Dupes of Non-Physical

In other words, a society characterized by zero technological growth as a policy of general practice is a dying society, a form of society morally unfit to continue existing. Repetition of modes of production and related cultural practice inherited from fathers, grandfathers, and so on, is the distinguishing policy of a dying society. For this and related reasons, all economic analysis and policy-shaping premised on systems of simultaneous linear equations, such as those proposed by the late John von Neumann and others, are worse than absurd.
Conversely, a successful form of society is characterized by technological progress. Such progress is the characteristic feature of the total activity of the labor force of that society. Technological progress is the precondition even for merely maintaining a fixed constant value of potential relative population density.
However, to overcome absolutely the apparent limits to growth associated with the "natural resources" of a fixed range of technology, there must be technological revolutions periodically, through which leaps in potential relative population density occur. Moreover, technological progress always tends to cause a net increase in the required social division of total labor, which in turn signifies an increase of population - and therefore of population density. Thus increase of potential relative population density is the irreducible datum required. It is human activity integral to effecting that increase of potential which is the irreducible definition of human activity.
It is that specific, irreducible datum of human activity which correlates directly with those qualities of the human mind which distinguish humanity absolutely from the beasts.
This "economic" form of human activity is mapped to the activity of the human mind by aid of Plato's conception of the hypothesis of the higher hypothesis. From the standpoint of hypothesis (e.g., rational problem-solving activity of the mind), the human mind has three distinguishing possible states: (1) Simple Hypothesis, (2) Higher Hypothesis, and (3) Hypothesis of the Higher Hypothesis. These are summarily defined as follows, using modern language.

Simple Hypothesis. On the lowest level of human problem-solving (rational) activity, we attempt to comprehend a problem by aid of the assumption that prevailing opinion is broadly correct. We seek to describe the problem considered in a manner which is credible and acceptable to either prevailing assumptions of general opinion, or the body of opinion associated with some chosen professional or other peer group of reference. This is what is sometimes described as an "other-directed" state of mind, which limits one's self-approved thoughts to such thoughts one imagines to be approved among neighbors, family, prevailing authorities, and so forth.
In scientific work, the peer group of reference is one's old university professors (who awarded one the social, professional status of a scientific degree), one's professional peers (as typified by co-workers and referees of professional publications), current or prospective employers, and so forth. The prevailing (e.g., textbook) lattice-work of algebraic formulations, and the axiomatic assumptions directly or implicitly underlying such lattice-works, are accepted as broadly inalterable, and similar assumptions are made bearing on prevailing professional opinion in the specialized domain of experimental practice in which the problem treated is assumed to lie. The formulation of the simple hypothesis seeks consistency with such lattice-works.

Persons in this state of mind will never discover anything of useful importance bearing upon fundamental issues of scientific knowledge. Worse, they will be hostile to creative discoveries, no matter how exhaustively, conclusively demonstrated, and will have enormous difficulty in attempting to master such discoveries. If obliged by pressures of practical circumstance to employ such a discovery, they will attempt to explain the discovery away, to reject the method by which the discovery was actually formulated.

