21 st CENTURY SCIENCE & TECHNOLOGY

Vol. 8, No.4 Winter 1995-1996

Features

22 Johannes Kepler's Mysterium Cosmographicum A Guide to the Harmony of the Mind and the Universe Ralf Schauerhammer Four hundred years later, Kepler's first work still tells us more about the solar system and human creativity than Newton or any other empiricist is capable of doing.

35 First English Translation: RIEMANN'S PHILOSOPHICAL FRAGMENTS

FOREWORD 36 Riemann Refutes Euler Lyndon H. LaRouche, Jr.

TRANSLATION 50 Philosophical Fragments Bernhard Riemann 50 Introduction to Second German Edition 50 Translator's Note 51 I. On Psychology and Metaphysics 55 II. Epistemological Issues GESAIlXELTE 57 III. Natural Philosophy MA'l'HEMATISCHE WERKE SUPPLEMENTARY MATERIAL WI8SY.NSCHAFTLICHER NAmILASs, 44 On the Hypotheses Which Lie at The Foundations of Geometry [excerpts] Bernhard Riemann 47 Riemann in English Translation 48 Euler's Lying Attack on Leibniz NACHTRAGE 52 Herbart on the Thought Process

M. NOETllER UND .... WIRTINGER

oon:R PUBUCA.TlO�S.INC. News Bernhard Riemann (7826- 7 866), with SPECIAL REPORT: THE DARWIN DEBATE title page from the second German 10 In Defense of Darwin edition ofhis works. 11 Bury Darwin-It's Overdue! FUSION REPORT 63 Tokamak Plasma Advances Made But Budget Cuts Threaten Program GEOMETRY 66 In the Footsteps of Kepler: On the cover: Two polyhedra built by Fa­ A Master Polyhedra Builder Demonstrates His Art ther Magnus Wenninger: The larger model is a perfect polyhedron with the vertices of the Archimedean icosadodecahedron, which has 30 rectangular faces and 20 per­ Departments fect hexagons. With it is a small stellated EDITORIAL VIEWPOINT dodecahedron. Philip Ulanowsky photo­ 2 5 8 NEWS BRIEFS graphed the models; cover design is by 4 LETTERS The Infamous 69 BOOKS Rosemary Moak. Delaney Clause EDITORIAL EDITORIAL STAFF

Editor-In-Chief Carol White

Managing Editor Ma�orie Mazel Hecht The Kepler Year Associate Editors David Cherry cience today is under very brutal at­ War II, but that is certainly not the root Marsha Freeman Laurence Hecht tack. The pay-as-you-go idea that all cause of the problem_ Nor even are the Carol Hugunin Sresearch must have an immed iate, prac­ openly Malthusian goals of the environ­ Rogelio A. Maduro Jim Olson tical goal means the death of fundamen­ mentalists at the root. Charles B. Slevens tal science. Then there are the myriad We could not have come to this pass Mark Wilsey environmentalist frauds promoted in the were there not a far graver problem, ex­ name of science_ Indeed, young people empl ified by the steri Ie orthodoxy of Books David Cherry today are taught pagan ideology-a res­ modern mathematical physics. Nature is urrection of the cult of the earth god­ expected to conform to a preconceived, Art Director dess Gaia-as science. If these trends axiomatically closed mathematical the­ Rosemary Moak continue, scientific inquiry will soon be orem structure, accord ing to the pre­ a thing of the past, and we will have cepts of Aristotelian logic. Advertising Manager Marsha Freeman doomed ourselves and our posterity to a At 27 st Century, therefore, while we misery and banality still unimagined deplore the present crisis in science, we SCIENTIFIC ADVISORY BOARD today. see it as an opportunity to get rid of the Francesco Celani, PhD Things were certainly better in the dead weight of the past, in order to al­ Hugh W. Ellsaesser, PhD BerthaFarfa n, MD United States of John F. Kennedy, but it low the birth of a new scientific renais­ James Frazer, PhD would be wrong to look for simple an­ sance, based upon the principles of cre­ Emmanuel Grenier swers to the question of how we got ative discovery. We commit ourselves Wilford Hansen, PhD Hideo Ikegami, PhD from there to here. One reason for the to this, in the spirit of Johannes Kepler, Lyndon H. LaRouche, Jr. institutional destruction of American who 400 years ago, in 1 S96, published Wolfgang Ullge,MD Ramtanu Maitra science today lies in the increasing bu­ his first major work, The Secret of the Giuliano Preparata, PhD reaucratization of science since World Universe_ B.A. Soldano, PhD B.P. Sonnenblick, PhD Jonathan Tennenbaum, PhD Daniel R. Wells, PhD

21st Century Science & Technology (ISSN 0895-6820) is published 4 times a year in 1995, every third month, by 21st Century Science Asso­ Those Impossible Waves ciates, 60 Sycolin Road, Suite 203, Leesburg, Va. 22075. Tel. (703) 777-7473. Address all correspondence to 21sl Cenlury, P.O. Box 16285, Washington, D.C. 20041. In the Solar Wind Second-class postage is paid at Leesburg, Va. and additional mailing offices. n July, three AT&T Bell Labs scientists th is should destroy the waves, the text­ Dedicated to providing accurate and compre­ reported their discovery that the solar books say. Finally, the solar wind even­ hensive information on advanced technologies I and science policy, 21st Cenluryis committed to wind-the flow of plasma from the tually becomes so rarefied and colli­ restoring American scientific and technological Sun-carries waves that originate in the sions so rare, that no wave could leadership. 2151 Cenlury covers the frontiers of science, focusing on the self-developing qualities vast number of vibrations or oscillations continue to propagate. of the physical universe in such areas as plasma physics-the basis for fusion power-'-as well as of the Sun itself. What is apparently But they do! biology and microphysics, and including ground­ happening is that the densities of the This is good news for solar-terrestrial breaking studies of the historical development of science and technology. Opinions expressed in various particles thrown off by the Sun science precisely because it upsets articles are not necessarily those of 21st Century have stable variations with time. That these fundamental ideas imposed on Science Associates or the scientific advisory board. is, they have a wave structure, and it the field by the Newton-Euler mindset. Subscriptions by mail are $25 for 6 issues or continues out into the solar wind. Indeed, the news continues, as of this $48 for 12 issues in the USA and Canada. Airmail subscriptions to other countries are $50 for 6 is­ This is not supposed to be possible, writing, to create excitement among sues. Back issues are $5 each ($6 foreign). Pay­ ments must be in U.S. currency. as can be seen in the comments of specialists, who express "surprise, won­ POSTMASTER: Send address changes to 21st other scientists reported below_ Accord­ der and skepticism"-in the words of Century, P.O. Box 16285, Washington, D.C. 20041-0285. ing to the textbooks, the upper atmos­ one commentator-even though they phere of the Sun is so in homogenous have yet to scrutinize those hegemonic, Copyright © 1995 that the neat patterns of the solar oscil-. fu ndamental assumptions that are im­ 21s1 Cenlury Science Associates lations would be disrupted and not car­ plicitly being challenged_ Printed in the USA ISSN 0895-6820 ried out into the solar wind_ Moreover, Presumably, the key is in the behav­ the solar wind itself is turbulent, and ior of the interplanetary magnetic field,

2 Winter 1995-1 996 21 st CENTURY EDITORIAL but certainly not in particle-particle in­ were all systematica lly higher by a factor in Physics Today in September, the re­ teractions. of 1.00078. Thomson et al. th ink the sults of Thomson et al. "are particularly So me Details factor of 1.00078 might be a conse­ interesting because they imply that the Since th is editorial is also the first re­ quence of a Doppler effect. Or, it might Sun's core and the solar wind are cou­ port of the discovery in 21st Century, be a variation in the solar cycle, since pled, although half a billion kilometers some details are in order here. In "Prop­ the two data sets were taken at different of largely turbulent plasma and 24 to 26 agation of Solar Oscillations Through points in the cycle. orders of magnitude in density separated the Interplanetary Medium" (Nature, July Charged particles from the Sun enter the solar core from where the satell ite 13), David Thomson, Carol Maclennan, Earth's magnetosphere, where they are measured the solar wind ion flux." and Louis Lanzerotti report on their best known fo r damaging spacecraft So we have a picture of these waves analysis of 1992-1 994 data from the electronics and inducing voltage surges "lasing" through the inhomogeneities of Ulysses spacecraft, with earlier Voyager in telephone and power lines. Now that the upper solar atmosphere and the tur­ 2 data as a cross-check. They find that the particles have been found to be or­ bulence of the solar wind. Additionally, the spectra of temporal variations of dered in waves, it would be useful to the waves continue to propagate even low-energy hydrogen and helium ion ask what implications th is has for the when the solar wind has become so flows coming from the Sun show very workings of nature on Earth. rarefied that, from the standpoint of sharp, distinct frequencies. percussive propagation, they Most of these waves should re­ should not. sult from g modes in the Sun, ac­ Ladbury goes further. Confi r­ cording to Thomson et al. These g mation of the results of Thomson modes are hypothetical standing and his colleagues, he writes, density waves in the Sun for "would go a long way toward es­ which gravity is said to be the tablishing their results as a truly restoring force, and which are revolutionary contribution to supposed to originate deep within space physics." the solar interior. Because waves Those are well-chosen words: with the periods predi cted for g "would go a long way toward .. .." modes have not been indepen­ Because to fu lly establ ish these dently detected on the Sun with results as a revolutionary contri­ any certainty, such solar g modes bution, the implicit falsification of the Newton-Euler model of remain hypothetical. SOHO, the Solar and Heliospheric Observatory, percussive causality, in favor of The three scientists thus could launched in December, will probe the Sun's oscilla­ the physics of Kepler, Leibniz and not link the ion waves they have tions and the solar wind. found in the solar wind to phe­ Riemann, would have to be taken nomena in the Sun at present, and so The Commentators to heart and carried into all related they pursued a flanking strategy. p While these results are exciting be­ fields, including the study of climate waves, for which pressure is said to be cause they send the textbook out the and weather. Lyndon LaRouche's arti­ the restoring force, are abundantly seen window, it is also encouraging to see cle, "Riemann Refutes Euler" (page 36), on the Sun with optical telescopes by that scientists recognize that conse­ speaks to this issue. helioseismologists. These p waves have quence and at least some of them seem The Next St eps periods of 4 to 20 minutes (frequencies to accept it. In a commentary on the There may be an early confirmation of 1,000 to 5,000 microhertz), while findings in the same issue of Nature, of the thinking of Thomson et al. with the expected periods of g waves range Douglas Gough of the Institute of As­ respect to the so-called g modes. from 40 minutes to a few days (frequen­ tronomy at Cambridge University SOHO, the European Space Agency's cies of less than about 400 microhertz). writes, "The discovery is amazing in the Solar and Heliospheric Observatory Thomson et aI., therefore, sought to light of current thinking about the solar launched December 2, may be able to find a clear link between these p waves wind, because such thinking is based detect these solar oscillations that are and those particles in the solar wind on the idea that the temporal variation predicted by the Thomson paper. that should be coupled with them. is predominantly the consequence of SOHO's 12 instruments, together These particles turn out to be energetic turbul ence, which has a relatively with those of the continuing Wind pro­ electrons. smooth spectrum." ject, and the new ground-based net­ Would the frequencies of the ener­ Gough also ind icates the other side work of helioseismology telescopes getic electrons, as detected by Ulysses, of the same coin in pointing out that called GONG (Global Oscillation Net­ be the same as the frequencies of the "more or less everyone has always as­ work Group) promise major discoveries known p modes? Of 118 frequencies sumed that any seismic disturbance in the ordering of the solar-terrestrial re­ between 1,588 and 4,200 microhertz, propagating through the chromosphere lationship. 90 matched to within 1.2 microhertz. into the corona would be washed out However, if the results are to be co­ This is the really sign ificant and fascinat­ by the substantial inhomogeneities in herent, the revolution in assumptions ing finding reported by the three. the upper solar atmosphere." referred to above is a necessary com­ Strangely, the electron frequencies In the words of Ray Ladbury, writing plement to the advances in technology.

EDITORIAL 21 st CENTURY Winter 1995-1 996 3 factors control the movement of ozone in the stratosphere. We don't know what part of the thinning is due to natural dy­ namics of the atmosphere and what part is due to the destruction of ozone by man-made chemicals. We don't know Letters much of anyth ing.. ..We've confused computer models of the atmosphere with the real thing. We're making huge Nobel Extrapolators? extrapolations based on nothing but models, and models are often wrong" This letter was sent to Chemical & En­ (The New York Times Magazine, March gineering News in response to its Oct. 9, 13, 1994, pp. 36-39 ). 1995, editorial attacking those who I have a question. On what criterion questioned the ozone depletion "con­ was the Nobel Prize awarded to sensus." It is printed here with permis­ Crutzen, Mol ina, and Rowland? sion of its author, Hugh W. Ellsaesser, (All quotes without attribution are PhD., who is a participating guest scien­ from the Executive Summary of the tist at the Global Climate Research Divi­ World Meteorological Organization's Nora Hamerman sion of Lawrence Livermore National Scientific Assessment of Ozone Deple­ Perin del Vaga 's 16th-century painting, Laboratory. Ellsaesser's article, "A Ratio­ tion, 1994. ) directly under Archimedes in Raphael's nal View on Stratospheric Ozone: The Hugh W. Ellsaesser "School of Athens," shows Archimedes Unheard Arguments, " appeared in the Livermore, California dra wing as he is about to be killed by a Fall 1994 issue of 21st Century. Roman soldier.

To the Editor [o f C&E News]: EUREKA! It's Not Euclid lieved to be Archimedes. This is attested In response to your editorial of Oct. 9, To the Editor : to by the image that Perin del Vaga, a may I present a few facts about stratos­ The handsome cover of your Fall pupil of Raphael, frescoed at that time pheric ozone. 1995 issue, headlined "Eureka! Red is­ directly under the geometry group for The original Rowland/Molina theory covering the Method of Archimedes," the "basement"-part of the walls up to predicted the major destruction of ozone shows a large detail of the right-hand the height of the doors, where the origi­ by chlorine would be at about 40 km. side of Raphael's famous fresco of nal decoration had been destroyed dur­ Observations show some decline there 1509, usually called "The School of ing the Sack of Rome in 1527. but generally less than that predicted; Athens." Some readers who are familiar Some years after I first read Oberhu­ this is described as "broad agreement." with the work, often reproduced, might ber's explanation, I happened to visit the Formation of the Anta rctic ozone be puzzled, however, that the bald man Stanza della Segnatu ra in the Vatican hole, which occurs between 12 and 22 drawing on a slate with a compass, Palace where the mura ls are, and km, was not predicted. who clearly represents Geometry, is snapped a photo of Perin del Vaga's Observations "show that much of the called "Archimedes." This figure, painting. The subject is unmistakable: It downward trend in ozone occurs below whose garment was signed by Raphael shows the aged Archimedes as he is 25 km"; therefore, this also was not pre­ with his own name, is almost always about to be killed by Roman soldiers in dicted. called "Euclid" whenever the picture is Syracuse, while drawing circles on the Models including the chemistry in­ published. ground. [See photo.] volving sulfate aerosol and polar stratos­ The correct identification of this figure By the way, Archimedes was greatly pheric clouds "sti II u nderesti mate the is due to Konrad Oberhuber in the 1972 admired in Platonic circles in Rome in ozone loss by factors ranging from 1.3 book, II cartone per la Scuola d'Atene, the early 16th century, because he com­ to 3." published in Milan by Silvana Editori. bined mathematical theory with physical As NASA's Dr. Robert Watson, orga­ Dr. Oberhuber, one of the leading schol­ applications, particularly in the defense nizer and director of the Ozone Trends ars of Renaissance art and especially of of the state-a timely issue in the turbu­ Panel, told Science, "[our ozone] mod­ Raphael, pointed out that few of the lent times when Raphael lived. (Archi­ els do not predict that ozone decreased identities of the personages in the paint­ medes was supposed to have invented the way it did over the Northern Hemi­ ing are known with certainty, apart from the "Greek fire," which the Syracusans sphere during the past 17 years" (Sci­ the central figures of Plato and Aristotle used to fight the Romans and other ene­ ence, Vol. 239, p. 1489, 1988). (not shown in your detail). mies. ) As Harvard's Professor Jim Anderson Accord ing to Oberhuber, the idea that Nora Hamerman to ld The New York Times Magazine: the geometer is Euclid did not appear in Leesburg, Virginia "The th inning of the ozone layer over print unti l it was suggested in 1864 by other parts of the Earth is accelerating, an English writer. However, it is known Mrs. Hamerman, an art historian, is and we don't know why, and we don't that during the papacy of Paul III, who senior editor of Executive Intelligence know how fast. We don't know what reigned 1532-1 547, this figure was be- Review.

