visualizing the complex domain

8/4/2019 Visualizing the Complex Domain

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The oldest known precedent for what we call physical science today, is reflected in ancient astronomical calendars.Clockwise from top left: (A) Cave drawing at Lascaux, France, ca. 14,500 B.C., thought to depict the constellation of Taur

the bull, with a map of the Pleides over its shoulder; (B) Stonehenge in England, ca. 2800 B.C., an ancient astronomical si(C) remnant of Ulugh Begs observatory in Samarkand, ca. 1420, where this large marble sextant was used for astronommeasurements; (D) one of five astronomical observatories built by Indian astronomer-king Maharaja Jai Singh II of Jaipur, cearly 1700s to measure celestial positions; (E) Carl F. Gauss with his telescope, ca. 1800; (F) the U.K. Infrared Telescope, onemany different telescopes at the Mauna Kea Observatory in Hawaii, with Orion in the background; (G) The Hubble SpaTelescope, photographed from the Shuttle during a servicing mission.

24 Fall 2003 21st CENTURY

Robin Phillips/UKIRT, Mauna Kea Observatory, Ha

HST/NASA

SCIENCEFOR TEACHERS

Visualizing

The Complex Domainby Lyndon H. LaRouche, Jr.May 30, 2003

Dr. Michael Rappenglu


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Ishall show here, that the unstated, but implied aspectof the charge which Carl Gauss delivered in 1799,against DAlembert, Euler, and Lagrange, lies in the

implication, that the latter were virtually Satanists, thatin the sense of the philosophical tradition of both themedieval William of Ockham and those founders ofmodern empiricism, Venices Paolo Sarpi and his per-sonal lackey, Thomas Hobbess teacher Galileo Galilei.I shall show here, without exaggeration of any kind, thatthat charge of Satanism is not merely relevant, but mustbe emphasized, to bring into focus the implicit, mostessential features, and political importance, of Gausssargument respecting mathematics itself. I shall also focussome exemplary attention on the leading role of empiri-cism in producing those widely accepted, incompetentdoctrines of economy, such as contemporary mone-

tarism, which have played a leading role in bringingabout the 1971-2003 collapse of the economies of theAmericas, Europe, Japan, and elsewhere.

21st CENTURY Fall 2003 25

arttoday.com

ABTA

clipart.com

Niels Bohr Library/ American Institute of Physics


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As I have shown in locations published earlier, the crucialquality of functional significance of philosophical reduc-tionism, such as empiricism, for physical science, is that itattempts to uproot knowledge of the existence of what thecelebrated geobiochemist V.I. Vernadsky identified as thosenoeticpowers of the human mind which distinguish humanbeings from beasts.1 Within the realm of political scienceand law, that denial of the distinction between man and

beast, is the philosophical basis for Satanism.2

Typical arethe Synarchist and kindred followers of G.W.F. Hegel andFriedrich Nietzsche.3 In a narrower aspect of that specificissue, as implied by Gausss devastating exposure of a fraudin the work of Euler and Lagrange, the specific philosophi-cal expression of Satanism called empiricism, is theaxiomatic basis for not only that radical positivists aberra-tion which is known as the so-called new math, but whathas been usually recognized, even earlier, as todays gener-ally accepted classroom mathematics, and the economicfads of the positivists.4

Within the bounds of a narrowly defined physical science, thecorrupting influence of empiricism, is its role as the doctrine oftodays politically powerful echo of the ancient Babylonian

high priesthood. That priesthoods traditions modern role inscience is such, that even many presumably sophisticated stu-dents and experts in physical science, are often victims of theirown fearful sense, that no argument by them on mathematical-physics subjects, will be tolerated among their so-called com-munity of professionals, unless the submitted argument confinesitself within the axiomatically aprioristic, soulless bounds of thecurrently prevalent, reductionist (e.g., empiricist) notions ofclassroom mathematics. The same perversion is at the root of

todays widespread two cultures syndrome of academic lithe categorical separation of the usually taught practice of tso-called mathematical sciences from the so-called liberal artThat commonplace folly of both academic mathematics and called liberal arts today, is the widely accepted, and intellecally crippling premise of the victims propitiatory effort to secueither academic, or popular acceptance for the social expresion of his, or her views.6

In mathematical physics, for example, submission to thkind of popularized classroom and textbook convention,the common source of the failures of attempted academde-mystifications of the complex domain, as the latdomain was properly defined by Gauss, Riemann, et alhave made reference to the specifically pro-satanic roots empiricism here, to force the readers attention to the usuaunsuspected moral effect of the efficiently corrupting, faprinciple underlying the empiricist mystification still prevlent in the university classroom, as elsewhere, today. Tmind-numbing influence spills over from mathematics, insuch forms as the evil done to the 1965-2003, growing infence of the free trade fads of such centers of gnossophistry as the American Enterprise Institute. It is common

expressed as todays customary misapplication of statisticfinancial accounting to economics generally. The pernicioeffect of carrying those statistical fads to their limit, is notabwidespread, as expressed by the Enron and other examplesthe proliferating effects of empiricism on social and politicpractice today.

As I shall show here, the influence of such reductionist crents of popular opinion is such, that the attempt to teach CGausss 1799 treatment of the fundamental principle of algbra, would often fail, simply because the teacher were lurinto attempting to prove the existence of the ontologicacomplex domain within the bounds of the presumptiowhich bow to the currently most widespread classroom a

related opinion. Classroom opinion on many topics is widepolluted, still today, by the prejudice, that all must be provaccording to the popular presumption that truth lies ultimaly, axiomatically, in the domain of the so-called real couing numbers of simple sense-perception, as distinct from t

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5. The allusion is to C.P. Snows Two Cultures(Two Cultures and the ScienRevolution, London and New York: Cambridge University Press, 1993 rep

6. For example, many brilliant, original discoverers among experimentalspend years of their life seeking to secure peer review acceptance of texperimental successes, by distorting their discoveries in ways which intended to make such opinions acceptable to the sterile Babylonian priehood of the contemporary, reductionist, peer review mafia. The case of hounding to which the friend of Albert Einstein, the brilliant Kurt Gdel, wsubjected, at the Princeton Institute of Advanced Studies, by the hyena-pof Bertrand Russells ideologues, is representative of the general pattern

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1. Lyndon H. LaRouche, Jr., The Economics of the Nosphere(Washington,D.C.: EIR News Service, 2001).

2. As I shall show in the course of unfolding this report, this use of the termSatanism, is not a matter of any one variety of religious belief. It is also a

category of political, and, as I show here, also physical science. Otherwise,apart from the matters I address in this report, its expression in variousforms is among the topics of the political practice of law, or, as in the caseof cults associated with Britains Aleister Crowley or Synarchist occultism,may pop up as a subject of public safety or even national security concerns.

3. Cf. Lyndon H. LaRouche, Jr., et al., The Children of Satan (Washington,D.C.: LaRouche in 2004, 2003).

4. The Bertrand Russell who was usually in error on matters of actual science,was nonetheless correct in stating that positivism, such as that of ErnstMach, was merely another name for radical empiricism. The same should besaid of reductionism generally. The function which empiricist thinking gener-ated as the evil of the utopian social doctrines of Bertrand Russell, NorbertWiener, John von Neumann, and MITs Marvin Minsky, expresses the con-nection between empiricist thinking in mathematical physics and satanicqualities of wickedness which that mathematical mind-set generates in thedomains of art and social practice. The presently continuing influence of thesystemically pathological economic dogmas of Wiener and von Neumann, istypical of the worst effects on world and national economies today.

A discussion during the question period of a Hannover,[Germany] event, prompted me to recognize the impor-tance of adding explicit emphasis on what I wrote in theoriginal publication (Executive Intelligence Review, July11, 2003) of this item on the power/passion function,respecting the actual conception of thought-objects as rec-

ognizable ideas. I have now added a few relevant interpo-lations in the originally published text, and appended asupplement on this point at the close. I have also restoredsome edited-out paragraphing, where this was required toconvey meaning.

Lyndon H. LaRouche, Jr., July 21, 2003

AUTHORS NOTE


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higher standpoint which Euler andLagrange maliciously libelled as thedomain ofimaginary numbers.

The point emphasized here, is that itwould be an intellectually fatal tacticalmistake, to attempt to show a devoutreductionist an argument for the Gaussiancomplex domain in terms he is willing to

accept: terms which are bounded by theessentially linear, axiomatic assumptions

of arithmetic reductionists such as Eulerand Lagrange. Therefore, for such anerrant discussion partner as one of the lat-ter ideologues, only that kind ofClassically Socratic argument for the rele-vant hypothesis, which would blow hisbeliefs apart emotionally, could actuallyshow him the incurable folly of Euler s,and his own argument, as I do in thisreport. The use of this method of hypoth-esis means attacking the falseness of thereductionists fixed ontological assump-

tions, not in his choice of method, deduc-tively, 7 but epistemologically: emotional-ly, rather than merely deductively.

