Part III
The Essential Role of
‘Time-Reversal’ in
Mathematical Economics

by Lyndon H. LaRouche, Jr.

‘When’ is the future? At what point in time?...
The answer to this seeming paradox, was already known by Plato,
by Augustine of Hippo, and therefore, also, Thomas Aquinas:
All time is subsumed under a general regine of simultaneity!
Related Articles

Fidelio, Vol. V, No, 4. Winter 1996
This article is reprinted from the Winter 1996 issue of FIDELIO Magazine.

For related articles, scroll down or click here.

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The Essential Subjectivity of Science

Above, we employed the example of Mozart’s Ave Verum Corpus to identify those features of B. Riemann’s discoveries which are characteristic of both scientific and technological progress, and also of progress based upon discoveries of rational principle within the domain of the Classical art-forms.65

We now turn to present the principal implications of that evidence: Contrary to simple-minded illiterates, and other superstitious persons, physical science is not “objective knowledge.” Science is not a reflection of the universe as simply reflected into our minds by our senses, as if by a kind of mirror. Science is premised upon the experimental evidence obtained through mankind’s relevant successes and failures in our species’ efforts to increase its power over the universe. The very term “scientific objectivity,” is a paralogism; it bespeaks a person afflicted with superstition. Only after we have acknowledged the essential subjectivity of knowledge, do we escape from that erotic bondage called “sensual science.”

Reference the general function identified above:


This, as indicated at an earlier point in this report, represents the role of hypothesizing the higher hypothesis as underlying all scientific and related progress in human knowledge and practice. This is a statement, in terms of a Leibniz-Riemann-referenced mode of analysis situs, of the axiomatic generality of all valid scientific knowledge: Since the history of man’s increase of our species’ power to command the universe to our species’ benefit, is a history of man’s hypothesizing the higher hypothesis, the term “science” is properly delimited in use to signifying rational comprehension of the process of hypothesizing the higher hypothesis. In that sense, we must think of the subjectivity of science.

In terms of the adding of relatively valid new theorems according to some fixed hypothesis, man’s power to increase the potential relative population-density of our species has a limit. Our species exceeds that limit; but, that success occurs solely through experimentally validated, axiomatic-revolutionary changes in hypothesis. It is such axiomatic-revolutionary changes, all within the domain of hypothesis, which constitute the action, by means of which mankind exceeds the bounds of any fixed theorem-lattice. This action is the change referenced by Heracleitus’ famous apothegm, “Nothing is constant, but change.” That is the same notion of change which Plato introduces as the crucial conception of his Parmenides. In first approximation, this change, this action, is located ontologically within the domain of higher hypothesis: the efficient, valid change, from one hypothesis to a higher one. The generalization of this notion of change, or Plato’s becoming, is located within the domain of hypothesizing the higher hypothesis.

Thus, the reality of the universe is comprehended by the mind, not the ignorant man’s blind, irrational faith in the bare experience of his senses. That is the definition of Reason, as used by Johannes Kepler; we have already referenced this here, above, as Leibniz’s notion of necessary and sufficient reason. The notion of the necessary, efficient existence of functional time-reversal, arises, as necessity, from these considerations.

The lesson of the progress of science, in these, Platonic terms of reference, is that the universe is, in effect, so pre-designed, that it is obliged to obey man’s will, whenever man’s will is expressed according to Reason: according to valid changes in hypothesis, from lower to higher hypotheses. The relevant action, by means of which the efficient principle of existence of the human species is defined, is the advancement of man’s operating hypothesis, from a relatively lower hypothesis, to a relatively more valid, more powerfully efficient one. In effect, the relevant changes are typified mathematically, in the form of an increase of the Gauss-Riemann physical-space-time curvature, by the relative, transfinite cardinality of action.

This is the essence of that which deserves the name of “science,” or of “Classical art.”

The experience of scientific, or artistic activity, so defined, is presented to our minds in two ways. On the one side as the form of analysis situs demonstrably cohering with the increase of mankind’s power over the universe. In physical economy, this form is correlated with mankind’s willful increase of the potential relative population-density of our species. On the other side, as Classical art typifies this, this activity of our minds is expressed in the form of the emotion associated with what Plato and the Apostle Paul identify as Agape.66 The mind is able to distinguish Agape from the erotic impulses associated with the materialist’s blind faith in sense-certainty.67