4 Winter 1995-1 996 21 st CENTURY LETTERS VIEWPOINT

The I nfamous Delaney Clause

ne of the primary instruments evaluating cancer risk to humans? used by environmentalist groups The test animals are routinely fed toO attack food producers, food proces­ "maximum to lerated dosages." This sors, and food consumers has been the means that any increase in the Delaney Clause of the Federal Food, amount of the chemical ingested Drug, and Cosmetic Act. This year, would rather quickly result in death Congress has an opportunity, in pend­ because of the cessation of normal ing legislative bills, to clarify the infa­ body functions unassociated with car­ mous clause and make its application cinogenicity. Also animals ingesting scientific rather than political. such massive doses often can barely In 1958, Representative James J. De­ by Dr. J. Gordon Edwards stay alive, and the dosage frequently laney entered a clause into the food causes the death of body tissues. As a additive provisions of the Federal is not possible to experimentally de­ result, there is a proliferation of new Food, Drug and Cosmetic Act (21 termine human carcinogenicity cell divisions, during which numer­ USCS 348) intended to permit only caused by food unless long-term, ous mutations naturally occur, and toxicologically insignificant amounts strictly regulated tests are carried out. the chances of spontaneous tumors or of additives in the food supply. Both In such tests the activities of a large cancers are also increased. Those mu­ Congress and the Health, Education, number of nearly identical, same-sex tations are scarce in normal tissues, and Welfare Department construed humans, exposed to the same food, but occur much more often during the Delaney Clause as specifying that drink, lifestyles, and other factors abnormally rapid cell proliferation. an insignificant amount of chemicals, would have to be monitored and Even more important, the data from including carcinogens, could be strictly controlled. Very high doses of those experiments cannot be extrapo­ legally permitted in human foods. a single test chemical would have to lated to humans living normal lives! They did not interpret the clause to be given daily to half of the experi­ How the EPA Redefined Cancer mean that "zero" amounts of chemi­ mental humans, but never to the oth­ When Rep. Delaney proposed his cals were required. ers (the controls). clause, the prevalent medical defini­ Section 408 of the act requires that Only after months or years of such tion of cancer was that it was a malig­ raw foods or produce conform with testing could it be reasonably hypothe­ nant, invasive growth that expanded tolerance levels establ ished by the sized that the high doses of that chem­ rapidly, frequently metastasized Federal Food, Drug, and Cosmetic ical might have been responsible for (spread to other organs and tissues), Act. If the levels are higher than the cancer formation in the "test humans," and might quickly kill the host. Tu­ permitted legal tolerance, the raw food but only if that type of cancer did not mors, on the other hand, were is considered adulterated and cannot also develop in the "control humans" swellings or lumps, some of which be sold. in the experiment. Such tests have might become malignant, but most Section 409 deals with the inten­ never been performed, and obviously would not. In experiments, tumors of­ tional addition of chemicals to never can be performed, on humans ten disappeared completely after the processed foods, as preservatives, in this country; therefore, that part of massive overdoses of test chemicals dyes, and so on. This section includes the Delaney clause is meaningless. were halted. the Delaney Clause, which states: "No However, the same sentence in the In October 1975, attorney Russell additive shall be deemed to be safe if Clause continues with "... or if it is Train, the administrator of the EPA, re­ it is found to induce cancer when in­ fo und, after tests which are appropri­ defined the medical term "cancer," ar­ gested by man or animal, or if it is ate fo r the evaluation of the safety of bitrarily seeking to make "tumor" and found, after tests which are appropri­ fo od additives, to induce cancer in "cancer" synonymous. He stated, "For ate for the evaluation of the safety of man or animals. " This might provide a purposes of carcinogenicity testing, no food additives, to induce cancer in method of actually reaching accurate distinction should be made between man or animals." conclusions, but it is necessary to the induction of tumors diagnosed as Inducing Cancer specify what animal tests are appropri­ benign and the induction of tumors di­ The first part of the Delaney Clause ate, and there has never been any agnosed as malignant." Under Train, ("No additive shall be deemed to be broad scientific agreement on that. safe if it is found to induce cancer Can doses thousands of times J. Gordon Edwards is an emeritus when ingested by man .. ..") is greater than those animals ever en­ professor of entomology at San Jose meaningless because it cannot be counter outside of laboratory cages be State University in Ca/rfornia, where carried out adequately. Obviously it considered appropriate for accurately he has taught fo r 46 years.

VIEWPOINT 21 st CENTURY Winter 1995-1 996 5 SAVE YOUR COPIES OF tists that most of the rats used in such experiments have been deliberately 21st CENTURY reared as cancer-prone strains, which These custom-made titled cases and binders are ideal to protect develop cancer extremely easily. your valuable copies from damage. Obviously, such tests are not "ap­ They're designed to hold two years' issues (may vary with issue sizes), propriate fo r the evaluation of the constructed with reinforced board and covered with durable leather· safety of food additives to induce can­ like material in blue, title is hot­ sl4mped in gold, cer in man or animals," as requ ired by cases are V·notched for easy access, the Delaney Clause. Representative binders have special spring Delaney later stated that "too many mechanism to hold individual egos, reputations, and careers are at rods which easily "The court finds you guilty as charged un­ stake; if you try to change things, the snap in. der the Delaney clause, and sentences you BINDER crazies just come at you with blow­ to banishment from the shelves!" torches and chain saws." Russell Train, ca_: 1-$7.95 3-$21.95 8-$39.95 who later became the head of the Binders: 1-$9.95 3-$27.95 8-$52.95 the EPA could consider harmless tu­ World Wildlife Fund, knew the conse­ 21 st Cenlury Science & Technology Jesse Jones Industries. Dept. 21 C mors as cancers and thus subject to the quences of his redefinition of cancer, 19134 199 Easl Erie Ave .. Philadelphia. PA provisions of the Delaney Clause. and made no effort to hide his convic­ Enclosed Is $ for __ Cases; __ Binders. Add $1 per caselbinder for Scientists disagreed with this tion that pesticides should be banned. postage & handling. Outside USA $2.50per easel binder (US funds only). PA residents add 6% sales change. For example, the Council for Natural Pesticides tax. Print Agricultural Science and Technology, As analytical techniques became ______Name, a consortium of more than 30 scientific more sophisticated, making it possible AddreSS' organizations, observed in its study of ___""N""O P"" . O" . Bo""x"'N""um""be'::.."'P:;:' ....:,-. ::-- --- to detect smaller and smaller levels of

City______the Delaney Clause, "Classifying as chemicals, scientists had an add itional carcinogens all chemicals that cause reason to worry about the potential for StatelZlp,______CHARGE ORDERS (Minimum $15): Am Ex, Visa, tumors ...greatly overestimates the misapplication of the Delaney Clause. MC, DC accepted. Send card name, *, Exp. date. 'cancer' risk." Charles C. Edwards, commissioner of CALL TOLL FREE 7 days, 24 hours 1-800-825-6690 Further criticism came from other the Food and Drug Administration in ___ SATISFACTION GUARANTEED ___ scientific groups and even from the 1972, said, "An all-or-nothing law EPA's own researchers. The American (like the Delaney Clause) should be Counci I on Science and Health re­ more flexible, allowing safe levels for ported in 1991 that "sound toxicologi­ use of additives in human food ." He Coming in cal principles are routinely flouted in also stated, "It is now possible to de­ lab rodent tests on behalf of govern­ tect very tiny amounts; thus the De­ 21st CENTURY ment agencies, and the results are fre­ laney Clause could be interpreted to quently inappropriately extrapolated requ ire banning animal and plant SCIENCE & TECHNOLOGY to humans." Toxicologists affi liated products containing natural carcino­ with the council also pointed out that gens, and a strict interpretation could • The Fraud inModern Physics "a rat is not simply a small human." even require banning certain essential The two species are phys iologically human nutrients."

• What the Suppressed Works of very different; thus they react differ­ Some chemicals, such as selenium Gauss and Weber Reveal ently to chemicals. and Vitamin A, are anticarcinogenic Rats, for example, which have been at low levels, but may become car­ the most common test animals, pro­ cinogenic at higher levels, indicating • Kepler in China duce a special protein (Alpha 2U that there are definite thresholds in­ Globalin) that makes them especially volved . (A threshold is the dose of a • Ancient Chinese Astronomy prone to develop tumors and cancers. chemical below which effects do not In 1991, the EPA pointed out that hu­ result.) "Carried to its logical ex­

• Climate Models Model Ideology mans lack this protein, which in fact treme," warned Edwards, "the De­ "could invalidate thousands of tests of laney Clause would ban all food con­ pesticides, preservatives, additives, and ta ining such carcinogenic environ­ • Environmentalism's other chemicals that have been banned mental contaminants as traces of ra­ Disease Death Toll on the basis of producing tumors in dioactive material," which all living rats in laboratories." Those tumors, the things naturally contain.

• The Herschels' Revolution in EPA spokesmen said, "are a species­ The issue of natural pesticides is not Astronomy specific effect," and "are not relevant trivial. Dr. Bruce Ames, head of the to human risks from those chemicals." Biochemistry Department at the Uni­ It is also troublesome to many scien- versity of Californ ia, pointed out in

6 Winter 1995-1996 21 st CENTURY VIEWPOINT carcinogenic activ­ ��.. Stal.mentofOwne...... 1P.M.n.g. m:!:!.."!���= THE DELANEY CLAUSE ity would have ��""'YSc i",.. POll r time. I year Tocb"'+hl:I'I'I.j.I'IQI•::� $16 . 75 l.."" been detected if _ - 4. higher doses had 60 SycoUn Road, SII.1te 20], t.elubuE"9. VA a2015

been applied" (em­ PO Box 16285, W.lhlngton. DC 20041 phasis added). :nat Century Sci.nc...... oct.t •• OSHA also stated Carol Wh t.4; ..l22fl PO � Box 16285 that "an assay that w:� !2A� is not positive fo r --m�W�c::PO Box lun WOIblnston pc?P°t! carcinogenicity is the same as if the chemical has never ----­ ._- been tested for car­ ._ .._--- cinogenicity." Rely- ';;"=�-- 16.24& 16,101 ... - .._------'" ing on these inter- ._- - - - � _ .. , ,,-,- 21).'39 19,145 '------... ------' pretations, OSHA . -�-...... - " - -- -- l.1H 3.700 any ... . 1987 that "we are ingesting in our diet could condemn chemical it '.161 3.729 at least 10,000 times more, by weight, wished to attack, again using the De­ 2.400 of natural pesticides than of man­ laney Clause as a weapon. - =''i,...

made pesticide residues." Ames also In 1988, the EPA sought to make the . __ ... " -,,-,- n.OOQ 26,000 -----­ noted that edible plants often contain Delaney Clause more reasonable by " .." ... - natural pesticides making up 5 to 10 permitting insignificant, harmless percent of the plant's total dry weight, amounts of pesticide residues in and that many of those tested proved processed foods. (This is referred to as to be carcinogenic. . the de minimis standard.) Environmen­ It is a fact that an abundance of nat­ tal extremists, bent on removing all urally occurring carcinogens is present pesticide traces from food products, in most foods, including meat, pota­ challenged that interpretation. In 1992, toes, berries, and fru it. They also the environmentalists, supported by abound in the liqu ids we drink. How the 9th Circuit Court of Appeals in San should we consider the thousands of Francisco, destroyed the EPA's efforts natural carcinogens that have been to proceed rationally. Evidently the added by the plants we eat? Those tox­ members of that court had again ne­ ins protect the plants from their ene­ glected to read the Delaney Clause or mies but are not food for the animals to review the findings of medical sci­ that eat them. entists and toxicologists! In food for human beings, these The U.S. Supreme Court declined to same chemicals may qualify as envi­ hear appeals by scientific and agricul­ ronmental hazards. Should these nat­ tural groups in this case. Perhaps the ural environmental hazards, nearly half Supreme Court intended to force Con­ Did you miss of which are potential carcinogens, be gress to accurately define "cancer," to something? subject to regulation under the De­ specify what laboratory tests for car­ laney Clause? As a result of biased in­ cinogenicity will be considered appro­ Back issues of terpretations of that Clause, food addi­ priate, and to acknowledge the lack of tives have been defined in a manner val idity of extrapolations from mega­ 2ptCENTURY that (1) includes many harmless syn­ dosed, cancer-prone laboratory rats to SCIENCE & TECHNOLOGY thetic chemicals that are legally pre­ humans who ingest concentrations of are available at $5 each sent in meat, vegetables, fruits, and li­ chemicals thousands of times lower bations, but (2) does not include the than the doses fed to the rats. ($6 foreign). naturally occurring environmental tox­ Such congressional actions might re­ U.S. CUlTency only. ins or carcinogens that are added by sult in the demise of the Delaney To receive the index for volumes the plants we eat! Clause and the establ ishment of hu­ 1-7, send a self-addressed enve­ From Bad to Worse man food safety guidelines based on x In a 1980 policy statement, the u.s. science rather than politics. Represen­ lope (9 12) with 78<1: postage Occupational Safety and Health tative Delaney was unfortunately cor­ to: Agency (OSHA) specified that "nega­ rect when he said that he would prob­ 21st Century tive results in carcinogenicity bioassays ably go to his grave "with that damned P.O. Box 16285 simply define a limit beyond which thing hanging around my neck!" Washington, D.C. 20041

VIEWPOINT 21 st CENTURY Winter 1995-1 996 7 NEWS BRIEFS

HOUSE HEARINGS CHALLENGE SCIENCE MAFIA ON OZONE, CLIMATE Congressional hearings on ozone depletion and on climate models, sponsored by the House Committee on Science's subcommittee on energy and environment, held Sept. 20 and Nov. 16, made it clear that the ban on chlorofluorocarbons (CFCs) is determined by pol itics, not science; that climate models known to be faulty were used to determine international policy; and that the science establishment is willing to act like a gestapo to prevent scientific dissent on environmental policy. Subcommittee chairman Dana Rohrabacher (R-Calif.) convened both hearings un­ der the title "Scientific Integrity and Public Trust: The Science Behind Federal Poli­ cies and Mandates" and invited both sides of the issues to testify. The ozone hearings were particularly vituperative. The airing of the main scientific arguments against the "The public has been misled, bamboo­ ozone hoax provoked some congressmen and administration spokesmen to attack zled, and otherwise manipulated, " Or. those scientists who disagreed with the "consensus" view as "fringe," "irresponsible," S. Fred Singer told Congress. Here, he and "without standing in the scientific community." chats with Rep. Rohrabacher (center) Dr. S. Fred Singer, head of the Science and Environmental Policy Project and an and Rogelio Madura (left), author of the emeritus professor of environmental science at the University of Virginia, and Dr. book The Holes in the Ozone Scare. Sallie Baliunas, an astrophysicist, came under particular fire. Baliunas testified that she had almost pulled out of participating in the hearing that morning because of the ongoing threats to her and her employer. She also told the committee that she was warned not to pursue lines of research that might show the ozone depletion theory to be wrong, because her institution might lose federal and other funding. Baliunas's testimony is available from the Marshall Institute (202) 296-9655; Singer's testimony is available from SEPP (703) 934-6940. Hearings in November on the validity of the global climate models were less stormy, but the same arguments were used to maintain that the global warming sce­ nario is correct simply because, allegedly, "the overwhelming majority of scientists" THE DENGUE EPIDEMIC IN agree that it is. SOUTH AMERICA

Brazil 112,939 GERMAN SPECTROMETER PRODUCES GLOBAL OZONE MAP IN 3-D Colombia NA A new German spectrometer called Crista, deployed on the u.s. Space Shuttle in Ecuador 1994, has produced the first high precision, 3-dimensional global map of ozone, an­ Peru nounced researchers from the University of Wuppertal, who designed the instrument. The ozone layer is a patchwork of large- and small-scale structures and not a uniform longitudinal phenomenon, the researchers said. Crista's preliminary results show that the currently accepted ozone models are "junk," they said at a Nov. 6 press confer­ ence. More details will appear in the next 21st Century.