On this account, epistemology, it was the relevant specificvirtue of that 1799 Gauss piece, which had prompted me tosituate it as the cornerstone of the initial educational programof the youth movement. The immediate issue of the disputeover that piece, from the close of the Eighteenth Century to thepresent day, has been, as Gausss enemies themselves empha-sized at that time, Gausss insistence on viewing problems ofmodern mathematical physics from the standpoint of aClassical pre-Euclidean, geometric treatment of those sameerrors which Gauss exposed as the products of the ivory

tower mysticism of Euler and Lagrange.8

For an example of the same mysticism I am attacking here, Ipoint to the errant argument which was made, by Felix Klein, andothers, Kleins false claim, that crucial features of Keplers,Leibnizs, or Gausss discoveries could be replicated by the errantmethods of such followers of the Enlightenment philosophersLagrange, Kant, and Laplace as Cauchy, Hermite, Lindemann, etal. The fraud implicit in the latters attempts, is their vicious exclu-

sion of the physical geometries of Leibniz,Gauss, and Riemann; so, the celebratedMaxwell confessed his politically motivat-ed complicity in this matter of suppressingwhat he knew had been the crucial contri-butions of Ampre, Weber, Gauss, andRiemann to electrodynamics. This ethere-al fraud by Maxwell et al., is typical of

widely accepted hoaxes still presented, onrecord, in todays classrooms, referenceworks, and textbooks.9

That fraudulent mathematics of thereductionists is avoided, only when theunderlying epistemological issues of count-ing numbers, such as those issues posedby Gausss Disquisitiones, are situatedwithin the realm of an essentially con-structive, synthetic anti-Euclideangeometry. So, Gausss work, employing histeacher Kaestners anti-Euclidean geome-try in this case, is the most crucial,make-or-break issue of modern mathe-

matics to be posed for the students com-petent introduction to modern mathe-

matical physics. The exclusion of critical consideration of theaxiomatically geometric roots of the orderings of numbers,was the premise of the relevant essential fraud perpetrated byEuler et al., and the common mistake of the credulous imita-tors of Eulers error today.

Such was the sad state of affairs in that education which hadbeen made available to me prior to my own suspicions con-cerning some of what was taught to me in classrooms and relat-ed kinds of sources on these topics. My own contrary views, asI developed them within that relatively hostile intellectual envi-ronment, proceeded along the lines I present in these pages.

Therefore, I insist today, that competent teaching requires thatthe teacher not rely on the putative authority of textbook mate-rial, but, rather, aid the student in reliving the successes of theoriginal (source) discoverers experience in making, or relivingthe relevant physical discoveries being presented. I explain thispoint from my youthful experience as follows.

On account of what was, for me, initially a much simpler,adolescents mere approximation of that same core issue

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7. On another of those rare occasions when Bertrand Russell did not mis-speak, he emphasized that reductionist inductive method is only borrowingagainst the presumed fruits of future deduction. So much for the delusion ofthe inductive sciences.

8. The complementary terms, pre-Euclidean and anti-Euclidean geometry,represent a conception introduced to modern European science by a leading

Eighteenth-Century mathematician, Gausss teacher Abraham Kstner. Anti-Euclidean geometry in the sense of the geometries of Gauss, Riemann, etal., is defined at the opening of Riemanns 1854 habilitation dissertation. Anti-Euclidean geometries are specifically contrary to so-called non-Euclideangeometries, such as those of Lobatchevski and Jonas Bolyai, which latterare reforms within the bounds of the principles of Euclidean a priorigeome-tries. Cf. Foreword, by Joseph Ehrenfried Hofmann, to Abraham GotthelfKstner, Geschichte der Mathematik(reprint edition), (Hildesheim-New York:Georg Olms Verlag, 1970) pp. XIII-XVI. Hofmann s praise for Euler,DAlembert, Lagrange, and Laplace, typifies the fraudulent opinion againstboth Gausss teacher Kstner and Gauss, which persists to the present time.

9. According to the influential Klein, for example, the definition of the mathemati-cally transcendental in general, and of pi, in particular, was originally accom-

plished by Hermite and Lindemann, working from what was, in fact, a fraudulentdefinition of that task, successively, by Euler and Lambert. In fact, the modernconcept of that transcendental was first presented, in a critical treatment of thediscoveries of Archimedes, by Nicholas of Cusa. The modern mathematical-physics definition of the transcendental, was introduced as an integral feature ofLeibnizs proof for a principle of the origin of the infinitesimal, a proof integral to

his catenary-cued definition of both natural logarithms and the principles of uni-versal physical least action. Leibniz-hater Euler, by denying the existence of theinfinitesimal, as, for example, in his 1761 Letters to a German Princess, createda fraudulent, radically reductionist substitute for Leibnizs infinitesimal, in Eulersown and Lamberts misstated definition of the transcendental. Hence, Kleinspro-reductionist praise for the work of the reductionist followers of Lambert,Hermite and Lindemann. The indicated errors include those who present so-called mathematical models of Riemann surfaces without any indicated notionof the physical meaning of such a surface. On the discoveries of Amp re,Weber, Gauss, and Riemann, in opposition to the reductionists Grassmann etal., see Laurence Hecht, The Significance fo the 1845 Gauss-WeberCorrespondence, 21st Century Science & Technology, Fall 1996; JonathanTennenbaum, An Introduction to The Significance of the 1845 Gauss-WeberCorrespondence, 21st Century Science & Technology, Fall 1996.

Stuart Lewis

Lyndon H. LaRouche addressing aWashington, D.C. audience in a live

webcast.


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which is posed by Gausss1799 paper, I have alwaysstubbornly insisted, since myfirst moment of encounterwith the ivory towersuperstitions taught as thedefinitions, axioms, and pos-tulates of secondary-school

geometry, that the matter ofthe optimal design of a func-tioning, real world, struc-tural beam, already sufficesto point out that the natureof mathematics must bedemonstrated from an exper-imental, physicalstandpoint,not a priori definitions,axioms, and postulates.

I point, now as then, to that experimental standpoint which,in fact, coincides with the relevant epistemological proofs ofthe experimental methods of hypothesis presented in PlatosSocratic dialogues, and echoed in the Apostle Pauls I

Corinthians 13. Then, in my adolescence, and, later, untilearly 1952, even before I came to actually master some part ofthe crucial, axiomatic aspects of the work of Gauss, Riemann,et al., I was already prudent enough to limit the claims whichI presented in my arguments, to the same Classical epistemo-logical premises which I have continued to employ since, ashere today. The spontaneous, childish ridicule unsuccessfullyheaped upon me by foolish teachers and classmates then,more than sixty-five years ago, in the secondary classroomsresponse to my rather obvious statement of fact to that effect,had only succeeded in convincing me, rightly, of the back-wardness of both the popular and classroom culture of thattime.

Since the post-war 1940s, I have developed and adopted aprogressively refined form of that same epistemological proofin all of my principled arguments respecting art and physicalscience. I restate it here in the same frame of reference I cameto know it during 1948-1953, including, especially, throughthe addition of my 1952-1953 comparison, and contrast of thestandpoints of the 1880s work of Georg Cantor and, the meth-ods I prefer to Weierstrass and Cantor at the latters pre-1890sbest, those of Bernard Riemann.

My leading motive for restating that case here, is to exposethe nature of the mental block which I have observed as a fre-quent cause of the students failure to grasp the deep implica-tions of Gausss 1799 paper. It is the need to strengthen ouryouth movements higher-education program on this pivotal

topic, on which my attention is focussed here. However, thesame argument is also needed by the wider audience which Iinclude here.

On that account, as I shall show, although the topicsimplicit in Gausss 1799 paper have been much more thanmerely ably presented by a number of my collaborators, Dr. Jonathan Tennenbaum, Bruce Director, and some of theyouth themselves, I think an additional degree of improve-ment in our program is needed. The epistemological issue ofthe functional difference between man and beast, should be

presented more emphatically, as part of the argument, awith that degree of qualitatively greater emphasis whichemploy here. In such topical areas within epistemologyhave become the relevant specialist. The deeper, epistemlogical issue, has been the intended, but sometimes mere

implied feature of all of my published work, including moriginal scientific discoveries on the principles of economthe crucial proof of the economic fraud of so-called infmation theory, and related matters. Here, in this presereport, I have thought it necessary to focus that same muchoned epistemological insight more sharply on the psychlogical aspect of the related physical-science issues of maematics as such.

The interdependent set of issues so brought into focus, isfollows.

1. What, Physically,Is the Complex Domain?

The subsuming, pivotal question implied by Gausss 17paper, is: What is the nature of human knowledge? In othwords: What is the experimental evidence which demostrates, that the existence of the human species as we knowdepends upon some universal principle of human individuand social behavior, a principle which is lacking in all othliving species?