(Notably: The indispensable function performed by successful Classical art-forms, is to bring forth the motive quality of Agape in its more concentrated expression. The Classical motivic thorough-composition of anti-Romantic, well-tempered polyphony, by W. Mozart, the later Joseph Haydn, Beethoven, and Brahms, is the typical expression of this, like the great and prolific well-tempered polyphony of J.S. Bach before them.68)

Hence, the fundamental distinction between Plato and Aristotle. Hence, the legitimately Aristotelean, modern, Venetian tradition of mortalism, traced through Padua’s anti-Renaissance Pietro Pomponazzi and Michel Montaigne, through the Seventeenth-century followers of Paolo Sarpi.69 Whereas, in the relevant tradition of Christian civilization, the Aristotelean, like the bathless hesychast, the Stoic, the Epicurean, and kindred schools of pornography, contemplates the world, the Platonist masters that world, and that out of a sense of the responsibility inhering in a creature “made in the image of God,” in the sense of the cup passed to Christ in Gethsemane. For the Aristotelean, such as the empiricist and irrationalist Immanuel Kant, the world is a construct, fabricated from the detritus of naive sense-certainty. Thus, for the Kant who purports to be the Apostle of Reason, it is the central feature of his Romantic reconstruction of empiricism, in his Critiques, that an efficient form of Reason does not exist.70 Out of the related version of empiricism, the Ockham simplification promulgated by Paolo Sarpi and his followers, we have that contemplative standpoint in mathematical formalism of Isaac Newton, Leonhard Euler, and their radical-positivist followers, such as Bertrand Russell, Norbert Wiener, John Von Neumann, et al.

Hence, given this fundamental controversy between the experimental standpoint of Cusa, da Vinci, Kepler, Leibniz, Monge-Carnot, Gauss, and Riemann, versus contemplative, “ivory tower” philosophies of science, any attempted approach to the issues of scientific method which is not rooted in rigorous study of the Plato-Aristotle controversy in philosophy, would be the bungling enterprise of a science-illiterate, one acting as a virtual charlatan. It is toleration of such charlatanry in the name of “generally accepted classroom mathematics,” which gave us the infamous Solvay Conferences of the 1920’s, the toleration of B. Russell’s hoaxes, and the narrow corners, such as Andrei Sakharov’s work, into which the evidence of “time-reversal” has been confined to date.

Man’s knowledge of the lawful composition of our universe is limited, by necessity to those processes of knowledge which have shown themselves to lead to mankind’s repeated improvement of the number, demographic characteristics, and per-capita power of our species over the universe. Let us agree to name that test of knowledge according to the spirit of Riemann’s experimental physics, “The Great Experiment.” The primary task of science is, therefore, to discern and define those processes within the sovereign domain of individual human cognition, by means of which the successful furthering of the process of hypothesizing the higher hypothesis is to be promoted. It is in that context, that a rational comprehension of the principle of “time-reversal” becomes accessible.

Riemannian Time-Reversal

The measurable impact of “time-reversal” must necessarily lie within the conceptual bounds of the crucial discovery at the center of Riemann’s habilitation dissertation. In other words, applying those methods of C.F. Gauss’ general principles of curved surfaces (which Riemann incorporated in the method of his own discovery), there must be a measurable difference in the implied curvature of physical space-time, reflecting the action of time-reversal upon the function as otherwise determined. For this case, measurement appears in two available expressions: (1) The measurement of extension, as this is extended from Gauss’ work on the higher expressions of biquadratic residues; (2) As expressed by discontinuities in attempted simple extension.

Once more, return to our referenced musical example, to define the form of this set of relations. What is to be emphasized here, as in reference to this musical case in earlier published locations, is that the characteristic feature of Classical art is the evocation of Agape, by means of the rigorous subordination of art to that Platonic principle of Reason, the which is expressible only by the form of development which employs resolving transitions to new hypotheses of a relative higher cardinality than the utterance of the preceding hypothesis. Thus, as Pablo Casals instructed his master-class students, in great art, as typified by his beloved J.S. Bach, there is never repetition, but always contrapuntally progressive variation.71

As we stressed earlier, here: In the referenced illustrative case, the progression through a series of polyphonic hypotheses, into the culminating hypothesis which concludes the composition, registers the composition as a whole as a process of development located ontologically within the domain of a specific proposition, that within the domain of higher hypothesis. Now, once that is apprehended by the performer, or hearer, every detail of the performance must be subordinated to that specific proposition otherwise defined only at the close of the piece. The result is a shading of interpretation in the shaping of each interval of the composition, both within the individual voice, and across the polyphonic voices. The effect is of a slight deviation of the “physical space-time curvature” in the performance: conductor Furtwängler’s doctrine of “performing between the notes.”

