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by Lyndon H. LaRouche Jr.
|This article is reprinted from the Spring 1996 issue of FIDELIO Magazine.
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How Hobbes' Mathematics Misshaped Modern History
by Lyndon H. LaRouche, Jr.
Putting to one side, as diversionary, the topic of today's aggressive fungus of trash curricula1: There is virtually no academic subject-matter currently taught in universities, which is not derived from the root of that specific strain of mathematics associated with Galileo Galilei, Thomas Hobbes, Rene Decartes, Isaac Newton, Leonhard Euler, the Marquis Laplace, or Augustin Cauchy. The significance of Dr. Jonathan Tennenbaum's Dec. 3, Eltville presentation on the subject of Paolo Sarpi's influence, from the standpoint of mathematics, is to be located accordingly.*
Again, overlooking the trivial course-topics proliferating in today's politically-correct academic curriculum, the fact is: There is no area of prevailing opinion in the fine arts, the so-called social sciences, in political-economy, in the teaching of theology, in doctrines of historiography, within the departments of philosophy, and so on, which is not premised upon the same, false, axiomatic assumptions which are derived from the mathematical-physics presumptions of the mathematicians Sarpi, Galileo, Hobbes, et al.
The topic we are addressing here, the role of so-called Enlightenment mathematics, in misshaping the teaching of non-mathematical learnings, is not an exotic sort of topic, relevant only to the specialists trained in the philosophy underlying mathematics.5 When we examine the way in which virtually all popular belief, even among the putatively uneducated, is hewn into either the empiricist, or the kindred, materialist form, we must find, that this issue of mathematics' influence upon social theory, accounts for the characteristics of response of most of our citizens, as voters, and otherwise. This shapes those citizens' response to issues in virtually every area of public policy and individual behavior.6
Without understanding the way in which Galileo's pathetic tradition in mathematics has induced the unwitting adoption of blind faith in such false, axiomatic, mathematical assumptions, throughout the academic curriculum and popular opinion, it would be impossible to render any competent account of the history of the Twentieth century, in particular, or to produce competent speculation on mankind's immediate future. Those pathological axiomatics, which the mostly unwitting citizen has adopted as principles of blind faith, act upon the citizen's will, to cause him, or her to tend to ignore or to reject, as if instinctively, those options of policy and decision which are inconsistent with the empiricist's dogmas respecting causality.
Galileo's Sarpian axiomatics is analogous, thus, to a mass psychosis, which has created a virtual reality in the victim's mind. To the degree he or she is acting under that influence, the victim refuses to acknowledge any evidence of the real world which is inconsistent with that virtual reality. In that sense, these often hidden axiomatic beliefs, are, thus, to modern society, as the goldfish bowl is to the typical populist among goldfish, who mistakes his bowl for the extent of his functional universe.
Today, the planetary society is poised at the brink of a threatened New Dark Age. Unless that New Dark Age is prevented by choice of effective action now, this world will be plunged, very soon, into a general catastrophe, worse in intensity than that which struck Europe during the famous New Dark Age, which depopulated Europe during the middle of the Fourteenth century.7 We have been brought to the brink of such a threatened disaster, through the influence of those mostly hidden axiomatic assumptions which have lately shaped the decisions of policy-makers, and which have fostered tolerance for such foolish, official decisions, among most of the citizenry. Without examining, and innoculating our nation's policy-shaping processes, against those axiomatic assumptions which have so misguided us, decision by decision, to today's brink of disaster, we shall not be able to choose the decisions upon which survival depends. The relevant issues are the identifiable, axiomatic presumptions of Newtonian social theory.
Since modern popular opinion is chiefly, directly or indirectly, a product of the trickle-down effects of classroom and textbook, it is the content of those textbooks and classroom dogmas, which is best searched for clues to the pathologies which have invaded the popular consensus.
Granted, some among the various symptoms of that pathology's impact upon modern university teaching in these fields, can be detected and exposed, as symptoms, without resort to those advanced topics in mathematics which lie within Dr. Tennenbaum's specialist's competence. However, one could never understand how the overall corruption of modern education works, without reference to the seminal issues of mathematical physics.
These are the same issues expressed as the central feature of the savage, and fraudulent attacks upon Leibniz by the avowedly Newtonian agent of Venice, Leonhard Euler, and the perfervidly Newtonian asset of the same Venice-directed salon as Euler, the Aristotelean Immanuel Kant. Those frauds by Euler and Kant typify the same issues upon which Bernhard Riemann's epoch-making habilitation dissertation is focussed: those are the issues at the center of the great fight within Nineteenth-century mathematics and mathematical-physics, with Gaspard Monge, Legendre, Gauss, Weber, Riemann, Weierstrass, and Cantor, on one side, and Laplace, Grassmann, Kelvin, Clausius, Helmholtz, Maxwell, Kronecker, and Rayleigh, on the other.
The Issue of Scientific Method
The proximate origin of all empiricist and related modern doctrines of taught mathematics and mathematical physics, is the Venetian Servite monk, arch-conspirator, and mathematician, Paolo Sarpi. Sarpi, who would fit the role of Mephistopheles in Christopher Marlowe's Dr. Faustus, is proximately the natural father of what became the Eighteenth century's founding of the Second Earl of Shelburne's and Bentham's British empire of the Georges. The begats follow. Galileo Galilei was mathematician Sarpi's lackey. Francis Bacon, the putative founder of British empiricism, was a protege of Sarpi's accomplices in England. Homo Sarpian Hobbes, who learned his mathematics from Galileo, became the personal secretary and intimate of Francis Bacon. Descartes was a tool of the circles established by Sarpi in the Netherlands, France, and England.
For the case of the modern English-speaking world, the matter is fairly summed up, by reporting, that during the span of several centuries, from the Seventeenth century of Paolo Sarpi's Sir Henry Wotton, through John Ruskin's Nineteenth century, literate England and Britain recognized the faction of Bacon, Hobbes, Locke, et al., and also the process of emergence of the British Liberal Party, by the generic name of Venetian Party. For example, Sir Winston Churchill's infamous ancestor, the First Duke of Marlborough, like King George I and Prime Minister Walpole, was a representative of that Venetian Party.
So, the terms Enlightenment, British liberalism, and Venetian Party, are implicitly interchangable, without change in meaning, down to the present day. We may describe Sarpian mathematics and its derivatives, such as Newtonian social theory, as literally Enlightenment philosophy, or Venetian Party policy.
All among this planet's cultures which had been established prior to the Fifteenth-century Europe's Golden Renaissance, were either failures by design, or simply outlived their limited usefulness after a time. Most of these pre-Renaissance cultures ended as manifest catastrophes. In the more fortunate cases, a culture faced with self-induced doom, met the challenge of its existential crisis, by generating a new, superior culture, as Fifteenth-century western Europe did most brilliantly. Among failed cultures generally, there is included a special type, a defective culture which was designed according to the intent to destroy an existing culture. Mathematician Paolo Sarpi's application of Occam's Razor to Aristotle, to make Aristotle's anti-Platonic formalism the hypothesis of a generalized, empiricist-materialist method, is a pathology of that latter type.
One can not understand this, or any other case of the latter type, without comparing it to that alternative which it has been concocted to destroy.8 Sarpi, shrewder than the leaders of Venice who preceded him, recognized that the strength, and corresponding vulnerability of emerging, modern European civilization, was its dependency upon the scientific method of Plato. In Sarpi's time, leading thinkers of modern European science, had meant, chiefly, Nicolaus of Cusa, Luca Pacioli, Leonardo da Vinci, the School of Raphael, Johannes Kepler, William Gilbert, and so on, a list which grew, later, to feature the leading role of Europe's last universal intellect, Gottfried Leibniz.