Proceed to that end by successive approximations.Begin by taking as an example, a comparison of the constru

tion of a solution for the task of doubling the cube, as solved the ancient Archytas, with the modern approach represented Gausss 1799 exposure of the folly of Euler and Lagrange on tpoint. When Gausss solution for the ontological problem

Cardans algebraic approach to cubic roots (as already solvgeometrically by Archytas) is used to demonstrate the principalready at work in the axiomatic issues of doubling the line a_________________________________________________________________________

10. Plato, arguing from the standpoint of pre-Euclidean notions of physgeometry, defined the concept of power, as reflecting those discoveriesmeans of which the human mind is able to increase the power of man s wful action upon the universe. (e.g., Theaetetus). This notion of power wopposed by Platos famous opponent, that sophistical reductionist Aristowho introduced that reductionists notion of energy employed in reductist thermodynamics since Clausius, Grassmann, Kelvin, et al. Cf. AntoPapert, private comments and lectures on Greek language and history.

New York Public Library Picture Collection

Carl Friedrich Gauss(1777-1855)

Library of Congress

Bernhard Riemann(1826-1866)

Vladimir Vernadsky(1863-1945)


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square, the existence of the complex domain, as a domain ofefficient power(in Platos sense of the notion ofpower), we mustrecognize that the physical reality of Gausss argument wasalready clearly, and conclusively shown by the pre-EuclideanClassical Greeks working in the tradition of Pythagoras.10 The

task assumed by Gauss in 1799, was to unveil that sameancient principle of pre-Euclidean (e.g., anti-Euclidean) geom-etry within the frame of reference of modern, post-Fourteenth-Century mathematical physics.

In other words, as I shall clarify this significantly below,modern mathematical physics must recognize those historiccircumstances specific to the history of modern economy,which prompted the successive steps of development, chieflyby the efforts of Gauss, Dirichlet, Abel, and Riemann, of solu-tions for the higher principles of a general notion of physicalspace-time curvature.

Modern developments, since that Fifteenth-CenturyEuropean Renaissance which founded modern European

civilization, have presented us with a new form of practical,social expression of the same issues of physical geometrytreated by Archytas, Plato, et al. The succession of develop-ments from such Renaissance founders of modern science asNicholas of Cusa, Luca Pacioli, and Leonardo da Vinci, andtheir outstanding, avowed follower, Johannes Kepler, creat-ed those Seventeenth-Century foundations of the validmathematical physics developed by Gottfried Leibniz andhis associates.

Unfortunately, the subsequent gaining of relative politicalhegemony by the contrary, decadent, pro-empiricist politi-cal currents of Eighteenth-Century Europes so-calledEnlightenment, provided that centurys empiricist follow-ers of Sarpi, Galileo, and Descartes the opportunity to near-

ly succeed in destroying science.11 The already referenced,two skilled ivory tower formalists of that time from amongmathematicians, the fanatical hoaxsters Leonhard Euler andLagrange, led that fraudulent attack upon Leibniz which,fortunately, Gauss refuted, essentially, in his own 1799paper.

Napoleon Bonapartes accession to what is to be termedtoday a fascist form of imperial power, and his sponsorship of

presentation of the empiri-cist dogmas of Lagrange,produced the opportunityand precedent for a new,Eighteenth-Century attemptto destroy Classical forms ofmodern French science.This assault was continued

with increased force in thepost-1814 role of theBritish-founded, French Res-toration monarchys favorites,Laplace and Cauchy, intheir attempt to eradicatethe original, Leibnizian pro-gram of the Carnot-Mongegeometric tradition of the

Ecole Polytechnique. That same hoax was continued in suchforms as the savage attacks on the foundations of modernEuropean science by the combination of the British empiri-cists and neo-Cartesian followers of Lagranges assault on theLeibnizian roots of Frances Ecole Polytechnique. As a result,

since that time, especially since the hoaxes of Clausius,Grassmann, Kelvin, Helmholtz, et al., that form of the con-flict between good, Classical science, and empiricist hoaxesin the name of science (reductionism), has persisted to thepresent day. Usually, reductionism has prevailed politically,so far.

That much said on those pivotal historical features of thoseproblems of modern science, I return to the trail of my princi-pal, ontological argument here.

Two elementary modern discoveries of physical scienceillustrate the method already employed by such ancients asthe Pythagoreans and Plato to solve such elementary para-doxes as the doubling of the line, square, and cube, and the

uniqueness, by construction, of the five Platonic solids.12

Themost elementary, and crucial modern applications of thesame Classical method, are Keplers uniquely original discov-ery of universal gravitation and the elaboration of Fermatsprinciple of universal quickest action, as continued throughLeibnizs original development of the infinitesimal calculus,and as the catenary-keyed universal physical principle ofleast action.

These works of Kepler, Leibniz, and their like, were the dis-coveries fraudulently attacked by those pro-satanic modernsophists known variously as the empiricists, Cartesians,Physiocrats, phenomenologists, and existentialists.13 The role____________________________________________________________________________

12. Again, Platos notion of power, as opposed to the ivory tower meta-physics of so-called energy.

13. Since this report was drafted, my associate Michael Liebig has stoutly andcorrectly emphasized his thesis, that the continuing root problem ofEuropean civilization, still today, is what Socrates and Plato attacked asthe essential form of pure evil in their time, the sophists, and, I add, suchpredecessors of the sophists as the reductionist Eleatics, such asParmenides, and the Delphi Apollo cult. The modern reductionists, suchas the empiricists, are essentially a continuation of that popularized cult ofsophistry which destroyed the civilization of ancient Greece, and alsoRome, from within. This sophist tradition is the same acid by which con-temporary European civilization, including that of U.S. popular opinion,has nearly destroyed the U.S.A. and Europe from within, over the recentfour decades. Sophism were better understood as a typical synonym forthe generality of the methods of reductionism.

AIP/Emilio Segr Visual Archives

Leonard Euler(1707-1783)

AIP/Emilio Segr Visual Archives, E. ScottBarr Collection

Joseph Louis Lagrange(1736-1813)

AIP/Emilio Segr Visual Archives, E. ScottBarr Collection

BaronAugustinLouis Cauchy(1789-1857)

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11. The method of Descartes is to be treated as a variant of empiricism.


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of the cult offree trade, is typical of the way in which suchforms of what I shall expose here as pro-satanic forms of belief,induce a people, such as many in our U.S.A., to tend todestroy itself, as by a flight from being the worlds leading pro-ductive power, to the floundering, post-1964 decadence of ourpredatory, pro-imperialist, consumerist culture, an increasingmoral, cultural, and economic decadence, which took overcontrol during the 1964-2003 interval to date. Look at the two

cases, gravitation and least action, successively, as caseswhich illustrate a crucial, most elementary ontological princi-ple of all competent scientific method. Failure to grasp the ele-mentary principle expressed by those cases, would cripple allsubsequent attempts to define a scientific way of modernthinking in general.

As our associations educational program has emphasized inits work to date, Keplers observation is typical of all valid sci-entific method, in pointing out the scientifically fatal errors ofjudgment common to the pro-Aristotelean astronomy ofClaudius Ptolemy, Copernicus, and Tycho Brahe. Contrary tothe mathematical presumptions of those pro-Aristoteleanastronomers, the planetary orbits were not only elliptical, withthe Sun situated as one of the foci; but, the motion along the

orbital trajectory was constantly non-uniform. As Kepleremphasized, explicitly, this evidence demonstrated, among

other things, that thproduct of reductioniknown as Aristoteleaniswas fraudulent.14 Aristotapriorism, which dgraded knowledge to tmere describing of senperception, was prov

false by a more competestudy of certain kinds irregularities in the observphenomena themselvKeplers discovery of gratation was the point of ogin of such crucial ladevelopments as Leibniuniquely original discoery of the infinitesimcalculus, and, as I shemphasize here, of tcrucially pivotal conceof a Riemann Surfa

Function.The sophist (reductio

ist) method denies texistence of knowabtruth, as the ancie

Aristotelean hoaxsters denied such knowledge, for astronmy or otherwise, and the famous modern hoaxster, tempiricist neo-Aristotelean Immanuel Kant did.15 The redutionist insists that we actually know only that which is psented to us by our senses.16 Contrary to the sophists, tmeasured characteristics of the compared planetary orbitsEarth and Mars, sufficed to exemplify the proof that we not know physical reality from our senses; we know real

through the specifically human power of hypothesizing, experimental determination of the validity of those hypothses which solve the contradictory paradoxes which oftarise when we attempt to explain the behavior of tobserved world by reliance on merely describing the expeence of sense-perception.17

Shadow and substance! (Passion!) Gravitation is experimentally proven hypothesis, which defines oknowledge of that universal physical principle as one whican not be detected directly by the senses, but whinonetheless efficiently affects the movement of those me

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14. Aristotle was deployed from Demosthenes school of rhetoric, to borefrom within Platos Academy. His Nicomachean Ethics is typical of thesophist method. Claudius Ptolemys scheme, which was based uponthe fraudulent method of Aristotle, was an effort to destroy the mostcompetent astronomy of that time, the legacy of Aristarchus andEratosthenes. Kepler deals explicitly with the methodological fallacy ofAristotle in his own report of the discovery of gravitation. Aristotle smethod is the reductionist method otherwise associated with the nameof sophistry.