SPREAD OF UNCONTROllED EPIDEMICS THREATENS WORLD POPULATION Top medical experts convened at the 25th anniversary meeting of the National In­

Puerto Rico stitute of Medicine painted an alarming picture of emerging and reemerging diseases Dominican Republic 1,252 Oct. 16 at the National Academy of Sciences in Washington, D.C. AIDS, Ebola virus, English Caribbean 282 tuberculosis, bubonic plague, yellow fever, dengue fever, cholera, and diphtheria Total 190,554 were among the diseases discussed. The presentations stressed that existing vaccines and antibiotic treatments are fai ling to deal with these diseases, and that the surveil­ Dengue and dengue hemorrhagic fe ver, lance networks and laboratories to study the emergence and spread of epidemics and a fo rmerly conquered disease, has in­ ways to combat them have been dismantled. creased as a direct result of the collapse Two weeks earlier, the World Health Organization announced the creation of a of mosquito control programs in the Division of Emerging Diseases, and a WHO delegation testified on the situation be­ past two decades. U.S. health officials fore Congress Oct. 18. "The recent outbreaks have shown that the potential of epi­ are concerned that the epidemic can demics is now vastly increased by the speed by which they are able to spread [and] easily spread here. by the unprecedented size, concentration, and mobility of populations," warned a WHO press release. Source: Countryreports to the Pan·American Health Organization, Oct. 25, 1995. 21st Century will report on the situation in the spring issue.

8 Fall 1995 21 st CENTURY NEWS BRIEFS BLUE RIBBON PANEl CALLS FOR BURNING SURPLUS WEAPONS PLUTONIUM A panel of international experts convened by the American Nuclear Society urged Protection the burning of surplus weapons plutonium as fuel for civilian power reactors in the United States, Russia, and other countries. The blue ribbon panel issued its report on and plutonium management in August. Burning plutonium as fuel is the fastest and most effective way of disposing of surplus weapons plutonium, the report says. The panel Management also recommended that the United States reverse its decision to stop work on repro­ of cessing and on 'breeding nuclear fuel. "Plutonium is a valuable energy resource, not a waste material to be buried," the report said. In addition, the report said that the de­ Plutonium veloping sector should not have "to forgo the benefits of abundant energy that the in­ dustrialized world has enjoyed for many decades" and that there is "no need for in­ ternational uniformity" in how individual countries configure the nuclear fuel cycle. The panel was chaired by Dr. Glenn T. Seaborg, who discovered plutonium, and included former government officials, weapons and disarmament specialists, and in­ ternational nuclear experts. Copies of the report are available at $20 from the Ameri­ can Nuclear Society in LaGrange Park, III., (708) 352-661 1. AmericanNudear Society Special Panel �

CHINESE TO RECONSTRUCT GERMANY'S ASDEX FUSION REACTOR The ANS report also called fo r the safe Frankfurter Allgemeine The German daily reported Nov. 29 that a team of Chinese storage of surplus weapons plutonium engineers was dismantling the German fusion test reactor ASDEX in Garching, in or­ in the short term under the "strict non­ der to reconstruct it at the South-Western Institute for Plasma Physics in Leshan, proliferation safeguards" of the Interna­ Sichuan province, where China is improving its biggest fusion research facility. tional Atomic Energy Agency.

CATATOMIC SOCIETY FOUNDED IN JAPAN FOR NUCLEAR CAT LOVERS Cat lovers who work in the nuclear community now have their own association. As reported in the Nov.-Dec. issue of the American Nuclear Society News, the Catatomic Society was formed by Prof. Yoshitsugu Mishima, professor emeritus at the University of Tokyo. Its first meeting in April drew 40 cat lovers, and the group rapidly became international. Membership is $20 and members receive a pin with the society's logo-a picture of a cat's face within the atomic nucleus. For more infor­ mation, contact Mishima at the University, 3-30-1 1 Matsunoki, Suginami-ku, Tokyo.

ACT OF CONGRESS TO END OBSTRUCTION OF MT. GRAHAM TELESCOPE Arizona Congressman James Kolbe plans to attach a rider to a suitable federal bill that will clear the way for the University of Arizona to build the Large Binocular Telescope on the best known site. Kolbe hopes to have the rider pass both houses by the Christmas recess. Construction at the telescope site has been halted since July 1994, when a federal District Court granted an injunction to 18 green groups on a technicality, requiring environmental studies for several more years. The rider would void the injunction. Arizona's congressional delegation unanimously supports the rider, and letters and resolutions asking for congressional action have come from towns and counties throughout southeastern Arizona, state legislators from the south­ ern part of the state, the governor, the speaker of the Arizona house of representa­ tives, and president of the state senate, among others. The state's major newspapers are also supporting the telescope in editorials. Stuart LewisiEIRNS BIOTECHNOLOGY INDUSTRY GROUP LAUNCHES INFORMATION CAMPAIGN Carrots with improved taste, texture, The Biolotechnology Industry Organization (BIO) launched a campaign to acqaint and shelf life; sweet, seedless minipep­ the public with the science of biotechnology Sept. 12 at the National Press Club in pers; and pizza made with a genetically Washington, D.C. BIO represents 560 biotechnology companies and organizations modified processing tomato were in 47 states and 20 countries. In addition to releasing a guide for editors and re­ among the biogenetically engineered porters on the major uses of biotechnology, BIO served biogenetically engineered products served at the BIO press confer­ food. For information, contact BIO, (202) 857-0244. ence.

NEWS BRIEFS 21 st CENTURY Fall 1995 9 t wo uld be incorrect to establish the I scientific paradigms for the 21 st cen­ tury using 18th and 19th century views as the only available data. This anachronous approach, however, is a main line of Carol Hugunin's paper, "It's Time to Bury Darwin and Get On with Real Science." The readers of 21st Century deserve a more up-to-date, more balanced presentation of Darwin's theory, which is still a cornerstone of modern biology. The critique of Hugunin's article that fo llows is the least that may be done. It looks as if the article appeared miraculously from a time capsule, where it lay for a century. One hundred years ago it could have been a state-of-the-art presentation of current topics in science and philosophy. Now it is, for the most part, just a zombie of 19th century dilemmas over Darwin and the German idealist-or even older-pre-evolution­ ary trends in natural philosophy. The au­ thor seems to have missed more than a century that has passed since. Virtually no current views are pre­ sented to support the main thesis, and the reader is left to accept the intuitions of Darwin's contemporaries as if they were ultimate authorities. I, personally, would doubt if the naturalists quoted would still adhere to all of their opinions, were they able to confront them with the current state of paleontology, genetics, evolutionary biology, and so on. Who knows what von Baer would think, for example, after reading Stephen Jay Gould's books and checking them against the raw data in technical jour­ nals? It is just as anachronous to set sci­ entific paradigms for the 21 st century us­ analysis of the current state of knowl­ ural origin of life. ing 19th century naturalists as the only edge as the title implies. I wonder how such sophisticated math­ experts available, as it is to offer readers Crypto-creationism ematics (or its mutations, like Fred a map showing Alexander von Hum­ Calling support from outdated sources Hoyle's "randomly assembled jumbo jet boldt's route of 1829 into the Soviet is however, not the only flaw in the au­ from a junkyard") can be seriously quoted Union via Leningrad and Gorki-a trip thor's reasoning. Many important scien­ in an apparently scientific journal. made decades before Lenin and Maxim tific points are misrepresented, usually in This kind of calculation of ex post Gorki were born and a map printed a "crypto-creationist" way, that is, never fa cto probabilities has been refuted long years after the Soviet Union ceased to explicitly denying the existence of evolu­ ago. One can find a popular example in exist [po 35]. tion, but using Creationist arguments The Blind Wa tchmaker by Richard The whole article is out of time. I am against Darwinism. Dawkins, for example. In the case of op­ not inclined to debate with 19th century (1) Chance and Random Changes tically active organic compounds, usu­ opinions, as such a belated refutation The author quotes calculations show­ ally both enantiomers (d issymmetrical would be unfair to the long-dead oppo­ ing almost zero probabilities of getting a forms) are produced randomly by chem­ nents. Many of their views were both molecule of optically active protein and ical synthesis. The fact that in living novel and scientific at their time. Most of proceeds to proclaim that "life could not things only one geometrical version is the paper is an interesting historical possibly have begun without bringing in found results simply from the fact that sketch of the development of 19th cen­ miracles from the outside." This is a typi­ most chemical reactions are catalyzed tury natural sciences, rather than an cal Creationist argument against the nat- Continued on page 12

10 Winter 1995-1 996 21 st CENTURY SPECIAL REPORT lowed to rapidly develop new and better ideas, leading to new and better tech­ nologies, inexpensive and un limited en­ ergy sources, more nutritious food, rapid advanees in med icine, and higher stan­ dards of living/ why would anyone bow dowlil to political power? Why would anyone kowtow to the brutish sort of po­ litical power that says, "I have a persua­ sive group of paid thugs, I have money, I have control of what is printed in text­ books and the press, and you will do as I say"? Why wouldn't we just laugh at such characters and put them in mental institutions? However, if future students are taught only ideas that are confusing and sterile, they will be less able to produce better teehnologies and higher I ivi ng stan­ dards. In this ' situation, everything be­ comes 'scarce, and that wealthy brute can continue to maintain power, by hoarding and speculating on food and on raw materials. And so, we, gullible humans that we are, are duped and intellectually inca­ pacitated by our lack of knowledge of the history of epistemological fights in science. In this regard, it is useful-and, in fact, essential, to look at what other scientific currents thought about evolu­ tion, during the period that Darwin was formulating his ideas. A Malthusian Swindle A look at the history of the period when DarwiA wrote shows that a Malthusian political-social thesis was pmjected iAto the realm of the evolution of life. In other words, the biological sci­ ences were swindled-forced into a po­ litical fram�w(:)rk. Darwin openly admits this. In his di­ ary entry dated October 1838, .he says ------EDITOR'S NOTE ------that he borrowed his hypothesis directly Carol Hugunin's article, "It's Time to Bury Darwin and Get On with Real from Thomas Malthus, a proponent of Science, " which appeared in the Spring 1995 issue (p. 32), provoked many re­ specific eugenics "solutions" to prob­ sponses. We print here, along with Hugunin's response, the comments of pale­ lems of England's poor, solutions later ontologist Ka rol Sabath, who is writing his doctoral dissertation on dinosaurs at codified as England's Poor Laws. Dar­ the Institute of Paleobiology of the Polish Academy of Sciences in Warsaw. win applied this to his biological data from the voyage on the HMS Beagle. lhe original title of Darwin's 1859 opus arol Sabath's critique of "It's Time to also political; in the bro.ad sense, it con­ was Ofigin of Species by Means of Nat­ KBury Darwin And Get On with Real trols the way the next generation will ura!'Selection, or the Preservation of Fa­ Science" is most interesting in terms of think. Not only is the factual content and vored Races in the Struggle fo r Life. his erroneous assumptions. the methodology of science textbooks Malthus, in turn, had taken his thesis First, it is a myth that science is apolit­ political, so also is the selection of thesis on carrying capacity from the Venetian ical. The funding for scientific research projects for graduate students. monk Giammaria Ortes.1 The Venetians is political. The determination of which Now, one may ask, why would politi­ were the ones who would do anything, scientific ideas are presented to naive cal forces be interested in controlling even pirating and selling their fellow Eu- undergraduate and graduate students is science? If the human species were al- Continued on page 13

SPECIAL REPORT 21 st CENTURY Winter.. 1 995" 1 996 11 Continued from page 10 by enzymes, which have shape-specific active sites. Thus, using racemic (mixed) versions of each biological compound would ne­ cessitate doubling the number of en­ zymes encoded in the DNA of each or­ ganism, which would be both redundant (duplicating each metabolic pathway) and stretching the chance cal­ culation even further toward zero (two meaningfu l sequences of DNA would be necessary for each active molecule, and the probability of getting such a pair each time a new metabolic func­ tion arises is much, much smaller than fo r a single gene).' The question of the nature of the uni­ verse (or at least whether it is entropic or not) is better left to astrophysicists than to Darwin. Anyway, it seems to me that Hugunin believes that the universe is nonentropic and nonrandom with only local entropy. It is worth noting that the consensus among scientists is just the opposite: The whole universe is Author Karol Sabath with the first skull of T. rex at the American Museum of Nat­ entropic (the Second Law of Thermody­ ural History in New York City. namics), and organisms (as well as the whole biosphere) are only local negen­ links. The author quotes the evolution of tween subsequent forms.3 tropic open systems (at the cost of en­ horses to prove this. She states that there Nor is it true, as claimed in a caption ergy from outside, of course, and only are only six stages in th is lineage, "start­ [The Evolution of the Horse, p. 44], that for a finite time). ing with Hyracotherium and Eohippus in "If evolution followed the linear model The development of man is not espe­ the Eocene period, but each intermedi­ of Darwin, the evolutionary path of the cially "sudden" and thus mysterious. If ate stage appears abruptly." At least this modern horse would not look like a we look at the measurable characteris­ is not only philosophical rhetoric, but complex tree with many branches ... . tics, like cranial capacity, we can see some facts. Instead it would be a straight line.. .." that during the last 4 million years ho­ And what do we see? First, that the Darwinian evolutionists use the tree as a minid brains have approximately dou­ author is as well trained in paleontology good model of phylogenetic pattern. Lo­ bled in volume (from ape level of about as she is in the history of Victorian sci­ cal populations encounter varying local 600 ml to about 1,400 ml in humans; ence. The Eocene is not a period, but an conditions; somewhere a random muta­ part of the increase is simply the result of epoch of the Tertiary period. Hyra­ tion appears that is absent in other changes in body size from australop­ cotherium and Eohippus are not two ani­ groups, and so on. ithecines to modern man). mals but one; Eohippus is a junior syn­ Thus the local populations begin to Such a doubling is hardly a miracle. In onym for Hyracotherium. And there are diffe r, and are transformed into new vari­ modern human populations the· largest only six separate stages in the classical ations, subspecies, species, and subse­ brains are twice as big as the smallest 19th century diagram by O.c. Marsh, of­ quently genera-shown as branches on ones (both being functionally normal). ten reproduced in textbooks. the picture. Some of them die out as the The average brain-size increase (or But if someone tries to change para­ conditions change, some migrate and cephalization increase, to use Dana's digms of the whole of modern natural give rise to new populations, and so on. term) in 200,000 generations would thus sciences, why not check such a fact in A straight line would result from the au­ be less than 1/1 000 of 1 percent per some current technical paper, instead of thor's favorite model: "directed, nonran­ generation, which is perfectly explain­ a simplified, and more than 100-year­ dom, purposeful, teleological." able within standard models of natural old schoolbook drawing? There are Directedness in Development selection and well below the actual rate many more fo ssil horses known than six, Again, we are presented with pre-Dar­ of evolution observed in many lineages. and they do not appear abruptly, where winian wisdom about final causes and Most human features have changed less the geological record is not abrupt for the beauty of the work of God the Cre­ dramatically than the brain in the last sed i mentary reasons. To the contrary, ator, his intellect and hands. This is an few million years.2 small variations and gradual changes in interesting piece of history of natural Another typically Creationist argument all features (like tooth crowns, fo ot struc­ philosophy and also a typical Creationist is the alleged absence of all missing ture, and so on) can be observed be- Continued on page 14

12 Winter 1995-1 996 21 st CENTURY SPECIAL REPORT Continued from page l' 1 Leonard, was a major. proponent of eu­ modern medicine ..' . sanitation ... ropean Christians into slavery, to main­ genics and he wrote a book titled The welfare ...pity." He also prol3osed tain power. Need fo r Eugenic Reform. Leonard wrote that the number of poor, feeble-minded Likewise, contrary to cpmmon belief, that the book was "dedicated to the human being?,c ould ,be Cl!lt in ba.lfwith Darwin and the Darwinians borrowed memory of my father. For if I had not be­ a policy of mass sterilization. the terms "survival of the fittest," and lieved that he would have wished me to Darwin's Eugenics Alive and Well "struggle for existence" directly from give such help as I could towards mak­ Darwinism is still alive and well, Herbert Spencer, well known as the fa- ing his life's work of service to mankind, deeply embedded in the free ente�prise I should never have ideology, which has the same arguments been led to write as the eugenicists of Darwin's day: The this book." poor should be dumped on the'scrap As, just these few meap, thus leaving more resources for items ind icate, there the genetically superior elite-in other is no Chinese wall words, for themselves. Proponents of separating Dan.yin this ideology argue that countries spol:Jld and his theory from not industr-ialize; instead they should ex­ the pol itical and so­ tract raw materials for export, and use cial, gol icy of eu­ only appropriate-technology agricl!Iiture genics; and the in­ to grow food or narcotic drugs', Their flueflce has not all raw materials often are processed and been in one direc­ sold back to the impoverished producers tion. at exorbitant prices. " Tbe same ties to Who controls the contents of text­ eugenics policy are books that teach this' ideology? Did it found among the ever occur to Mr. sabath, that it is more author.s of the mod­ effective and less costly to enforce polf­ ern synthesis of Dar­ cies that are not in the self-interest @f a winism: Sir Ronald pOplulation by controlling textbooks and Aylmer Fisher, the the media, than by employing thugs? British 'geneti,dst, A recent variety of this elitist argument was the Galton pro­ is that man's development in general is fessor of eugenics at bad for biodiversity because it tmmples the Francis Galton on other species. One version ,of the ar­ laboratory of Uni­ gumeht-that human economic.:.: dev�l­ versity College, Lon­ opment hurts the environment-by No­ don from 1933 to bel economist Kenneth Arr0w and

