Through repeated replications of such original discoveries, as opposed to the process of the acts of merely learning, as by young chimpanzees, the student must replicate some of the cumulative results of those original discoveries. Through continued practice in this way, the student does much more than merely come to know those original discoveries of principle. In this case, such education in matters of universal physical principle, is dominated by a cognitive approach to solving ontological paradoxes. In this setting, the student's progress in education, tends to foster the growing awareness of some higher principle of ordering, a higher principle governing the generation of an unfolding manifold of validatable universal physical principles. It is implicit in the way in which Plato sets forth the paradoxes of his Parmenides, this sense of a higher principle of ordering exists, as an underlying, single principle, which subsumes each and all of a manifold of validatable universal physical principles. This shows, that there exists a higher form of hypothesis.
Riemann's notion of a series of multiply-connected manifolds of universal physical principles (a manifold of successive manifolds), which replaces all geometries of an aprioristic form of physics, replacing such as one subsumed by a Euclidean or quasi-Euclidean geometry, is an example of such a higher form of hypothesis, an anti-Euclidean principle of higher hypothesis. In Riemann's Leibnizian approach, each such manifold of a series of manifolds, exists as a distinct idea, an idea distinguished by its specific, experimentally demonstrable, Leibnizian physical characteristic of action. This notion of Riemann's is already implied, or, one might say, begged, in Kepler's exposition in his The New Astronomy, where Kepler details proof that a common, formalist fallacy underlies the failed astrophysics of Claudius Ptolemy, Copernicus, and Tycho Brahe. The relevant comparison of the successive work of Kepler, Leibniz, and Riemann, suffices to show, that, contrary to scientifically illiterate gossips, there never was a "Copernican revolution" within the historical development of modern Europe.[15] In the domain of physics, this historically shaped emergence of Riemann's revolutionary notion of an implicitly orderable series of multiply-connected manifolds, corresponds to what Plato identifies as a notion of higher hypothesis.[16] This notion of higher hypothesis is congruent with the principle of universal change, as Plato illustrates the point in his Parmenides. This signifies a principle subsuming the notion of well-ordered, successive, validatable changes in the composition of a series of multiply-connected manifolds, as distinct from the hypothesis which defines but one principle to be introduced, as correction, to define but a single new axiomatic mind-set. Call this higher, subsuming ordering principle, a continuing, ontological principle of change.
Consider the practical significance of that principle of higher hypothesis. Consider the question: What is the practical significance of a student's ability to replicate several individual, validated discoveries of universal physical principle, and to have insight into a qualitatively superior method within the domain of cognition, a method by means of which, an unfolding series of such discoveries can be generated. Consider the question: What is the difference between cognitive knowledge of certain universal physical principles, and an assured capacity and method for generating entire series of original such discoveries?
The crucial question, as directly relevant to economics, is: What is the causal form of action which generates a general increase in the relative general productivity of the economy? That action is not simply production, as by labor in and of itself. That action is the expression of a principle of change, a power which generates a principled change in the potential relative population-density of the society. The cause of increased productivity lies in the fruits of cognition, not the simple act of labor as such. Hence, the functional notion to be employed, can be nothing other than change, as defined by Heraclitus and Plato, as a power-generating change. The question is not how to make a valid individual discovery of a universal principle; what is required, is the method for generating an unending series of successive such revolutions. What is required, is the deployment of the principle which assures that latter result. The question is: how do we shape the economic policies of a society, to ensure that that result is fostered. How do we develop the discoverers, and how do we ensure that the society is disposed and otherwise prepared to assimilate such benefits to the effect of advancing the potential relative population-density of the human species? All that is written hereafter, in this report, should be considered with that statement of this report's assigned mission prominently in mind.
To that latter end, we must approach that challenge by, first, developing a clear conception of the specific distinction which sets the truly cultivated creative-scientific intellect apart from the relatively more pedestrian sort of qualified professional. This is to be found in the implications of this notion of higher hypothesis. Such is the fertility of the creative intellect of an Eratosthenes, a Dante Alighieri, a Brunelleschi, a Nicholas of Cusa, a Leonardo da Vinci, a Kepler, a Leibniz, a Gauss, and a Riemann.
This latter distinction among qualities of scientific thinkers, is not merely a matter of degree. The distinction is, as I have said, qualitative. This point is made explicitly by both Gauss and Riemann, in their replacement of the notion of connectedness among empirically validated axiomatic principles, by the notion of a multiply-connected manifold and its associated characteristic.[17] This notion of characteristic, together with the associated notion of general principles of curvature, so situated, is a conception of crucial importance for the founding of an urgently needed new set of principles of cost accounting. The equivalence of the notion of higher hypothesis, as summarized here thus far, is crucial for the effective shaping of general, long-range economic policies, both within sovereign nations, and in their choices of long-range cooperation.
This same notion of higher hypothesis, when so situated within the domain of physical economy, shows the dangerous error embedded axiomatically in the mistaking of sense-experience as such, for a standard of truthfulness. This notion of higher hypothesis, extended from the domain of physical science, to include validatable and universal Classical principles of artistic and related composition, constitutes the domain of reason. Cognition, defined in this way, is the cognate of the notion of reason, the latter as distinct from mere deductive logic. This distinction is not a merely formal one, but has immediate moral consequences for society, both within the domain of scientific practice, and otherwise. It is in that sense, and only that sense, that the term reason is used hereinafter, by me.
To sum up our discussion thus far. Thus, cognition, as typified by the experience of replicating the argument of Plato's Socratic dialogues, rather than sense-perception, is the only faculty by means of which the individual human mind, and society in general, can actually know the truth in any matter of universal principle.
Here, in this report, our emphasis is upon curing those heretofore commonplace fallacies, the which inhere in the way in which today's customarily taught doctrines of political economy and cost accounting, especially so-called "standard cost accounting" have been presented. The point to be emphasized, most of all, is that those customary practices falsify the knowable, physically efficient principle of action underlying the apparent connection among the dots of perceived financial-accounting events. It is customarily assumed, that the connection among the dots, is deductive in nature, and therefore linear. There lies the most common folly within today's generally practiced financial analysis.
The axiomatic error characteristic of such customary practices, is twofold. The first error is the assumption that we may define the functional aspects of a political-economic process, by substituting simply defined prices and other quantities, as mere nouns, for the verbs which a competent functional notion of economic process requires.[18] In other words, the mere "dots" of sense-perception are substituted for that action, which, instead, should be reflected in the proper use of verbs.