Sarpi recognized the potentially fatal strategic blunder of those Venetian leaders who sought to eliminate the influence of the Council of Florence, and of science, by bloody and other varieties of inquisitional methods. The increased productive powers of labor, fostered by the newly-created modern nation-state, had a military implication. Already, beginning with France under Louis XI, it was repeatedly shown, that, per capita, modern nation-states were more powerful than their feudal adversaries. To defend the oligarchical tradition of Babylon against the Christian form of modern nation-state, Venice must penetrate to the innermost essence of emergent, modern European civilization, and strike it a deadly blow in that essence.
The Enlightenment is the instrument developed by Sarpi and his followers to that oligarchical purpose.
On the subject of mathematics itself, the general argument on behalf of the work of Leibniz, Riemann, et al., against Galileo, Newton, Euler, Cauchy, et al., is supplied in other published locations.9 Our subject here, is not mathematics as such, but, rather, those two, underlying, axiomatic assumptions of Sarpi's mathematics, which misshape the characteristic features of a wide assortment of liberal arts topics, in addition to commonly taught classroom mathematics. Our primary concern is to strip away all of those secondary features which distinguish one liberal-arts subject-matter from another, to unveil, thus, the common axiomatic feature of all. For that more limited, stated purpose, we select two crucial issues of scientific method, which reveal the way in which Sarpi's mathematical assumptions define the mental behavior underlying virtually every liberal arts textbook and classroom of today.
Those two, broadly relevant assumptions are, first, the false belief in perfectly continuous extension in space-time, and, second, the Enlightenment' s rejection of the principle of reason, substituting the idea of mechanistic causality. Combined, the two assumptions represent the central issues of scientific method, in every field of inquiry, since Plato's founding of the Academy of Athens, through the work of Archimedes and Eratosthenes, and through the writings of St. Augustine, Nicolaus of Cusa, Leonardo da Vinci, Kepler, and Leibniz. The implication of the first assumption is more easily recognized; we address that first.
The Issue of Continuity
Respecting the deepest axiomatic implication of the fallacy of perfectly continuous extension, it is sufficient to summarize, and then situate the argument with which this author has elaborated the point, in numerous earlier locations.10 To wit:
Until Bernhard Riemann's 1854 habilitation dissertation, all those formalities of the classroom mathematics which are generally taught still today, were derived from a model of geometry adopted from Euclid's Elements.11 The materialist and empiricist view of that geometry, was based upon the presumption that the four dimensions of Euclidean-Cartesian space-time, were each and all extended into bad infinity without limit, and were extended everywhere, always with perfect continuity. The materialist version of this, assumed that those four dimensions were supplied to an Aristotelean tabula rasa, the newborn human mind, by the human senses, whose sense-impressions were presumed to be a reflection of the composition of the material universe outside the human mind itself. The empiricists made more limited claims respecting the alleged reality of sense-perceptions, but shared with the materialists the presumption that all knowledge was limited to those facts attributed to the self-evident authority of isolable sense-impressions.
In the real world, which exists only outside such presumptions of Aristotelean virtual reality, the increase of the potential relative population-density of the human species, from the level of a putative man-ape, several millions living individuals at most, to the vastly higher population-levels and life-expectancies of civilized existence, is the result of categories of ideas which violate the empiricist's and materialist's presumptions respecting sense-perceptions, and respecting ideas as defined by Plato.
These ideas do arise from investigation of the domain of sense-experience; but, they arise from those stubborn paradoxes which show the Aristotelean view of nature to be absurd. One of the most readily demonstrated classroom models of the way in which such ideas are obtained, is the case of the estimate of the curvature of the Earth by Eratosthenes, a leading member of Plato's Academy of Athens. The crucial point of relevance to our discussion here, is that that curvature was not to be seen (that is, as a sense-perceptible object) by any person until 2,200 years after Eratosthenes' measurements of this unseen principle of reality.12
Those, Platonic qualities of empirically demonstrated, non-sensory ideas, are to be recognized in all rigorous natural philosophy as validated discovery of new scientific principles. These discoveries have the formal quality of being new axioms, axioms which changed radically the set of axiomatic assumptions upon which depended the entirety of a previously adopted body of formal scientific opinion. The result of such a change, is usefully identified as the replacement of the entirety of the existing, extensible theorem-lattice, associated with previously established sets of axiomatic presumptions, by a new theorem-lattice premised upon the modified set of axioms.
The term hypothesis, as used by Plato and his Academy, through the time of Archimedes and Eratosthenes, signifies, formally, such a set of axioms.13 As a matter of formalities, a change in hypothesis signifies nothing less than, nothing other than, a validated change in the set of axioms underlying a previously established body of scientific knowledge.
In this view, the term knowledge does not signify what students have learned to accept as today's authority's teaching, respecting contemporary, customary bare fact or doctrine; it does not signify information, as that latter term is commonly employed today. Knowledge signifies: either that the mind of the original discoverer of a new, validated principle (hypothesis) has lived through the experience of the act of identifying and validating that new principle, or, that a student has successfully reenacted the original discoverer's mental act of discovery of both that concept and its proof.
Knowledge is not textbook or kindred learning of approved doctrine. The quality of knowledge is typified, essentially, by those relatively more valid principles of nature which the individual has discovered through the successful application of his, or her individual's, distinctly human, creative power of cognitive reasoning, to solve an existential quality of paradox within previously established scientific opinion. Whether the mastery of such a valid principle occurs as an original discovery, or as a student's form of reenacting the mental act of original discovery, the result is, that that principle is known, rather than merely learned. Thus, knowledge is typified by the Christian-humanist methods of education employed by the best among the Brotherhood of the Common Life, and in the Schiller-Humboldt form of Classical Humanist secondary education introduced in Nineteenth-century Germany.
Notably, the term Geistesmassen, as used by Riemann, signifies a quality of cognitive thought which is expressed as a valid discovery of natural principle, as opposed to the false notion, that ideas are rooted in mere reflections of sense-perceptions.14 Thus, Riemann's employment of that term is synonymous with metaphor.
To define such a metaphor, a different kind of object replaces and supersedes the derivation of a particular sense-perception. Eratosthenes' determination of the curvature of the Earth's surface (within a reasonable estimate of the length of the polar meridian), is typical of the fact that all valid principles of science are Platonic ideas (Geistesmassen), which exist only outside the domains of empiricism and materialism, existentialism generally, and outside the sickly dogmas of phenomenology in particular.
Thus, as elaborated by the present writer in the indicated, earlier locations, such metaphors are the active principle underlying those formal mathematical discontinuities (or related singularities) which mark the transinfinitesimal break in continuity occurring at each Riemann phase-shift of a process, from a phase representable by a formal theorem-lattice of n dimensions, to a superseding lattice of n+1 dimensions.15 The metaphor is not contained within the mark; the mark is the footprint which valid metaphor leaves in its passage through the efficient development of (for example) mathematical physics to successively higher levels of competency. Physicsor, experimental physicsexists outside, and above the mere mathematical physics which scrambles in its efforts to mimic reality, as a shadow on the wall of Plato's cave mimics that which it misrepresents. As the frequently referenced case of Eratosthenes' estimate of the meridian illustrates this point, physical ideas exist only outside formal, classroom blackboard mathematical physics.16 Physical ideas, such as Eratosthenes' referenced discovery, exist only as metaphors, or, as Riemann says, Geistesmassen.