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15. (Kant, previously a rabid empiricist from the school of David Hume, pduced his series of Critiques premised upon a syncretic expressionempiricism incorporating the teachings of Aristotle.) Meanwhile, while

was being edited for release, my associate Bruce Director elaborated same essential point, in contrasting it to the revolutionary discovery psented by Bernhard Riemann in the latters 1854 habilitation dissertatCf. Bruce Director, Defeating I. Kant,Riemann for Anti-Dummies, no. at www.theacademy2004.com.

16. Thats only a theory! is the typical protest of the sterile intellect steepin the dogmas of simple sense-certainty. The curious fact of the mattethat the advocate of such views miraculously fails to grow the tail whwould manifest at least the species-sincerity of his doctrine.

17. Actually, as I have occasionally illustrated this point, this discoveryKepler requires the implied notion of a Riemann Surface Functionthe means for representing the mental image of Kepler s concvisually.

Illustration by Jan van der Heyden, courtesy ofNew York Public Library Prints Division

Johannes Kepler (1571-1630), the founderof astrophysics and modern mathematicalphysics, discovered universal gravitationusing an anti-Aristotelean method. His

ordering of the orbits of the planets (right) tocohere with the ordering of Platonic solidswas not based onsense perception.

Reproduced from Keplers 1596 Mysterium Cosmographicum


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shadows which are the sensed aspects of our world. Thispoints the mind of the intelligent observer to the fact, thatour sense-apparatus is merely part of our organism. Whatour senses report to us, is, at best, the effect of action by theworld outside on those sense-organs, not the image of thatefficient action itself.18 The senses show us, at best, shad-ows cast by a universe which exists beyond the directobservation of the senses. The domain of sense-perception

presents us the mere shadows of the real principles whichoperate in a universe outside the domain of direct sense-perception. The same point was made in Platos treatmentof the doubling of the square (Theaetetus)19 and the con-struction of the Platonic solids.20

Shadow and substance! (Passion!) Fermat discovered thatthe propagation of light follows a pathway of quickest time,rather than shortest distance. The continued refinement of thatdiscovery, successively, by Huyghens, Leibniz, and JohnBernouilli, most notably, led to Leibnizs interrelated discover-ies of that principle of universal least action, which is theunique basis for the infinitesimal calculus, the related physicalprinciple of logarithmic functions, and the role of the catenaryas an expression of the most characteristic feature of what

Gauss and Riemann later defined, successively, as the com-plex domain.

Both of the outcomes of those exemplary cases, Kepler suniquely original discovery of the principle of gravitation, andLeibnizs defining of a universal physical principle of leastaction, defy that naive, false presumption which teaches thatour senses show us directly the realuniverse in which we exist. These,and comparable discoveries of uni-versal physical principle, show usprinciples by means of which wecan increase our willful, and alsovisible control of the universe; but,

they also show us the nature of thatuniversal principle of physicalhypothesis, the faculty ofnosis21by means of which we areable to adduce the existence of,and effect the practical (emotional)mastery of those specific physicalprinciples.

The acquisition of such efficient-ly practical knowledge of princi-ples beyond the powers of senseperception, enables us to define theefficient function of sense-percep-tion within that real universe which

lies within nothing less than thecomplex domain, a universebeyond the shadow-world of

sense-perception as such. Describe this relationship by aid ofthe following illustration.

The Case of the Nighttime SkyThe oldest known precedent for what we call physical sci-

ence today, is reflected in ancient astronomical calendars. Thederivation of the notion of science today, is traced in Europeancivilization from a geometric study of astronomy which the

pro-Egyptian Pythagoreans namedspherics.

The notion ofuniversally efficient physical principles today, is derived from

study of the regular behavior of the wanderers of our SolarSystem, as seen against the background of the clearer momentsof opportunity to view the nighttime stellar sky.22

As man begins to approximate a normalization of thenighttime sky, to compensate for the fact that any observa-tion from a point on Earth, is viewing immediate sights froma point on the surface of a rotating and moving quasi-sphe-roid, our planet, a certain notion of what we call a uni-verse emerges. The question is thus posed: What are weseeing, up there?

From a normalized position on Earth, the stellar displayappears to lie on the interior surface of a spherical space of

great, but undetermined radius. In ancient times, solar eventsseemed to many to be willfully insolent wanderers against thebackdrop of an array of seemingly fixed stars, stars apparentlylying along the internal surface of a celestial sphere. Call thisupward-looking view of the universe, the relevant starting-point for mankinds notion of a universal Sensorium, a view of


A

D B E

C

Pierre de Fermat (1601-1665), French philosopher and mathematician, discovered thatthe propagation of light follows a pathway of quickest or least time, rather than least

distance. A light ray beginning at point A in air, and entering the water at point B, willdirect itself towards the point C in the denser medium, the total time of travel along thepath ABC being the least possible.

____________________________________________________________________________

18. Again, the image conveyed by the notion of a Riemann Surface Function.

19. On this, see, once again, Antony Papert on Platos use of the notion ofpower, here, in opposition to the reductionist term, energy, subse-quently introduced by Platos adversary Aristotle.

20. In this instance, I reference Platos treatment of the implications of thatconstruction in his Timaeus.

21. Vernadskys term for those uniquely human powers of creative reason, by

means of which individuals discover those hypotheses which prove,experimentally, to be universal physical principles, principles which existbeyond the abilities of lower forms of life, and beyond the direct reach ofour powers of perception.

22. The deep pit method used by Eratosthenes and others, provided a wayof viewing the stars during midday. E.g., the method of observationemployed to assist his celebrated estimation of the curvature of theEarth.


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that universe as it is presented to our sense-organs. Those whomade the mistake of assuming that our senses show us the realuniverse directly, tended toward the belief that the measure-ments of what could be read as constant angular, or straight-line motion of observed bodies, would be the simply statisti-cal form of expression of laws directly governing the universe,lawful effects which were thus misinterpreted as merely lyingwithin, confined to the bounds as of a universal Sensorium

within which the existence of our Earth was presumably situ-ated.Similarly, as in the example of the typical modern dupes

misunderstanding of cyclical and related periodic movementswithin financial markets, the dupe assumes that charting thoseapparent patterns produces knowledge of supposed laws ofthe marketplace. That dupe fails to grasp the point that finan-cial markets, like sheep-shearings, are deployed to trap andstrip the victim-investor by aid of the investor s own simple-minded cupidity, his foolish faith in seeing is believing, as inhis substitution of patterns of simplistic statistical readings forwhat should have been his attention to physically efficientcauses of effects.

That said, turn ones attention in two directions. In one

direction we have, contrary to the reductionists, those moreinsightful ancients who viewed the universe within the boundsof that Sensorium from a pre-Euclidean standpoint akin to thatof Thales and the Pythagoreans. We have also, their propersuccessors, including the Aristarchus who demonstrated thatthe Earth orbitted the Sun, and the Eratosthenes who measuredthe curvature of the surface of the Earth (with remarkableapproximation) by observations made from points, in thevicinity of the Mediterranean, on the surface of our planet.Then, we have modern science, which erupted within theFifteenth-Century, Italy-centered Renaissance.

I shall bring our attention back to that fact at a relevantpoint, later in this report; for the moment, focus on the fact that

this Renaissance revived ancient Classical Greek knowledgeof the methods of physical science from the relative intellec-tual dark ages of Roman imperial traditions, and did this in thesetting of giving birth to the first modern sovereign nation-states, those of Louis XIs France and Henry VIIs England. Thiswas also the birth of modern European civilization out from along dark age which dominated Europe under the emergingRoman Empire and the subsequent prolongation of feudal-ism.23 It was also the birthplace of modern science, as typifiedby the work of Brunelleschi, Nicholas of Cusa, Leonardo daVinci, and their follower, the founder of the notion of a com-prehensive modern mathematical physics, Johannes Kepler.The historical circumstances most relevant to this report, are,

in summary, the following.Although the fact of the Earths orbitting the Sun was know

to mid-Fifteenth-Century founders of modern experimenscience, such as Nicholas of Cusa, Inquisition-ridden, poA.D. 1511 Europe returned to the failed Aristotelean, ivotower methods of astronomy of Claudius PtolemCopernicus, and Tycho Brahe: until Kepler. All three of thepre-Kepler copiers of Aristotles reductionism, portrayed tuniverse as lying within the apparent linear-statistical regul

ity of motion within the internal surface of the astronomicSensorium.

Now, centuries later, the Sensorium is conceived in depthis imagined that an expanding universe of galaxies, and highly complex and vast configurations within each galaxyto be considered. However, such latter discoveries do not yaddress the crucial question: Is the Sensorium, so defined, seevidentlyreal? This forces our attention to the function of tmodern, pro-Platonic nation-state republic, in giving a neednew definition to the meaning of science.