The second of those two errors runs as follows. A typical clinical demonstration of the pathological implications of today's widely accepted opinions on matters of political economy and cost accounting, is the delusion that a mere financial gain, such as a financial capital gain, even one premised on the virtual gambler's side-bets called financial derivatives, is a contribution to the nation's prosperity, its estimatable Gross National Product. The delusion, that money as such is wealth, is the specific form of the sometimes fatally ruinous, fatuous delusions common to such cases as the historical tulip and John-Law-style financial bubbles of the Seventeenth and Eighteenth Centuries, the evaporation of money itself in Germany's 1923 hyperinflation, and the mortally cancerous financial bubble which accounts for most of the nominal financial wealth popularly attributed to the U.S. and the world today. It was never truly wealth; it was only a wish expressed on paper. So, often, sly merchants have traded wishes for horses.
Physical science and productivity
From the outset of my referenced 1948-1952 studies, I adopted the following, somewhat simplified, but appropriate representation, of the functional connection between the discovery of universal physical principles, and the ensuing generation of new technologies of product design and productive practice.
In brief: Of necessity, the appropriate experimental validation of a new scientific hypothesis, must feature, as expressed within the design of that experiment, a direct reflection of the universal principle being tested within the chosen experimental medium. That latter feature of a successful such experiment, is the most appropriate functional definition of a technology, as distinguished from that universal physical principle from which that technology is thus derived.
To maintain coherence in this ongoing report, I select, here again, the example of Wilhelm Weber's experimental proof of the Ampère angular force. A study of the experimental apparatus employed for Wilhelm Weber's proof, and measurement, is an excellent choice of example, of the way in which a test of proof of a specific universal physical principle, must include elements of the experimental assembly which correspond to the way in which that principle subsumes one or more implied technologies.[19] The measurement of universal constants, by aid of such apparatus, as in the case of Weber's measurement, is a readily recognized example of this kind of connection.
However, since the relations among physical principles and technologies, must be situated within a valid sort of multiply-connected manifold of the Gauss-Riemann type, we can not limit the notion of technology to so relatively simple a case, as the validation of a single physical principle within a single choice of experimental medium. A rich plenum of experimental measurements remain to be considered. First, there is the matter of physical-experimental determination of characteristic curvature of the domain in which the new principle is situated. Next, the issue of multiple-connectedness, invades the manufacturer's department of experimental testing and design, whenever technologies are combined in a new way.[20]
That latter word of caution, represents an extended view of the same matter addressed in the concluding portion of Riemann's habilitation dissertation. The characteristic curvature of multiply-connected manifolds, is to be determined by the methods of measurement used for test of principle in physics, not the methods of a merely formal mathematics. Similarly, the significance of multiple-connectedness haunts the designer, whenever technologies derived from known principles are combined in a new way, within a single design. Those combinations of technologies, must be measured as to their effects upon the characteristics of the assembly as a whole. Similarly, when technologies are generated in new choices of media, and new combinations of media, this change must also be tested according to Riemann's principle.
Therefore, any cost-conscious corporate management so reckless, as to imagine it might be permitted to reduce costs by substituting so-called mathematical modelers, for the type of design-engineering developed for the tasks of testing new universal physical principles, should be promptly discharged, that out of consideration for urgent issues of managerial incompetence.
Overzealous cost-cutters must be forewarned, with suitable penalties attached, against neglecting this matter of principle. On principle, neither financial-accounting projections, nor other enterprises in mathematical modelling, have any intrinsic competence, beyond the application of what have already become empirically validated combinations of known principles, technologies, and media of application employed.[21] Indeed, for precisely this reason, safety reasons included, empiricists and existentialists should be excluded from positions of supervisory authority in scientific development, in design of products and productive processes, and in cost accounting and medium- to long-range budgeting of large enterprises, national economies, and long-term economic relations among states.
As I shall indicate at a later point in this report, attention to these kinds of issues of economic policy, bearing upon the functions of science and technology, must be shifted from confinement to application within the relatively small scale of the individual firm and locality, to the large, and from the relatively short-term, of one to several years duration, to the long term considered in the spatially large. Otherwise, the results will be akin to the catastrophic consequences for the passengers on a ship of fools, of relying upon a transoceanic navigator who is passionately persuaded, by limiting his education to study of very small areas of space, that the world is flat and the universe four-square.[22]
That said by way of introduction to the following point, look at the entire matter of economic policy, in the very large that is to say, nationally, or globally, and in the long term, a decade, a generation ahead, or even longer.
Therefore, at this moment we interpolate, and emphasize the way in which the definition of human nature, as defined by cognition, assumes the role of the determining consideration in economic analysis and related matters. I situate the connection to be made with a few pertinent background observations.
If the human species were a type of great ape, the human population of this planet would never have exceeded several millions living individuals. Such would have been the ecological state of affairs for such a species under the conditions existing on this planet during any part of a period of approximately the past two millions years to date.
The actually known increases of the potential relative human population-density, consist chiefly of some known historical accounts, dating presently from no earlier than approximately 12,000 years before the present, plus artefacts which date known human existence and activity, to no later than several hundred thousands of years ago.[23] The most notable associated difficulty confronting the paleontologist on this latter account, is to determine whether a relevant relic represents the remains of a human individual, or some higher-ape-like creature. This distinction requires nothing different than evidence which associates that relic with artefacts of clearly human activity.[24] In light of the known ability of higher apes, such as chimpanzees, to learn, and to transmit learning to their offspring, such artefacts, whether as assessed singly, or in combinations, can not be securely identified as products of human activity, unless they are, without doubt, products of human cognition, rather than merely the kinds of transmittable learning associated with the higher apes, for example.
As I have already reported here, the earliest secure such dating known to me, has been identified by relevant scientists as dated to several hundreds of thousands of years ago. The artefacts associated with that site, well crafted throwing spears, reflect the existence of a culture existing in Europe, during what was probably an inter-glacial period, a product of a culture which must be dated even earlier, to many preceding generations. However, precisely because of approximately two millions years of glacial cycles, the repeatedly glaciated regions of the northern hemisphere, are not the likely places in which to locate the settings of the earliest phases of human cultural development and its transmission.[25] Such a broad-brush overview, is sufficient for our consideration here, on the topic of cost accounting, respecting the general state of currently available knowledge respecting the antiquity of human culture.
Such background evidence taken into account, there is no doubt, that the increase of the human species' potential relative population-density since the Fifteenth Century European Renaissance, has been qualitatively greater than in any other known or suspected case prior to that time.[26] The figure for population growth shown here, [Figure 2] has the double significance, that it has been used repeatedly, as a statement of fact, by each of two diametrically opposing factions, both the pro-Malthusian and the anti-Malthusians. I use it here to illustrate the correlation between the emergence of the institution of the sovereign nation-state, during the Fifteenth Century Golden Renaissance, and the emergence of the indicated long-range trend of increase of potential relative population-density. Those who promote drastic reductions in the human population, the modern Malthusians, such as U.S. Vice-President Al Gore, for example, use it as evidence to show the urgency of eradicating the modern sovereign nation-state. The latter propose to arrest technological progress, reduce sharply the life-expectancy of selected portions of the human population, as savagely as Adolf Hitler attempted, and to destroy the sovereign nation-state, in favor of a return to the kind of world government which existed under both the Roman Empire and European feudalism.[27]
The functional basis for that increase in potential relative population-density, as brought about by globally extended modern European cultural progress, was the establishment of the modern, sovereign form of nation-state. This was a form of state organized around that same Fifteenth Century commonwealth principle, the principle of the obligation of government, to promote the general welfare for all of the population, the principle of a true republic, which was later adopted in the opening paragraphs of the U.S. 1776 Declaration of Independence and the 1789 Preamble of the U.S. Federal Constitution.