From Geoffrey West, Charles Darwin: A Portrail' (New Haven: Yale University Press, Hj38}. 1943. �rnst �M3yr others, titled "Economi6 C,rowtn,. Carry­ Charles Darwin, shown here in 1854, fit 'his theory to the was director of the ing Capacity, and the Environment,"3 Malthusian mold. American Eugenics was refuted at length by economist Lyn­ Society in 1985 and don LaRouche, whose concept makes it ther of Social Darwinism an� an ae:tive 1986. Theodosius Dobzh.ansky was di­ possible to measure the demographic ' proponent of culling the human species rector 'ofthe Eugenics Society from 1964 correlates of discontinuous transform a- ,of its "good-for-nothings." to 1973, and chairman of the board of tions in technological development.4 Darwin wrote in The Descent of Man, the Eugenics Society from 1969 to 1975. "at some future period, not very distant Sir Julian Sorrell Huxley was a member "Man has no fixetf biological as measured by, centuries, the civil ized of the Council of the Eugenics Society in way of life; he has n() races of man will almost certainly exter­ Engl:and (its executive council) from minate and replace the s':l.Vage ,races 1931 to 1932, vice president of the EI:J­ geneticallf determined:job throughout the, world." In 1837, after genics SocietY from � 937 to 1944, and description." Darwin returned from his voyage, he its president from 1959 to 1962.2 lived with his older brother, Erasmus, in Huxley, perhaps the most famous of London, and Erasmus's common-law those involved in creating the modern The appHcation of Darwin's ideas to wife, Harriet Martineau, who was synthesis, wrote in a 1924 letter to the the politica l-economic realm might known politically as the outspoken pro­ editor of The New Statesman: "baboons make Sabath uncomfortable, given the ponent of the aging Malthus. In 183.1, or Austral ian savages can have all these , infamy the Nazis .3chieved by imple-' Martineau wrote a work called "Poor [cultural] advantages, and will not blos­ mentihg eugenics ideas!' But, these are Laws and Paupers Illustrated." som beyond their lim its-limits set by Darwin's ideas, and their application Charles and Erasmus's cousin, Francis their inheritance." In the same letter, does lead to fascism. Daniel Dennett Galton, is considereG'l to be· the father of . Huxley also said, "The selection for sur­ r.ecpgnizes .this in his book, Darwin's British eugenics. Charles Darwin's son, vival has been enormously weakened by Contihued on page 15

SPECIAL REPORT 21 st CENTURY Winter 1995-1 996 1-3 Continued from page 12 The attitude toward evolution of concluded that the species originated as argument, but the author seems not species (as hardly explainable) and varieties, which became strongly defined aware that since the 19th century such higher taxa (impossible to explain in (now we would say: reproductively iso­ arguments have been refuted by show­ Darwinian terms) is borrowed directly lated). This is the idea of evolution itself, ing how the supposedly "purposefu lly from creationists : They also reluctantly and this is how modern biologists see designed" structures and functions came accept the idea of minor genetic varia­ species! into being. tion and even speciation within "created As a positive example of continental Because she invokes Riemann's ad­ kinds," but strongly reject any explana­ science, the author offers a long quota­ miration of the perfection of the ear and tions of origins of higher taxa by Darwin­ tion from von Baer ("by 1834," in fa ct the hearing, I can only again suggest read­ ian means. quote was assembled from his writings of ing Richard Dawkins, who brilliantly Here Hugunin proceeds to demon­ 1827 and 1828, but decades before Dar­ analyzes such concepts in his book The strate that "Darwin, who wrote a monu­ win's On the Origin of Species) . We are Blind Wa tchmaker. Paleontologists mental work on the origin of species, presented here with the well-known hier­ have also shown how the archy of biological system­ human ear developed from atics plus a fuzzy "scientific the jaw apparatus in fishes explanation" of the ob­ through amphibians and served pattern: "The cause mammal-like reptiles, by re­ must lie in the essence of modelling hyomandibular, the forms themselves." Or: articul ar, and quadrate "all potential for variation is bones into middle-ear ossi­ not actually developed be­ cles. But this knowledge cause environmental fac­ comes from hard evidence tors must be conducive for gathered in our century; that the potential capacity in or­ is, from the period neglected der for variation to be real­ in Hugunin's paper. ized." (2) Continuous, Gradual If this is the way "real Mutation science" should look ac­ After recapitu lating "as­ cording to Hugunin, I'd sumptions" and "hypothesiz­ rather stick to Darwin. ing" of evolutionary mecha­ (3) Survival of the Fittest nisms leading through gen­ The author claims that etic changes to speciation, "the Darwinian view Hugunin asks, "But then stresses a fierce dog-eat­ how could one explain dog competition: survival much larger changes, such of the fittest," and in the as ...the differences in dif­ penultimate sentence of fe rent fam ilies within the an­ this section: "the Darwin­ imal kingdom?" ian model of individual The answer is simple. dog-eat-dog fights to the What we now see as fa milies death." were once genera, and even One need only look into before, mere species, not On the Origin of Species much different from each or into most textbooks to other. It is only ex post fa cto see that this suggestion is that we can say: "In 20 mil­ From Geoffrey West, Charles Darwin: A Portrait (New Haven: Yale University Press, 1938). fa lse. Natural selection I ion years the descendants of Darwin in 1881. does not normally operate this fossil species will de- by cruel duels between velop into a family A and those of its does not even bel ieve in species!" She members of the same species, but by the sibling into fam ily B." It is as if we were proves this (again in a typically Cre­ differential survival of different individu­ to say: "We" , we understand how isola­ ationist way) by manipulating a quota­ als, with the main mortality factors being tion produces dialects, and we know tion. Darwin wrote that he came to "the predators, illnesses, and so on, not mor­ that American English naturally diverged heterodox conclusion that there are no tal combats within species. from British English. But how could one such things as independently created Another old charge against Darwin­ explain much larger changes, such as species. That species are only strongly ism, now often repeated only among those between the Engl ish and German defined varieties." Creationists, is the supposed tautology of languages, or in the Indo-European lin­ The key words are, of course, "inde­ the "survival of the fittest," where the guistic fa mily?" Again, exactly the same pendently created species." In other fittest is the one that survives. The reason applies: by accumulation of minor words, Darwin no longer bel ieved in in­ that it is not a tautology is that the sur- changes in separate lineages. dependent creation of each species. He Continued on page 76

14 Winter 1995-1996 21 st CENTURY SPECIAL REPORT Continued from page 13 gument is made that there is a long, changes to have occurred by chance. Dangerous Idea.s Dennett correctly as­ long time for each little change to occur Real time, as accurate as science can serts that Darwin's ideas are a sort of by chance. But this also is a fallacy; in currently determine it through paleon­ universal acid, and says that they can reality, the Earth cooled at a specific tology, leads to the same paradox,6 and have been applied in ways that de­ point in time, life evolved at a specific The Errors of Fundamentalism stroy the civilized nature of human life . point in time, eukaryotes evolved at a Another wild assumption Sabath Darwin the marl' may be long gone, specific point in time, and man evolved makes is that anyone who argues that but his ideas and his method of thinking at a specific point in time-all of which man is higher than a beast must be a are still having corwsive effects on suc­ are known, within a certain margin of Christian fundamentalist. Wait a ceeding generations. error, to science by various techniques minute! The Creationists have an irra­ The same can be said fo r Darwin's im­ for dating rocks. This means that tnere tional, literal interpretation of the Bible. pact in the biological sciences today, are shar[iltemporal boundary conditions That is a direct denial of the role of where the major assumptions of Darwin­ ian science are st ill alive and well. For example, Darwin argued that an accu­ mulation of very small changes slowly , creates a divergence of populations, from which new species emerge. The modern synthesis argues the same thing, adding that those genetic changes are random, gradual, very small changes on the gene level. The scientific opposition to the mod­ ern synthesis argues for punctuated equi­ librium, governed by, in Stephen Jay Gould's words, "contingency," a pseu­ donym for chance. Why should scientists accept a situa­ tion where the choice is between very gradual cn anges governed by chance, or very abrupt radical changes governed •. by chance? How can Sa bath explain his own ex­ istence by chance or by its eorreJative, entropy? If the universe is governed by chance and entropy, how does Sabath explain the fact that we can each argue in a possibly ingenious, possibly even creative manner, each heatedly defeFJd­ ing his own hypotrnesis abol!l't the way the universe works? Isn't it ironic, ac� . cording to Sabath's view of the uni­ StuartK. LewiS/EiRNS verse, that what he most cherishes "Human beings have genetically changed at a much slower rate than rats or mon­ about himself is nothing but a tempo­ keys because humans use creativity to evolve further, whereas lower species are rary mistake (or a series of temporary more dependent on genetic changes to evolve. /IHere children making sundials. mistakes) that denies the laws of chance and entropy? or limits, within which all those myriad man's mind, man's ability to think Sabath mentions the arguments of tiny changes would have to occur to get metaphorically, in receiving the divine Richard Dawkins, but beware the sleight from a cooling Earth, with a solidified message. of hand in such w0rks of Dawkins as crust, to the evolution of life. And this is precisely the point: man1s The Blir.uil Watchmaker! According to Once one starts looking at those tem­ difference from animals is his ability to the laws of prol!Jability, a change does poral boundary conditions, one begins think metaphorically. To assert that any­ not become more probable if one huge, to discover that it is not possible for all one who says man is not an animal complicated, rapid change is broken those tiny changes to have each oc­ must be a fundamentalist, is a very seri­ down into a series of tiny steps, each of curred sequentially by chance. There ous error, which, in fact, denies the which must occur sequentially to arrive was not enough time. It is not necessary truth of Christianity and Judaism: Man is at the same end at which the large, to use that strange Creationist view of not a beast, but was created in the like­ punctuated change would arrive. time, in which the Earth cooled shortly ness of God as Composer or Creator of It may become, more plausible to the before recorded hist0ry, to run out of the Universe, imago viva dei. This credulous reader, particularly if the ar- time fo r. all those sequential tiny Continued on page 17

SPECIAL REPORT 21st CENTURY Winter 1995-1- 996 15 Continued from page 14 apes (which, I guess, are "the highest" In nature such a fo rm would be vival is not entirely random. It means mammals), some live in bigger groups quickly eliminated, because natural se­ that survival is only the common de­ (chimps) and some in polygamous fa mi­ lection is not concentrating on any par­ nominator, and the lower mortality ratio lies (gorillas). Thus the social structure is ticular feature, but on the overall fit­ of a given phenotype is a convenient about as elaborate as in the pricklefish, ness; that is, the reproductive success. measure of fitness, but the reason for it is and much simpler than in ants. Some There are also natural selection mecha­ determined by adaptive features. even live as isolated couples (gibbons) or nisms preventing inbreeding in natural Let's look at an example. If we take a solo (orangutans). None exhibits "exten­ populations.4 Nevertheless, some population of cockroaches and spray sive collective nurturing of the young"; analogies with the human-bred cham­ them with an insecticide, some of them usually it is the mother who carries and pions can be found in nature, in cases will survive, thus proving they are the feeds her offspring. of sexual selection. fittest (in these environmental condi­ I wonder which mammals the author In these cases, where the reproduc­ tions). But they are not the fittest because tive success depends strongly on pleas­ they are survivors, and not survivors be­ "No one is preventing ing some particular and exaggerated ex­ cause they are the fittest. They are both, pectations of members of the opposite because they possess some particular ge­ non-Darwinian scientists sex (just as the reproductive success of a netic feature, in this case perhaps a more from getting 'down to some domestic animal depends on possessing efficent detoxifying enzyme or more im­ really hard work' and particular traits favored by the farmer), permeable exoskeleton. the selection can lead to otherwise We do not need to wait and see if answering all the poorly adapted "champions" (males the animal survives in order to assess fundamental questions with a huge, apparently counter-adap­ its fitness. If we knew the individual posed by Carol Hugunin. tive burden of enormous antlers, bright resistance to the insecticide in all feathers bringing predators' attention If they find answers that roaches, we could point to the fittest and making flying difficult, and so on). individuals even before the survival are both novel, testable, So here natural selection is very much test. Normally, diffe rential survival and and anti-Darwinian, like artificial selection. reproduction just show which individu­ then it will be time It is not clear why Hugunin links the als are the fittest. inbreeding problem with, and seriously to bury Darwin." Here Hugunin shows lack of knowl­ refutes, the absurd "view [which] as­ edge, implying that survival of particular sumes that the environment-nature­ individuals in "Iower species" "may ap­ remains fixed and stable." Certainly it is pear superficially to be the result of had in mind. The reproductive strategy not a Darwinian view. Darwin opposed chance," and that this chance survival is of "higher" and "Iower" species need the idea of fixed nature and replaced it what the "Malthusian-Darwinian view" not be "so drastically different" as the with the idea of evolving nature. Just assumes. The whole idea of natural se­ author implies. Of course, birds and because each living and evolving thing lection implies that the survival is not mammals, being endotherms, can afford is an important element of others' envi­ entirely the result of chance, but of dif­ more intense parental care than other ronment, evolution proceeds in a ferential fitness. Totally random survival, vertebrates, but there are also sharks that changing environment (not to mention not discriminating in respect to adapted­ bear live young (and few of them). the climatic changes, and so on). Dar­ ness or fitness, is postulated by non-Dar­ (4) Inbreeding vs. Outbreeding winism never assumed that organisms winian models of evolution. And a Pointing to limitations of inbreed ing should be selected for lack of flexibility prodigious number of offspring and/or of better varieties by human breeders and vigor, as the author strangely seems cannibalism versus parental care of a (increase in serious genetic diseases, to assume. Such terms as "coevolution", few offspring is not related to being poor temperament, and so on) is an­ "evolutionary arms race," "Red Queen "Iowest" or "highest" species, whatever other Creationist argument. Artificially hypothesis" all explore the dynamic na­ that means. (Is a bee higher or lower bred domestic animals come from very ture of adaptation. than a frog or a coconut palm higher or limited populations (few breeders can Some species are more specialized lower than an oak?) afford a stable population of, say, and stenotopic (adapted to a narrow It is just the K-strategy versus the r­ 10,000 race horses), and thus are often range of environmental parameters) and strategy. The latter maximizes reproduc­ close kin. This increases the risk. of ho­ some are more generalized, eurytopic. tive success by means of producing as mozygous lethal or sublethal gene alle­ The former can thrive in very stable con­ many offspring as possible. It is typical of les. Natural selection, however, oper­ ditions (ocean depths, caves), the latter organisms living in variable, unpre­ ates on larger populations, and this risk pay a price of less than perfect adapta­ dictable habitats. Inhabitants of stable is minimized. tion to any given habitat, but can survive habitats are usually K-strategists (a small Another difference is that people usu­ even drastic changes. The adaptations number of well-equipped offspring). ally breed animals or plants for a single can be of diffe rent form, and both nar­ I was also amazed to read that "most trait (milkier cows, brighter flowers, larger rowly specialized and more adaptable higher mammals have elaborate social grain, and so on). Thus they often get a forms can occur in closely related taxa. structures and extensive collective nur­ maximum performer in one respect, but Let's take the example of our genus, turing of the young." Even within the one that is flawed in other respects. Continued on page 18