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23. The emergence of the modern nation-state out of the morass of ancientimperial Rome and ultramontane feudalism, is to be studied, chiefly, as animpulse toward the freeing of society from the Romantic s ultramontanenotion of imperial law. This process is chiefly divided between two periods.The first of these steps toward freeing mankind from the ultramontane, istypified by the rejection of the fraudulent Donation of Constantine, fromCharlemagne through Dante Alighieri. That first period is treated by legalhistorian Friedrich August von Der Heydtes Die Geburtsstunde des sou-vernen Staates (Regensburg: Druck und Verlag Josef Habbel, 1952).The second phase is the birth of the modern sovereign nation-state repub-lic during the course of the Fifteenth-Century Renaissance, as expressedby Louis XIs France and Henry VIIs England. A comparison of the twocases has been made public by my wife, Helga Zepp-LaRouche.

Gil Riviere-Wecks

The courage of Joan of Arc in the Fifteenth Century ma

possible the first nation-statea united France under LouXI, which made it possible for the majority of the populatito rise above the status ofhuman cattle.Here, a statue Joan in Paris.


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What was the pathological assumption which promptedpost-1511 official, relatively decadent, then predominant,Venice-centered, reactionary authorities in Europe, to attemptto turn back the clock of science to reductionist superstitions,such as the methods of Aristotle and William of Ockham?What is the simplest way of making clear the systemic featuresof that Venice-orchestrated rampage of moral decadence dur-ing the 1511-1648 interval of religious warfare? Consider the

social origins of the decadence, first, and then focus upon theepistemological consequences.As I shall emphasize here, the underlying political issue

posed by the Venice-led attempt to reverse the progress of theFifteenth-Century Renaissance, is the fight over the proposi-tion: Is man a higher form of beast, or a species categoricallydistinct from, and superior to all lower forms of life? In otherwords, this issue is, once again: What is the functional natureof specifically human knowledge, which sets the humanspecies apart from the beasts?What are the conditions underwhich the members of a culture are confronted with proof ofsuch considerations?

The Fifteenth-Century, Florence-centered Renaissance is thehistorical benchmark which separates emergence of modern

European civilization from the admittedly still lingering aro-mas of the declining, philosophically irrationalist, Romanticworld of feudalism. The central intellectual figure of that rev-olutionary moment of historic change is Cardinal Nicholas ofCusa, whose Concordantia Catholica prescribed both an ecu-menical reform of the then shattered Papacy, and the replace-ment of the feudal system by a community of principle amongsovereign nation-state republics,24 and whose De DoctaIgnorantia provided the initial approximation of a comprehen-sive definition of what became known as modern physical sci-ence. The crucial complementary development to that effectin Italy, was the transition, pioneered by the courage of JeannedArc, which made possible the first modern nation-state, a

united France under Louis XI. The second modern nation-statewas England under Henry VII.The correlated political development was Christopher

Columbuss voyage of discovery, implementing a post-A.D.1453 project which organized by Nicholas of Cusa, and car-ried out according to maps and other designs which Columbusplanned and conducted, on the basis of materials he obtainedfrom Cusas collaborator Toscanelli. The irony of Columbuss1492 re-discovery of the inhabited land across the Atlantic,was that it coincided with the precedent of that brutish sav-agery of tyrannical Spains monstrous persecution of the Jewsand Moors.25 The latter brutishness opened the door for whathas been called modern Europes little new dark age ofrecurring religious and related wars of the 1511-1648 period.

Despite the brutish horrors of those chiefly Venice-orches-trated religious and related wars of the 1511-1648 interval, the

secular thrust of the entire span of 1401-1789, and beyond,through all ebbs and flows, was the net progress, over the peri-od taken as a whole, toward forms of society which liberatedEurope from that prevalent degradation of the mass of human-ity to the status of either hunted or herded human cattle. Forthe first time, the principle ofagape, of Plato and Christianity,found expression in a notion of political society as rightly gov-erned by that principle of natural law which appeared later asthe fundamental constitutional principle of law in thePreamble of the U.S. Federal Constitution. That principle is

expressed summarily by the combined names of an interde-pendent notion ofnational sovereignty, general welfare, andposterity.

This doctrine of natural law meant three things in practice.That a nation-state republic must be perfectly sovereign. Thatthe rulers had no moral right to reign except as they were effi-ciently dedicated to the general welfareof all of the popula-tion, and that society placed the benefits to posterityabovethose enjoyed by the presently living. It followed, thatalthough states must enjoy sovereignty, they are bound,


____________________________________________________________________________

24. Concordantia Catholicais, in principle, the successor to Dante Alighieri sDe Monarchia. The latter, which reflects the totality of Dante s principalwork, defined the proposed emergence of a form of national societiesfreed from the shackles of ultramontane13th and 14th centuries Venetian-Norman feudal hegemony.

25. This expulsion of the Moors and Jews, was the crime against God andmankind which set the pace for the brutish self-destruction of 1511-1648Spain, and for the subsequent eruption of Carlism and such fascistsequels as the pathological doctrine of Hispanidad.

Philip Ulanowsky

Columbus sailed to the New World in a project organized by

Nicholas of Cusa, using maps and materials from Cusascollaborator, Paolo Toscanelli. This statue of the explorerstands at Columbus Circle in New York City.


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according to natural law, to promote these three rights andbenefits among all peoples; hence, those concurring condi-tions represent the basis in natural law for a community ofprinciple, rather than a system based on the prescription ofinevitable conflict, such as that of the empiricists Hobbes andLocke.

This Fifteenth-Century, Renaissance-led revolution in state-craft, as typified in approximation by Louis XIs France and

Henry VIIs England, was the date and place of the birth ofactual political-economy. This birth of political-economy gave

practical expression of a new, lawful definition of the propernature of government of both the human individual and soci-ety. This notion of the states moral accountability for fosteringthe general welfare of all persons and their posterity, is thebirth of modern society, the progressive freeing of that formerunderclass, the majority of mankind, from the social-political,and economic status of being treated as virtually merelyhuman cattle.

It was this modern conception of natural law, rooted in afunctional notion of the promotion of the general welfare of allpersons and their individual and collective posterities, whichis the basis for any competent notion of law and political-

economy in particular, and of physical science in general. It isfrom the standpoint of the Fifteenth-Century notion of modernscience, that we adopt the ancient Classical precursors of sci-ence, such as the pre-Euclidean Pythagoreans, as an imper-fectly developed, but integral part of the foundations for emer-gence of a competent modern science today.

Earlier, that larger mass of mankind, which had been treatedconventionally as hunted or herded human cattle, had few law-ful rights under feudal imperial (ultramontane) law which dif-fered little, even unwittingly, from those forms of rights accord-ed to fairly treated herded cattle. This same feudal doctrine,expressed by the Anjou-like Anglo-French Fronde tradition ofthe Sixteenth and Seventeenth centuries, was the premise of the

neo-feudalist dogma of the Physiocrats, as defined axiomati-cally by Dr. Francois Quesnay. Quesnays doctrine of laissez-faire, like that of Turgot, and of the Adam Smith who plagia-rized his free trade dogma largely from Frances Physiocrats,was premised on the proposition, that the serfs of the estate hadno more rights than those enjoyed by herded, non-human cat-tle, and that, therefore, the profit of the estate was a magicalexpression of the Cathar-like benefit of the charter expressed bythe patent of lordship over the estate held by that usually lazyparasite currently the decadent, aristocratic landlord or othertitleholder to property-right or shareholder value.

Prior to the new, modern conception of law, a notion of lawtypified by such works of Cusa as his inherently complemen-tary Concordantia Catholica and his subsequent De Docta

Ignorantia, the reduction of the foreigner and lower classes tothe virtual status of human cattle, defined the latter as merelyat the service of the ruling classes, as cattle are, rather thanmeasuring societys performance in terms of the included ben-efits expressed in the uplifting of the whole population.

For example. Following the U.S. Civil War, the policies ofeducation of the slave represented by the work of FrederickDouglass, were widely superseded by a doctrine which low-ered the standard of education and intellectual life of the freedslave to the level sufficient for a workaday life of menial work.

Earlier, the worlds leading economist of that time, Henry Carey, documented the case, the pre-1865 U.S. national ecoomy, had lost money on the work of the slaves, while tprofits of that slavery were enjoyed chiefly by British intereand their American Tory accomplices. The ultimately castrophic collapse of the internal economy of Italy under tslavery-ridden Roman Empire, is typical of the kind of falmerely superficial and temporary prosperity enjoyed by

nation which obtains the apparent prosperity of the fethrough the looting of the land and persons of the many, whiloots, thus, both that land and those lower classes whichtreats as virtually human cattle.

The collapse today, of a U.S.A., which had been the worlleading producer-power under Presidents Franklin RooseveEisenhower, and Kennedy, into a predatory, decadent, ruinconsumerist culture, reflects the ruinous effects of U.S.-direed post-1971 monetary-financial policies of the IMF on tnations of the Americas which those U.S.-directed IMF pocies have driven to collapse. The parasite which thus destroits host, is thus condemned to collapse out of its own recklefolly.