Consider the blind faith of the Aristotelean, the empiricist, materialist, or phenomenologist, his smug confidence, that the universe of experience is implicitly representable mathematically as a Euclidean space-time, extended limitlessly, within perfect continuity. That is a popular notion, but also a delusion; it is literally a form of mass-psychosis. The core of the argument to be offered against that delusion, is, summarily, as follows.
Man's knowledge of the universe is derived solely from the human species' increased mastery of nature (as expressed by rising potential relative population-density). That advancement in the human condition, is brought about through a unique quality of the human individual, absent in all inferior species: the ability to change society's behavior willfully, and radically, to such effect, through valid fundamental discoveries. That progress is entirely the result of those creative mental powers of successive, valid discovery of superior natural principle, in art, as in science.
Focus upon the fact, of the efficiency of the method by which valid and superior hypotheses are generated,17 as metaphor, through the effectiveness of the creative reason of the human individual in uncovering more powerful principles of nature. From this standpoint, increase of mankind's potential relative population-density demonstrates the predisposition of the universe to submit to the creative powers of reason of the human individual.
The universe customarily defies all arbitrary, individual and popular opinion; it is obedient only to valid metaphor. The success of mankind in mastering the universe according to Plato's principled method of hypothesis, supplies the only possible proof of the nature of the laws of the universe. This is the proof that the universe is predisposed, as by design, to obey the faculty of individual creative reason, the faculty of valid metaphor, rather than the always transitory, and usually doubtful authority of mere learned opinion.18 That empirically manifest predisposition of the universe is the content of the idea of Natural Law, of the existence of universal physical law, of those commonly underlying universal characteristics which subsume, combined, non-living, living, and cognitive processes.
These discoveries occur only in the form of Platonic ideas (metaphor), which are reflected upon the domain of formalist mathematical, and other, thinking as discontinuities, or, as singularities.
To attempt to create an imaginary world of human experience, in which such occurrence and impact of Platonic ideas is not the central feature, is to concoct a vicious species of virtual reality, a virtual mass-psychosis, upon which the pseudo-science called information theory converges. The latter type of delusion, is an axiomatic characteristic of the Sarpi-Galileo-Hobbes-Newton-Euler venery in mathematical physics. Centuries before Professor Norbert Wiener's founding of the cult of information theory, there was already Paolo Sarpi's Enlightenment, and, before Sarpi, Aristotle, Bernard of Clairvaux, and William of Ockham.
Thence, from such mathematical-physics, the same delusion is extended, to serve as the central, axiomatic feature of all Newtonian social theory: all presently, commonly taught political science (co-created by the positivists Saint-Simon and Madame de Stael), and, also out of positivism, all of today's commonly taught ethnology, anthropology, sociology, behaviorist psychology, modern criminal law, grammar/prose style, behaviorist and Freudian psychology, and so on.19
In the work of the founder of modern science, Nicolaus of Cusa, and among such Cusa followers as Leonardo da Vinci, Kepler, and Leibniz, the notion of lawfulness of the universe is derived from the work of Plato. The most relevant features of Plato's work on scientific method, are found in those, later dialogues, which his Parmenides serves as a de facto prologue. That most fundamental principle of scientific method, which is savagely violated by virtually all currently taught classroom mathematical physics, is the principle of memory. This point is most readily illustrated by reference to the composition of the Classical form of strophic poem. This principle of Classical poetry carries over into Josef Haydn's discovery of what he termed Motivführung, as that was given revolutionary further development by, chiefly, Wolfgang Mozart, Ludwig van Beethoven, and Johannes Brahms.20
Respecting this particular point, the role of the principle of memory in defining scientific ideas, virtually all today's mathematicians are, relatively speaking, science illiterates. This crucial principle is key to the subject of the present report. It is crucial, not only for professional mathematicians, but, also, professionals representing all empiricist and positivist varieties of the commonly taught versions of liberal-arts subject-matters.21 This Platonic principle of memory combines with that principle of universal discontinuity, central to Leibniz's Monadology, to define the axiomatic basis of the presently hegemonicand, potentially fatalEnlightenment culture of modern European civilization world-wide.
Our pedagogy on this point, is organized as follows. As a benchmark, note Thomas Hobbes' proposal to outlaw metaphor from the English language.22 It should be understood, that this Hobbes manifesto against metaphor, is typical of an epidemic of related attacks, on both metaphor and the use of the classical form of the subjunctive,23 which continued through the centuries to the present-day pagan priesthood of the Modern Language Association (M.L.A.). Note the agreement between Hobbes and the Romantics on this point, as the Romantics substitute symbolism and hyperbole wherever Shakespeare, for example, employs metaphor.
That noted, we must, then, emphasize afresh, that each valid discovery of more advanced scientific principles, has occurred in the form of a nameless idea, to which a name was later assigned. This idea had no simple referent in any single sense-perception: it had the form, therefore, of metaphor. The Romantic adversary of metaphor would seek to avoid that fact, by attributing that idea, symbolically or hyperbolically, to some simple perception, such as the symbolic or hyperbolic definition, Aristotle is a featherless biped. That is the implication of Hobbes' referenced argument against metaphor, and also the kernel of the empiricist objection to the strict subjunctive.
For example, referring again to Eratosthenes' estimate of the meridian: once we have identified the fact, that no man had yet seen that curvature of the Earth, the quality of his discovery as a Platonic idea, as a metaphor, is forced to our attention. Similarly, all microphysics is based upon metaphor, rather than sense-perception: despite the hysterical efforts of the allies of Ernst Mach, to reduce Max Planck's quantum to a matter of symbolisms. Similarly, one can not directly see the distance between the Earth and the moon, as a sense-perception, from the surface of the Earth.24
Look at metaphor, then, from its central place in the competent composition and performance of both Classical strophic poetry, and, in Classical musical composition: motivic thorough-composition in the exemplary cases of Haydn, Mozart, Beethoven, and Brahms. Examine this principle of Classical composition, from the standpoint of Plato's treatment of the principle of memory.25 Look, then, at the way in which this principle of memory defines Reason's role in defining the lawful ordering of the universe. Consider, then, the monstrous impact, for modern society, of the fraud inhering in Galileo's mechanistic notion of causality.
Consider the role of the principle of memory in four, successive settings: Classical poetry, Classical Motivführung,26 Classical tragedy, and, finally, physics.
A Classical strophic poem has the form of a series of stanzas, each of which, with two leading, possible exceptions, faithfully mimics or parodies the prosody of each of the others.27 This form is very ancient, antedating written language by millennia.28 Music is derived from the singing (i.e., vocalization) of such poetry according to principles brought to light more clearly in bel canto methods of training of the singing and speaking voice.
This tradition of vocalization of Classical strophic poetry, is the probable origin of what we know as scientific thought and scientific method today. Whatever the history of the matter might prove to be, it is from the musical view of such Classical poetry, that Plato elaborated the principles of scientific thought. Remember, that the science of memory, as embedded in the composition and peformance of such a Classical strophic poem, is the most fundamental formal principle of all human knowledge. Remember, that this principle of memory, is key to mastering metaphor, in art, and in matters bearing upon knowledge of universal principles of nature.