Prior to the Golden Renaissance, and the resulting new form of sovereign state under France's Louis XI and England's Henry VII, the majority of the human population, under all governments, was treated as human cattle, virtually owned, used, or culled, by choice of either a ruling oligarchy, or by an imperial power, such as the Caesars, which had been chosen to represent and regulate such a ruling oligarchy. It is the demographic and related benefits of that modern form of sovereign nation-state republic, which are reflected in the Figure shown here.
That commonwealth, or republican principle, as President Abraham Lincoln defined our republic (but neither Presidents Theodore Roosevelt nor Woodrow Wilson), was the immediate and principled cause for the doubling of the national income of France under the short reign of Louis XI. It was as a by-product of those measures taken in France, then, and England shortly after that, that the conditions of life, national income, and potential relative population-density of European population, have enjoyed the long-term rate of improvement experienced, in net effect, during the half-millennium since.
The fact that this improvement continued, as a long-term trend, until the turn for the worse, thirty years ago, with the introduction of the cumulatively disastrous floating-exchange-rate monetary system, reflects the combined impact, and interdependency of several fruits of the nation-state institution itself. These fruits included the political and social reforms in aid of the general welfare, the promotion of the role of the state in both economic-protectionist measures and building of basic economic infrastructure according to the requirements of the general welfare, and the related promotion of education in physical science, technology, and Classical culture. That interdependency of these cited influences, that under the indispensable role of the institution of the sovereign nation-state, defines the point of birth of modern political economy.
At this point in this report, our attention is focussed upon the functional role performed, to this physical-economic effect, by promotion of scientific and technological progress. The interrelated role of the latter with social and political reforms in the practice of political economy, we shall examine at a later point in this report. At this point, our attention is focussed on the causal (functional) relationship between discovery and validation of universal physical principles and increase of potential relative population-density.
The listing of the immediately preceding considerations brings us, to the way in which the most specific distinction of the individual person, the universal principle of cognition, defines the characteristic features of both mankind's functional determination of increases of its potential relative population-density in general, and the underlying principles of a modern political economy, in particular. To situate this phase of the report, I return your attention, briefly, to my work from the 1948-1952 interval, focussing on a work being done circa 1948. In the effort to sort out the tumult which my undertaking against statistical information theory, had generated within me then, I compared the problem of defining the impact of technological progress, with the seemingly analogous problems of defining living processes, other than in the customary clinical way, as the axiomatic issue of the functional nature of life itself was addressed in Professor Nicolas Rashevsky's two texts on mathematical biophysics.[28]
As to the matter of physical principle, it was then already clear to me, that increase of potential relative population-density, must be defined as a function of the application of additional, validated universal physical principles. It was also clear, that the role of the new technologies derived from validation of such universal principles, were a subsidiary function of the demographic function, a function driven primarily by the unfolding of new physical principles. However, it also became clear to me, and increasingly so, over the course of the years 1948-1951, that, for elementary epistemological reasons, the kind of mathematics employed so cleverly by Rashevsky et al., could not describe such a demographic function. Had Rashevsky's approach been premised on an epistemologically sound conception, of the crucial, axiomatically categorical distinction of living from non-living processes, the problem would have remained, that the categorically axiomatic uniqueness of human cognitive processes, among living species, was clearly the root of the stubborn difference between the cognitive nature of the human individual, and the qualitatively inferior quality of all other living species.
Therefore, it was made clear to me then, that the possibility of uncovering the specific quality of superiority of the human individual, to that of any other species, could not be found in any formal-mathematical modelling; it could be located only in an empirical approach to the event-experience of cognition itself. I have described the elementary expression of that event-experience (paradox, cognition, validation) above.
The most direct way to get at "the structure" of the interior of that kind of event-experience, was to note the equivalence between the role of metaphor in the composition of Classical poetry, and the re-enactment of a validatable, cognitive generation of universal physical principle. For various reasons, the most reliable way of defining this aspect of Classical poetry, was to focus upon certain song-settings of Classical poetry. The strictly defined metaphor of Classical poetry, has the same characteristic features as the ontological paradox of Plato's Parmenides, and, also, the prompting of a validatable discovery of a universal physical principle.
The meaning of such a poem, can never be located in the mere grammatical ordering of the words themselves; it depends upon the correct, polyphonic rendering of the poem's utterance, the quality of polyphonic rendering typical of the song-settings of Classical, and also folk poetry and song. Such are the methods of motivic thorough-composition, as typified by the methods shown in the span of Classical composition, from Wolfgang Mozart's Das Veilchen through the Four Serious Songs of Johannes Brahms. Such song-treatments of Classical poetry, come nearest to making implicitly clear the idea of the poem itself,[29] and the appropriate literate form of prosody essential to enabling the individual hearer to replicate the cognitive idea of the poem in his or her own cognitive experience. Civilized people do not recite poetry; they sing it. The best musicians never sing the mere notes, and the best actors never recite the mere words; they sing the music heard in the cognitive processes of the mind. They sing, to convey that music heard in the cognitive processes of their own mind, into the mind of the audiences. As the great Classical poet, John Keats, wrote: That music of the mind, that sweetest sound, so composed, so performed, subsumes the appearance of the mere notes--the mere "dots" of sense-perception.
The cognitively witting scientific thinker, recognizes a connection between the emotional function of such sung Classical prosody, and the passion of concentration required to generate a validatable discovery of a universal physical principle. This is the same passion which Plato identifies as agape¯, the passion for truth and justice, and the same notion of agape¯, elaborated by the Christian Apostle Paul's I Corinthians 13. Without that specific quality of passion, common to scientific discovery and the expression of the same quality of passion in such artistic forms as great Classical song-prosody, valid replication of a validatable universal physical principle, were not possible.