Higher Hypothesis. In this approach to problem-solving, the thinker rejects the "other-directedness" of simple hypothesis. He is interested chiefly in those kinds of experiments which test one or more of the underlying, axiomatic assumptions of prevailing opinion, and expects to be able sooner or later to overturn one or more of such assumptions through a "crucial" experimental demonstration. This creative thinker is inherently an "iconoclast" in the eyes of his "other-directed" fellow professionals, and they "philistines" in his eyes, as such were in the eyes of Plato's Socrates. He is "inner-directed"; he must prove everything for himself, especially those features of the logical lattice-work of established opinion which are underlying, axiomatic.
The formulation of the higher hypothesis is best accomplished by a thorough education in the internal history of ideas, especially scientific ideas, with reliance upon the original sources of the present and past. This historical approach to contemporary scientific work emphasizes those kinds of axiomatic assumptions which are ontological, which bear directly on identifying which aspects of the universe as a whole are properly treated as efficiently substantial, and also how such ontological assumptions implicitly determine the method of adducing the lawful principles governing action in the universe. From such an historically-informed vantage point, the thinker is able to recognize that the elaborated logical lattice-work of the algebraic formulations associated with some branch of scientific inquiry is a kind of "hereditary" elaboration of the axiomatic ontological-methodological assumptions which underlie those constructed edifices of algebraic formulations. From this vantage point, the thinker is enabled to recognize that certain classes of experimental problems put an entire edifice of that sort into question, that certain classes of experimental problems, properly defined in that light, have implicitly a "crucial", or "revolutionary" significance for scientific knowledge in general.
So, the formulation of a higher form of experimental hypothesis is addressed to some selection of empirical evidence, evidence which is appropriate to prove whether or not certain prevailing assumptions of scientific work must now be overturned in order that scientific (and, technological) progress might continue. If this experiment is successful, a greater or less scientific revolution - or, the equivalent in some other aspect of knowledge - results. If this occurs, the entire edifice of mathematical knowledge resting hereditarily upon flawed assumptions collapses, and a new, replacement edifice must be constructed according to the hereditary implications of the newly proven principle.
In the final analysis, the question whether such experimental proof of a new principle is valid or not, is determined: does this discovery implicitly lead to an increase of the potential relative population density of society? Does the discovery effect an increase in mankind's per capita power over nature as a whole?

There are many false discoveries which purport to be of this form. Everywhere, this or that anarchist whose ego has been inflated by a little professional learning, prankishly deludes himself that iconoclasm for its own sake, merely being eccentrically different, constitutes valid discovery. The case of so-called modernism in art today, or nineteenth-century romanticism, is illustrative. Fellows who have never mastered Albertian perspective, to say nothing of Leonardo's system of convex-spherical mirror projection, delude themselves that childish smears, echoing infantile smearing of feces on walls, constitutes an expression of "creative freedom". In music, those who have no comprehension of the principles of coherent contrapuntal development (such as that of the post-1782 Mozart or Beethoven), delude themselves to surpass the classical masters by the anarchistic chromatic imbecilities of a Liszt or Wagner or the irrationalist nihilism of Webern and Schoenberg. In scientific work, such feces-smearing artistic productions would be regarded as the bungling of illiterate tinkerers.
In significant degree, the toleration of such artistic and social sciences frauds by society today echoes a breakdown in primary and secondary education. If students today were educated at standards of classical education associated with the eighteenth-century French-Italian Oratorians, the leading schools of the young United States, or the Humboldt program in Germany, the graduates of secondary institutions would already possess a much higher degree of education in fundamentals than is commanded by more than a tiny minority of professionals holding terminal degrees today. The steeping of the student in the original classics, beginning with Greek classics, is not unnecessary exposure of the student to dead languages and "outdated" opinions. It is affording the student both a familiarity with the past 2,500 years of development of the ideas of Western civilization, and the power to think of ideas in terms of universality and historicity. Out of such education emerges a sense of rigorous thinking, the power to discriminate between new eruptions of what has been proven trivial nonsense many times in the past, and genuinely new solutions to problems left unresolved from the entirety of whole spans of work of mankind up to the present.
For example, all fundamental accomplishments in modern European mathematical physics over the recent five hundred years are derived most directly (hereditarily) from the work of Cardinal Nicholas of Cusa. Cusa's adolescent training was under the Brothers of the Common Life, education based on rigorous reworking of the classics prior to mid-adolescence. Cusa's principal discoveries in science centered around his thorough reworking of the writings of Archimedes, most emphatically Cusa's rediscovery of the isoperimetric principle of topology as a superior approach to that of Archimedes in treatment of the problem of quadrature of the circle. The genius of Karl Gauss, the greatest thinker of the past two centuries, is typified by and centered in his thorough reworking of the work of Kepler. In Georg Cantor's Grundlagen, in which Cantor summarizes the solution to comprehension of transfinite manifolds, Cantor devotes much of the writing to reviewing the preceding centuries' work in that same direction.
The work of formulating valid higher hypothesis is not less rigorous than that of formulating simple hypothesis; it is far more rigorous, more demanding upon the historical education in depth and concentration span of the investigator.
Once one has worked through one such discovery (as the author experienced this in the culmination of five years of work in 1952, in his fundamental discovery in economic science), one has broken through into the inside of the matter of method, and from that vantage point, to descend once more into the lower realm of simple hypothesis is like eating bad dishwater for soup. The term, "genius", for persons associated with fundamental scientific discoveries, is an unfortunately mystical, and therefore wickedly misleading choice of term. "Genius" is learned, as a development of a potential inherent in every newborn (biologically undamaged mental apparatus) human individual. Depth and width of development of that potential, strongly motivated "inner-directedness", and the experience of one good, worked-through true discovery, are all that is required to bring forth such potentialities in almost any human being.
From this vantage point, we must view as criminal the educational policies associated with John Dewey, and the more radical steps in the same direction fostered by the National Education Association under influence of the National Training Laboratories during the more recent decades. Where proper education might have produced legions of true "geniuses", we permit our children to be encouraged in irrational infantilism, to "protect them" from the "oppression" of rigorous development of their creative potentials in depth and breadth of classical and pre-science education, and to deny them the development of that rational maturity indispensable to survive psychologically as adults.