At this instant, it is indispensable, for practical reasons, that we supply the following warnings against the way in which poetry, and its recitation, is generally misunderstood among university liberal-arts graduates today. The point we have to make, respecting the role of memory in composition and performance of poetry, involves the special qualities of Classical poetry as a medium for communication of metaphor, a medium which is mastered presently by only a vanishing few, aging professional actors. Thus, one could not recognize the point we are making here, if one mistook the way in which poetry is presently recited (or as the subject of poetry currently taught), for the medium which Plato knew, and to which the writer is referring.
The problem today, that problem of the medium which we are addressing here, is the academic popularity of the cult of written text.
Today, unfortunately, the ability of even most professionally trained modern-language specialists, to say, or even to understand such a poem, is either virtually non-existent, or, no better than profoundly impaired by the present conventions, which examine all literature from the standpoint of doctrines of written text. Written text is presented as it were not only an independent mode of speech; it is, sometimes, even the assumption of practice, as by the devotees of Professor Jacques Derrida, that written speech ought to have been the original form of utterance.
Exemplary of this cult of the written text: Speeches read from written text, are usually boring, when not calculated titillations accomplished either by premeditated perpetration of that which is both trivial and popular, or simply a crude cartoon of trivial ideas seasoned with the manic-depressive jock's spice of soap-box ranting. When this tactic is not employed as a method of pre-censorship, the function of the pre-written text for a speech, is chiefly as a mental crutch for the speaker who lacks a clear preconception of what he or she is about to say.
A good oral address is an art-form, with some crucial points of absolute distinction from those commonly taught notions of English prose style employed for composition of written text. Indeed, if an oral address might be transcribed appropriately in a style of punctuation not offensive to the Columbia University School of Journalism and New York Times style book, the product transcribed must have been an intellectually sterile concoction.
A good oral address is closer to poetry, and to the prosody of Shakespeare's and Schiller's tragedies, than to that which is currently taught as university-schooled prose. A good address works backward from a subsuming idea, that in the form of what Plato would have recognized as a Good idea. Like a qualified teacher's lesson-plan, the address is developed, as a Becoming, to fulfill the necessary determination of the Good idea, as the metaphor-solution of the paradox posed by the Becoming.
Thus, the Good idea of the intended presentation, as a totality, determines that parade of metaphors which is the order of the address as a Becoming, each among which, in turn, subsumes the construction of the paradox implying that particular metaphor in the succession. The further requirement, is an ironical form of coherence among that succession of stages of development ordered according to the series of metaphors.
During the recent two generations, the illiteracy of university instruction on this account has been increased geometrically, through the loss of a culture of reference rooted in the bel canto modes of voice-training. This mode is indispensable, not only for the singing of the Classical-musical repertoire and to provide instrumentalists with an indispensable grounding in the principles of the bel canto singing voice. It is essential to poetry, and to the performance of Classical forms of drama on stage. Among the numerous difficulties confronting the student of poetry today, the greatest obstacle to even the barest comprehension of Classical poetry (and music), among professionals and others, is the prevailing tendency to degrade oral speech into a matter of rules for reciting written text.29
The immediate practical point of concern here, is the following. If the reader recites a strophic poem in the manner of supplying today's conventional classroom variety of recitation of written text, the oral delivery will be an illiterate's abomination. Directly to the point of relevance: Among the evils so perpetrated, will be the reader's tendency, either to mimic the first strophe in the delivery of second and third, or to apply a strained, or otherwise inappropriate sort of variation in the expression of each. It will not be poetry; it will be a recitation of text, more or less as bad as actor Sir Laurence Olivier's ranting torment of Shakespeare's prosody.
The failure to comprehend poetry as sung (vocalized) oral speech, rather than written text, signifies that the reader would command about as much recognition of the medium for which the poem is composed, as the tenor who imagined that Mozart composed the Picture Aria of his The Magic Flute as a part for performance on the musical comb. There is nothing in any poem which might have been composed for the medium of written text, which corresponds to the principle of composition of Classical poetry; the meaning of a Classical poem is contained solely in the poetry of bel canto-vocalized, oral utterance, not written text.
By combining the characteristics of the medium of bel-canto-vocalized oral utterance, with strophic prosody, the Classical poet is able to employ the multi-media character of such recitation as a contrapuntal device. By means of this ruse, the poet plays the singing voice's intonation against the oral text, to achieve the effect of conflict among suggested meanings, the effect known generally as irony.30 It is relevant to note, that Beethoven's last string quartets use the special counterpoint of motivic thorough-composition, to achieve the same sort of result.31
Compare this view of such poetry, with the exemplary case for scientific discovery of principle, Eratosthenes' estimate for the meridian.
There is an exemplary succession of development, from that estimation by Eratosthenes, through Blaise Pascal's development of the cross-ratio, through the role of refraction of light in Leibniz's and Jean Bernoulli's supercession of algebraic by non-algebraic (transcendental) mathematics, through Carl Gauss's work on biquadratic residues and geodetics, and Riemann's habilitation dissertation. The common characteristic of these developments, is the practise of driving the axiomatic assumptions of an existing theorem-lattice measurably beyond their limits, into a well-defined paradox.32 So, the repeated strophes of a Classical poem proceed, adding irony upon irony, stanza by stanza. Each stanza, compared to its predecessors, demands a metaphor. The concluding utterance of the repeated strophic characteristic of the poem, transforms everything, including the preceding metaphors, provoking the new metaphor which subsumes the entirety of the development of the poem through all of its successive stanzas. So, each of the observations in Eratosthenes' study of the curvature of the meridian proceeds.
Classical music is composed according to this model of strophic poetry. Shall we perform the repeat? one of the musicians says to the other. The recording company frequently answered, No! The musically illiterate would imagine that the repetition is merely repetition; in Classical music there are no mere repeats; the repeated section of the Mozart sonata is never performed exactly the same way as the first statement of that section. The repetition occurs as antistrophe to the strophe. As Pablo Casals instructed the students of his master class: In Classical music, there is always variation.
It is not arbitrary variation. Variation is not the embellishment of the bare score by the performer's arbitrary choice. In the simplest version of the movement of the Classical sonata form, the order of development is statement, restatement, development, and recapitulation, each of which occurs as reponse to, in order, the statement, the statement plus restatement, and the statement, restatement, and development. Each among these four successive elements of such a movement, is analogous to the corresponding stanza of a four-stanza strophic poem. That ordered variation is implicitly built into the performance by the composer. The performer's task, is the exercise of musical insight into the metaphorical intent of the composer; technique is a matter of the performer's resourcefulness in bringing out that progression in the domain of metaphor. Interpretation is not a matter of personal taste; it is a matter of the performer's ability to comprehend, and to realize the distinction between right and wrong.
The strophe provides a repeated, yet varied structure for the poem as a whole. The change of vowels and consonants, in contrast of one strophe to each of the others, provides a degree of contrapuntal irony to the repeated common aspect of the successive strophes. The imagery of ideas in the verse as such, provides another degree of contrapuntal irony. It is the juxtaposition of these ironies, which generates paradoxes. The form known as the classical strophic poem, provides the poet, thus, a medium whose potential is a nest of paradoxes: within the stanza, among the stanzas, and in the poem taken as a unit-whole.