This quality of passion can not be expressed in nouns; it is associated with the verb, but, that only in the case that the use of the verb corresponds to a form of action which results in a change in state of some stated or implied object, subject, or both. This includes all literate uses of the verb "to be," those which express the notion of becoming.[30]
This notion of the proper role of the verb in rigorous use of language, is determining in both Classical artistic composition and physical science, as the philologist Panini stressed this point. The strict, correct usage of the term "non-linear" in physical science, is also associated with that employment of the verb in literate forms of language and Classical artistic composition in general: something--my self or some other agency--is acting to change the universe from what it was during an antecedent moment. This same notion is the pivotal feature of competent forms of cost accounting and economic forecasting. This view of the role of the verb, is crucial for grasping the Riemannian non-linearity of the form of action which generates those transformations which link one dot to another, as in cost accounting and economic forecasting.[31]
The fundamental principle of the science of physical economy, is the anti-entropic effect of the efficient application of an expanding, Riemannian, multiply-connected manifold of universal physical principles, expressed as an increase in the general potential relative population-density of society.[32]
In the history of science, this use of the term anti-entropy, or negative entropy, in the science of physical economy, was borrowed from biology. It signifies the principled difference between the axiomatic type of behavior exhibited by developing living organizations, as contrasted with non-living ones of very similar, or closely related, organic chemical composition.
The demonstration of that fundamental principle of physical economy, implicitly generates the following, most important ontological paradox of all physical science.
The fact, that the universe submits consistently, in that way, to such application of advancing discovery and application of all validatable universal physical principle, and not otherwise, shows, in first approximation: that the universe is implicitly pre-disposed, as if by pre-design, to submit to mankind's will, on this account, whenever mankind acts on behalf of those discoveries of universal physical principle. Since the effect of this cooperative social application of the sovereign power of individual cognition, is to increase mankind's power in and over the universe--per capita, and per square kilometer of the Earth's surface, that connection shows, that the characteristics of the underlying laws of the universe, and the characteristics expressed by the processes of cognition, are congruent. That is to say: the underlying law of the universe, is expressed by the same principle of higher hypothesis which is expressed by the generalized processes of well-ordered individual cognition.
This expresses a unique quality of experimental evidence of a universal principle. The implications of that principle may be read, either as the secularist version 1) the universe generated the emergence of a species, mankind, which could manage, and become a cause for the continuing, noetic self-development of that universe; or, in other words, the Biblical view, 2) that the Creator of the universe made men and women of such a human nature as in His own image.[33]
The corollary of this, is that these considerations define a corresponding, implied body of natural law, truthfully knowable by means of cognition, which is the highest body of man-made law, superior in authority to all man-made constitutions, or other man-made law. On this account, the fundamental principle of constitutional law, is, that the only source of legitimate authority of government, is the state's unshirkable duty and unique power, to promote the general welfare of all the living and their posterity. So, for example, the first three paragraphs of the 1776 U.S. Declaration of Independence, and the corresponding 1789 Preamble of the U.S. Federal Constitution, are the sole ultimate authority in law for the U.S.A.
Not only are those latter conceptions epistemologically legitimate ones. Without taking these explicitly into account, there will never be a competent conception of the proper meaning of the term "physical science," nor of the underlying, fundamental principles of political economy, either. Therefore, let us briefly draw out the practical implications of what I have just emphasized.
The prevalent, false portrayal of physical science, as expressed, wittingly or not, in today's typical university and its textbooks, is a reflection of the imposition of the same aprioristic notion commonly underlying both the mortalist, neo-Aristotelean doctrine of Padua's notorious Pietro Pomponazzi, and the so-called empiricist, Voltairean, or Enlightenment tradition of Venice's Paolo Sarpi and Antonio Conti. This is the aprioristic view expressed as the central principle of Thomas Hobbes;[34] John Locke and Isaac Newton;[35] Bernard Mandeville's pro-satanic The Fable of the Bees;[36] François Quesnay's pro-feudalist, mystical dogma of laissez-faire;[37] Adam Smith's axiomatically irrational doctrine of "free trade;"[38] and British Foreign Office head Jeremy Bentham's 1789 An Introduction to the Principles of Morals and Legislation.[39] Notably, this array of rabid, hedonistic irrationalists, represents the continued building of the foundation of the ruinous British doctrine of political-economy, to the present day. This is also the most important of the anti-Renaissance influences which, by no mere coincidence, have continued to pollute the teaching and practice of physical science, from the time of Padua's Pietro Pomponazzi, to the present.
Consider a frequent expression of that same crucial element of irrationalism, in the behavior of even today's otherwise gifted science professional. Observe the incidence of those cases, in which one among them protests against my view. In my experience, a typical such professional, may either profess, that he has no professional responsibility to understand economics, or, much worse, he gives his implicit political support to the dogmas of such figures as the Mont Pelerin Society's Friedrich von Hayek and Milton Friedman, or even Vice-President Al Gore's lunatic political-economic "algorerythms." Physician, heal thyself: such are typical of the conceptual aberrations prevalent among today's science professionals. Recognizing the nature of such behavior among some specialists in physical science, sometimes even otherwise outstanding such figures, should evoke compassion for the related conceptual shortcomings found among so many of today's accountants and financial analysts, who, typically, lack a competent education in the basics of science.
The simplest approach to understanding the source of such aberrations among scientists, is to trace the problem to the increasing popularization of mathematical models, both in classrooms, and in the daily practice of today's scientists and engineers. The outlook so induced in the mind of the victim, is a certain, induced habit of thinking about the physical universe, a practice which implies, that universal physical laws pre-existed, prior to mankind, in the form of the mathematical models widely adopted, ex cathedra, today.
For example, as what appears to have been typical of him, Bertrand Russell carried this pathological view of science to a point even beyond its deductive limits, during an utterance of the late 1920s. He asserted the coming end of scientific progress. He argued, that the available, untapped hoard of such universal mathematical-physical laws, represents nothing but a rapidly vanishing residue of what had been, from the start of Creation, a fixed set of such discoverable mathematical laws.[40] Many scientists might disagree with Russell's argument, as to the quantity of discoveries still available to be made. After the rampant decay of university education, during the course of the recent decades, relatively few remain, who would be able to identify correctly the precise nature of the systemic fraud implicit in Russell's argument.
The point here is, that it is only in that view of economic processes supplied by a science of physical economy, that the proof of the validity, and nature of universal physical principles, could be securely established. To test each principle individually to that purpose, would represent a fallacy of composition. The test, to be rigorous, must be defined in terms of larger, multiply-connected aggregations, as phase-spaces. The designer of such tests, must think, on a broad scale, in terms of long waves, of general scientific and physical economic progress. Such waves must be correlated with the growth of per-capita and per-square-kilometer productivity over significant periods. Study such patterns, under conditions within periods both of stagnation in, and during bursts of investment in scientific and technological progress in agriculture, manufacturing, and basic economic infrastructure-building in the public sector.
To illustrate that, study the manner in which Benjamin Franklin's great-grandson, Philadelphia's and West Point Military Academy's Alexander Dallas Bache, played a key role, in bringing the impact of the scientific work of the circles of Germany's Gauss and Alexander von Humboldt into the United States. Think of Bache's role, in terms of such outcomes as the "Thomas Edison phenomenon," the rapid electrification in the U.S. and Emil Rathenau's Germany. See this leading to an explosive upsurge in U.S. industrial productivity, during the early Twentieth Century. That result is typical of appropriate economic demonstrations, of the efficacy of scientific discovery, as demonstrated by the increase, as under France's Louis XI, of the potential relative population-density of the human species.