Hypothesis of the Higher Hypothesis. The fact that successions of higher hypothesis (scientific-technological revolutions) prompt increase of potential relative population density of society, implies that such a succession of scientific revolutions has an ordered character. In other words, the succession of higher hypotheses subsuming such an ordered succession of scientific-technological revolutions has an ordered character. This defines a new experimental problem for hypothesis, the experiment which isolates the consistent feature of successive scientific revolutions, the common principle of discovery uniting revolutions which are otherwise different. This defines an hypothesis of the higher hypothesis.
Just as no experimental hypothesis can be the last word in human knowledge, the same is true for successful hypothesis of the higher hypothesis. It cannot be perfect, and it need not be perfect. It is required that the successive improvements in this hypothesis successfully direct man to the needed next step upward through scientific revolutions.

It is in this latter activity, successful testing of the hypothesis of the higher hypothesis, that true human scientific creativity lies. This is the irreducible feature of human mental activity which distinguishes man from the beast, the irreducible datum of a science of the human mind. SM-LL-6,7&8


First, let us consider the issue in terms of a purely formal problem.
Either the whole of musical development represents a coherent domain, and this coherent lawfulness is therefore the primary reality of music, or the notes of the twelve-tone scale are the self-evidently "atomic" sensualities of music. If the former, then the notes are determined in value by the requirements of a system which is coherent with respect to all of the lawfully ordered development within music. If the latter, then the values of the notes, as self-evident "atoms" of sensuality, can be determined by any variously arbitrary or consistent standards apart from music. In the latter case, music is axiomatically degraded to a matter of sensual effects.
The former standpoint is the Platonic (or, Neoplatonic) epistemological standpoint, as exemplified by Plato's Timaeus. The latter standpoint is that of Aristotle and his successors, and coincides with the classical arguments of the British Secret Intelligence Service in adopting Rameau as its prophet during the British monarchy's attempted inquisition against J. S. Bach during Bach's period at Leipzig.
The Aristotelian standpoint was also the common standpoint of Goethe, Mendelssohn, and Richard Wagner, among others, in those persons' philippics against the line of development of musical composition exemplified by Beethoven. The same issue was reflected, although in an often confused form, in both of the principal Wagner controversies of the late nineteenth and early twentieth centuries, between Wagnerians and Brahmsians, in the once case, and Wagnerians and Verdians in another. Although both Brahms and Verdi reflected the depressing influence of the romantic decay of nineteenth century musical (and other) aspects of European culture, relative to the Wagnerians they were the sane currents, and represented to that extent a continuation of the thrust of Bach, Mozart, Beethoven, et al.
From the Platonic standpoint, the notes of the well-tempered system are ephemerals. The student must not be left misguided on the significance of that term. "Ephemeral" is not equivalent to "sloppy", "arbitrary", "illusory". Indeed, individual life is an ephemeral in the whole development of humanity, yet an individual person is not only definite, but what he or she may do to secure a meaningful place in the process of human development as a whole is also a definite matter. The notes within a well-tempered system have a determined, exact value as notes. There is no caprice, no margin for indifference within the range of audible discriminations, or within a tolerable range of beats produced by the variation between produced tones of the same nominal set of values.
When we insist that the values of notes are ephemerals, we are merely insisting that the values of musical notes are not determined a priori, independently of music. We are merely insisting that the principles of lawful development necessary to effect beauty within musical composition rigorously determine the values of notes, with no obligation to any aprioristic assumption of what those sensual values must be independently of beautiful music.
From the standpoint of the Aristotelian and irrationalist (empiricist-positivist) schools - such as the Frankfurt School's protege Arnold Schoenberg, downward through Webern into Stockhausen and John Cage - the values of the notes are either properly determined as if they were self-evident atoms, prior to any musical consideration, or purely arbitrary valuations might be given to them. IG-LL-9