As in the idea of curvature of the meridian, in Eratosthenes' measurements, the solution to the paradox of what is explicitly stated, lies outside any individual sense-perception, any mere symbolism. Until the Twentieth-century development of rockets and supersonic jet-aircraft, led by Hermann Oberth's team, the idea of curvature of the Earth's surface existed only in the domain of metaphor. The ideas of microphysics exist always only in the domain of metaphor. The distinction between non-living and living processes, is measurable in its effects, but has primary existence only in the domain of metaphor. The idea of the poetic stanza, of the poem as a whole, exists only in the domain of metaphor, but in neither sense-perception nor symbolism.
Similarly, musical ideas exist only within the domain of metaphor. In all cases, the fact of the difference is measurable, but the cause of that difference is not a matter of sense-certainties.
Once we have the concluding metaphor of a Classical strophic poem, or motivic-thorough-compositional form of Classical musical composition, we have struck, at least implicitly, upon the deepest principle of scientific method.33
Scientific Method in Poetry and Music
That veritable metaphor of metaphors, the concluding metaphor which is established by the concluding stanza of a strophic poem, or (for example) a motivic thorough-compositional mode in Classical musical composition, corresponds to the identity of that composition taken in its entirety.
Any qualified musician, or Classical actor, presented with that fact, will recognize that the proper way in which to perform the relevant musical or poetical composition, is to use that concluding idea of the composition as a whole, as the guiding rule shaping the succession of steps of performance in the development of that composition, at every point in the performance. This is the exemplification of the fundamental principle of scientific method, as encountered in Classical art-forms generally. This is the kernel of the Socratic method of Plato's Academy of Athens.
The immediate argument may be summarily stated, as follows.
Once this metaphor of metaphors has been established in the mind of the performer, for any Classical strophic poem (or, a comparable musical composition), that idea remains a fixed concept in the mind of the performer, from the beginning to close of his next presentation of that artistic work. In this way, that next performance of the work is dominated by the interplay of two ideas: first, the metaphor of metaphors, which remains constant, from the moment of silence prior to beginning the performance, through the closing instant of silence, which immediately follows the completion of that performance; second, the constantly changing idea of the work-in-progress, as the performance moves from one stanza to the next, and, so, through the close.
In Plato's terms, the unchanging idea representing the metaphor of metaphors, has the form of the Good; in other words, that idea is chosen by the mind of the performer, for that occasion, at least, as the alpha and omega of the composition taken as a whole; it is an unchanging idea, which does not undergo any change in itself during that developmental process which it directs.34 In contrast to that unchanging, controlling idea, we have that evolving notion of the unfolding composition, which is reached at each point within the progress of that same performance, which has the form to which Plato ascribed the name of Becoming. Thus, in any successful performance of such a Classical poem or musical composition, the interaction between these two forms of ideas, Good and Becoming, generates a tension within the performance which the audience may perceive as energy.35 Exactly the sense of tension and energy is required for all great poetry, including the soliloquies and related excerpts of Shakespeare's tragedies.
Examine the structure of that tension: an awful, beautiful truth takes shape, within the early morning mists.
Consider the case of the Classical performer presenting a poem or musical composition. From the stillness of the moment which must always precede the beginning of the piece's opening enunciation, through to the concluding momentary silence, the performance is governed by an unchanging goal. That purpose, is the realization of the cognitive necessity of the metaphor whose existence appears only in the conclusion of the composition. That unchanging metaphor's realization, is the purpose, the Good of the composition. Against this fixed conception of purpose, the mind of the performer is experiencing the developmental process, the Becoming, moving toward that goal: a developmental process which yearns toward, but which, within itself, does not yet know the conception which is that goal.
Thus, two conceptions coexist within the mind of that performer, during each instant of the unfolding of the performance: one fixed, and relatively perfect, one relatively imperfect, changing. True counterpoint. There is an additional, awfully profound difference between the two qualities of ideas thus juxtaposed. The latter difference may be described as follows.
Let the order of the development of the composition serve as the measure of relative time. At each moment of the process, the idea which has the form of the Good, comes as if from the future; it expresses the existence of that which is yet to be made known to the audience in the future unfolding of that composition in progress; whereas, the changing idea which has the form of the Becoming, comes from the embodiment of the past in the occurrence of that particular instant. In this contrast in time, lies the tension referenced above. Here lies the awful, beautiful truth about all human knowledge, expressed as art, science, or both. This is the key to comprehension of the laws of the universe.
The scientific principle of universal lawfulness, as understood by Plato, by Kepler, and as Leibniz's notion of necessary and sufficient reason, is of this same form as such a Classical composition in poetry and music.36 The notion of lawfulness as Reason, corresponds to the sense, that any perfected metaphor subsuming (as from the future), the composition through which knowledge of that metaphor is coherently generated, is the Reason of that composition's unfolding, the lawfulness which governs that composition. In contrast, Sarpi's Galileo outlaws Reason, and substitutes the deductive-logical outcome of blind, percussive causality. For that Ockhamite atheist, and Servite monk, Sarpi, the motive for the present must be found in the past, not, as for Plato and the Christians, in the future; for him, as for such followers as Hobbes, Locke, Mandeville, François Quesnay, Adam Smith, and Jeremy Bentham, and the libertarian Mont Pelerin Society of Friedrich von Hayek and Milton Friedman, the Good, firstly, should not exist, and secondly, if it did exist, must not be allowed to interfere with the present.37
Science, like Classical art, is the inference of the necessary character of the future, from the assessment of the process of Becoming as coherently subsumed by a Good.
By virtue of the same principle we are examining here and now, the full comprehension of the implications of what we have just described, requires reference to Plato's Parmenides; without considering the Parmenides in this dawning light, it itself could not become adequately understood.
The Parmenides poses the problem of conceptualization of any formal theorem-lattice. Implicitly, as the other later dialogues of Plato make clear, the Parmenides considers not only a theorem-lattice, but also a manifold of the type which Riemann treats in his habilitation dissertation. The latter is a manifold of successive hypotheses, all related, but each of a higher rank of relative truthfulness than its predecessors. The latter case, in which the elements of the series are each hypotheses, so qualified, supplies the minimal definition of a Platonic Becoming. Consider the implied two cases. First, the inferior case, in which the subject is a lattice of theorems. Next, the superior case, in which each particular element of the lattice is an hypothesis of a Riemann series, rather than merely a theorem.
On both of the levels just described, both that of the theorem-lattice and of the hypothesis-lattice, we are confronted by a succession of elements, each of which, at first impression, has a unique, distinct individuality, analogous to that individuality attributed to any particular sense-perception. It appears, at first, to be an array of particular facts, or, of particular theorems, or, of particular hypotheses.
The Parmenides notes, as if in an ironical aside within that dialogue, that the inability of the character Parmenides to find a conception commonly subsuming all of the members of each array, is the result of the Eleatic reductionists' refusal to take the principle of change into account. For, if one could show that the pairwise difference among the elements of a functionally related collection might be expressed adequately by some functional notion of change, that notion of change would acquire the significance of transfinite, or Becoming, in Georg Cantor's work. In that case, a collection of related facts leads to a subsuming theorem, the elements of a consistent theorem-lattice lead to an hypothesis, and an orderable series of validated hypotheses, each and all generated in the same mode of discovery, through creative reason, defines what Plato identifies as an higher hypothesis. In such cases, the relevant theorem, hypothesis, or higher hypothesis, comes into existence, as a Platonic idea.