16 Winter 1995-1 996 21 st CENTURY SPECIAL REPORT Continued from'page 15 means that man, emulates the Creator, to the best of his ability, by transforming the universe, Imago viva dei does not mean that God is in man's image, but that marl is in the Composer's image, inasmuch as he is capable of participating in the mind of the Composer of the universe, to understand causally how the universe developed and to apply that knowledge to further transform the universe, Man is higher than a mere beast because he has this metaphorical (that is, nonliteral) capacity to hypothesize a higher hy­ pothesis. True, the monotheistic religions agree that man will never have an absolutely perfect under-standing of the nature of the universe, but all assert that man can approximate this understanding with greater and greater perfection, It is part of the fallacy of fundamentalist thinking to assume thanhe Bible (or Koran) must be taken literally, so that God's time, the time of the Eternal, of the Infin ite, is

reduced to man's simple notion Of From Geoffrey West, Charles Oarwin:-APortrait (New Haven: Yale University Press, 1938). everyday alarm.:.clock time. What makes Darwin's older brother, Or. Erasmus Darwin (above), and Erasmtls's common-law this approach evil is that it denies the wife, Harriet Martineau, were active in the Malthl,Jsian eugenicist fa ction in the - mind of man. It says to each child who mid- 19th century. asks "why?" that "You can ''lever know why. God made this, and this -God is man site, thought to be from about it in some crude way as a tool, but he unknowable." 20,300 years ago. This particular carved would not take advantage of how it was In its denial of man's mind, Creation­ tusk is not a boomerang that returns to designed to be used. Nor would he have ism, and other forms of fundamentalism, the thrower when thrown, but rather a any idea of how to make another one, or come together with extreme materialism. killing stick with lift; it fl ies about 123 how to experiment aerodynamically to The great mechanist and Marxist, Freder­ feet when thrown into oncoming wind, develop a still better carved tusk. ick Engels, claimed that the key to man's which gives it the lift. The glacier-d0mi­ Clearly, contrary to Engels' claims, development was h'is ppposab,l,e nated Europe �f 20,300 years ago fa­ aIJes and man are two totally different ' thumb-in effect, the capacity of sOme vored 'grasslands populated with large speci�s! with completely diffe rent ways ape to hold a stick.and use it to push ter­ grazing mammals, such as reindeer, of livi'ng.Ther e is a true discontinuity be­ mites Ollt of a termite colony, In this which could be killed readily with such tween them. When man first evolved, he claim, Engels makes exactly the same an instrument. was no longer an upright scavenger with hideous mistake as the fundamentalists: What kind of species would delibler­ some funny opposable thumb. He was He denies what is sacred about man, his ately carve something in a shape that employing creative ideas-ideas ability to think, to create, to emulate di­ would give it lift? We might look at this couched in. metaphors of language and rectly his Creator by continuing creation. tusk as simply some kind of tool. If we culture, including poetry, music, and Why sh0uld �aving an opposable gave it to different species, what would cave paintings. thumb be important? There are other, they do with it? 'Man's ideas, albeit imperfect ones, in­ non-primate species that employ things A d0g, for example, wou ld be de­ cluded thoughts about aerodynamics, that can be construed as crude tools, but lighted. He would drag it around, per­ particularly (initially) as tt:Jey might apply none of them, nor non-human primates, haps even shake, it back and fo rth. Even­ to the task of hunting under the strange can do what man can do with his cre­ tually, he would settle down to explore it conditions imposed by the ice ages. And ative reason. in a very dog-like way: by chewing on it. his ideas were about hunting strategy, or The Uniqueness of Man Does he understand it as a potential astronomical cycles, or about the devel­ One of the best examples of this tool? Obviously not. opment of a whole succession of more comes from Polish archaeology. Polish What if we gave it to a quasi-upright anq rnore sophisticated tools and other scientists discovered a carved ivory ape? He too would be delighted. He more advanced technologies. His ideas mammoth tusk, roughly resembling a would drag it around, throw it around, also concerned the earliest uses of fire- boomerang in shape, in a prehistoric hu- use it fo r poking at things. He might use Continued on page 19

$PECIAl REPORT 21 st CENTURY Winter 1995-1 996 17 (a) Directed, nonrandom, (b) Nondirectional, purporseful, teleological ? random, contingent ? "2 '� Evolution �• . '. ," ? '( . 'l ",' . --.., £.N ,. , ., I � • . .. .- ffl'T < '� : 0 · ·1Iluf " - ..., ;

, .... , , /7?t� . - .. :. � .. r

.... � ... . r-� '� _ . .... "

TWO VIEWS OF EVOLUTION Of the two philosophically possible models of evolution that Ka rol Sabath has sketched here, he argues that only (b) is supported by the fossil record.

Continued from page 16 adapted to the place where we evolved, created it, in fact. They also changed our Homo. One fo rm of human was and to our ancestors' hunting and scav­ atmosphere into one conta i n i ng free adapted physiologically to harsh enging mode of life. oxygen, without doubt a major change, periglacial conditions. The Nean­ Neither are we extremely weak. Hu­ which occurred more than 1 billion derthals of both sexes were extremely man beings can endure longer runs than years ago. On the other hand, I do not heavily muscled, thus producing a lot most other mammals, which develop see many recent additions to the animal of metabolic heat; their noses were symptoms of thermal shock. Of course, kingdom' (except Homo sapiens) that very big to allow efficient flow and our strategy of adaptation has for a long would show.remarkably greater capacity "conditioning" of the air, fueling the time not relied on muscle strength or to transform the biosphere than the ear­ metabolic oven with lots of oxygen. other physiological adaptations, but lier fo rms did. They needed more calories, so they rather on cultural ones. Darwinism does I would also be cautious in comparing specialized in eating large mammals of not state that all adaptations must be the number of species extinctions the Ice Age. Another, closely related physiological, however; there are many caused by humans with those resulting lineage of humans has "chosen" an­ examples of behavioral adaptation. from prior environmental changes, Nei­ other strategy: cultural adaptation (bet· There is no "general lawfu lness of ther drifting continents nor asteroids ter tools, more efficient cooperation, evolution that is not unique to man: Life have consciousness or moral responsi­ more diverse diet, extensive use of fire forms evolve to generate new species bility. Humans are the main extinction and clothing instead of stronger mus­ with greater versatility and greater ca­ factor in the last thousands of years. See, cles and larger noses). pacity to transform the biosphere." In my for example, the data on Pacific Islands Thus it is absurd to state that "man ap­ opinion these assumptions are fa lse. The birds exterminated by human settlers.s pears in DarWinian terms to be the least most versatile forms are microorganisms. About one quarter of all bird species in adjusted to environmental conditions, They live in both hot springs and glaci­ the world has become extinct in the last being both weak and naked." I wonder if ers, in ocean depths, and in other organ­ few thousand years; this is already a sud­ the author ever imagined our ancestors isms. They have managed to survive suc­ den mass extinction by paleontological running after prey in the African sa­ cessfully for almost 4 billion years. standards. vanna, under tropical sun, in a thick fur Microorganisms also have a great ca­ And many more people have de­ cover. Our naked skin is perfectly pacity to transform the biosphere. They Continued on page 20

18 Winter 1995-1 996 21 st CENTURY SPECIAL REPORT Continued from page 17 ing the resonating cavities in his head. they have a well-developed communica­ not just accidentally to char meat, but Therefore, he was able to articulate a tion system, akin to a primitive language. systematically to- develop more and language, a very sophisticated form of Parrots have fine resonating cavities in more sophisticated tools by developing communication. Is this the process that their heads and can babble away, .mim- . them at higher and higher densities of makes man human-or is the theory icking any human language devised, energy throughput. Likewise, he devel­ backwards? without the slightest clue as to what they oped ideas about fishing strategies and Consider th is: Dogs speak "dog," a are repeating. Again, they have no con­ even navigation at sea, ideas about plant combination of moans, grunts, growls, ception of how to make a tool, or what and animal husbandry, and so on. and other tones, with considerable non­ to do with one. Not Just Language verbal sign language conveyed by body Human beings developed sophisti­ Let's discuss another illusion about posture and a tremendous focus on the cated languages becau�e they had pro­ what makes man human. Some say, face, especially the eyes. Most dog own­ found conceptions to communicate; that man is man because he talks, he can ers, to the degree that they have been is, after becoming the human species, communicate; he uses some differenti­ able to teach their dogs much in the the species of ideas. They did not be­ ated combination of grunts, moans, and rea lm of obedience or wo rking skills come human because the shape of the other tones, with considerable nonverbal (herding, police work, seeing-eye work, skull changed, for whatever reason. sign language, focused on the tremen­ and so on), also speak dog. It's a com­ Man, the species of ideas, of higher dous expressiveness of the human face, mon other-species commun ication sys­ hypotheses, clearly continually improves _ especially around the eyes. tem known to humans. on the resources offered to him by raw' This theory holds that ape-man started Dogs, however, have not a clue as to nature, even to the degree of developing cooking his food, and this changed the how to make a tool or what to do with irrigation networks, artificial fertil izers, geometry of his mouth and skull, chang- an existing tool. Yet, as social creatl,lres, Continued on page 27

A Species of Ideas

his 20,300-year-old killing stick, a throwable Tweapon carved from a young mammoth's tusk, was found in the Oblazowa cave in the Polish 1 :.! :3 �. (�:.:> .;/-;....�. > Carpath ians among other artifacts of Upper Palae­ ol ithic human culture. It is identical in size and shape to the Queensland, Australia, non-returning wooden boomerang, but the Queensland boomerang is much lighter and considerably less stable when thrown un­ der varying wind conditions. ,: One side of the mammoth's tusk has been polished to create a convex blade edge, and the handle end is more rounded for safer grip. This design generates lift when th rown into the wind-from downwind of the rei ndeer or other game. Subtle details in the way the tusk was carved improve the weapon's stability and ballistic qualities, indicating that the carver had con­ siderable knowledge of aerodynamics based on a long tradition of making weapons of this sort. (The drawing shows cross-sections and their correspond­ ing locations on the stick.) Europe in the period 22,000 to 20,000 B.C. was a glacial grassland populated by large grazing mam­ mals and dominated by a mile-high glacier covering Dietrich Evers and Pawel Valde-Nowak, 1994, "Wurfversuche mit dem Jungpalaolithischen most of the British Isles, all of Scandinavia, and end­ Wurfgerat aus der Oblazowa-Hiihle in den polnischen Karpaten: ArcMologisches Korres- . ing just short of what would be today London, Ham­ pondenzblatt, Vol. 24, Heff 2, p. 137_ burg, and Warsaw. The French cave paintings (Las­ caux, Grotto Chauvet, and so 'on) come from this period were mined and combined with binders to produce pig­ and show serious study of animals-bulls, rh inoceroses, ments; ed ible nuts, fruits, and other plants were collected; horses, bears, elk, re indeer, bison, lions, hyena, and oth­ and salmon, bird, and mammal migration patterns were ers. studied and exploited. At th is time, man had developed the use of a spear In short, man was a species of ideas, relying on intelli­ thrower; ivory sewing needles were used to fashion hide gence, skills, and developing technology and culture, rather·­ clothing;' primitive torches and lamps were used; minerals than brute strength and wooden clubs. ' !.

SPECIAL REPORT 21st CENTURY Wihter 1995-1 996 19 Continued from page 18 trabestial space. From the top of the tra­ long-ago rejected model: a mixture of stroyed various "beasts" than ever got to jectory, a jumping flea cou ld take pho­ science, religion, and philosophy, both the Moon, of which the author is so tographs of the dog, using a micro­ vague and strongly influenced by sub­ proud. The blue-green algae changed camera (bought at theflea market). Ana­ jective intuitions (or the com mon sense the entire planet into a habitable place lyzing the "satellite images," and com­ of a given time). (you can thank them for the oxygen you paring them to the data collected at the In reading Hugunin's paper, I feel as if breathe, and for the protective ozone surface, the reductionist fleas cou ld I am being confronted with Creationists' layer), and so what? Are they the image reach quite a good approximation of the school brochures that try to hide the real, of God the Creator, and humans the im­ dog geometry. religious reasons behind re jecting evolu­ age of Daemon the Destroyer? As for the British holists, I never heard tion. Even the arguments are the same. (5) Man Just a Beast? of J.B.S. Haldane (or any one of them) Actually, I am surprised that the author Here it should be stressed that eugen­ worshipping the deteriorating conditions did not declare herself a Creationist, be­ ics and Social Darwinism are neither of living, or their subject of research, nor ing so influenced by this view. part of the original Darwinian theory of practicing human sacrifices of fellow sci­ An "axiom of science" that "Man is in evolution, nor part of the modern syn­ entists. Maybe it is irrelevant, but as far the image of God" appeared modestly thesis. No scientific theory can be falsi­ as I know, that was rather the practice of only in the table on page 38. Now, she fied by exposing its abuse by politicians. some Christian-Platonics who praised takes a hybrid view: believing in all tra­ The Hiroshima bomb did not falsify Ein­ natural disasters and infectious diseases d itional, Creation i st anti-Darwi n ian stein's theory or physics in general. Dis­ as a deserved and beneficial punishment tenets and yet still talking about evolu­ crimination against poor people or other by the Supreme Being and who occa­ tion that is somehow driven by miracles races did not begin with Darwin. Forced sionally burned someone at the stake to to a final point, with no proof given. labor, slavery, and injustice existed be­ appease its anger. Anyway, I think that Such a post-modern, New Age-like, po­ fore and were then (and later) justified the treatment of holism is here defi nitely I itically correct, conglomerate rei igious by religious arguments. For example, biased and unsubstantiated. ("Christian-Platonic") view is only a sign South African apartheid was justified by (7) The End of Darwin of getting lost in contradictory argu­ abuse of the Old Testament, and the dis­ I wonder where else, except in Cre­ ments, but is not a constructive scien­ crimination against Indian pariahs was ationist writings or some distorted early tific proposition. justified by Hinduism. journalists' reports on the "punctuated I am amazed that a "biologist on the And the "continental sc ience" and equilibria" hypothesis, could the author staff" of a scientific journal that aims at philosophy, so praised by the author, find a claim that "the views of Darwin the 21 st century could show such a bla­ was involved in the terror of the French and friends do not stand up well to the tant misunderstanding of a fundamental Revolution, justifying tortures by the po­ massive amount of scientific evidence idea of modern biology. I believe that lice, use of phrenology to indicate innate accumulated about how evolution readers deserve a fair treatment of this inclinations toward violent behavior, works" or that "from the standpoint of important matter. and so forth. the paleontological record and similar Cuvier made his political career-ris­ evidence [no evidence was shown by Notes ------1. For a brief resume of current ideas, expressed ing to the post of police minister in Huguninl, the Darwinian hypothesis is during a conference on the problem, see Jeffrey France-in the period when poor people a miserable fa ilure," or that one needs L. Bada, 1995. "Origins of Homochirality." Na­ were branded and sentenced to the gal­ to expose "the fraud in the still-taught ture, Vol. 374, pp. 594-595 (April 13). 2. See Ann Gibbons, 1995. "When It Comes to leys for minor crimes. dogma that modern biology and physi­ Evolution, Humans Are in the Slow Class," Sci­ Why blame Darwin for all prejudice cal anthropology rest upon Darwin's ence, Vol. 267, pp. 1907-1908 (March 31). and injustice in the world? fudamental discovery." 3. Conceming the number of fossil horse species and their mode of evolution, see for example, (6) Darwin Duo: Reductionism Of course, no one is preventing non­ Bruce J. MacFadden, 1984. ·Systematics and And Holism Darwinian scientists from getting "down Phylogeny of Hipparion, Neohipparion, Nannip­ pus and Cormohipparion (Mammalia, Equidae) In this satire [pp. 36-37], we see that to some really hard work" and answer­ from the Miocene and Pliocene of the New Hugunin does not speak of the real Dar­ ing all the fundamental questions posed World," Bulletin of the American Museum of win, who could not be reductionist and by Carol Hugunin. If they find answers Natural History, Vol. 179 (1); B.J. MacFadden, 1988. "Fossil Horses from 'Eohippus' (Hyra ­ holist at the same time. She just uses his that are both novel, testable, and anti­ cotherium) to Equus. 2. Rates of Dental Evolu­ name to denote any modern natural sci­ Darwinian, then it will be time to bury tion Revisited," Biological Journal of the Lin­ ence that is not explicitly Christian and Darwin. nean Society, Vol. 35 (1), pp. 37-48; R.C. Hulbert, Jr. and B.J. MacFadden, 1991 . "Mor­ full of supernatural assumptions. It is difficult to understand why the au­ phological Transformation and Cladogenesis at First of all, I would expect Hugunin to thor shows such an urge to get com­ the Base of the Adaptive Radiation of Miocene Hypsodont Horses," American Museum Novi­ show in her ironic style how the Christ­ pletely rid of Darwin. Normally, people tates, 3000; as well as the references cited in ian-Platonic flea scientist wo uld reach who feel that some old idea is wrong these papers. the proper answer about the nature of present a new, coherent theory that 4. L.F. Keller et aI., 1994. ·Selection against Inbred Song Sparrows during a Natural Pop­ the beast they live on. By divine illumi­ sooner or later could win majority sup­ ulation Bottleneck," Nature, Vol. 372, pp. nation, or what? port and become a new orthodoxy. In­ 356-357. I can only point out that the reduc­ stead, Hugunin first of all misrepresents 5. David W. Steadman, 1995. "Prehistoric Extinc­ tions of Pacific Island Birds: Biodiversity Meets tionist team of fleas would probably the view she dislikes, then as a replace­ Zooarcheology," Science, Vol. 267, pp. 1123- launch some of their number into ex- ment she proposes an even older and 1131.