In these, as all related matters, the test of truthfulness in expressed opinion, is a test of the efficacy of the powers of that anti-empiricist faculty, Socratic cognition, as typified in variety by Plato's Meno, Theaetetus, and Timaeus, in producing validatable discoveries of universal principle. In the final analysis, the only valid test, on which the truthful authority of all opinion depends, is the willful increase of mankind's power in and over the universe, as measurable per capita, for the entire population, and as measurable per square kilometer of the Earth's surface-area. It is upon that standard, as defined by the science of physical economy, that the validity of any presumed universal physical principle, depends.
Thus, stating the matter in these appropriate terms, so the authority of the putatively trained scientific professionals must be measured. So, their competence must ultimately be judged. They are all, whether they wish to acknowledge this fact, or not, subject to that standard of a science of physical economy. Indeed, the authority of all opinion depends upon that same test of man's power to increase his power in and over the universe. That physical-economic, cognitive standard, is the ultimate scientific measure of truth in all matters, including the domain of mathematical physical science. So, a professional, in any profession, is to be judged, primarily, as a human being. Otherwise, science itself might be left to roam perilously, unguided, like a Bertrand Russell or John von Neumann, near the outer rim of Jonathan Swift's floating island of Laputa.
To summarize the argument made, up to this point, we have the following.
Consider the case of those pitiable illiterates, such as the licentiously liberal doctrinaires of the ultra-Conservative, Mandevillian Heritage Foundation, who insisted upon a separation of "pure" from "applied" science. Their argument, typified by the case of Heritage's since-deceased Lt.-Gen. (ret.) Daniel Graham, was that the process of discovery and validation of new physical principles, such as the discovery of principles of nuclear fission and fusion, of space exploration, and so on, was the work of impractical, "ivory tower" academics. It thus appeared to escape his attention, that none of these discoveries would have been effected without governmental funding. On these premises, Graham proposed, that instead of investing in discovery and development of validatable new physical principles, government development programs should be limited to what would be in fact technologically obsolete new assemblies, composed of technologies already gathering dust on the shelves of Wall Street-owned private military contractors. He made this the theme of a virulent attack on the proposal, and upon me, personally, for what became the Strategic Defense Initiative (SDI), during 1982, before it was adopted; immediately after its adoption, he led in the preponderantly successful campaign, to exclude all those viable lines of fundamental research, which might compete with off-the-shelf approaches to the technologies of Wall Street-controlled military vendors.
The case of the Heritage Foundation's Graham, although a lurid one, the more clearly and simply illustrates the general problem. As if in loving memory of the Roman Emperor Diocletian and his Code, the advocates of such distinctions between pure and applied science, are arguing against any direct or indirect, putative subsidies of scientific progress, by government, either in the form of direct grants of government funds, or indirectly, through taxation policies and other forms of regulatory measures. Theirs is that sick mentality which fosters rabid cuts in taxation on purely speculative, and therefore parasitical forms of financial capital gains, while refusing to consider a President John Kennedy-style of investment tax-credit, which has been shown, repeatedly in our national history, the best suited to promote the kinds of capital investment fostering the increase of scientific progress, and of its productive and related applications.
Pose the view directly contrary to that of the Heritage Foundation and its like. Does science have a moral responsibility for promoting, both the discovery and economic realization of those advances in technology, which flow, as products, from the discovery and validation of universal physical principles? Does government not have a profound, unshirkable responsibility, under the general welfare principle, for promoting both such scientific progress, and its realization as the fostering of improvements in the potential relative population-density of present and future generations? Is this not an integral part of the axiomatic prerequisites, something akin to the Hippocratic Oath among physicians, for the role of government in qualifying a professional as a scientist according to the constitutional principle of the general welfare? Is it not, therefore, clearly, the case, that a nominal scientist who views himself and his work as a kind of "ivory tower" practice, is not morally qualified to be considered as a scientist, not fit to be considered as implicitly morally trustworthy as a true expert, in his proclamations? Are we not obliged to end the trend toward replacing competent scientists, by Heritage's reign of money-grubbing yahoos? Are not all qualified scientists to be held morally accountable, not only to promote no unnecessary harm, but also not to neglect the duty of promoting benefits for the general welfare, including the promotion of the increase of the potential relative population-density of the human species as a whole?
More important than the case of the individual scientist, or relevant policy-shapers in industry, education, and government, is the need to define the responsibility of government itself accordingly, especially its economic policies. As accountability for efficient promotion of the general welfare is the only legitimate premise for even the very existence of a sovereign nation-state, this policy respecting the function of scientific progress, is a matter of a test of the government's moral fitness to exist. Since the functions of accounting and financial analysis impinge upon the policy-shaping of government in this respect, those professions must adopt a congruent standard of truthfulness respecting the profferred product of their professions.
On this account, the referenced policies of the Heritage Foundation and its Daniel Graham, represented implicitly culpable fraud and negligence. Indeed, that liberal school of empiricist political-economy and related policy-shaping, is less of a profession, than an infectious disease preying upon humanity, that in the same manner the economists associated with the British East India Company's Haileybury School, authored such genocidal atrocities as the organized famines which the British Empire deployed to regulate the population of Nineteenth and also early Twentieth Centuries' India. "Free trade" for everyone? Or, better said, perhaps, rendering "Vogelfrei" those deemed "useless eaters," as Wall Street's approach to looting of health-care and related entitlements, increases the morbidity rates of entire strata within the U.S. population itself.[41]
`Non-linear': What does it mean?
I shall now indicate the reasons why the results of any application of what have been, heretofore, generally accepted methods of financial accounting, to cost accounting and to cost-accounting-related, functional forms of financial analysis and forecasting, must be judged intrinsically incompetent, by definition. The practical side of that matter to be addressed in this location, is: how are these incompetencies to be recognized, and what general remedies must be adopted to remove them?
At this point, we shall limit our attention, to emphasizing those features of the case which must become obligatory knowledge among cost-accounting professionals. This signifies that, in this location, we cling as closely as possible to the bare axiomatic issues of the matter. Therefore, our approximately bare-bones account of the matter runs as follows.