The principle of the sovereign nation-state gave the serf t

right, taken from him by ultramontane feudalism, of beihuman, under a new conception of the law of sovereination-states. The development of the productive powers the individual and the right to participate in the fruit producby that development, became the intentof the natural lawthe newly introduced institution, the modern sovereign natiostate. Under this law, the people and land of the nation weno longer mere cordwood to be consumed for the warmththe oligarchs and their lackeys; the defense and improvemeof the welfare of all the people and their posterity became tcalculable form of obligation on which the continued authoity of the government depended. That is the elementaexpression, in first approximation, of the modern instituti

called political-economy.Rendering this new order of society in that implicitly calclable form of organization, by defining political-economy cates the setting which was indispensable for the FifteenCentury birth of modern European science. The possibility an improvement of the conditions of life of both current afuture generations, depends upon the objective interdepenency of two forms of specifically human activity, by means which man accomplishes what no other living species can dthe effecting of willful increases of the potential relative poplation-density of the human species.

These two forms of activity are typified in their effect first, the efficiently used discoveries of universal principland, second, those insights into the principled role of Classic

artistic composition, such as the Classical tragedy Aeschylus, Shakespeare, and Schiller, in enabling society intend to cooperate willfully and efficiently in efficient pmotion and use of the benefits of physical-scientific progres

The difference between those two cooperating impulsesthat in the fundamental discoveries of universal physical prciple, the individual creative mind is acting in individual retionship to the physical universe. In the principles of Classicartistic composition, the individual is acting in an emotiodriven relationship to the principles of those social process


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through which society cooperates in the application of dis-covered universal physical principles. The benefits of thoseactivities are the only actual source of what should be regard-

ed as the physical form of economic profit by society. There isno other source of true and legitimate profit than the com-bined benefit of the action of discovering and adopting thesetwo kinds of universal principles.

This view of science, within the context of political econo-my, forces modern society to confront itself with a new kind ofview of the difference between man and the beast. As we canshow clearly from the doctrine of Moses, the work of Plato,and the principles of Christianity, for example, exceptionalindividuals of earlier society were able to adduce an essen-tially correct definition of the nature of man which sets ourspecies apart from, and above the beasts; but the modernnation-state republic, as seen in Nicholas of Cusa sConcordantia Catholica, was the first appearance of a form of

society whose passions are efficiently ordered for the promo-tion of forms of progress consistent with the special nature ofthe human being, as a creature whose characteristic activity isthe passion for discovery and application of those two classesof universal principles.

The modern sovereign nation-state republic, is a form ofstate which must be efficiently dedicated to that higher author-ity of the doctrine of natural law expressed as the Preamble ofthe U.S. Federal Constitution, which does not recognize theexistence of a right to class interest by any social class; the

notion of shareholder value spread in modernnations today exists only as a specifically fascistdoctrine of the Romantic law-tradition of theaccomplices Hegel and Savigny, and their followerthe Nazi Carl Schmitt. Like science, republican nat-ural law measures intention and performance bynothing less than universal standards: specifically,the universality of mankind, and mankinds implic-

itly assigned role of exerting increasing control over,and responsibility for the welfare of mankind, andimprovement of the universe we inhabit.

With the Fifteenth-Century Renaissance, the ideaof man in the universe, as a universal being soexpressed by willful practice, became the guide forthose changes in mankinds practice which deservethe name of progress. With the 1789 adoption of the

Preamble of the U.S. FederalConstitution, an impassionedmoral standard was estab-lished for all modern Europeancivilization, under which soci-ety obliged itself to regulate

itself according to the measur-able progress of its entire pop-ulation, toward the improve-ment of the general welfare ofall of its people and their pos-terity. With that continuationof the Fifteenth-CenturyRenaissances founding of themodern nation-state, the 1648Treaty of Westphalia, the 1776

U.S. Declaration of Independence, and the 1789 U.S. FederalConstitution, a form of lawful physical economy was invokedas a model of reference for a supreme law of nations, which,

when served, represents a measurable form of the true natureof mankind. Hence, the very name of modern history, and therelated notion of modern science, must be so dated.

These missions of the modern republic can be accom-plished in no other way than accumulated knowledge and useof those discovered universal physical principles which existbeyond the mere shadow-world of naive sense-perception.This proper view of mankind, its power, and its mission,begins when we seek those principles, of those two kinds,which, by their nature, are hidden from mere sense-percep-tion, by knowledge of which man may reach out toward con-trolling the invisible ordering of events in the Sensorium whichis reflected to our senses as the nighttime sky.

It was under those political preconditions, that modern sci-

ence adduced the notion of the complex domain from theprecedents of the ancient Platonic tradition.

2. The Complex Domain andMans Immortality

The proof that the universe contains efficient universal prin-ciples which are not themselves directly objects of the senses,presents us with the need to think of the individuals relation-


The founding of theU.S. Republic, basedon the ideas ofLeibniz and his

Renaissancepredecessors, createdthe conditions formodern physicaleconomy, scientificand social progress,and a referencemodel for relationsamong nation states.

Nicolaus of Cusa(1401-1464)

Gottfried Leibniz(1646-1716)


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ship to nature around us in terms of two geometries. The firstof those is what I have defined, in the preceding pages, as theanti-Euclidean form of the geometry of the universalSensorium; the second is a geometry based on nothing but anexperimental reading of the measurable relations within a setof inter-relationships among those discoverable, and experi-mentally validated universal physical principles which aregenerated by Platos method of hypothesis. The first, is approx-imately the shadow-world geometry of sense-perceptualspace-time. The second, is the unperceived universe of those

actual principles which produce those paradoxical sensoryeffects which prompt the recognition of the existence of theunperceived, but efficiently existing universal physical princi-ples. The two geometries are everywhere interacting.

We shall consider this, first, as it impacts the work of thephysical scientist. Later, we shall turn to the matter of Classicalartistic composition.

In the first of those two instances: The known interaction ofthose two geometries, perceptual and physical, is the effectreflected in modern mathematical physics as the notion of theactuality of the Gauss-Riemann complex domain. Within thiscombined notion, the relationship of the second, the physical-ly efficient action, to the first, the physical geometry of the vis-ible domain, is expressed as the shadowy impact of physical

principles on the Sensorium; these, combined, are the subjectof the general notion of a Riemann Surface function, as elab-orated by Riemann on, chiefly, the foundations of Gauss snotions of the general principles of curvature.26 For first

approximation, consider this case for gravitation as Kepdefines it. Next, in second approximation, consider the evotionary development of Fermats concept of quickest time, tnotion which was to appear in a more developed form Leibnizs catenary-pivotted concept of universal least action

Kepler situates the physical principle of gravitation wrespect to evidence bearing upon the successive treatmentsthe implications of the construction of the Platonic solids Plato,27 Luca Pacioli,28 and Leonardo da Vinci. Kepler pceeds from this insight into the ostensibly elliptical harmon

characteristics of the set of solar orbits, to make the first geeralized leap of insight into what became known later as tphysical nature of the complex domain. This insight led Keplers defining a set of orbital values characteristic of a neessary, but also necessarily exploded planet, lying in a desnated orbit between Mars and Jupiter, an exploded planwhich Gauss proved, nearly two centuries later, to be tremains known as the Asteroid belt.

These considerations by Kepler define an unseen, but efcient action occurring everywhere in the perceived SoSystem, action causing that system to behave differently, every visible point, than can be accounted for in terms of costant action among visible movements. Therefore, we mucreate the mental image of a new space-time, which, on t

one hand, corresponds to perception, but, on the other hanmoves perceived action by the intentionexpressed as somimpassioned, knowable, but imperceptible universal physiprinciple. The conjunction of these two actions, respectiveshadow and substance, defines a new geometry in which boeffects, perceived and causal, are combined as one geomtry.29 That becomes the complex domain of Leibnizs princip

Thebel canto method, which defines six types of human singing voices, and thesocial relationships this implies, is a necessary feature of Classical composition.Classical performance requires human thought and passion, not simply playing or

singing the notes. The conductor Wilhelm Furtwaengler called this playingbetween the notes,a quality startlingly evident in recordings of his performances.

C C C C C

64 128 256 512 1024

Middle C

do re mi fa sol la ti do re mi fa sol la ti do re mi fa sol la ti do

F

Soprano

F# F F# C

C#D

Contralto

D C# D

Baritone

AF# Bb Eb En A

D

Bass

Ab C# D

EbF

Alto (mezzosoprano)

En Eb En BnBbA

BA

Tenor

C F F# B C F

First Register

Second Register

Third Register

Fourth Register

Berlin Press Agency, 1

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29. Hence, what Euler mistakenly discards as imaginary, is the real, awhat Euler calls real, is the product of the sensory imagination!

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26. Bernhard Riemann, On the Hypotheses Which Underlie Geometry (berdie Hypothesen welche der Geometrie zu Grunde liegen) BernhardRiemanns Gesammelte Mathematische Werke (New York: DoverPublications reprint edition, 1953).