20 Winter 1995-1 996 21 st CENTURY SPECIAL REPORT Continued from page 19 totelians and the Platonists. The Aris­ rior to inductive laws generalized from better mining technologies, and so om totel ian dominance of academia has what we observe about nature. Man creates his Q�fJ superseding tech­ hidden the better approach of the PI'!,­ However, if such reasoning by anal­ nologies, which totally transform and re­ ton ic currents: the Christian Platonic ogy is mistakenly taken literally, reason define what can be considered as re­ tradition that developed the concept of aborts itself, and one is back to the steril­ sources. No other species can do that; man a? imago vivq, dei, ity of Gaia, in which npthing is know­ other species are trapped by the fixed bi� The "Philosophical Fragments" of able. The biosphere evolves, in interac­ ological nature of their way of life. Bernhard Riemann [see page 48, this is­ tion with the mantle of the Earth and For a fixed way of life, there are only sue], give a conceptual overview of this astrophysical phenomena as if it had a fixed resources and a fixed limit on pop­ alternative. In the -traditiorj of Plato, as mind, as if it were a thinking being­ ulation density. Man, has no fixed bio­ defined by Nicholas of Cusa, Leonardo planning the best of all possible worlds logical way of life ; he has nq'genetically da Vinci, Johannes Kepler, and Gottfried to set up the.ba?is for future evolution of determined job description. He is not Leibniz, Riemann develops a hydrody­ life. The biosphere acts in a purposeful limited to whatever' can be accom­ namic approach to the universe in manne�; yet to think of it as a living be­ plished by manipulating an opposable which the universe transfo rms itself by ing with a world brain is a dead end. thumb. Man, with a whole su€cession of generating singularities. These singulari­ To my knowledge, the last scientist to technologies, nurt�red by developing ties redefine the potential and topologi'­ take this sort of teleological approach culture, has transformed his potential cal characteristics (including change in was Lawrence Henderson in his 1913 population density by three orders of metric and change in state) of the space­ book, The Fitness of the ,Environment, magnitude'since the most primitive men time manifold oi that uni,verse. which argwes that the Earth, with its hy­ first inhabited Earth. In short, Riemann develops a notion drosphere, is physically, chem ically, The Evolutionary Clock of an evolving, hydrodynamic self-trans­ and in terms of protective climate, the 1J'lciting the concLusion that "When it forming universe, in w�ich entropy is best of all possible wodds-for the evoh,J­ comes to evolution, humans are in th� not primary, Lyndon LaRouche is the tion of life.9 slow class" (from Science, March 3·1, most prominent thinker today develop­ HeFlderson states that the old teleol­ 1995), Sabath is del iberatelY' ignoring ing ideas basep on this tradition. ogy�the fundamentalist teJeology that, ; the point being made by population ge >. The Vernadsky Example claims God made everything and hu­ neticist Li Wen-Hsiung of the. University In the earlier 20th century, the Ukrain­ mans cannot know how or why-is of Texas at Houston.? According to the ian scientist Vladimir Vernadsky (1 863- dead. However, he says, scientists can metric of DNA mutation rate�; human 1945l l00ked at the evoilltion of life and must develop a ne'A( teleology, be-· beings have genetically changed at a from a Riemannian perspective. Basing cause the mechanistic hypothesis devel­ much slower rate than rats or monkeys himself on the work of Riemann, Curie, oped out of the realm of Epicurean ,. because humans use, creativit)! to evolve and Mendeleyev, Vernadsky began to chance cannot account for the purpo�e­ furtner, whereas lower species are more elaborate that study. He was the first (at fulness found in nature. dependent on genetic changes to least the first known to this author) to The challenge posed in my ,previous evolve. elaborate the notion of the biosphere, as article remains: We have to j;ev�ve the Human beings evolve on a different · that portion of that Earth's crust arig, at­ method of Riemann and do the really level from other species; they evolve on mosphere that is dynamically trans­ hard work necessary to answer the ques­ the level of ideas. This is what Li says, formed by the development of a power­ tion, What is life and how did it evolve? which, as he points Qut, makes the idea ful singularity: Ufe. . of a universal biolog'ical molecul.arclock Life has totally reworked the geologi­ Notes ------(the rate of DNA mutations) a flawed cal surface of this planet's crust. But the 1. Lyndon H. LaRouche, Jr., 1995. "Kenneth Ar­ row RUns Out of Ideas, But Not Words," 21st. construct, insofar as it assumes that . emergence of man is still another power­ CentUlY, Fall, pp. 34-53. species evolve at the same rate. ful singularity transforming the character­ 2. Information concerning eugenics society mem­ The molecular clock concept is also istics of the biosphere, and its potential bers comes from records of the British and American eugenics societies compiled by re­ flawed and problematic because it as­ rate of change. This development­ searcher Kathy O'Keefe. slimes only vertical genetic change­ man's transformation of the crust of this 3. Kenneth Arrow, et aI., 1995. "Economic Growth, Carrying Capacity, and the Environ­ from parent to offspring. In reality, hori­ planet and its atmosphere-Vernadsky ment," Science (April 28), p. 520. zontal genetic change-the transfer 'of refers to as the noosphere. Because the 4. See note 1. genetic material from organism to organ­ school that developed around Vernad­ 5. Daniel C. Dennett, 1995. Darwin's Dangerous Idea (New York: Simon & SChuster). ism (of the same or different species) by sky's ideas is itself heavily influenced by 6. For a broader review of the argument of viruses and other parasites-is also pos" the empiricism that dominates modern Richard Dawkins. see Lyndon laRouche, "On the Subject of God," Fidelio (Spring 1993), p, sible under some circumstances. science, an honest treatment of Vernad­ . 1� . Should we, therefore, give up science sky would take considerable space.8 7. Ann Gibbons, 1995. "When It Comes to Evolu­ and join the fundamentalists in declar­ What's wrong with the empiricist ap­ tion, Humans Are in the Slow Class," Science ing the subject to be the unknowable proach of modern science? 'Riemann is (March 31), pp. 1907-1 908. 8. For space reasons, a section on Vernadsky's act of an unknowable Aristotelian God? very explicit: in dealing with the teleo­ work was eliminated from my previous article, I think not. Instead we should broaden logical nature of the evolution of the "It's Time to Bury Darwin." 9. Lawrence J. Henderson, 1913. The Fitness of our study of epistemology and look at biosphere and even the noosphere, rea­ the Environment (Gioucester. Mass.: Peter the historic fight between the Aris- son by analogy"':-"'by metaphor-is supe- Smith, 1970). .

SPECIAL REPORT 21 s� CENTURY Winter 1995-1 996 21 JOHANNES KEPLER'S MYSTERIBM · C0SMOGRAPHICUM

A Guide to 'the, Harmony of the Mind And: the Universe

by Ralf Schauerhammer

Four hundred years later, Kepler's first work

stitl tells'" IJS more about the solar system and human creativity than Newton or any empiricist is capable of doing.

ohannes Kepler discovered the harmonic ordering of the Laplace on Kepler's work. Laplace saw Kepler's ideas as J solar system in July 1595, precisely 400 years ago. The dis­ "chimerical speculations" and thought that Kepler's search for covery was so important to him, that he recorded the date a universal harmony was "depressing for the human spirit." for posterity in the foreword to his Mysterium Cosmograph­ Another great scientist, however, the mathematician Georg icum (Mystery of the Universe). While he was alive, and after Cantor-whose theory of manifolds was based on the same his death, in the middle of the horrors of the Thirty Years War, Platonic conceptions to which Kepler also subscribed­ the fundamental features of Kepler's work were misunderstood warned against the "empiricist sect," which reduces explana­ and fo rgotten. Today, it is claimed that Kepler was the fo rerun­ tions of nature to pure descriptions of phenomena (with formal ner of the Newtonian theory of universal gravitation, but this is "models") and makes real natural science impossible. a complete misrepresentation of Kepler's genius. Kepler's This "empiricist sect" has since puffed itself up to the rank of physics and epistemology go far beyond anything that Isaac orthodoxy in science. That is why the significance of Kepler's Newton, and the school named after him, are capable of work is still misunderstood; despite myriad symposia and re­ knowing and explaining. search projects in the history of science. Kepler was not the How diametrically opposite the two ways of thinking are, is forerunner of Newton and that kind of empirical science expressed in the judgment of the "Newtonian" Pierre Simon which, following Newton, "makes no hypotheses." For that

22 Winter 1995-1 996 21st CENTURY A statue honoring Kepler in his birthplace We il der Stadt, a town near Stuttgart.

very reason, Kepler can provide us a crucial stimulus: It was entire manifolds of hypotheses in creative freedom and yet Kepler, and not Copernicus, Newton, or Galileo, who made "lawfully" and, ultimately, empirically verifiable. astronomy, cosmology, and physics into an entirely new sci­ If we look upon the paradoxical quandary in which today's ence. What Kepler can teach us is the method for developing cosmology has entangled itself, or if we reflect upon the con-

------EDITOR'S NOTE ------The original German-language version of this article appeared in Fusion, June 1995. Its Kepler quotations were taken fr om Max Caspar's German translation of the Mysterium Cosmographicum, published in 1936 by Or. Benno Filser Verlag, Munich. Caspar, the fo remost Kepler scholar of this century, rendered the original Latin into German in the style in which Kepler himself wrote in German. The English translation here of Kepler's quotations is by George Gregory, and is taken from Caspar's German. A more literal English translation can be fo und in the Abaris Books publication of the Mysterium Cosmographicum (New York, 1981), translated by A.M. Duncan with an introduction and commentary by E.}. Aiton. The fo otnotes that appear with the text were added by Kepler when the text-unchanged-was republished 20 years later. Ralf Schauerhammer works with the Fusion Energy Foundation in Germany and is the coauthor of The Holes in the Ozone Scare: The Scientific Evidence That the Sky Isn't Falling, published in 1992 by 21 st Century.

21st CENTURY Winter 1995-1 996 23 ceptual contradictions of quantum theory, to which Werner longer give a meaningful answer to the' question of the har­ Heisenberg pointed shortly before his ,death,:we see contradic­ monic ordering of the distance-relationships of the planets in tions that have been ignored rather than solved. And if we no­ today's Newtonian physics, we look. around for a substitute, a tice the trend toward increasingly reckless ad hoc hypothesis way of differentiating-or at least explaining-the actual plane­ and epicycles, then it is quite natural. to hope for a new Jo­ tary orbits among the infinitely many possible orbits. We find hannes Kepler. this explanation in the development of the solar system in time. A number of important selections from Kepler's fi rst work, The issue is not that Kepler assumed the solpr system and the Mysterium Cosmographicum, are presented here. These the universe to be fixed; he, too, hypothesized a development are intended to allow the reader to immediately relive Kepler's in time. But since Kepler's conception,of harmony is missing in own thinking. The selec'tions may inspire some readers to read Newtonian physics, this physics must be based on a temporal the entire work, and also others of Kepler's works, his Wo rld development that permits the individual planetary movements Harmony or the New Astronomy, for example. to be calculated backwards, from their present positions. This ·Whoever does that with an open mind, will recognize how must also be causally calculable from one step to the next, all rich Kepler's thinking was. First, it will probably seem striking the way back to the time when God originally wound up the that Kepler does not think that the three planetary laws, great clock of the universe. named after him, are as important as is commonly assumed Today, of course, we no longer speak of a clockwork of the today. This assumption results from the already mentioned universe and about God. We talk about a "Big Bang," and we mistaken approach, which claims that Kepler was a "forerun­ commit the blunder of thinking that we,have fo und out some­ ner" of Newton, because the basic laws of Newtonian plane­ thing meaningful about the universe if we can design a model tary mechanics can be derived easily from Kepler's laws. It for what happened in the first nanosecond of these billions of will become evident in a number of passages that Kepler fu lly years: a self-contradictory and methodologically ridiculous en­ understood the . quantitative :features of. ·the relationship of terprise-and all of that, because we do not have Kepler's idea mass,- space, and time, which are explained by universal of harmony! gravitation accord ing to Newton. 'Kepler, in fact-in his Kepler's concept of harmony is anything but the sort of mys­ Dream 'of the Moon-was able to correctly predict the bio­ ticism that some New Age fanatics wdJwkl like to make of it. logical effects of minimal "gravitation" of the Moon's surface Kepler explicitly states: "I do not want to prove anything with upon potential living beings. No such document by Newton the mysticism of numbers, and I also do not think this is possi­ is known . . ble." Instead, Kepler simply acknowledges the fact that the Kepler's physics was far richer than that of Newton, Laplace, multiplicity of geometrical forms cannot be taken from sense and other Newtonians. Kepler's harmonies imply a relativistic experience, but that they have their origins in the human en­ conception of space, which reemerged and was generally rec­ dowment of Reason, which is the prerequisite for knowledge ognized in physics only in this century, in a different form, on and scientific research about the world. Empiricist ideology ve­ the basis of earlier mathematical work by Bernhard Riemann. hemently denies this, and stubbornly throws itself into the "ob­ The depth of Kepler's method in physics is apparent when we jective" description of the first millisecond of- creation. look at the question of why the planets in the solar system ro­ c' , , tate around the Sun with precisely those distance-relationships Creativity in the Human Mind....L.and the Universe they have, and not with others. This question cannot be an­ Kepler, to the contrary, tells us, that we can only know swered today, in any meaningful way, by the limited methods something, as human beings endowed with Reason, to the ex­ of Newtonian physics. tent that we "look over our own shoulders" when we know In the macrophysical realm, it has become · impossible to something; that we can only know something new to the ex­ pose the question of harmonic relationships (or "quantum or­ tent that, in the act of knowing, we learn about our own cre­ bits"). But in the microscopic realm, we are compelled to op­ ative capacity; and that we can only know nature, because the erate with harmonically ordered orbit-systems, such as the Reason in our minds and hearts corresponds exactly to the orbits of electrons in the atom, for example. Why do the em­ quality of the development of the universe, which we experi­ pirical data of the atomic spectrum in the microcosm lead us ence outside of our own persons. to harmonic quantum orbits, while the harmonic relationships In Kepler's words, this means: of the orbits of the planets, which Kepler calculated from the observational data of the visible anomalies of planetary move­ od wanted to allow us to know the world ments, are inconceivable from the standpoint of today's when He created us in His image, so that physics? And why have the extremely precise relationships of we may participate in His own thoughts. harmonic intervals, which Kepler calculated for the planets in For what besides numbers and magnitudes his World Harmony, remained the same as they were then, de­ are in the mind of the human being? Only these do spite reciprocal influences (that is, the "perturbations" in the we correctly apprehend, and indeed, if piety permits terminology of the Newtonian theory of gravitation)? And, one it to be said, our knowledge is of the same kind as more question: Why was it possible to locate the planetary or­ the Divine, at least so fa r as we are able to bits for Uranus, Neptune, and Pluto, discovered after ·Kepler's understand anything in our mortal lives. death,' precisely in these musical intervals? . Even with such questions, we have hardly reached the end If Kepler's religious way of expressing himself seems irritat­ of the problems confronting today's physics. Since we can no ing, we should remember that God is the Creator who pro-