The more general of these incompetencies, is simply the use, and reliance upon today's generally accepted statistical methods, for interpreting the array of financial and related events. The incompetence of the extension of such financial accounting practices, to cost accounting and functional financial analysis and forecasting, is most readily located simply in the fact that the methods of financial accounting and related analysis rely upon the implicit assumption of a child's game of "connect the dots." The essence of the incompetence at issue, is approximately the same as in the case of Sarpi lackey Galileo's use of nothing other than the same childish notion of "connect the dots," to define what become known as the basis for his, like Isaac Newton's, fraudulent claims to have discovered a universal principle of gravitation and other action.[42] The crude notion of "action at a distance," as attributable to Galileo, typifies the axiomatic incompetence of the employment of common statistical methods in financial accounting and related practice. It is the intrinsic absurdity of that assumption of "action at a distance," which is the kernel of our treatment of the issue of "non-linearity."
It was consistent with the homicidal enforcement of the reductionist dogmas of Pomponazzi, Sarpi, et al., during the interval of the anti-Renaissance, Conservative reaction and its religious wars, 1513-1648, that only a few souls dared to speak publicly, of any suggested composition of the universe contrary to what would be still considered today as standard classroom Euclidean geometry's definitions, axioms, and postulates.
After Kepler, the first crucial attack on the kind of axiomatic linearization associated with Galileo, was by Pierre de Fermat, in his physical demonstration that the refraction of light was governed by a principle of least time, rather than shortest (linear) path. However, for a time, this was treated as a demonstrable anomaly (a paradox), within the framework of a physical universe assumed to be, axiomatically, one defined as consistent with "Euclidean," a priori presumptions of limitless linear extension of space and time. The deeper implications of Fermat's discovery began to be made clear during the middle of the Seventeenth Century, through the intersection of a leading student of Kepler's work, Blaise Pascal, with the collaboration which began in Paris, between 1672 and 1676, between Christiaan Huyghens and Gottfried Leibniz.
The demonstration of both an isochronic and least time characteristic, for gravitation and refraction of light, by the combined work of Huyghens,[43] Leibniz, Römer,[44] and Jean Bernouilli,[45] provided the experimental proof of the universal physical principle, that action in physical space-time did not conform to those linearized notions of time, space, and matter associated with Galileo, Descartes, and Newton. The demonstration, by Huyghens, and also his followers, that the pathway of gravitational action could be shown to be not straight-line, but a curved pathway, which was isochronic, and, also, relatively,[46] of least time, and, that this was also true for refraction of light, was experimental proof that physical space-time is not Euclidean, and that action in that physical space-time is not elementarily linear, not Cartesian, not Newtonian.
Thus, the first implication of Fermat's discovery of an experimental principle of least time, was his introduction of a devastating paradox within the pre-existing, Euclidean domain of a priori physical space-time. The cognitive generation, by Fermat, of an hypothesis of least time, begged the development of experimental tests whose included obligation must be, to begin to define a universal notion of physical space-time in which the recognition of a newly discovered universal physical principle, would define a domain freed of the paradox posed by Fermat's discovery. Huyghens' work in developing his pendulum clock, and his generalization of those results, led to the introduction of the isochronic principle, and least time, into the physical space-time of constrained falling bodies. Related work on determining the characteristics of the speed and refraction of light, by Römer, Huyghens, Leibniz, and Jean Bernouilli, situated Leibniz's superseding of simple least time, by a more general principle of least action. This provided the setting in which the future refutation of the Newtonian dogma on light and electromagnetism, was accomplished by the collaborators Fresnel, Arago, and Ampère. The work by Leibniz's follower Kästner, contributed crucially to the setting of the development of anti-Euclidean geometries, successively, by Gauss and Riemann.
There are many lessons to be adduced from that and related elements of the history of the development of the Gauss-Riemann notions of anti-Euclidean hypergeometry. The lesson to be emphasized here, is not those events, but rather that subsuming process of development, which the pattern of those unfolding discoveries expresses. In science, it is not the individual discovery which is the essence of the matter; it is, rather, the adducing of the process which subsumes a series of successive discoveries of principle, as in the historical series which I have just outlined. It is in that process, that the true, categorical meaning of "non-linear" is to be situated.
The practical point of this, for cost-accounting practice, is that the ordering of those events which we might perceive as sequential "dots" in a time-series, is not an axiomatically linear order. Therefore, the series of such data is not necessarily ordered in a way which can be competently approximated by linear approximations, such as deductive methods. The same applies to the data-field in which the series of choices is located. Therefore, the use of statistical methods of financial accounting, to construct what is represented, thus, as a functional (e.g., "cause-effect") analysis of such a series, is an intrinsically incompetent form of general practice, on principle. Under certain special circumstances, such crude approximations may be harmless; but, as a matter of general practice, they are intrinsically incompetent, recklessly so.
Consider the implications of what I have just said, in the following terms of reference. These are the terms to which we shall return, repeatedly in the later, successive phase of this report. Let us zoom in upon some of the relevant problems to be addressed in the production of products. These illustrations will provide the framework, in which to situate the issues of non-linearity in practical terms of production and related practice.
Choose any relatively simple case, in which a combination of materials is brought together in such a fashion, that a transformation occurs in that combination, with the result we recognize as production. The transformation may be mechanical, chemical, etc., in nature. In the analysis of production, we focus upon the immediate relationship between the individual functioning as an operative, such as a farmer or a factory workman, and the quality of physical transformation which depends upon the active role of that operative, in respect to the process for which he is responsible. In other words, the operative is performing some necessary, controlling function in relationship to the physical transformation occurring at that point in the productive process. Such transformations, are to be represented by intrinsically non-linear orderings.
At a later point in this report, when I shall return our attention to that relationship, we shall focus upon the internal features of the operative's role as such. For the moment, now, take the necessary role of the operative in the productive process as a given fact; that said, focus on the physical transformation, as this is occurring in the process which the operative is controlling in some way.
In any such physical transformation, the function described by that localized productive function, involves primarily, three crucial kinds of distinguishing elements: physical principles, and also specific technologies, as the latter are subsumed by both these principles, and, thirdly, the choices of physical media in which the transformation is occurring.
Once we have identified those categorical features of the ongoing transformation, we must take into account the scale on which the relevant features of the transformation are occurring. The relevant scales include, for example, the astrophysical, the molecular, the atomic, the nuclear, and the sub-nuclear, and include accounting for both the wave-length and "energy-flux density" of the relevant actions. The qualities of action to be considered, include the functional distinction which deeply underlies the functionally determining differences between a living process and one which has just ceased to be living. In respect to human behavior bearing on the productive process, the qualities of action to be considered, include the functionally determining, principled, physical distinction between animal learning and human cognition. In all of these matters, there are qualitative distinctions peculiar to specific ranges within the respective domains of astrophysics, macrophysics, and microphysics. The relevant "local laws" of physical processes may change, as we pass from one such range to another.