Such a theorem is a claim against the future. Such an hypothesis is also a claim against the future. Each, so conceived as a relative future, has the approximate quality of form of a Good, akin in this respect to the concluding metaphor which then subsumes that poem or musical composition by means of which its cognition as an idea is generated. This view of theorem, hypothesis, and higher hypothesis, is the notion of Reason, of a universal lawfulness knowable to the cognitive powers of individual creative reason. Plato, on this account, recommends that we think of God as the Composer, and regard His universe as a lawful Composition.38
These principles of Classical poetry and music occur within the domain of natural-science practice, as, for example, Riemannian physics. In the LaRouche-Riemann domain,39 the Many are represented by a collection of hypotheses, each ranked and ordered, relative to the others, according to the increase of man's per-capita power over nature (potential relative population-density), and as one hypothesis serves as necessary predecessor for its successor. The immediate solution to the challenge of unifying cognition of such a series of hypotheses, is the principle of discovery subsuming the generation of each and all of the open-ended array of hypotheses: the Becoming. That latter, transfinite principle of discovery is designated as an higher hypothesis.
The development of the Platonic idea of higher hypothesis, at each instant of progress in human knowledge, presents us with a metaphor. This metaphor, is to be applied retrospectively to the process of development of relatively valid hypothesis. This is done according to the same principle of memory which governs the tension between the opposing Good and Becoming respecting the performance of a Classical strophic poem, or relevant musical composition.
*Jonathan Tennenbaum, Why 'Standard Classroom Mathematics' Makes People Stupid: Paolo Sarpi and the Fraud of the Enlightenment, speech to a conference sponsored by the International Caucus of Labor Committees and the Schiller Institute, Eltville, Germany, Dec. 2-3, 1995; 21st century Science & Technology, Vol. 9, No. 1, Spring 1996 (to be published).
1.Sometimes referenced as socially significant basket-weaving.
2.The generic term is hedonistic calculus.
3.For example, some quiddling victim of indoctrination in empiricism, might propose the correction of our text: that instead of, All modern empiricist ... versions of modern academic social theory, is derived ..., the plural of the verb, are derived, should be employed. In defense of that critic, we concede, that a spokesman for the relevant, pathological standpoint in method, such as Aristotle, or the Ockhamite Aristoteleanism known as empiricism, would be inconsistent with his own deepest principle, if he neglected to demand that grammatical correction. As Dr. Tennenbaum pointed out on an earlier occasion, that is the import of Aristotle's lunatic Metaphysics, a book which is essentially a maenad's rant against Plato's Parmenides dialogue.
4.Cf. H. Graham Lowry, How the Nation Was Won: America's Untold Story (Vol I:1630-1745) (Washington, D.C.: Executive Intelligence Review, 1987), p. 50: quotation from Cotton Mather on the distressed state of the intellect and morals of the 1696 Massachusets Bay Colony, after the capitulation to the reforms imposed by William of Orange: There seems to be a shameful Shrink, in all sorts of men among us, from that Greatness, and Goodness, which adorned our ancestors: We grow Little every way; Little in our Civil Matters, Little in our Military Matters, Matters, Little in our Ecclesiastical Matters; we dwindle away, to Nothing. The present writer knew his grandparents, who were born during the 1860's, and had bare acquaintance with one great-grandparent, born a generation earlier. He knew, of course, his parents' generation, born at the end of the last century, and, also, his own generation of young veterans of World War II. He knew each of these four generations better, by knowing the literature and art which informed the opinion of relevant strata in each. He considers the baby-boomer generation, and its progeny, now entering adult occupations, in similar terms. Relative to the degree to which the American people have descended in cultural level over the course of these six generations, bridging the 1840's to the present, closing decade of the century, the Little Massachusetts citizens of 1696 were as intellectual and moral giants, relative to the level which we have descended, as a people, over the course of the present century.
5.See Lyndon H. LaRouche, Jr., Riemann Refutes Euler, 21st century Science & Technology, Vol. 8, No. 4, Winter 1995-1996. See also, Lyndon H. LaRouche, Jr., Non-Newtonian Mathematics for Economists, Fidelio, Vol. IV, No. 4, Winter 1995-1996 (also appeared in Executive Intelligence Review (EIR) weekly, Vol. 22, No. 32, August 11, 1995). On the formal proof against Euler, see the treatment of Nicolaus of Cusa's conclusive proof, that @dp is a transcendental value, see Lyndon H. LaRouche, Jr., On the Subject of Metaphor, Fidelio, Vol. I, No. 3, Fall 1992.
6. Compare this with the present writer's thesis, on the subject of the present crisis as end of an epoch, as presented in the second part of his presidential campaign paper of Oct. 11, 1995, The Blunder in U.S. National Security Policy, and his Dec. 2, Eltville, Germany, address on the subject of The End of An Epoch, published in the Jan. 1, 1996 edition of EIR (Vol. 23, No. 1).
7.See Executive Intelligence Review, Jan. 1, 1996, passim, on the diagnosis of the present condition of the global I.M.F. monetary-financial system, as terminal.
8.The most appropriate precedent to be considered, is the role of Aristotle as the enemy of Plato. The widespread academic cant, to the effect that Aristotle bases himself upon, but also corrects Plato, is a fraud, invented and perpetuated by apologists for Aristotle's method. Specifically, the revival of Aristotle by the Byzantine Emperors who followed Diocletian, was introduced as part of the imperial social-control design for introducing a gnostic, syncretic blending of paganism and Christianity. Christianity, by its nature, is anti-oligarchical, opposed to that degradation of man which is inherent in, for example, the institutions of both feudal landed aristocracy and bourgeois financier oligarchy. Diocletian, the lawgiver for the tradition of European feudalism, decided that it were more prudent to coopt Christianity, than to continue with the futile tradition of bloody persecutions. Constantine legalized Christianity within the pagan pantheonic system, and imposed his selection of bishops, such as the infamous Arius, and the influence of pro-Aristotelean hesychasm, as worms, to enervate, hopefully to destroy Christianity's substance from within. The Byzantine Empire outlawed Plato, and imposed Aristotle and his method as the arbiter of Christian theology and doctrine. This policy was spread into western Europe from Byzantium, and from Venice. The focus of these imperial assaults from the east, was against Augustine and the method of Plato inhering in Augustinian Christianity, as in the Gospel of St. John and Epistles of Paul. The policies of Venice's leading Sixteenth-century opponents of the Council of Florence, such as Pietro Pomponazzi, Gasparo Contarini, Francesco Zorzi, and Paolo Sarpi, are a direct outgrowth of the Byzantine emperors' using the replacement of Plato by a canonical Aristotle, to corrupt Christianity into a syncretic form acceptable to an oligarchical social order.
9.See footnote 5, above.
10.From the locations published during the recent ten years, the author's following books and papers are exemplary. The Science of Christian Economy (Washington, D.C.: Schiller Institute, 1991). From the Fidelio quarterly's series on the cognitive principle of metaphor: On The Subject of Metaphor, Vol. I, No. 3, Fall 1992; Mozart's 1782-1786 Revolution in Music, Vol. I, No. 4, Winter 1992-1993; On The Subject of God, Vol. II, No. 1, Spring 1993; History As Science, Vol. II, No. 3, Fall 1993; How Bertrand Russell Became an Evil Man, Vol. III, No. 3, Fall 1994; The Truth About Temporal Eternity, Vol. III, No. 2, Summer 1994; and, The Fraud of Algebraic Causality, Vol. III, No. 4, Winter 1994-1995. Also, from Fidelio, on the subject of the role of metaphor in economic science, On LaRouche's Discovery, Vol. III, No. 1, Spring 1994; and, Non-Newtonian Mathematics for Economists, Winter 1995-1996 (also appeared in Executive Intelligence Review (EIR) weekly, Vol. 22, No. 32, August 11, 1995.) From EIR Why most Nobel Prize economists are quacks, Vol. 22, No. 30, July 28, 1995.