24 Winter 1995-1 996 21st CENTURY duced the laws of nature for which empiricism has hunted in with our eyes, even were no other utility connected vain in the form of the Big Bang. with it. And as the other creatures, so also the human Let this suffice as an introduction. We now turn to Kepler's body is sustained with fo od and drink, so the soul of Mysterium Cosmographicum. man, which is diffe rent from the whole of man,· kept alive by that sustenance of knowledge, enriched, and in a certain way promoted in growth. He who

--- DEDICATION OF THE FIRST EDITION -- has no yearning for such things in him, more resembles a corpse than a living being. do not want to speak of the fa ct, that my subject is a weighty testimony fo r the fact What a scathing critique of many people today, and most of of creation, which the philosophers have modern science, which has given up looking for the "being of denied. For here we see how God, like a things" and penetrating "to the causes of their being and be­ human architect, went about the work of designing coming," and instead limits itself to making "models" that only the world, according to order and rules, and "describe" empirical data and thus "more resemble a corpse constructed everything according to measure, so that than a living being." one could think, that it is not art which takes nature PREFACE TO THE READER as its model, but God Himself in His Creation ------looked to the design of the fu ture human beings. ven during the time, six years ago, when. I This is the most important hypothesis for all of science: The zealously devoted myself to association world is knowable by human Reason, because the laws of na­ with the renowned Master Michael ture are in accord with that Reason; but this natural lawfulness Maestlin, I sensed how inadequate, in has to be understood more profoundly than is usually done to­ many respects, the usual view about the construction day, and must also encompass, for example, the laws of "cre­ of the universe is. I was thus so excited by ativity" of classical works of art. Kepler continues: Copernicus, who my teacher mentioned quite often in his lectures, that I not only often defended his ndeed, must the value of divine things be views in the disputations with the candidates, but measured like a dinner in pennies? But, I also authored an elaborated disputation oli the please, someone will say to me, of what thesis that the "first movement" originated with good is the knowledge of nature to a the rotation of the Earth. I also began to ascribe to hungry stomach, of what good is all of astronomy? the Earth the movement of the Sun, fo r physical, Now, people ofReason do not listen to the ignorance or, if it better pleases the reader, fo r metaphysical which shrieks there, that such studies must not be reasons, just as Copernicus does it fo r mathematical undertaken. We tolerate the painter because he reasons .... entertains the eyes, the musician the ears, although they are otherwise of no use to us. Yes, the pleasure This expresses the fundamental difference between Kepler we derive from their works is thought to be not only and Copernicus. Copernicus wants to reassert uniform rota­ appropriate to human beings, it also does him honor. tional movement of the heavenly bodies, which the Ptolemaic What ignorance, what stupidity, therefore, to gainsay system only pretended to preserve. Kepler takes the Sun in the the spirit a pleasure which is a fitting honor to him, center of the universe as the starting point of a new physics, but not to gainsay this pleasure to the eyes and ears! and his equivalence between physics and metaphysics shows He does combat against nature, who combats against how diffe rent Kepler's notion of physics is from that of today's these pleasures! For the benevolent Creator who science. Just what is meant by that, will become evident in the called Nature into existence out of nothing, did He excerpt below (p. 27) from Kepler's Chapter 2. not bequeath to each creature that which is necessary, and both beauty and desire in plentiful bounty? �iI here were three things, especially, whose Shall he have left the spirit of human beings, the causes, why they are the way they ar:e,and master of all Creation, his own image, alone without not differently, I incessantly researched, the inspiring delight? Yes, we do not ask fo r what number, magnitude, and movement of the pleasure the little bird hopes, when it sings; fo r we orbits. I was led to dare this by those beautiful know, it takes pleasure in singing, because it was harmonies of things at rest; that is, the Sun, the fixed created to sing. Likewise, we may not ask why the stars, and the intervening space, with God the human spirit expends so much effort to seek out the secrets of the heavens. Our architect created the spirit .. Dear reader, fo rgive the beginner his not entirely correct manner of fittingto the senses, not only so that human beings speech. Philosophy, to be sure, seeks in the body something that is diffe rent fr om the human being, since the body undergoes continuous change, while may earn their livelihood-many sorts of creatures the human being remains an identity. The spirit, however, is that which can do that more skilfully with their unreasonable makes a human being human: so, the spirit is not something that is diffe rent fr om the human being. But what I wanted to say, remains: The spirit requires souls-but also to that purpose, that we may its sustenance, and that is diffe rent fr om the sustenance of the body, and it also penetrate to the being of things which we do not see has its special pleasures.

21 st CENTURY Winter 1995-1996 25 next. Now, at the points where the sides of the triangles intersected, there emerged a small circle; fo r the radius of the circle inscribed in such a triangle, is half of the radius of the circumscribing circle. The ratio between the two circles looked very similar to that of Saturn and Jupiter, and the triangle is the first of the geometrical figures, just as Saturn and Jupiter are the first of the planets. At once, I tested out the distance between Mars and Jupiter with a square, and the third distance with a pentagon, and the fo urth with a hexagon. Since the eye is also required fo r the second distance between Jupiter and Mars, I added a square to the triangle and to the pentagon. I could not stop, I wanted to try out everything. The end of this fa iled attempt was at once the beginning of the last one, successfully. My idea was, that is, that I would never reach the Sun by proceeding this way, if! wanted to maintain the order among the figures, and that I would find no reason why there should be 6, rather than 20 or 100 planets. But the figures pleased me. They are truly quantities, and they are The universe of Ptolemy: Heaven and Earth were of different natures and the Earth did something that existed before not move. the heavens. For quantity was created with the body at the Father, the Son, and the Holy Spirit. beginning, the heaven was created on the second I lost nearly the entire summer in this difficult day. So, I thought, if five figures can be fo und work. Finally, upon an entirely unimportant among the rest, and infinitely many others, fo r the occasion, I came closer to the truth. I believe it was magnitudes and the ratio of the six heavenly orbits, through divine Providence that I obtained by which Copernicus hypothesizes, fi gures that have accident that which I had been unable to obtain the advantage over others, that they have special previously through my work; I believe this all the characteristics, then the plan would go as I wished. more, because I always prayed to God to let my plan Now I pressed fo rward anew. What do figures in be successful if Copernicus had proclaimed the truth. the plane have to do with spatial orbits? The three­ Then, on the 19th of July 1595, as I wanted to show dimensional bodies would have to be dealt with my listeners how the great conjunctions always leap first. You see, dear reader, now you have my over eight points of the zodiac, and gradually discovery and the material fo r the whole of the little transpose from one triangle to another, I drew many book lying in front of you! For, if you tell that to triangles in a circle, if one can call them so, so that someone, who has just a little knowledge of the end of one always fo rmed the beginning of the geometry, then the five regular solids with their

26 Winter 1995-1 996 21st CENTURY Tetrahedron Cube Octahedron

Icosahedron Dodecahedron

Th e fi ve Platonic solids.

SKETCH OF MY MAIN PROOF ratios to the circumscribed and inscribed circles immediately leap into his eyes; he will recall at once n order now to come to my subject and to that fa mous corollary of Euclid to Postulate 18, Book substantiate the just described theory of 13, where it is proven that it is impossible that more Copernicus about the new world, I want to than five regular solids exist, or that they be go through the matter briefly from the conceivable. It is amazing: although I did not yet beginning. clearly understand the ordered succession of the It was body [substance] that God created at the particular solids, yet, on the fo undation of a beginning. If we have this conception, it becomes supposition, derived fr om the known distances of the somewhat clear why God created body at the planets, without any confirmation, I hit my target of beginning and not something else. I say that God had the ordering of the planets so successfully, that later, in His mind quantity; in order to realize it, He when I investigated the matter with specific reasons, needed everything that belongs to the essence of there was nothing that I had to change. body, and in this way, the quantity of body, insofar as I recall that I communicated the theorem just as it it is body, be the fo rm and starting point of its occurred to me, and in words I expressed it thus: definition.... "The orbit of the Earth is the measure fo r all the other orbits. A dodecahedron circumscribes it; the This means: God created the world "according to Reason," sphere circumscribing this is Mars. A tetrahedron so that things were created in an order of succession that is circumsubscribes it; the sphere circumscribing this is also knowable by reason. Jupiter. A cube circumscribes the orbit ofJupiter; the sphere that circumscribes this is Saturn. Now lay od wanted quantity to come into existence an icosahedron into the orbit of the Earth; the sphere before everything else, chieflyso that a inscribed to this, is Venus. Lay an octahedron in the comparison of curved and straight could orbit of Venus; the sphere inscribed in this, is occur. Mercury. There you have the reason fo r the number Nicholas of Cusa and others seem to me so of the planets." divinely great just fo r the reason, because they esteemed the relationship of the straight and curved In his first chapter, Kepler develops the reason for the cor­ toward each other so highly, and dared to ascribe the rectness of the Copernican theory and he explains it. In the curved to God and the straight to created things. second chapter, he goes on to his proof: Therefore, those who attempt to comprehend the

21 st CENTURY Winter 1995-1 996 27 Creator through the likewise become perfect, creatures, God through Prodromus it is evident, that accord­ human beings, divine DISSBRTAtlONPM COSMOGKAPHICARPM. ing to these laws that thought through human t,nt;n"" God prescribes to thoughts, hardly Himself in his goodness, accomplish work that is MYSTERIVM God could take the idea more useful than those COSMOCRAPHICVM for the foundation of the DE ADMIRAB I LI PRO P 0 R T lONE OR­ who seek to imagine i:he world from no other biumax:k�u?,: dcquc nu(j.ca:l�rum numeri. m.gni­ curved through the tudinis,moruumquc pcnodicorum ge_ thing than His own nuirili&propriis. straight, the circle essence. How excellent ... G.. l1Ittr;r•• through the square. DtI1lMfl'IIlIl1llP"fUillfNl,,,o£ui.co'p . and divine this is, may l.ibellusprimwn T6bi ngzin Ineem duus Anno Chrilll Although that alone M.DXCVl. be considered in two sufficed to establish the i respects, first, in c.M. IOANNE KEPLEIIO YYIIITI!M6EIIGICO. TYNC TSMPO_ purpose God had with the ,;,IRttjlri.m Stpi4tn.inri.lilU1ltM�h t11llJiu. Himself, insofar God is

quantities and the special Nunc�ero pollannos lJ.abeodcmauthorc rccognitusJ & Noris noubiliffimf. one in essence and partimcmendarus, partl� cxpli�rus,partim conlirmatus : dcniq; omnibus luil importance of the curved, mcmbClscolla(u�. ad aha cognati argument.. operl.qu� Authorcx ilJo rem .. threefold in the person, something else came into pore (u bduorum Impp. Rudolph. &:Macthiza u(piciisi cfiam" iQ and then in comparison Illunr. Ord. Authiz Supt-Alli(anzclicnre1a it in addition, something diucrfiilociscdidlt. with the creatures. ,,,fIi.1tua Mlil'!flr,,J,,,«ufil llliol" iI,HD'm,";rlMoJi, JiOiJli,f fa r greater; that is, the f.t/"#l"ff. llllti.",.ltrU &,.tI",. This image, this idea, NA.... AT.O IOACIll image of the triune God Add!tJ.!flcmditt M. C�o ..GU IWI R.HITlCI.d� God wanted to stamp . de LibnsReaohlDOnQtD.Itqueadnlirandls namno.ordinc. & diRanliit Sphn•• in the area of the sphere, rumM�d.ihypochtlibw:.crcdtrntiffimi Ml themltici,IO(iu('luc A n...onorni&R.r-­ upon the world. That fillUXOrd D. NICOLAI Co ...... Ct. of the Father in the center, I r.,,- the world might become (OAIIM littf4- •• ItJ..'l. I al1"r-o,mH '0100 of the Son in the surface, ,.Daonfo-"""::;::::'..".;m)lal;,"'''''''""""",,A ...... ". the best and most of the Holy Spirit in the beautiful world, that it C.. PrillilcpoCWno...... equality of the position be able to take up this between the point and the idea, the omniscient surface. For that which Creator created Fa ANCo',arl.

Cusa ascribes to the circle, Rccurus Typis E ...ASM I KEMPlI!... ..fu hlptibu5 magnitude and and others to the space of GODI'.. 'D' TAN'ACHIL conceived the quantities, the sphere, that is what I "",,"0

28 Winter 1995-1 996 21 st CENTURY bases his proof, among other things, on the prominent world, because they are infinite in number and thus importance of the surface of the sphere. For the same unsuitable fo r an order.* The bodies, of which there reasons, even fa rthest fixed stars still have this fo rm, are an infinite times infinitely many kinds, we now although no movement is ascribed to them; this fo rm want to examine, and select some of them on carries the Sun as the center-point in its bosom. That account of certain characteristics; I am thinking of the other orbits are round results from the movement those where there are equal edges or the angles or of rotation of the stars. That, therefore, the curved the sides, individually or in pairs or in some certain fo und application fo r the decoration of the world, shared lawfulness, so that one can come to

requires no fu rther proof. . . . something finite with a good reason. If now one species of bodies, defined by certain conditions, Kepler here is still assuming circular planetary orbits and indeed consists of an infinite number of kinds, but not elliptical orbits, as he would later. It is not possible to see resolves into an immense multiplicity of individual a fixed-star's parallax with the naked eye, and it took many bodies, then we want to use the corners and the decades until the telescope was sufficiently developed that midpoints of the sides of these bodies to represent the different distances of the fixed stars could be observed. the multiplicity, the side and position of the fixed Moreover, today's microwave background of the "Big Bang" stars, if it is possible. If, however, this surpasses the ' corresponds conceptually to an external spherical shell of power of a human being, then we want to postpone the universe, which is the sphere of the fixed stars, according determining the number and position of the fixed to Kepler. stars, until someone can tell us all of them, according to number and magnitude. For that lthough we see three kinds of quantities in reason, we leave the fixed stars aside, and leave them the world, that is, form, number, and body, to the omniscient Architect, who alone knows the we find the curved only in the fo rm. The number of the stars, and calls each by its name, and content is not important, and indeed, we turn our view to those that are closer, which exist fo r that reason, because a figure inscribed in a similar in fe wer number, the movable stars. figure with the same center (for example, a sphere If we now finally make a selection among the within a sphere, a circle within a circle), either bodies, and push to one side the entire lot of those touches everywhere or nowhere. That which is that are irregular, and only keep those whose sides spherical, since it represents an absolutely unique are all equal and all of equal angles, then those five quantity, can only be associated with the number 3. regulaT solids remain, which were given the . If, therefore, God had considered nothing but the fo llowing names by the Greeks: the cube Of the curved at the creation of the world, there would be hexahedron, the pyramid or the tetrahedron, the, nothing in our world structure but the Sun at the dodecahedTon, the icosahedmll, ,and the octahedron. ;t center, which was the image of the Father, the sphere of the fixed stars, or the water of the Mosaic report

upon the surface, which was the image of the Son, .. Oh! That is bad. We want to leave them out of the world? Yes, in the and the heavenly ether filling everything, that is, the Harmony [ called them back again fo r reason of the right of return. Why do extension and the fi rmament, which was the image we want to ban them? Because they are infinite in number and completely unsuitable fo r an order. But it is not they that are unsuitable, but [ was un­ of the Holy Spirit. But because the fixed stars exist in suitable, on account of my ignorance at that time, which [ had in common uncountable numbers-although the wandering with most to comprehend their order. Thus, in Harmony I, I made a selec­ stars are a determinate number, and because the tion among the infinitely many, and discovered the beautiful order that exists among them: For what should we ban the lines from the original image of magnitudes of the individual heavenly orbits are the world, where God Himself made use of the lines in his work fo r its rep­ diffe rent, we must necessarily seek the cause fo r all resentation, that is, through the movement of the planets? The manner of ex­ pression, therefore, must be improved, in order to maintain the sense. In the of this in the concept of the straight. We must then establishment of the number of the heavenly bodies and of the breadth of the assume that God made something in the world spheres, the lines should indeed be left aside initially; in classifying the move­ haphazardly, although the best and most reasonable ments, however, which occur in lines, we cannot leave the lines and surfaces to one side, which alone are the <)riginsof the harmonic proportions: plans are available; and no one will be able to t The prominent importance of the solids lies in their simplicity and in convince me, that this plan is only valid fo r the fixed the equal distances of the sides from the center of the figure. For, as God is stars, whose positions are the least regular, as if deter­ the norm and rule fo r the created ,things, so is the sphere fo r the solids. This, however, has the previously mentioned characteristics: (I) It is the simplest, mined by the chance fa ll of a seed. because it is enclosed in a boundary, that is, by itself. (2) All of its points have Let us, therefore, now consider the straight the perfectly same distance from the center-point. Of all the solids, the regu­ lars are the closest quantities. Just as we previously chose the spherical to the sphere in perfection. Their definition lies in the re­ quirement that they (I) have edges, (2) sides, and (3) vertices, which are the surface because it is the most perfect quantity, we same in kind and magnitude; therein lies the simplicity. From this definition, now move with one leap to the bodies (solids), it fo llows, without fu rther ado, that (4) the center-points of all sides are equally distant from the center-point (of the figure), because they are the most perfect among the straight (5) that the figure in­ scribed in a circle touches it with all the vertices, (6) that they sit firmly quantities, and consist of three dimensions. That the within it, (7) that they touch an inscribed circle with the midpoints of all the idea of the world is perfect is established. But we sides, (8) that the inscribed circle sits firm without movement, (9) that they have the same midpoint as the figure. That brings about anotlier similarity want to leave the straight lines and surfaces out of with the sphere, which consists in the'equality of the distances from the the finite, best ordered, and perfectly beautiful sides.'