That must not be over-simplified. Each locality within the composition belongs to one among the sequence of polyphonic hypotheses, and must be so performed; but, that hypothesis must be affected in the shading of its performance by the proposition which locates the development process of the composition as a whole within the domain of higher hypothesis. The image of Gauss’ development of, and Riemann’s apprehension of higher implications of biquadratic residues, is forced to our attention, thus. In music, it is the ability to hear, to recognize, and to anticipate the distinction between appropriate and inappropriate shadings of difference of “curvature” within the performance, which is crucial. In music, as otherwise, such music must be heard first in the mind, and, after that, what is heard so in the mind must command the instruments employed.72

Those differences in manifest “physical space-time curvature,” are, relatively speaking, the more readily accessible feature of the principle of “time-reversal”: Its efficient presence can be measured so, whether in musical performance or physics as such. The more profound aspect of matter forces our attention to the functional implications of true discontinuities. The crux of the matter is efficiently introduced by the following proposition.

How is it possible for the human mind to perceive a mental object, whose form does not originate from within the domain of sense-perception? To most, that question immediately suggests the domain of microphysics; it must be recognized that the concepts of microphysics are but a derivative of the general category of Platonic ideas. Restate the proposition in other terms: How are singularities, such as metaphors, afforded discrete distinctness within the mind? The answer from any literate person should be: by the juxtaposition which we term irony: a “double meaning,” the which can not be resolved deductively.

The quality of “definiteness” attributable to a Platonic idea, is derived from the association of such an idea with a formal discontinuity. This involves a “non-linear” transition, as from one hypothesis to another, a transition which occurs in such a manner that it must appear to a deductive mind-set as a “leap” of comprehension across an incomprehensible gap. This may be a valid metaphor, in poetry, Classical drama, painting, or music; or, it may be the introduction of the need to consider a new quality of principle (a new hypothesis), as a precondition for accounting for the actual continuation of a process, as in the case of Riemann’s Fortpflanzung paper, referenced here earlier.

On this same point, consider a “map” of science in general, which we have identified in locations published earlier. If we seek to outline the full domain of scientific inquiry from the standpoint of the relations of hypothesis, we have the following, general, preliminary result.

We divide the domain of inquiry among three classes of phenomena and three categories of relationship of judgments to methods of empirical inquiry. The three general classes of phenomena are: (1) Ostensibly non-living processes, both organic and inorganic in ostensible composition; (2) Living, but presumably non-cognitive processes; (3) Cognitive processes. The three categories of inference are: (a) Astrophysics, (b) Microphysics, (c) Macrophysics. This yields a table of nine cells. Since the existence of this evidence is conditional upon the existence of human cognition, it is the driving of the cognitive processes to the ever-expanded limits of inquiry into astrophysics, microphysics, living processes, and cognition itself, which underlies this nine-cell domain of science as a whole.

All of the permutations of relations among the nine cells are defined in terms of strict boundaries, strict discontinuities. Consider the most exemplary such case, the transition of what is ostensibly the same living process into a non-living state, and the distinction between living processes which are typified by cognitive functions, and those which are not. What are the transitions which separate these states? Define them functionally. The difference in organization of the three states is expressed as a difference within hypothesizing the higher hypothesis, a difference, however apparently subtle, in the effective curvature of the process.

On this account, the peculiarity of living processes, and also cognitive ones, is of the form of time-reversal: the apparent pre-determination of the next phase-state in a way which either distinguishes a living from a non-living process, or a cognitive from a non-cognitive activity within a living process. For this, the conceits of A.M. Turing and his followers will not do. Once we have identified the necessity of time-reversal for one class of processes within the array, we have identified the necessity for the generality of functional time-reversal.

The introduction of the notion of time-reversal, obliges us to face up to the implied questions: What is the efficient future to be considered? What is the efficient scope of the relevant past?

The truth is always elegant and lovely, but the delusions which commonly obstruct access to that truth, tend toward the ugly sentimentalities of the rutting Yahoo class. The clinical problem to be addressed, is illustrated by reference to those commonplace, pathetic commentaries upon musical compositions, the which inhabit concert program notes, or the dust jackets of recordings. According to that Romantic irrationalism, the which has dominated British taste since Thomas Hobbes outlawed metaphor, the purported explanation of a Biblical text or a musical composition is to be found in the orgasmic domain of erotic symbology.73

One might say, that our perennially prissy British art critics, like their American mimics, are as irrationally symbol-minded in their artistic opinions, as in their lunatic, low-church notions of the future, their so-called Biblical prophecies. Indeed, if we understand the mental breakdown of such critics, when faced with “time-reversal” as it occurs in poetic speech or music, we have ready insight into the pathetic mental condition of that homicidal, American, “Lost Cause” variety of Protestant cults, the which predict, that erecting a Hebrew temple on the site of Jerusalem’s Dome of the Rock, will unleash “End Times” events, leading to the Rapture, thus, presumably, freeing them from the obligation to meet next month’s mortgage-payment.