11.See LaRouche, Non-Newtonian Mathematics for Economists, loc. cit., passim.
12.See Riemann Refutes Euler, op. cit., pp. 39, 41. See, also, On the Subject of Metaphor, op. cit.; Cusa's proof, by geometrical construction, of what was later termed the transcendental character of the ratio of circumference to radius of a circle, is a more sophisticated version of the same method employed by Eratosthenes in the case of the meridian.
13.As Riemann emphasized, Isaac Newton's famous use of hypothesis (... et hypotheses non fingo), was a scientific illiterate's application of that term. Unfortunately, Newton's illiterate use of the term has been popularized within today's customary classroom usages. See Bernhard Riemanns gesammelte mathematische Werke, ed. by Heinrich Weber [Stuttgart: Verlages B.G. Teubner, 1902] (New York: Dover Publications [reprint], 1953), p. 525.
14.Bernhard Riemann, Zur Pyschologie und Metaphysik, in Riemann's Werke, op cit., pp. 509-520. For an English translation supervised by W.F. Wertz and Renee Sigerson, see 21st century Science & Technology, Vol. 8, No. 4, Winter 1995-1996, pp. 50-55.
15.See LaRouche, Riemann Refutes Euler, op. cit., passim.
17.I.e., the Riemann phase-shift from a theorem-lattice of n dimensions, to one of n+1 dimensions. This is the method of hypothesis, Plato's method of hypothesis.
18.In theology, this is to be received as another way of stating the King James' Version's Genesis 1:26-28.
19.To sedate the captious, the following: Axiomatically, all empiricism was axiomatically radical, in the sense of radical empiricism. As Bertrand Russell argues, Oxbridge Britons tend to prefer the term radical empiricism, while acknowledging that this is pretty much the same thing as French and Austro-Hungarian positivism. For our purposes here, the only grounds for preferring the term positivism over empiricism or radical empiricism, would be to lay the stress upon products specific to the French or Austrian schools of positivism. Thus, although the single most influential architect of the frankly radical empiricist dogma of Jeremy Bentham's Principles of Morals and Legislation, is the same Venetian monk Giammaria Ortes whose work Thomas Malthus plagiarized for his own On Population, the immediate authorship of the branches of liberal arts known as political science, ethnology, and sociology was the Simon-Simonist school of Laplace, Cauchy, Comte, et al., while Freud's psychoanalysis owes characteristic methodological traits to Freud's role as a devotee of Ernst Mach.
20.See, Lyndon H. LaRouche, Jr., That which underlies motivic thorough-composition, EIR, Vol. 22, No. 35, Sept. 1, 1995. For author's use of the term Motivführung, he is obliged to the former primarius of the Amadeus Quartet, Professor Nobert Brainin, who had discovered the importance of this about two decades ago. Although Motivführung referenced, proximately, the first movement of Haydn's Opus 33, No. 3 [NOTE HARTMUT CRAMER TO MSG LHL] [from Haydn's Russian Quartets], it overlaps a phenomenon in Classical musical composition known generally as the germinal influence of the way in which Wolfgang Mozart's K. 475 Fantasy, and his related compositions, treated the implications of J.S. Bach's discovery in his A Musical Offering. Recently, Professor Brainin led a seminar co-sponsored by the Schiller Institute, at Slovakia's Dolna Krupa, in which he presented Beethoven's revolutionary further development of Mozart's discoveries in Motivführung, as key to the Beethoven late string quartets Opera 127, 130, 132, and 133and, implicitly, also, Opera 95, 131, and 135.
21.On this account, for example, behaviorist psychologists are shown to be quacks.
22.See Hobbes' Leviathan, or The Matter, Form, and Power of a Commonwealth Ecclesiastical and Civil (1651), chaps. 4-5 [see: Box, p. XX, this issue].
23.Especially the use of the Platonic-Greek model for the English subjunctive.
24.As the present writer has not yet tired of restating, over the recent decades, physics defines experimental knowledge as strictly divided among four immediate domains: astrophysics, microphysics, macrophysics (the scale of sense-perception), and the implicitly absolute difference between non-living and living processes in general. In addition, we have the domain of cognition's efficient impact upon all non-living and living processes combined. The universal characteristics which subsume inclusively non-living, living, and cognitive processes, as they are encountered on the scales of astrophysics, microphysics, and macrophysics, subsume the domain of experimental-physics inquiry. To omit any one of these, in considering any other one of these, is, implicitly, to perpetrate a fallacy of composition.
25.In this connection, one must reference the work and influence of the Platonist Ramon Llull and his Ars Magna.
26.Haydn's, and Professor Brainin's choice of term, Motivführung, is otherwise identified by the descriptive term, motivic thorough-composition.
27.The two leading locations for significant change in the strophe, are the last couplet of a concluding stanza, and also a change in the prosody of one of the middle stanzas, the latter change analogous to Haydn's, or the pre-1782 Mozart's frequent use of quoting a minor-key section within a movement stated in a major-key signature.
28.Ancient Vedic hymns, transmitted from the oral tradition of Indo-European central Asia circa 6,000-4,000 BCE illustrate the point. See, the relevant two texts of Bal Gangadhar Tilak: The Orion, or Researches into the Antiquity of the Vedas (1893) and The Arctic Home in the Vedas (1903) (Poona City: Tilak Brothers, 1956).
29.It will probably be helpful at this point, to view the modern emphasis upon reciting of written text as analogous to a similar reading of the bare text of musical score. The score of a Classical musical composition, must be thought of as a mnemonic device, a short-hand transcript of the heard composition, rather than conceiving the performed composition as a transcription of the written score. It must not be permitted, that musical performance reflects rules for reading written score aloud. The actual score to be performed, lies not within the individual notes of the written score, but, as conductor Wilhelm Furtwaengler said, between the notes: see LaRouche, That which underlies motivic thorough-composition, op. cit.
30.The present writer first developed the thesis, respecting poetry, being recapitulated here, during the interval 1948-1952, as an integral part of his work on the role of creative reason as the historical determinant of rising productive powers of labor. As part of the same undertaking, the writer also developed a large portion of his related, present argument respecting both the Classical Lied (taking examples from Mozart, Beethoven, Schubert, Franz, Schumann, Brahms, and Wolf) and Classical tragedy. In the treatment of metaphor, as the form of creative reason, during that interval, he employed William Empson's celebrated text, Seven Types of Ambiguity, as his foil of reference. He did not follow Empson consistently, but rather required of himself that wherever he deviated from Empson on irony, that his own reasoning be rigorously justified. Hence, the marks of the wrestling with Empson during the late 1940's are sometimes visible in the argument presented afresh today.
31.For the professional musician, or qualified amateur, the Schiller Institute has captured Professor Brainin's seminar at Dolna Krupa on stereo, broadcast-quality videotapes. Otherwise, the special nature of the counterpoint employed by Beethoven in the Opus 132 (for example), is sketched by Bruce M. Director, What Mathematics Can Learn From Classical Music, Fidelio, Vol. III, No. 4, Winter 1994-1995.