Themes in music are as lines to a poet. They are musical ideas, even on the level of primitive culture's comprehension of music. A theme must "parse", it must have the preconscious form of a musical-idea utterance, such that the mind seizes that utterance as a gestalt, something corresponding to a musical-idea statement in and for itself. The process of composition then presents the mind with an ambivalence. Each of the musical-idea statements subsumed in the developmental process is at first glance an ordinary musical-idea statement. Yet it is also essentially something else, a mere predicate of the developmental process whose meaning is essentially the latter. It is the polemical struggle within the mind between the two kinds of meaning which is the musical experience of the audience.
However, to put the composition together as a unity, the mind must subordinate the theme-by-theme hearing to hearing the developmental process. The simple statement corresponds to ordinary knowledge, the developmental process in a great musical composition corresponds at best to the higher hypothesis of Plato. Hence, the difference between the master of existing musical knowledge, Johannes Brahms, and the creator of new musical knowledge, Beethoven. Brahms is satisfying as a composer because he achieves lawful creative processes of musical development; he is uninspiring, relative to Beethoven, because Brahms's mastery of music seldom touches those processes which correspond to the higher hypothesis. Brahms is to Beethoven as Immanuel Kant stands as a poet with respect to Friedrich Schiller.
This sort of use of predicated objects to force the mind to a higher-order process-conception is identical with the notion of higher hypothesis in Riemann's great habilitation paper and the notion of transfinite in Cantor's work. Process-conceptions occur as distinct mental notions in terms of transfinites, as Cantor defines transfinites. The higher hypothesis of Plato is the highest-order transfinite possible in Cantor's implicit schema. Conversely, examining the lawful ordering of Bach's well-tempered system from the standpoint of both Beethoven and Cantor's notion of transfinite orderings, we have a more advantageous standpoint from which to comprehend both the general principle of the well-tempered system and contrapuntal methods generally.
What defines the well-tempered system for al-Farabi and his European followers through Beethoven is not the matter of agreement of tones as such. The well-tempered system is defined by the process of musical composition under contrapuntal rules. Counterpoint within any lawful ordering within modes leads inevitably to juxtapositions which are paradoxical: they contradict the apparent law and yet they arise through the realization of the law under contrapuntal conditions. These paradoxes are dissonances - lawful dissonances, or singularities within the domain of law. These cease to be unlawful if they are properly developed as transitions to other modes. Hence, the system of law within composition is not conserved except by allowing for the implicit, concurrent existence of every other mode within each mode. The well-tempering principle is determined by this principle of necessary agreement. The values of tonalities are those which admit of coherent lawfulness within the process of musical composition as a whole.
Music is not located in the physiology of a human ear, or the neurophysiology of the acoustico-lateral lobe; music is located in the creative-mental processes peculiar to the human being. It is as music is defined accordingly that the distinction between the human and the bestial in various proferrings of so-called music is determined. This was understood by Plato, by al-Farabi, by ibn-Sina, and by their European continuators.
The distinguishing feature of rock, of Elvis Presley, Bob Dylan, and other aspects of the guitar-strumming "modern folk-song" cults is that they combine monotony with arbitrary dissonances. The "modern folk-song" side of this overall spectrum is the most boring sort of monodic strumming, relieved scantily by occasional transpositions. The addition of the arbitrary dissonance, sometimes merely whining or cacophonous bellowing into a microphone, is the element of "personal style" - irrational idiosyncrasy - added on the tensible pretext of relieving the internal monotony of the rest.
There is no doubt that a gifted chimpanzee could replicate every cognitive aspect of this sort of performance. In a chimpanzee, the spectacle would represent - in brief, occasional zoo exhibitions - a certain kind of achievement, at least to the purpose of clarifying the cognitive levels of an Elvis Presley, a Bob Dylan, or of any one of a large accumulation of grunters, strummers, and squirmers - of bedrockers. CM-LL-23