The name of the issue underlying each and all of those mental disorders of the symbol-minded, is “Bad Infinity.” In gnostic parodies of Christianity, such pathetic symbol-mindedness may assume the form of “End Times” prophecies. In respect to Classical art, it appears as the inability to accept the notion that a future event, the apprehension of the metaphor at the close of a poem or musical composition, must efficiently shape the development of the composition at each preceding point in time. Thus, the distaste for Classical poetry and music among the cognitively illiterate, such as the wont for the rage-brimming, Brechtian soap-operas of “Country and Western” whines, like the wont for today’s rutting-and-gore, story-free Hollywood entertainments, reflects the flight from Agape to Eros.

The Classical composition, in any medium, follows the underlying model of the Greek Classic, the same Classical humanist model found in the educational programs of the Brothers of the Common Life and in the Schiller-Humboldt program for Classical Humanist education in Germany. Such education, and such art, submits to the policy, that the development of the mind of the young, must be the student’s experience of the reenactment of the actual process of original discovery of a principle of nature within the sovereign domain of the individual student’s mind. The re-discovery of the principle, at the end of that reenacted experience, is, thus, akin to the final hypothesis of Mozart’s Ave Verum Corpus; in music, as in Paul’s I Corinthians 13, as in life, the “test of death” returns our thought to an agapic vision of life’s meaning.74

As Mindy Pechenuk’s description showed, Mozart’s setting of this motet, leads the music through a succession of hypotheses, thus impelling the singers and audience into the kind of excitation of the sovereign cognitive processes of the individual mind, which evokes the experience of re-creating Mozart’s discovered principle, and thus evokes the quality of emotion which Plato and the Apostle Paul identify as Agape. Thus, music, so employed, evokes the highest level of Reason.75 This is the same Reason employed to effect either an original, valid discovery of natural principle, or the reenactment of that original, sovereign mental act of discovery.

Motivic thorough-composition, a revolution effected within the domain of J.S. Bach’s well-tempered polyphony, demonstrates the twofold absurdity of the claims upon which Immanuel Kant bases the entirety of his famous Critiques. Mozart’s Ave Verum Corpus demonstrates not only that the principle of valid original discovery of principle is cognizable, but that the same principle of Reason which Mozart employed for this composition, is the principle of Reason underlying all valid scientific discovery. The most fundamental principles of either art or science can be comprehended, only if we reject the irrationalist war-cry of Kant’s Critique of Judgment, Savigny’s hermetic separation of natural science (Naturwissenschaft) from art (Geisteswissenschaft), to recognize the underlying interdependency of art and science, as did the founder of comprehensive mathematical physics, Johannes Kepler. The notions of potential (i.e., cardinality) and efficient time-reversal, as adduced from Classical musical compositions such as this, are general for art and science: they involve identical cognitive potentialities of the individual mind.

Employ this musical context to explore a deeper meaning of “the future acting upon the present.” At first, the thought will be a stunning one; then, gradually, the initial shock of astonishment will gave way to the consoling reassurances of Reason.

“When” is the future? At what point in time? Similarly, what is the beginning-point in time from which to define the cumulative past with which the future is to collide? The answer to this seeming paradox, was already known by Plato, by Augustine of Hippo, and, therefore, also, Thomas Aquinas: All time is subsumed under a general regime of simultaneity! (See box on Raphael’s The School of Athens) The highest expression of change, is that lattice of higher hypotheses which expresses the transfinite notion of hypothesizing the higher hypothesis. What underlies that lattice? That lattice is underlain by what Plato distinguishes as the Good. In the analysis situs of hypothesis, that Good is “simultaneously” efficient in all times and places which might exist. Thus, in those terms of reference, the past and future, as hypothesis, are existent as efficient agency in each present moment.