27. E.g., Timaeus.

28. E.g., De Divina Proportione.


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of universal least action, the complex domain as defined, suc-cessively, by Gauss and Riemann, in concert with their col-laborators, such as Lejeune Dirichlet, and others, such asAbel, on whose work the product presented by Riemanndepended in most significant degree.

Such is that quality of passion which separates true geniusfrom pedantry, in both physical science and Classical artisticcomposition and performance.

I shall leave it to our collaborators to work through the ped-agogical exercises required by the geometries my outline hasthus implied. The included purpose of that assigned exercise,is to break through the barrier which separates simply percep-tual visualization of events in sensory space-time, from theconceptualization of higher geometries arising from syntheticvisualization of the unseen principle of action revealing itspresence at each point. The readers attention will be returnedto some implications of that matter, below, after we have com-pared this case to that presented by the notion of a Classicalprinciple of artistic composition. Therefore, reasons for thisdecision by me will be clarified a bit later in this report.

The Subject of Classical Irony

In an effective staging of a Classical tragedy, or of a Classicalmusical composition, the images on stage are superseded by adrama performed on the internal stage of the individualaudience members imagination. The comparison of the twostages, the shadows perceived and the imagined reality,involves contrasted human mental states analogous to thecontrast between sensory perception and recognition of theunseeable universal principle governing the movements ofthat which is perceived. Every successfulClassical performer,dramatic or musical, is implicitly aware of this, and is gov-erned by a prescience of such relationships.30 This is the keyto the definition of all Classical artistic principles; it is also thekey to all political practice which leads nations along an

upward course of social self-development of the humanspecies as a whole.Those introductory remarks on the matter now immediately

before us, are intended to point attention to a question: Whatis the object which corresponds to the individuals mental actof hypothetical discovery of what proves, experimentally, tobe a universal physical principle?That mental act correspondsto what Vernadsky defines as (biogeochemical) nosis.

In true nosis, our subject is the existence of ideas whichreside outside the scope of sense-perception; yet, they are def-inite, experimentally efficient ideas, of the same degree of dis-tinctness, as ideas, as might be ascribed to any sense-perceived object.31 These are referenced under the heading of

powersby Plato.32 Therefore, out of respect for the definitenature of such ideas of principle, I refer to these distinct con-ceptions as thought-objects.33

To hone my foregoing observation to a fine point: what isthe thought-objectrepresented by the act of discovery of a uni-versal physical principle? What is the recognition of such athought-object in one mind by another person? What is thekindred thought-objectwhose controlling presence defines the

successful composition, or performance of a Classical tragedy,or musical composition, as distinct from the mere sensational-ism of Romantic and modernist artistic composition or per-formance?34

Both of these compared types of thought-objects, physicaland Classical-artistic, have the ontological quality we meet inmy earlier references, here, to the original discovery of anexperimentally validated, hypothetical physical principle. Thebest choice of introductory exercises for acquiring a sense ofthe equivalence of universal physical principles to the thought-objects of Classical artistic composition and performance, isthe study of the collection of Plato dialogues. In that collectionas a whole, the student encounters the thought-objects calledPlatonic hypotheses, which pertain to physical principles; the

same method yields those insights, also called hypotheses,which pertain to the principles of social processes.

The latter class of insights into social processes, populatethe domain of Classical artistic composition, and are, as Ihave often emphasized in earlier utterances, the key to rec-ognizing the interdependency between Classical artisticcomposition and a competent force of a political science ofhistory-making.

In Classical composition, as in the discovery of experimen-tally validated universal physical principles, the entire compo-sition is both generated by a single act of insight, and neverdeparts from being an expression of that single insight. Take amusical example of this principle. The late Beethoven string

quartets Opus 131 and 132 are a work of genius even by thestandard of Beethovens best earlier compositions, the mostnotable, most coherent, and highest expression, to date, of acompositional principle of well-tempered counterpoint firstdefined by J.S. Bach. Properly apprehended, these composi-tions, properly delivered, like related cases of so-called lateBeethoven compositions, fascinate the minds powers of con-centration, subjecting it to an impassioned, kaleidoscopic suc-cession of exciting acts of discovery, as coherent development,from start to the aftermath of the close.35 The ordering princi-

____________________________________________________________________________30. The task of the playwright or composer, is to foresee the arrangement of the

shadows represented by the seen and heard action on stage, and toarrange those shadowy elements deployed in such an ironical fashion as toprovoke the audience to search its own mind for the reality to which thoseshadows correspond. It is as if God arranged the visible motion of the SolarSystem to cause Keplers mind to recognize the reality of a universal princi-ple of gravitation. So, the adequate performer of a Classical musical com-position crafts his or her performance to force the real intent of the compos-er upon the audience. The greatest conductor of the Twentieth Century,Wilhelm Furtwngler, referred to this as performing between the notes.

31. Cf. B. Riemann, 1. Zur Psychologie und Metaphysik,Bernhard RiemannsGesammelte Mathematische Werke, pp. 507-538. N.B. pp. 509-520.

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32. A. Papert, op. cit.

33. There are those who recognize such thought-objects, and those whoprotest, I Kant!

34. Exemplary is the disgusting practice of director theater arrangements ofClassical drama, the one more disgusting than the version it superseded.

35. The performance of any similarly qualified Classical composition, requiresthe performers, and audience, alike, to make the unfolding, unifyingprocess of the completed composition ones own. This is accomplishedby reducing the entire compositions process of development, from an omi-nous moment of silence before its beginning, to a moment of silence at theend, to a single principle of development. The late Beethoven quartets areperhaps the best cases to consider from this standpoint. Instead of a suc-cession of stages, there is a seamless process of transcendental devel-opment, a notion of development which expresses the unfolding of theentire composition as a single idea, an idea comparable to Keplers notionof the organization of the Solar System.


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ple which subsumes that succession, is a thought-object. Thatthought-object is the generating idea of the compositionsunity of effect.

A great performance of a Classical tragedy has a similareffect.

That said, begin the definition of Classical composition ingeneral with a crucial question: How does the individualsmind discover the set of principles of both composition and

performance; how does this relate to the individuals sover-eign act of generating an experimentally validated universalphysical principle? In other words, what is the feature ofthought-objects which is common to discoveries of principlein both physical science and Classical composition? Howdoes the answer to that question make clear the reason whywe must see Classical artistic and opposing forms of artisticcomposition (or, performance) as placed into qualitativelyopposing categories. Classical and Romantic artistry are notcontrasting views of art; they are different species of exis-tence, opposing one anothers existence in a way comparableto the interspecific sterility enjoyed between mammals andreptiles.

The key to the answer to that question so posed, is already

reflected, typically, in the account of Pythagoras definition ofthe musical comma. That account states that Pythagorasderived the proof of that comma by, in effect, comparing thedivision as of the octave, by a singing-voice and a monochord.In such an experiment, the comma is generated consistentlyonly when the human singing voice is one developed to itsnaturally optimal potential by methods equivalent to thatFifteenth-Century Florentine bel cantosinging-voice traditionassociated with the musical knowledge referenced by the frag-mentary remains of Leonardo da Vincis book De Musica. Theresult is the same characteristic of the human singing-voicereflected in the systemic conflict between Bachs well-tem-pered counterpoint and the empiricists equal-tempered key-

board.In the Florentine bel cantotradition, for example, the act ofplacing of the tones and phrasing of the human singing voice,is established in memory as a set of ideas in the sense ofPlatonic thought-objects as ideas.36 This notion of the belcantosinging voice, is the pivotal feature of Classical compo-sition of not only music, but also, as the German and ItalianClassical song and opera which the Classical poetry anddrama of those musical compositions require. The same is therule of passionfor the composition and performance of poet-ry, or the musical substructure of what is to be delivered as thedrama for the Classical stage.

There is some more, which is of crucial performance in dis-tinguishing music as Classical art, for example, from a musical

physics.The bel canto musical scale divides the categories of

human singing voices among six types of human singingvoices, as determined by what are known as natural regis-ter-shifts, and otherwise determined by secondary differen-tiations within voice-types. The combined effect of these

and related features of the properly developed natupotentials of the human singing voice, define music associal, rather than an individual expression of the use of thuman creative powers for generating and sharing expeence of the generation of thought-objects as ideas. This sof social relations integral to the chest of human singivoices, and the essential role of counterpoint in Classicmusical composition, defines Classical musical compo

tion and performance, as a domain of Classical artiscomposition, rather than a type of mathematical physiceven though the definitions of human thought-objects fClassical art and physical science are otherwise perfeccongruent.

Thus, as Bachs Well-Tempered Preludes and Fuguillustrate the case, the social characteristic of musical ideis expressed by the principles of Well-Tempered countepoint. On this account, Classical musical performanrequires that instrumentalists impose the characteristics the bel canto-trained human singing voice on the instrments; otherwise, the attempted instrumental aspect of pformance of even Classical compositions degenerates ina mimickry of Romanticism, such as that of Liszt a

Wagner, or even modernism. Competent performers nevplay the notes of the score; the score is a mnemonic devica mere shadow of the Classical composer s intentiowhich must be back-translated into the process, the uniing thought-object, the principle, which is the intendcomposition as an indivisible single conception to be tranmitted to the audience.