The higher formal ordering of joking, as we identified it above, is suggestive of the principles of creative genius. By being made conscious of lawfulness in the use of a good joke to bring forth important conceptions simultaneously in the minds of a substantial portion of a definite audience, the person experiencing that awareness is made conscious of lawfulness in the ordering processes of his or her own judgment.
Thus, a poor joke - or poorer joke - is one which simply plays upon the ambiguities of simple consciousness, without structuring the experience to bring into play a forced reflection on a process of a lawful ordering of insight.
What is required is a truly great joke: art. This must be a quality of joking one qualitative level higher than the evoking of self-consciousness by good joking. Instead of being merely conscious of the lawful ordering of one's preconscious processes, one must have a great joke which prompts one to be aware of a lawful principle for transforming those preconscious processes.
This achievement brings forth the laughter of great, fundamental scientific discovery. This brings to consciousness a knowledge of the lawfulness of those mental processes by which one may willfully effect a qualitative advancement in one's mental-creative powers. PC-LL-20


By wide-ranging observations and measurements, Leonardo da Vinci and his physicist collaborator Luca Pacioli, demonstrated that the morphological patterns of living processes were harmonically ordered according to convergence upon the principle of the Golden Section. Leonardo applied this knowledge to his design of machine technologies, where the principle of the Golden Section and self-similar spiral rotation is used to concentrate the power and increase the energy-flux density of the machine, thus accomplishing work. Leonardo recognized that the same principle of negentropy governs the lawful development of the physical universe and the human mind. SM-LL-5


Formal algebra, like syllogistic systems, is based on the function of the middle term. This middle term has the associated significance of stating such things as "equal to", "identical with", "not part of", "part of", "greater than", "lesser than", and so forth. The objective of formal mathematics of this sort is to assemble all knowledge, or at least a great part of it, into one gigantic, continuous syllogism, such that one might trace one's way from the subject of a single syllogism, by way of middle terms, through every syllogism in that entire part of human knowledge. In other words, a syllogistic lattice-work.
All knowledge, or purported knowledge, of this syllogistic form, is either anarchistic nominalism, such as the irrationalism of William of Ockham, or is formal nominalism, like that of the neo-Aristotelian scholastics. The one is Dionysian, the other Apollonian; both are pure nominalism, noun-ism.
The practical issue is posed by stating that the nominalist approach chooses nouns as the data of experimental inquiry, whereas the negentropic approach chooses data of the form of verbs.
In the latter method, the verb "to be" adopts the self-reflexive transitive form of itself: "to cause itself to become". This is another way of stating the verb "to create", or to "cause to exist". Wherever the verb "to cause" is employed, the meaning of that verb is referenced "hereditarily" to the verb "to create", "to cause to exist", and to the ultimate verb, "to cause itself to become". All verbs, at least as they are employed to define data of scientific thought, must be defined by the hereditary principle of connection to "to cause itself to become".
Insofar as this pertains to the work of classical philologists, we leave the rest of that aspect of the discussion to them, to report how these principles may be located within Sanskrit writings, or at least some among them, and the form of classical Greek used by Plato. Having identified this aspect of the point, we proceed onward. SM-LL-24