Stunning? Consider, and remove the false assumptions which might be attributed, mistakenly, to what has just been uttered here. Does this signify that each and all events are predetermined—“predestined.” No: recall the conditions of analysis situs which we have imposed, repeatedly, upon this report’s content, from the outset. Everything we have said here on this matter, to the present moment of writing, is premised upon, and delimited to statements respecting the set of relations defined by the general principle of hypothesis, even as Riemann’s 1854 habilitation dissertation expresses that Platonic principle as its pivotal foundation. The general set of relations defined by the principle of hypothesis are otherwise describable as relations within an hierarchy of available “pathways of change.” The ordering principle underlying this hierarchy is cardinality, as we have indicated that principle of ordering of Riemannian physical space-time manifolds here. It is in terms of efficient choices of pathways of change, that the future acts upon the present. So, the choice of conception (higher hypothesis) reached with the conclusion of a Classical piece of motivic thorough-composition, determines the potentialities of each subsumed hypothesis, and, thus, of each interval of tolerable counterpoint, within the composition as a whole.

Therefore, we must anticipate the implications of time-reversal to be manifest in those instances a change in choice of hypothesis, to one of relatively higher cardinality, is demanded of us, as by the eruption of an undeniable anomaly from within the domain of experimental physics.

Physical Economy As ‘The King of the Sciences’

Look at that from the standpoint of the science of physical economy. C.F. Gauss famously identified mathematics as “The Queen of the Sciences,” which, the feminists must excuse us, was intended to indicate that mathematics must not be king. As for Nicolaus of Cusa, for Leibniz, and for Riemann, the essence of physical science lies with the employment of measurement to demonstrate those valid principles of nature accessed through either experimental physics or similar methods of inquiry. It is through experimental physics, and similar methods, that we demonstrate that every valid discovery of principle increases man’s power of local intervention into the universe. However, it is only in the domain of physical economy, that we demonstrate the same principle applies to the relationship of mankind to the universe as a whole. Physical economy is “The King of the Sciences.”

The principle of hypothesis affects the potential relative population-density of mankind by two pathways. In the guises of Classical art-forms, mankind discovers new, higher qualities of institutions, such as the constitutional modern nation-state, the institutions of education, the institutionalization of scientific and technological progress, and so on. In the guise of contributions to progress of science and technology, the productive powers of labor are advanced. It is the interrelation between the two aspects of these changes for human progress, that mankind’s functional relationship to the universe is defined.

Human history, and pre-history, so read, shows that the universe is so designed, that whenever man’s demand upon the universe is expressed as valid hypothesis, the universe obeys man. That, whenever man’s demand upon the universe is expressed as a valid change in hypothesis, the universe obeys man’s will. Thus, the pathway of change marked by valid directions in hypothesizing the higher hypothesis, expresses, as experimental physics, and as the increase of potential relative population-density, the lawful ordering of the universe. That demonstration is the essence of science; it is the only source of knowledge of that which we might regard as the laws of the universe. In that sense of the matter, we are obliged to end foolish babbling about “scientific objectivity,” and think of “scientific subjectivity,” instead.

In that sense and degree, the ordering within the domain of valid hypothesis does define the lawful ordering which governs the universe. It is upon that premise, that we may be certain of the efficient principle of “time-reversal” in physics, as well as Classical musical composition.

Consider as a relevant case, the choice of the future expressed by formulation of economic policy by the government of a modern European model of nation-state republic, such as our Federal republic under the anti-British, anti-Metternich, anti-“free trade,” American System of political-economy, embedded as the intent of our Federal Constitution.

Contrary to the sewage which has spoiled the mainstream of economic-policy thinking the recent thirty years, the making of U.S. economic policy during all successful periods of our history, since the earliest period of the English colonies here, has been premised upon a commitment to investment in scientific and technological progress. Under the governance of such a higher hypothesis of national self-government, each promoted change in patterns of investment, production, employment, and trade, has represented shifts from practice of relatively lower cardinality to higher cardinality. Or, to say the same thing, in effect: In choosing the hypothesis of relatively higher cardinality, we have chosen the better future inhering in the latter hypothesis.

To provide the relevant contrast: Without introducing such considerations, of change of hypothesis, into policy-shaping, the relationship of future to present becomes as paradoxical as it was for Nobel Prize-winner Kenneth Arrow.76 It is the transitions from one phase-space to a higher one, under penalty of “entropic” technological attrition if we do not so change, which display the functions of time-reversal in a clearer, relatively more immediate way.

It is so in life, as Mozart seeks to remind us in his setting of the Ave Verum Corpus. “The test of death”: How shall I choose to live under the impact of the certainty of death? From the standpoint represented above, the answer is neither obscure, nor remote.