In all such matters, the specific way in which the connections among the relevant "dots" of the transformation are ordered, may change in characteristic local curvature, from one case to another. Thus, the determination of the way in which the transformation proceeds, from one observed "dot" of that process, to the next, may rarely correspond, in fact, to a simply linear connection of a Euclidean or Cartesian type. In the practice of cost accounting and forecasting, it is essential to recognize this principle of non-linearity, and to be guided thus in knowing when linear approximations may be tolerable, or not. The importance of making that distinction is magnified, sometimes perilously, by any effort to forecast long-range consequences from short-term apparent changes, or the observer's failure to look behind the superficial indications of a lack of apparent changes in trends.[47] In such cases, it were prudent to have re-enacted Gauss's laborious discovery of the asteroid orbits from several relative momentary observations, a labor which, as viewed in retrospect by Gauss himself, provides an excellent demonstration of the long-term significance of recognizing characteristic expressions of non-linearity, even in the relatively very small.
Mathematical knowledge of the characteristic types of changes which may be applicable to the task of connecting the dots, has increased in known ways over the recent millennia. The known methods for estimating [pi], for example, have changed from those on record as used by the ancient Egyptians, for example: from series of fractions, to the irrational magnitudes mistakenly adopted by Archimedes for the quadrature of the circle, to the proof of the existence of the transcendental nature of [pi] by Nicholas of Cusa, as in his work founding modern experimental physical science, De docta ignorantia.
The corresponding definitions of each class of numbers which might be employed to trace the determining pathway between two observed dots, rational, irrational, and transcendental, or higher orders of the transfinite, are supplied in two distinct ways: arithmetic-algebraic, or geometric.
The model distinction among number types, is that originally provided by a leading follower of Plato, the so-called "sieve" of the famous ancient astrophysicist Eratosthenes. This sieve was updated by mathematician Georg Cantor, to include higher orders, such as the transcendental and higher transfinite. As Plato's Meno, Theaetetus, and Timaeus illustrate the point, the method of Plato's Academy, including Eratosthenes, was essentially the geometric method. Cusa discovered the correct definition of the transcendental, by geometric methods, during the middle of the Fifteenth Century. The more elaborate, inferior proof of the distinctness of the transcendental, is that formalist one developed centuries after Cusa's original discovery, by Euler, Lambert, Hermite, and Lindemann. However, the issue, which method, algebraic or geometric, is superior, is actually governing, was settled in principle, in favor of the geometric, by the successive work of Gauss and Riemann in the domain of number theory. Riemann's treatment of the prime number domain, correcting the initial attempts by Euler, and continuing that of Lejeune Dirichlet, is exemplary.[48]
A modest few remarks on the history of this matter, are of crucial significance at this point.
Even beginning at the simplest level of classroom instruction, the paradoxes arising in the effort to define simple agreement between multiplication and division, for example: the theory of numbers becomes increasingly a thicket of paradoxes, thus assuring employment for both many number theorists, and also any supercomputer which might otherwise sit idle. The question this fact poses, is: "What does all this really mean?"
The case of Gauss's youthful dissertation, his Disquisitiones arithmeticae, published in 1801, exhibits the mind of a master of number theory whose method of thinking was essentially geometric.[49] The geometer's view of the density of paradoxes which appear in the number domain, demystifies arithmetic, and aids us in appreciating the geometric standpoint of physical space-time, as the location where the significance of such number-theoretical paradoxes is to be uncovered, as such masters of number theory as Gauss and Riemann illustrate the point.
That is to say, that numerical operations should be understood to be reflections of some corresponding physical operations, the latter to be comprehended from a geometrical standpoint. One outstanding example of this, the origins of ancient astrophysics, expressed in terms of relatively simple, but relevant illustrations, up through the discoveries of Eratosthenes, will suffice for our purposes here.
The characteristic features of ancient Vedic astronomy, as studied by Europeans, from Kepler on,[50] include the great equinoctial and other millennial or longer cycles, which correspond to a language reflecting prolonged earlier association with a transoceanic form of ancient maritime culture. Harvard Professor Barry Fell's solving the mystery of the Egyptian discovery of the Pacific coast of South America, using the methods of celestial navigation developed by Eratosthenes, has similar implications, to which I shall make reference here.[51] The fact, that the founders of what became known to historical times as ancient Greece and Cyrenaica, established maritime colonies of the type of the legendary, transoceanic Peoples of the Sea, is highly relevant to our illustration here.
Look up to the stars. What do you observe? Chiefly, nothing but regular, zodiacal, angular, apparently circular motion. Such observations assume qualitatively more significance, when they are made, for purposes of navigation, by members of a transoceanic maritime culture, especially when those travels carry the party in question from the northern into the southern hemisphere. The position of Egypt on our planet, with its long history of astronomical work, is notable on this latter account.
For purposes of reference, consider the specific case of Captain Rati and navigator Maui, two Egyptians of Cyrenaican extraction, recording their voyage in the writing of an ancient Cyrenaican language. They, using the astrophysics of Eratosthenes for this purpose, led a flotilla of large wooden Egyptian ships typical of that time, for an attempted west-east circumnavigation of the planet [Figure 3]. The eastward voyage of that flotilla was halted, by encounter with the Pacific coast of South America, and probably, as navigational logic and some other evidence indicates, also parts of Central America, too. They gave up the effort to continue the eastward journey, after going south to seek a passage around South America, returning to a cave located near today's Santiago, Chile, to record their discovery of the continent, and to claim it for Egypt's Pharaoh.[52]
At that time, prior to the devastating cultural decline hitting the Mediterranean region with pagan Rome's rise to dominance,[53] not only the size of the Earthball, but also the Earth's orbitting of the Sun, had become well known. The measurement of the circumference of the Earth by the Platonic Academy's Cyrenaican, Eratosthenes, was part of the science which, according to the record of navigator Maui, guided Egypt's flotilla eastward, through the Indian Ocean and across the Pacific. Notably, the accomplishments of Eratosthenes reflected a direction of Classical-Greek, Egypt-linked scientific progress since Pythagoras and Thales. Notably, ancient Egypt's accounts attributed the founding of Egypt to colonization by an ancient maritime culture. My point here, is to prompt the reader to think of the notion of non-linearity, from the geometric standpoint of the legacy of transoceanic and kindred maritime culture, in ancient Greece and Egypt.
Look at Plato's Meno, Theaetetus, and Timaeus, as also the work of Eratosthenes, from this vantage-point. Read the Meno and Theaetetus as, in each case, Plato's use of the example of the education of a young boy, to demonstrate the necessity of use of the cognitive functions of the mind, as the basis in geometric thinking, for the education of young persons into becoming future scientific thinkers.[54] The Timaeus has a different, higher quality of aim, in its address to the same essential topic, the principles of cognition.