Insight into these functions of Classical musical compositiderived from the natural, bel canto, characteristics of thuman singing voice, leads into insight into the cognitifunctions of the human speaking voice itself. These connetions are best explored by attention to the role of Classicforms of sung prosody in ancient through modern forms of t

poetry of sundry languages.37

Modernist compositions autterance of poetry and prose are an expression of forms decadence which have resulted in the victims critical lossthe ability to compose and utter such prosody, or even to copose the forms of spoken and written utterance required convey what Percy Bysshe Shelley identifies as profound aimpassioned conceptions respecting man and nature. Tloss of the power of intelligible communication of importaideas, has become increasingly acute in European languagduring the course of the recent forty years since the beginniof the popularization of a rock-drug-sex youth-countercture as a mode of attempted eradication of the influenceClassical culture.38

One of the notable effects of the post-1963 spread of t

so-called cultural paradigm-shift among those enteri

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36. This conception of music is that which Kepler adopted from both the impli-cations of Platos treatment of the determination of the five Platonic solidsand the treatment of the same matter by Luca Pacioli and Leonardo daVinci.

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37. Cf. the comparison of the modern Classical Italian and German modesthe bel cantohuman singing voices application to Classical song comsition. See: A Manual on the Rudiments of Tuning and Registration, BoI: Introduction and Human Singing Voice, Project Editors John Sigersand Kathy Wolfe (Washington, D.C.: Schiller Institute, 1992)

38. In decadent forms of composition, or of misreading of Classical compotions, the passion is attached to the sensual effect of the perceived ssations; in Classical composition and performance, the passionattached to the idea, the act of insight whose object lies beyond the limof sense-perception as such.


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adolescence in Europe and theAmericas during the middlethrough late 1960s, is a wide-spread impairment of the literateuse of language. Much of thisimpairment is a reflection of thedestructive impact of the rock-drug-sex youth-counterculture

on the sense of the role of musi-cality (i.e., bel canto-rootedprosody). This was aggravatedby other, coincident factors. Thelatter factors included the shift ofthis generation away from thefuture-oriented culture of earliergenerations, to the NowGenerations loss of a sense ofpersonal historical perspective.The result of that qualitativemoral down-shift in perspective,is that most of those nowbetween fifty and sixty years

of age have undergone an exis-tentialist, emotional-intellectual impairment of the cognitivepowers comparable to the synarchist cults pathologicalend of history dogma.39

This accelerating cultural down-shift of recent decades, isreflected in a loss of that power of prosody in speaking whichis rooted in the principles of Classical poetry and song, with aconsequent diminution, or even loss of the power of commu-nicating actual ideas.

The apparent exceptions to that aspect of a general culturaldecline in recent generations capacity for intelligible prosody,include the substitution of a kind of Romantic sing-song whichis mistaken by the credulous for pretty speech, a sing-song

proffered as a substitute for the quality of utterance needed toconvey the kinds of ideas typified by, but not limited toClassical scientific discovery of universal physical principles.In other words, the location of the passion is shifted fromhuman ideas, to beast-like sensations of both objects and per-

ceived monkey-equivalent moods (screaming, cooing, and soon) of other persons.40

Consider the exemplary case of the leading pro-fascist ide-ologue on the present U.S. Supreme Court, Justice AntoninScalia. Scalia is notorious for his shameless admission of hisdenial of the existence of any historically defined principles oflaw, and for his repeatedly, publicly uttered, explicit insistenceon a substitute for reason, in his Orwellian, dictionary-nom-inalist dogma of what he calls text. On that account, Scaliahas flunked the reading of even the Preamble of the U.S.Federal Constitution.

Consider, for example, the principle ofsovereignty.

The Irony of SovereigntyIt is notable that the empiricist Thomas Hobbes expressesexplicitly his own and the positivists seemingly instinctiveabhorrence of irony in general, and metaphor most emphati-cally. As I have already noted, as the central theme of thisreport, the reduction of the definition ofrational to a mech-anistic, connect-the-dots kind of description of experience,has the effect, and intention of outlawing acknowledgment ofthe existence of any reality which is not a kind ofconnect-the-dots reading of sensory experience. Charlatans such asBertrand Russell and his acolytes, such as Norbert Wiener, John von Neumann and their like, carry Hobbes satanicdogma to an extreme.

Contrary to Hobbess and Antonin Scalias implied diction-

ary nominalism, only forms of human mental behavior fairlydescribed as schizophrenic could assume that what mighthave been intended as a literal meaning of words encompass-es human knowledge. The sane use of any language begsrecognition of similarities to the Gauss-Riemann complexdomain. Words are used literally, to designate perceptions ofobject-like subjects, or perceptions of emotional impulses.

Mississippi Office of the State Auditor

Two peas in an empiricist pod: Thomas Hobbes (1588-1679) and U.S. Supreme CourtJustice Antonin Scalia.

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39. The prevalent decadence of the so-called Baby Boomer generations of(most notably Europe and the Americas), is a reflection of the combinedeffects of the 1961-1964 succession of such events as the Bay of Pigs,Cuba Missiles Crisis, Kennedy assassination, and launching of the officialU.S.A. war in Indo-China. The flight of relatively privileged strata of emerg-ing post-adolescents into the rock-drug-sex-counterculture, was merely oneof several expressions of the decadence this experience promoted amongthose recruited from numerous socio-economic strata currently in their 50sor 60s. The commonly underlying feature of the sundry is what is fairlydescribed as a special kind of cultural desensitization. The result was theassortment of expressions of flights into crude sensationalism, includingneurotic flights from one becoming boring life-style fugue into the mayflyexistence of a successor. The result, in all variations, is the common pathol-ogy of a flight from the reality of a producer society s culture to that of a con-sumerist culture. The lust for experiencing of decadent forms of cultural sen-sations, rather than ideas of the future social outcome of one s living, is thecommon feature of the decadence which grips most of those in those BabyBoomer age-categories today. The passions are diverted from the real uni-verse into the Romantic-existentialist fantasy-world of my immediate feelingexperience. The attachment of passion is shifted from the universe inhabit-ed by the human mind, to the universe of animal-like sensations, with theresult that the victim tends to act toward man as beast toward beast.

40. This use of location corresponds roughly to Sigmund Freuds notion ofcathexis.

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41. There is no room in Classical art for mere symbolism; no condoning ofsymbolism is intended, or allowed by me here.

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But, sane human speech is never simply literal; sane speechhas its own version of the complex domain. By means of ironyin general, or metaphor most emphatically, intelligent speechencompasses notions of realities which operate, like universalphysical principles, beyond the realm of literal descriptions ofsense-perception. Sometimes, the ironies are misleading, evenfalse; but, the existence of truthful ironies is indispensable fortruthful human communication of ideas, true or false.

Classical poetry, for example, is based entirely upon the basisof that higher order of intention shared between speaker andhearer.41

These subtler, higher meanings permeate the folklore of apeople, and are encountered in their more refined expressionin Classical plastic, as much as non-plastic art. Typical is thedistinction of Classical from Archaic modes of ancient Greeksculpture and the related original redefinition of perspectivefor painting by Leonardo da Vinci. Great Classical sculpturepresents the mind with a body, not as fixed, but recognizableby the mind as captured in mid-motion; the mind senses theexistence of that motion, as John Keats describes this effect inhis Ode to a Grecian Urn. This kind of art expresses princi-ples, in the same sense that the complex domain expresses

principles of continuing development in action, as the mathe-matics of Galileo, Euler, Lagrange, and Cauchy does not.Folklore and Classical art convey the sense of principles ofaction which lie beyond the comprehension of the reduction-ist form of literal statements.

Thus, intelligent communication among a people reliesessentially on those ironical, anti-reductionist meanings whichlie between the cracks of literal imageries. The introduction ofnew, principled ideas to a people, depends largely on the shar-ing of that store of such ideas within the practice of the exist-ing language-culture.

In general, therefore, it is only to the degree that a peoplehas the approximation of a Classical language-culture that it is

able to discover, and to deliberate upon new ideas. What iscalled the freedom of the individual members of a society,depends upon processes of deliberation within the societywhich are based upon the accumulation of ironies embeddedin the general language-culture of that society. Without thosefunctions of a literate form of irony-rich language, the mem-bers of a society are degraded to the functional status of virtu-al human cattle, unable to participate efficiently in shaping thecommon national destiny.

The problem on which our attention is focussed here, is thesame issue ofpassionwhich has been repeatedly referenced inpreceding portions of this report. Pause here to reflect on acommon expression of the problems involved. Focus on thefactor of irrational rage which permeates the reductionists

attempts to explain the occurrence of any phenomenon whoseexistence corresponds to a true universal physical principle (orClassical artistic compos

visualizing the complex domain

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