If I am conscious of the content of my own knowledge and practice, in the manner underlying a Classical humanist form of education, then I know that most of what I know represents valid discoveries of principle effected by individual original discoverers, some known by name, more unknown, most located deep in the lost pages of pre-history. In reenacting their discoveries of principle, I have relived in my mind, moments from the interior of their own. I am closer to these long-deceased persons than to most of the daily associates of my childhood, youth, and adult life. If I aid in transmitting these precious gifts from the past, into the countless generations of the future, and perhaps add one or two such gifts of my own, I am certain that my life will have been a necessary one: both a fulfillment of the past, and a gift to the future. I have thus met “the test of death.”

That illustration implies the crucial point. It is in the terms of the relations of hypothesis, and in no other way, that the issues of scientific principle are rendered intelligible, even the rudimentary consideration that all processes in the universe are subject, as Wilhelm Weber’s appreciation of Ampère’s work, or Max Planck’s related discovery attest, to an alteration of their curvature by efficient “time-reversal.” That principle is already implicit in the deeper meaning which Plato’s Parmenides supplies to Heracleitus’ maxim, “Nothing is constant, but change”—nothing is real, nothing is efficient, but the quality of change which is located in the analysis situs of those relations defined by the architecture of hypothesis.

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65. The rational employment of the term “Classical” is a choice of term which references the Classical period of ancient Greece, with emphasis on the Athens-centered culture, from the time of Solon through Alexander the Great’s destruction of the Persian Empire. Otherwise, the rational use of the term “Classical,” is limited either to certain Classical Greek models, or their reflection in modern forms of art and science. In western European civilization, from Augustine of Hippo through the Classical humanist followers of Friedrich Schiller in Nineteenth-century Germany, the term “Classical” signifies art and science cohering with the rational principles of Plato and his Academy at Athens. In practice, “Classical” signifies contempt for arbitrary beliefs, in both art and science: e.g., those not governed by Reason. It signifies contempt for arbitrary, erotic effects in art. As noted earlier here: The principles of Classical musical, motivic thorough-composition exemplify the coherence of Reason (e.g., John Keats’ “truth”) and Beauty in art, and a degree of rationality which is identical with the function of Reason in science.

66. I.e., Plato: love of justice, love of truth. Cf. Paul, I Corinthians 13. The charismatic “feeling” according to Agape is never irrational, but always an expression of Reason.

67. The deepest secret of the Romantic existentialism of the proto-Nazi Friedrich Nietzsche, the Nazi Martin Heidegger, Jean-Paul Sartre, the irrationalist Martin Buber, deconstructionist Jacques Derrida, et al., is implicitly disclosed by the notorious Liebestod of “Young Europe” terrorist R. Wagner’s Tristan and Isolde (as by Wagner’s operas and music-dramas generally). A comparison of Jean-Paul Sartre’s (“Sartre-Masochismus”) autobiographical rant, with the notion of “thrown” central to the doctrine of the Nazi ideologue Heidegger, tells us much about the underlying kinship among French existentialists, German Nazis, and also existentialists of the Hannah Arendt and Martin Buber types. The kernel of the doctrine of existentialism is the impulsion to give freedom to (unleash) the “inner pig” one adduces as the essential kernel of one’s innermost self. The lunatic Nietzsche, who has the distinction of being the most candid among the degenerate breed called existentialists, rightly attributes the ancestry of his cult to the Apollo-Dionysus dualism of the satanic, Delphi cult of Gaea-Python/Dionysus-Apollo, and, thus, implicitly, to the Hellenistic cult of Isis-Osiris: the victim whose erotic impulse has carried him, like Adolf Hitler and Heidegger, deep into the depths of Hell.

68. Hence, the intrinsically religious quality of virtually all of the music of these composers. Hence, for related reasons, the intrinsically satanic implications of bringing the dionysiac “Christian rock” into the churches.

69. Cf. Webster G. Tarpley et al., “From Napoleon to Nashville,” The New Federalist, Sept. 23, 1996 (Vol. X, No. 37).

70. During World War II, the British propaganda service enlisted Heinrich Heine’s prophetically insightful Religion and Philosophy in Germany, in warning that Immanuel Kant was a spiritual ancestor of Adolf Hitler’s acceptance within Germany. Notable, is the strain of neo-Kantianism running through the positivism of Madame de Staël, her collaborator Saint-Simon, and Auguste Comte, in France, and Hegel’s accomplice, Karl Savigny, in Germany. The Volksgeist irrationalism flagrantly displayed in Kant’s Critique of Judgment, running through Savigny’s Romantic school of law, and Hegel’s philosophy of history, supplied the rationale for Germany’s fatalistic submission to the Anglo-American financier-oligarchy’s imposition of Adolf Hitler’s rule in the “legal” coup d’état of 1933-1934. On the Anglo-American backing for the Hitler coup, see Webster G. Tarpley and Anton Chaitkin, George Bush: The Unauthorized Biography (Washington, D.C.: EIR News Service, 1992); pp. 26-62.