To know, rather than merely learn, the significance of the appearance of the subject of the five regular solids in the Timaeus, think of the view of the universe by one who knew, at that time, that the Earth is a planet of approximately spherical shape, as the Greeks of Plato's time knew this. Look at the subject-matter of those solids through the eyes of ancient navigators. Look at that matter on the scale represented by transoceanic navigation. Explore the paradoxes, as shown by comparing a global map with Mercator's projection, which the evidence of that navigation poses to simple sense-perception. Then, it is more readily clear, that the five Platonic solids have the immediate significance of being characteristic of the projection of a specific choice of curved form of astrophysical space-time, as opposed to the arbitrary conceit, of bodies floating within a homogeneously four-square space-time. In other words, the characteristic action of that physical space-time is curved, not linear, not to be determined by quadrature. The fact that it is curved is certain; the question is, what kind of curvature?
Return to our earlier exposition of the concept of cognition, of cognitive knowledge, as distinct from the kind of learning from the simple experience of direct, naive sense-perception. Transoceanic navigation requires true knowledge, not mere learning, as navigator Maui recorded his praise of the scientific achievements of Eratosthenes, midway en route to the Pacific coast of South America.[55] Here lies the significance of the transcendental, as Cusa is the first known to have discovered it, that from the geometric standpoint of Plato and Eratosthenes. Here lies the crucial role of Cusa in that work of Paolo dal Pozzo Toscanelli, which gave Columbus the map reflecting the discoveries by Eratosthenes, and supplied the strategic impetus used for the rediscovery of the Americas.
Plato uses this demonstration of the five solids, relative to the characteristic differences between living and non-living processes, to expose a more general, deeper principle, the principle reflected in the very title of Cusa's De docta ignorantia, the universally cognitive nature of knowledge, that as opposed to mere learning. This is the principle which was re-established in European science by Cusa, Pacioli, and Leonardo, and, through them, occupied a central place in the founding of both modern astrophysics and also a comprehensive form of mathematical physics, by Kepler.
To be fair, entire chunks taken from this work of Plato and his Academy, are reflected in the latter part of the Thirteen Books of Euclid. As I have stressed earlier here, and, repeatedly, in other locations, the evil of classroom Euclidean geometry lies not in the work of Euclid, but in the imposition upon the mind of the young, of the a priori notion of infinitely extended (to both the large and small) linearity of space and time, the same aprioristic folly which foolish Leonhard Euler and his fellow-ideologues adopted, in defense of Newton's follies, against Leibniz.
Apply such considerations to the real-life problems confronting the hardy entrepreneur in his management of a technologically progressive manufacturing enterprise. Like Gauss's choice of approach to the problem of defining the asteroid orbits, that entrepreneur must make long-ranging investment decisions, on the basis of the relatively few crucial experimental measurements available. The differences are small, but the longer-term implications may be enormous.
So, the characteristic curvature which, in physical reality, connects the dots of cost accounting's observations, can not be safely presumed to be linear. In important cases, it is not. In crucial cases, failure to recognize that principle, has proven disastrous. We must now wait to complete the immediately foregoing discussion of this matter, at the appropriate later point, after we have first addressed the prerequisites respecting the role of culture in cost accounting. Then, after that, we shall complete the discussion under the heading of budgetary and cost-accounting principles.
3. Culture as a cost of productivity
As summarized in the opening portion of the preceding section of this report, the possibility of cooperation in applying validated discoveries of universal physical principle, among persons considered pair-wise, or the members of society in general, depends upon what I presented there, as the three-step prerequisites for sharing such knowledge among two or more persons.
I also stressed there, that to achieve the same quality of knowledge of past time's discoveries of universal physical principles, the student, or other living member of society, must replicate the original enactment of that discovery, in accord with the same three-step prerequisites required for sharing such knowledge directly with a living acquaintance.
I stressed there, that, in this way, the accumulation of a living person's actual knowledge of such principles, produces in that person's mind, an array of images of both those earlier, and contemporary discoverers of such validated universal principles, an array typified by the example of Raphael Sanzio's celebrated The School of Athens. Such persons from the past, although deceased, have, nonetheless, spoken directly to the living individual child's, or adult's mind, through the transparent medium of time, through that medium of communication called cognition. Those persons from our past, constitute an assembly of conscience, a court of living personalities, seated, at our beckoning, within the simultaneity of eternity. So, at our calling, they are constituted as a great council, before whom we must defend and judge the truthfulness of all among our own opinions, including new hypotheses. Only among those about us, who are sterile formalists, virtual Yahoos, or outrightly malevolent persons, is this not so.
Some, or all of such members of that great council of truthfulness, may be in error in appearing to oppose my opinion, but they must be countered on that issue in a certain, specific way, a way which compels that council of immortals to judge whether or not that proposition is truthful, even if it contradict what they had believed before. To saints of such distinction, from such a council, a devout person might justly, and fruitfully pray for guidance. So, aided by such resident immortals, conscience disciplines true statesmen, scientists, and poets, in the art of being truthful, in opinion, and in the submission of practice to uncompromising service of cognitively defined universal principle.[56]
Within the mind whose individual cognitive powers have been cultivated to such effect, that great council of truthfulness, is the living essence of the unfolding of past, present, and future scientific knowledge. All of us who have acquired cultivated minds, have such a council readily at hand, our old friends such as Plato, Eratosthenes, Cusa, Leonardo, Kepler, Leibniz, and so on, many of whom one knows by a familiar name, who are called from the past, to express cognitive moments from their living personality, within us, in some present moment.
That same council, is also the only true choice of place where the greatest compositions of Classical art, are composed and justly performed afresh. There dwell some of the greatest Classical poets, musicians, dramatists, painters, architects, and sculptors, and other masters of true metaphor, of the past. The subject of great Classical artistic compositions, is always, essentially, a celebration of those powers of communication through which we, as individuals, are able to share the ongoing development of our individual cognitive powers. The subject of art, is the rudimentary expression of this sharing of truthfulness, as that is also expressed by the three-step method of validating a discovered, universal physical principle.
Truthfulness is not von Hayek's cafeteria, not some "greasy spoon," from whose steam-table, or salad bar, one might select liberally one's choice of dish. The attempt to separate scientific from artistic truthfulness, as the irrationalist Immanuel Kant does, is the mark of an intrinsically immoral personality.[57] Truth rules one's choice of what each of us is morally permitted to select. This is true in science, in economics, in statecraft generally, and in the composition, selection, and public performance of artistic compositions.
Such a commitment to truthfulness, respecting both science and art, is the only mode in which anyone among us might become his, or her true self. Unfortunately, few, especially nowadays, succeed in becoming their own true self. Yet, seeking that Socratic pathway to truthfulness in opinion and practice, is the only course which does not lead the deceased individual, ultimately, as failed, or even evil souls, into waiting before the great council seated in the simultaneity of eternity, to await judgment on their prospective relegation to the rubbish-bin of true history.
In successful approaches to these Classical forms of artistic composition, the underlying subject-matter is the same cognitive social relationships, the which are the substance of the sharing of the discovery and validation of solutions to well-defined scientific paradoxes. In Classica