32.From the standpoint of blind faith in Sarpi-Galileo-Newton space-time, the primary limits exceeded are the axiomatic presumptions of limitless extension in perfect continuity. To drive an established scientific opinion, to the limits at which one or both of those two assumptions breaks down, either in measurable degree, or by the appearance of a disruptive singularity, is the general principle of, for example, experimental physics.
33.The immediately following argument recapitulates the central argument of That which underlies motivic thorough-composition.
34.There is no great performer of Classical works, or composer, whose notion of this Good of a particular work does not undergo significant change over time. For example, the author had not only the advantage of comparing his hearing the Amadeus Quartet perform some Beethoven in Munich, during the mid-1980's. with the Polydor recordings of about two decades earlier; but, the opportunity to discuss related matters with Norbert Brainin. Already, at the beginning of the 1960's, the Amadeus Quartet represented a standard of performance; they represented that Beethoven tradition transmitted directly via Josef Böhm's Vienna School of Violin performance, via Joseph Joachim, Carl Flesch, and the Amadeus members' teacher, Max Rostal. The referenced Dolna Krupa seminar on the subject of Motivführung, supplies us indication of Professor Brainin's notion of the nature of the improvement in conception which developed over the course of the decades. It is similar for the cases of composers such as Wolfgang Mozart, Ludwig van Beethoven, and Johannes Brahms: we may trace the evolution to the idea of motivic thorough-composition, from Mozart's initial 1782-1783 approach to the coincident conceptions of Haydn's Opus 33 and J.S. Bach's A Musical Offering, through Beethoven's Opera 95-96 onward, as capped by the late quartets, and the new dimensions of a quoted late Beethoven, in the hands of Brahms. Despite the changes in the performer's or composer's notion of a fixed metaphor of metaphors, the idea undergoing such change retains the form of Plato's Good.
35.The most compelling examples of this are typified by, but not limited to, seven slow movements from Beethoven works. Slow movements have the pedagogical advantage of avoiding the popularized musicological delusion, that the sensuality of velocity, other pyrotechnics, are the source of energyi.e., excitementin musical performance; the fallacy of that Romantic view of sensual effects in art, is exposed by the imposition of the practice of passage work in the performance of a Classical composition, and related destruction of the idea-content of the work ostensibly being performed. Begin with the long phrasing of the opening passage within the second movement, Adagio expressivo, from Beethoven's violin-piano sonata, Opus 96. Compare this, as Max Rostal proposes, with the second movement, Adagio molto expressivo, of Beethoven's Opus 30, No. 1, the slow movement of Wolfgang Mozart's B-major (Tdrinasacchi) sonata K. 454, and the second movement, Molto adagio, of Beethoven's second Rasumovsky Quartet, Opus 59, No 2. [Max Rostal, Ludwig van Beethoven: Die Sonaten für Klavier und Violone (Munich: F. Piper & Co. Verlag, 1981)]. The second Rasumovky's Molto adagio should be compared with the Heiliger Dankgesang movement of the Opus 132. From Beethoven's keyboard repertoire, compare the second movement Adagio sostenuto, of Opus 106, and the concluding movement, emphasizing the long coda, of that Opus 111 which Beethoven derived from a quotation of Mozart's K.475 Fantasy. Each of these compositions are characterized, in competent performances, by a concentration of relative energy, energy supplied by the tension of the long phrasing required to sustain the unfolding of the motivic germ into the immediate aftertaste of the concluding tones. The source of this quality of tension in such passages requiring long phrasing, is the specific stress of sustaining change within the Becoming of the composition's development, this under the authority of an unchanging metaphor in the form of a Good.
36.To most modern ears, this sentence is offensively shocking. Among German readers, for example, one hears captious hissing of ritual reference to Professor Friedrich v. Savigny; the critics' conceit may be expressed in the form of the following argument, Naturwissenschaft [natural science] has no place in Geisteswissenschaft [e.g., the arts], nor is either to be confused with what Savigny prescribed to the axiomatically amoral domain of statecraft, Rechtswissenschaft [e.g., law]. Savigny, whose smallest distinction is that of having been Karl Marx's Berlin professor of law, was, like the founder of sociology, Professor Emile Durkheim [The Rules of the Sociological Method 1895], a rabid follower of the positivist dogma of Immanuel Kant, most emphatically Kant's Critique of Judgment. The distinction between the simple Sarpians of Newtonian social theory, and the positivist and existentialist followers of Newtonian fanatic Kant, including, ironically, Friedrich Nietzsche and Nazi philosopher Martin Heidegger, is that, whereas the simpler Sarpians, those whom Kant described as philosophically indifferentist [e.g., Kant's Preface to the first edition of his Critique of Pure Reason], such as Pierre-Louis Maupertuis, Giammaria Ortes, Adam Smith, and Jeremy Bentham, sought to derive every doctrine of social science from Sarpian mathematics (Newtonian social theory), the followers of Kant, such as Savigny, adopted the conclusion reached in Kant's last Critique, that there are large areas of human activity, such as art, and law, in which there is no underlying moral or rational principle, but, at most, the irrationality of merely customary behavior. While official Prussian state philosopher, and Prince Metternich agent, G.W.F. Hegel still lived, he and Savigny dominated the university at Berlin, in Byzantine defiance of the efforts of the Humboldt brothers to introduce the teaching of modern science to that institution. Not accidentally [as Heinrich Heine warned in his Religion and Philosophy in Germany], the irrationalist school of Kant, Hegel, Savigny, and their fellow-romantics and existentialist followers, laid the foundations upon which Martin Heidegger's Nazi Party was later erected. Those persons who react viscerally against this writer's mixing up art and science, should, therefore, reexamine more critically the roots of their own malignant prejudices.
37.Empiricism, therefore, demands such wicked notions as Locke's contribution of life, liberty, and property [emphasis added] to the Constitution of Britain's puppet-entity, the Confederate States of America, in savage hostility to the U.S. Federal Constitution's ... promote the general Welfare, and secure the Blessings of Libery to ourselves and our Posterity [emphasis added]. The Confederate constitution's emphasis upon property is made in explicitly Lockean hatred against Gottfried Leibniz's life, liberty, and the pursuit of happiness, the latter the burden of the U.S.A.'s Declaration of Independence from the evils of the British monarchy.
38.E.g., in the Timaeus.
39.The term, LaRouche-Riemann Method, was adopted during November-December 1978, to designate the subsuming body of conceptions under which the Executive Intelligence Review magazine's 1979-1983 Quarterly Economic Forecast was generated, according to an array of linear inequalities supplied by the present writer. The core of the method was the writer's 1948-51 discovery (directly in opposition to professors Norbert Wiener and John Von Neumann, et al.) that the sole proof of any argued scientific principle is the increase of society's potential relative population-density, effected through those fundamental discoveries which each, in turn, represented discontinuities in the fabric of a preexisting scientific doctrine. The problems of measurement posed by this discovery, led, during 1952, to a close examination of the work of Georg Cantor, and, thence, a reexamination of Riemann's treatment, in his habilitation dissertation, of the metrical problem of physical-space-time curvature under the condition of a succession of hypotheses ordered in the (n+1)/n mode. (This is not to be confused with the failed differential geometries which presume the axiomatically efficient existence of linearity in the very small.) Thus, the descriptive term is LaRouche-Riemann, rather than the seemingly conventional, but careless and misleading Riemann-LaRouche.
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