71. Among the greatest enemies of Classical music, on several grounds, are the leading recording companies. Exemplary of these firms’ endemic, mercenary artistic imbecility, is the question often expressed by a performing ensemble: “Shall we do the repeats?” In Mozart and Beethoven, for example, there is never carbon-copy repetition, even when repetition might be suggested by the printed text of the score. That is to say, neither Mozart nor Beethoven intended mere repetition, but rather a recapitulation which is apposite to the initial utterance of the text. This is a device borrowed, so to speak, from Classical strophic poetry, which must be performed (and heard in the mind) as a process of constantly ongoing development, never as monotonous sing-song prosody. In the works of these composers, the “repeat” is always a lead into a new development.

72. The performance of music must never be from text to instrument, but through the digestion of the hearing as performed in rehearsal by no other instrument than the mind itself. Only in such a domain of memory, can the mind “hear” the interplay among all hypotheses and conclusion as if in relative simultaneity, relative to every interval of the relevant moment of performance. It is in replaying compositions, so, within the polyphony of the mind, and constantly adjusting one’s interpretation according to all these considerations at once, that these notions can be mastered by the performer, or the musical audience.

73. Unfortunately, there are performing musicians who attempt to breathe the spirit of such program notes into their performances, with all-too-common catastrophic results. Such obscenities could please no one but music critics and other devotees of the satanic cult of the Zeitgeist.

74. Thus, the importance of the Requiem Mass as a musical subject for Mozart and Beethoven. What joy could be found in the interment of a family member, or close friend, except that we return from such ritual refreshed in our commitment to free living from enslavement to the banal eroticism of petty things, to live a life whose duration shall have become durably necessary for humanity even long after one’s passage through life has ended. This is not a matter of symbolisms; it is a matter of Agape, in the sense of the term common to Plato and the Apostle Paul. In all art, all science, the composition whose conclusion defines, retrospectively, every moment of its unfolding, is the heart of the matter. Thus, the “test of death”; thus, the Agape of the Lacrimosa of Mozart’s Requiem, as contrasted with the ugly erotic parody of this Mozart Lacrimosa within the gnostic Hector Berlioz’s blaring, Bonapartist Requiem.

75. In this way, the true “religious feeling”—Agape—is evoked, by Reason, not as irrationalist, Romantic, psychotomimetic exaltation.

76. Loc. cit.

On the Curvature of Physical Space-Time.
In 1696, the mathematician Jean Bernouilli issued a challenge to the scientific world, to solve the following problem: “To determine the curve joining two given points, at different distances from the horizontal and not on the same vertical line, along which a mobile particle acted upon by its own weight and starting its motion from the upper point, descends most rapidly to the lower point.” Or, expressed another way: “If the curve is replaced by a thin tube or groove, and a small sphere placed in it and released, then this [sphere] will pass from one point to the other in the shortest time.” This curve, he called the brachistochrone, from the Greek words for “shortest time” [Figure 2(a)].

The curve in question, Bernouilli discovered, was the cycloid [Figure 2(b)]—a curve which had been investigated earlier by Christiaan Huygens (1629-1695), and described in his book The Pendulum Clock. Huygens determined that a weight falls along a cycloidal path in the same amount of time, no matter from what point on the cycloid it begins its motion. This curve, he called the tautochrone, from the Greek for “same time” [Figure 2(c)].

Bernouilli described his amazement, when he discovered that the two curves were the same: “But you will be petrified with astonishment when I say that precisely this cycloid, the tautochrone of Huygens, is our required brachistochrone.

His amazement did not stop there. Bernouilli went on to write that the same property also applied to the refraction of light [Figure 2(d)]: “I discovered a wonderful accordance between the curved orbit of a ray of light in a continuously varying medium and our brachistochrone curve. ... The brachistochrone is the curve which would be traced by a ray of light in its passage through a medium whose rarity is proportional to the velocity which a heavy particle attains in falling vertically. For whether the increase in the velocity depends on the nature of the medium, more or less resistant, as in the case of the ray of light, or whether one removes the medium, and supposes that the acceleration is produced by means of another agency but according to the same law, as in the case of gravity; since in both cases the curve is in the end supposed to be traversed in the shortest time, what hinders us from substituting the one in place of the other? ...

“Thus I have with one stroke solved two remarkable problems, one optical and the other mechanical; ... I have shown that the two problems which are taken from entirely distinct fields of mathematics are nevertheless of the same nature.”

[Quotations taken from “Bernoulli on the Brachistochrone Problem,” in A Source Book in Mathematics, ed. by David Eugene Smith (Mineola, N.Y.: Dover, 1959), pp. 644-655.]

—Susan Welsh


Model of a brachistochrone. A ball that rolls down the cycloidal track, reaches the bottom faster than one rolling down the straight track.


The cycloid is the curve traced out by a point on a circle, as the circle rolls along a line.


The tautochrone: Huyghens used the cycloid to make a pendulum clock, because the time of a cycloidal swing reminas constant, as a swing height decreases.


Bernouilli proved that the cycloid is also the path taken by a ray of light passing through a medium of constantly increasing density.

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Stand facing the famous “School of Athens” ... .

Above: Personalities gathered together by Raphael.
1-Plato, 2-Aristotle, 3-Socrates, 4-Xenophon, 5-Æschines, 6-Alcibiades, 7-Zeno, 8-Epicurus, 9-Federico Gonzaga, 10-Averroes, 11-Pyhthagoras, 12-Francesco Maria Della rovere, 13-Heraclietus, 14-Diogenes, 15-Archimedes, 16 Zoroaster, 17-Ptolemy, 18 Raphael’s self-portrait.
Diagram courtesy of Vatican Museums.

Raphael Sanzio, “The School of Athens” (1509)

As you stand there, call that mural to life. Look around inside that mural; which of these are old friends of yours? You never met any of them face to face, but most of those in the hall never met one another in the flesh, either. Yet, you have relived a most intimate moment of the mind of each of some of them, reliving one or more of their creative moments of discovery. First, pick those whom you know in that way. You know Plato, and are acquainted with Aristotle. Are there not two or three in the foreground? As you focus upon the ideas, especially those ideas which represent original axiomatic-revolutionary discoveries, or something proximate to that, one figure after another within this busy hall comes alive for you. As for the others, I believe you know most of them already by reputation.

Think of the number of generations of history spanned by the personalities gathered here within this hall! Radiating from that hall, there is a sense of being embraced, where you stand, by some living intelligence proximate to Temporal Eternity. That radiance fills the small room in the old papal apartments.

Raphael understood the point well enough to design and trasmit a message, this mural, which would reach both of us, nearly five centuries later, standing with our minds within that mural’s assembly within the great hall. It is no fantasy; it is a painting of a scene the like of which this writer has seen within his own mind, many times. It is a scene which Raphael painted from life, with the gathering of the inhabitants of his mind as living models. It draws from life those relationships within Temporal Eternity which are higher, and more efficient than any drawn in ordinary space or ordinary time. Those are the direct relationships of creative minds’ ideas, which dissolve centuries into the span of a pleasant day’s assembly, and bring vast spaces comfortably into a room no larger than that which contains this mural.

This mural is no mere symbolism, nor an imagined room in Paradise. It is a moment of deja vu! It is a portrait of Raphael’s relations to the most intimate acquaintances of his daily mental life, all captured so to share the companionship of a moment in Temporal Eternity. ...

When the relationship of the individual person to mankind in general, and other persons in particular, is measured in the space and time of the generation and transmission of those qualities of ideas associated with valid axiomatic-revolutioanry discoveries, what a short distance a mere few centuries become! The order of necessary predecessor and necessary successor is preserved: the intelligence of the timeless Absolute is not zero-motion; the lack of spatial division is the consequence of being simultaneously everywhere, such that there is nothing in between any two experiences which would require us to experience time, except as, for us the onlookers, a sense of a timeless ordering of development. For us, the onlookers, just so, the duration of space and extent of time shrink almost to the vanishing-point. ...

... Truth lies accessible to us on condition we are able, as Raphael’s mural tells us, to comprehend the reality of Temporal Eternity as a form of human existence measured in terms of efficient relationships among axiomatic-creative qualities of ideas. ... While that though occupies one’s mind, move through the rooms of the old papal apartment more thoughtfully, catching every aspect of Raphael’s work there. Does it not occur to you, that the [last 3,000 years of history], is a moment of Temporal Eternity which could be such a mural as one of those Raphael left as messages for us?

—Lyndon H. LaRouche, Jr.
from “The Truth About Temporal Eternity”

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