21 st CENTURY Winter 1995-1 996 .29 For the proof that there can not be more than these of six spheres. five,see Euclid, Book XIII, the note fo llowing Now, if any other age had examined the order of Theorem 18. * the world on the basis of the assumption that there Because now the number of these solids is definite are six movable orbits around the immovable Sun, and very small, but the number of the remaining ones this was, by all means, a result of true astronomy. is uncountable or infinite, then there must be two But Copernicus has, infa ct, six orbits of this sort, which species of stars in the universe also, which distinguish have proportional relationships to each other pair-wise, themselves by an evident characteristic (such as are such that the five solids fit peifectly within them; that is rest and motion); the one species must border on the the essence of the fo llowing discussion. So, one will infinite, the other must be narrowly limited, like the have to listen to Copernicus until someone poses number of the planets. This is not the place to discuss hypotheses which agree even better with our the reasons why these planets move but the others do philosophical observation, or until someone teaches, not. But assuming, that the planets are in need of that that which has been directly gained from the movement, then it fo llows that they must obtain principles of nature by means of the most rigorous circular orbits in order to maintain this movement. procedure of proof, might have smuggled its way, Thus, we arrive at the circular orbit through quite by accident, both into the numbers as well as movement, and at the bodies through the number of into the human spirit. For what could be more magnitude. What other choice do we have, than to surprising, than the fact that that which Copernicus say, with Plato, that God is always practicing discovered in the phenomena, in the effects, a geometry, and, in the construction of the wandering posteriori, just as a sculptor supports himself with his stars, he inscribed bodies in circles and circles in cane (as he used to say to Rheticus), more through a bodies fo r so long, until there was no body left that fo rtunate whim than through a reliable procedure of was not accompanied by movable circles within and reasoning, and fo rmulated, that all of that, I say, can without. From the theorems 13, 14, 15, 16, and 17 of be established and comprehended from reasons, the 13th book of Euclid, it is evident to what a high which are derived a priori fr om causes, from the idea degree these solids are suited by nature fo r this of the Creation? process of inscription and circumscription. If now But if someone should want to take these the five solids are embedded in each other, and philosophical conclusions of reason unreasonably and spheres are added both between them and outside of reject them in mockery, fo r that reason that I, a them to bound them, then we obtain just the number novice, present them toward the time of the end of the world, while the old lights of philosophy are

* That note reads as fo llows2: There can be no other solids in addition to silent, to such a person I would introduce Pythagoras the fi ve named, enclosed by equally sided and equally angled sides. For no fig­ as a leader, guarantor, and guide from the most ure can be formed from two triangles or two other figures. distant antiquity. I have mentioned him often in my From three triangles, however, there ensue the vertices of the pyramid, out of fo ur those of the octahedron, out of fivethose of the icosahedron. lectures. For, since he understood the excellence of From six equally sided and equally angled triangles, which come together the five solids, he came to the insight 2,000 years ago, at a point, no solid vertex can be fo rmed. For since the angle of the equally through considerations very similar to mine today, sided triangle is 2/3 of a right-angle, six such angles taken together are fo ur right angles. And that is impossible. For the entire solid vertex is fo rmed that it was not unworthy of the Creator to take from less than fo ur right angles (Euclid Book XI, Theorem 21). consideration of them, and he ordered For the same reason, no solid vertex can be fo rmed out of more than six such angles. nonmathematical things, on account of their nature The vertices of the cuhe ensue from three squares; fr om four squares there and their special accidental qualities, according to ensues no solid vertex, fo r its angles, taken together, are fo ur right-angles. esteemed mathematical things. The Earth he The vertices of the dodecahedron ensue from three equally sided and equally angled pentagons. But no solid vertex ensues from fo ur of them. For equated to a cube because both are stable, which is a since the angle of the equally angled pentagon is one 115th of a right angle, quality not only of the cube. The heavens he assigned fo ur such angles would be larger than fo ur right angles. And that is impossi­ to the icosahedron, because both can rotate. He ble. Solid vertices also cannot be fo rmed by other polygons, because that would result in something impossible. It is, therefore, clear, that no other assigned the pyramid to fire, because these have the solids can be fo rmed than the named five, which are enclosed by equally sided fo rm of a fl ickering flame; the other two solids he and equally angled sides. Therefore: distributed between air and water, because in both cases, the one part is related to the other. But No. of No. of No. of Inscribed Pythagoras had no Copernicus who might have told Type of face faces edges vertices sphere him .first of all what exists in the universe. Starting Cube Quadrilateral 6 12 8 Medium fr om that, he w�uld doubtless have fo und out why it

Octahedron Triangle 8 12 6 Equal to is so, and this arrangement of the heavenly orbits cube would be as well known today as the five solids en themselves, and would be as accepted as was the case, Dodecahedron � Pentagon 12 30 20 Largest in the past, with the belief in the movement of the Icosahedron Triangle 20 30 12 Equal to dodeca- Sun and the immobility of the Earth. hedron But let us investigate fu rther, whether the Tetrahedron Triangle 4 6 4 Smallest proportions of the five solids prevail between the orbits of Copernicus. First of all, we shall make a

30 Winter 1995-1 996 21st CENTURY and Saturn represent the second largest diffe rence. The first is only a little more than the half of the latter. A similar diffe rence occurs in the interior and exterior circle of the cube. Saturn thus circumscribes the cube, while the cube circumscribes Jupiter. Nearly the same proportion prevails between Venus and Mercury; it is not dissimilar to the proportions of the circles of the octahedron. Venus circumscribes this solid, while Mercury is circumscribed by it. The two remaining proportions between Venus and the Earth, as well as between these and Mars, are the smallest and are nearly identical to each other; the interior orbit is three quarters or two thirds of the exterior. In the icosahedron and the dodecahedron, the proportions of the distances of the two spheres are likewise identical, and here they are in fa ct the smallest among the regular solids . .It is therefore probable that the distance of Mars from the Earth is determined by the others. Thus, if I am asked, why there are only six movable orbits, then I shall answer: because there cannot be more than five proportions, The Copernican system, in which the Sun has been put at the center of the universe. Coper- so many, that is, as there nicus's theory was an important point of departure fo r Kepler's revolutionary discoveries. are regular solids in mathematics. But six rough estimate. According to Copernicus, the largest magnitudes result precisely in this number of difference in distance exists between Jupiter and proportions. . . Mars, as may be seen in the representation of the hypotheses in Figure 1 [not shown] and fu rther ------CHAPTER 13 ------­ below in chapters 14 and 15. The distance of Mars ON THE CALCULATION OF THE SPHERES INSCRIBING from the Sun is not even a third of the distance fr om AND CIRCUMSCRIBING THE SOLIDS Jupiter. We must therefore seek that solid fo r which the difference between the circumscribed and tiC d;«"",;on th", [" """ only to '"ppon inscribed sphere is the largest (permit me to use the the theorem we have posited with reasons hollow solid rather than the firm solid); this is the of probability. Now we want to move to the tetrahedron or the pyramid. The distances of Jupiter rIl determination of the astronomical orbits 21st CENTURY Winter 1995-1 996 31 Table 1 PROPORTIONS OF CIRCUMSCRIBING AND INSCRIBING SPHERES TO THE FIVE SOLIDS

Radius of the Length of Radius of the circle Radius of the circumscribing sphere the edge circumscribing a face inscribed sphere

Cube 1,000 1,115 816112 577

Tetrahedron 1,000 1,633 943 333

Dodecahedron 1,000 71 4 607 795

Icosahedron 1,000 1,051 607 795

Octahedron 1,000 1,414 816112 577*

* [Kepler's note on the lable]: By Ihe way. Ihe radius of Ihe circle inscribed in the octahedral square is 707.

and to geometrical investigations. If these investigations the solids must be taken in the order of succession as do not agree, then all of our effort has been in vain. First I established above, fo r inherent reasons. of all, we want to see in what proportions the spheres, inscribed and circumscribing, stand to the fivesolids. Kepler compares the values he found in the previous chap­ ter with the distances of Copernicus, and obtains the approxi­ Kepler now calculates the values in Table 1, which is the mation in Table 2. basis for the calculation and the comparison with the distances Kepler continues: as Copernicus had determined them. If one adds the lunar system to the thickness of the ------CHAPTER 14 ------­ Earth orbit, and lets 1,000 units be the standard fo r THE CHIEF PURPOSE OF THE BOOK; THE the interior of the orbit of the Earth and the Moon, ASTRONOMICAL PROOF, THAT THE FIVE SOLIDS LIE then the exterior of the orbit of Venus is 847, IN BETWEEN THE HEAVENLY ORBITS according to Copernicus. The exterior of the Earth's ...Since I have taken it upon myself, at the orbit with the Moon is 801, if the interior of the orbit beginning of my work, to derive from the five solids of Mars is 1,000. Please refer time and again to the the reason why the omnipotent Creator always left chart preceding this discussion [Table 1], where I just so much space between two planets, and to show have represented the embedding of the solids. that the individual solid figures determine the spaces And now see how the corresponding numbers in between, in succession, we now want to see with approximate each other. For Mars and Venus, they what success this book shall be crowned; we want to are the same. For Earth and Mercury, they are not so bring the issue before the judge's bench of astronomy very diffe rent from one another; only fo r Jupiter do fo r judgment, and Copernicus shall explain it to us. I they diverge greatly, but, at that immense distance, shall let the orbits themselves be as thick as required no one should be surprised at this. One also sees what by the rising and setting of the planets. If the solids a great diffe rence the small circle of the Moon makes are so arranged as I have said, then the interior side fo r Mars and Venus, if the thickness of the Earth's of a sphere above it must coincide with the sphere orbit is added, although this little circle has hardly surrounding a solid, the exterior side of the next three parts, while the Earth's orbit is 60. sphere must coincide with the interior sphere; but It is evident from this how easily one would have

Table 2 KEPLER'S ORBITAL DISTANCES COMPARED WITH THOSE OF COPERNICUS

Radius of the Sphere of the planet Orbital distance according Chapter interior sphere beneath it to Copernicus no!

Saturn 1,000

Jupiter 1,000 577 635 9

Mars 1,000 333 333 14

Earth 1,000 795 757 19

Venus 1,000 795 794 21 and 22 - Mercury . 1,000 577 or 707 723 27

* in Book V of Copernicus

32 Winter 1995-1 996 21st CENTURY noticed, and what great discord in the numbers had The haughty enemy, who shows contempt occurred, if our experiment had turned against the For thee, and shows contempt fo r law and justice. nature of the heaven; that is, if God Himself had not Yet, to believe thy Godhead is within taken account of these proportions when He created This spacious sphere, let me look up astonished the Universe ... At thy achievement of this mighty heaven. The work of the great Craftsman, miracles CHAPTER 15------­ Of thy strong hand; see how thou hast marked out THE IMPROVEMENT OF THE DISTANCES AND THE The fi ve-fold pattern of the starry spheres. DIFFERENCE OF THE PROSTHAPHERESES Dispensing light and spirit from their midst; See by what law thou dost control the reins The prosthapheresis is the angle which an orbit of an interior Of their eternal course; see how the Moon planet passes over when viewed from a certain point on the Varies her path, her toils, how many stars orbit of an exterior planet. In the Mysterium Cosmographicum, Thy hand has scattered over that boundless field. Kepler develops a precise table of his model in comparison to Great Builder of the Universe, what plea the Copernican distances. Table 3 is derived from Kepler's Of the poor, humble, small inhabitant table. All magnitudes are given in astronomical units (A.U.); Of this so tiny plot compelled thy care that is, where the distance from the Earth to the Sun is 1. The For his harsh troubles? Yet thou dost look down higher value is the maximum orbital distance of the planet On his unworthiness, carry him up from the midpoint of the Sun; the lower is the minimal value. On high, a little lower than the Gods, Column 1 gives the values calcu lated on the basis of the Bestow great honors on him, crown his head Prutenic Tables according to the Copernican system. Column Nobly with diadem, appoint him king 2 shows the results from Kepler's model of the five Platonic Over the tokens of thy handiwork. solids. Column 3 gives the values accepted today. Column 4 Thou makest all that is above his head, shows the difference between Kepler's model and the Coperni­ The great spheres with their motions, bow before can values, and column 5 shows the difference from today's His genius. All creatures of the Earth, accepted values. The herds bred fo r his works, and fitted fo r The numbers in Kepler's model represent the thickness of The smoking altars, and the generation the spherical shell within which the orbits of the planets lie, Of wild beasts, which remain to dwell in woods, where he takes the distance of the Moon (the Earth's Moon was the only known Moon in the solar system at that time) for the thickness of the Earth's orbit, and not the difference be­ Table 3 tween the perihelion and aphelion. KEPLER'S MODEL OF THE ORBITS The largest divergences result with respect to the Earth, COMPARED WITH THAT OF COPERNICUS A.U.) which is understandable, because Kepler's Earth orbit was (all figures are in The largest deviations of the two models arise in the case conceptually somewhat different from what Copernicus or to­ of the Earth. The significance of this, however, is that day's measurements understand by the Earth's orbit. Kepler's Kepler's Earth orbit is conceptually different from what . orbit would actually have to be called the Earth-Moon orbit. Copernicus and today's measurements understand by Kepler's values for Jupiter and Saturn are even closer to to­ day's values than the Copernican values, but, for the interior Earth orbit. Kepler's orbit would properly have to be called the Earth-Moon orbit. For Jupiter and Saturn, Kepler planets, only the aphelion of Mercury agrees exactly. Kepler was even closer to today's values than the Copernican val­ was well aware of the discrepancies between his model and ues, while for the inner planets only the aphelion of the Copernican values. Mercury agrees exactly. Kepler was aware of the discrep­ ancies between his model and the Copernican values. ------CHAPTER 23 ------­ ON THE ASTRONOMICAL BEGINNING AND THE ASTRONOMICAL END OF THE WORLD, AND ON THE Column no. 2 3 4 5 PLATONIC YEAR

In this last chapter, Kepler ends his work with the following poem. Not wishing to deprive the reader of its simple beauty, it is here reprinted in fu l1.3

reat God, Creator of the Universe, And our eternal power, how great thy fa me In every corner of the whole wide world! How great thy glory, which fl ies wondrously Above the fa r-flungrampa rts of the heavens

With rushing wings! The babe salutes it, spurning Mercury 0.49 0.47 0.47 -0.02 0.00

The breast, replete, and with his halting lips 0.23 0.22 0.31 -0.Q1 -0.09 Bears powerful witness-witness which confounds

21st CENTURY Winter 1995-1 996 33 makes a claim fo r the harmonic relationships seen from the standpoint of the Sun, between the angular velocities at ex­ treme points of the or­ bits (that is, aphelion and perihelion) of the planets, which suppos­ ed ly means that he gave up the hypothesis of the Mysterium. Kepler delivered an appropriate answer to all of these academic argu­ ments: Two decades af­ ter the publication of his first work, Kepler re­ printed it completely un­ changed, merely adding a few footnotes. That which no for­ malist understands is quite simple for Kepler's creative thinking. There is no contradiction be­ tween the Mysterium and the World Har­ mony, because the har­ mony they both de­ scribe is a process. Kepler says that he set out to discover the har­ mony of a crystal in the Mysterium, and then, in the World Harmony, he found one in fact that is living. Both models cor­ respond to the nature of Kepler's model of the universe, a copper engraving from the fi rst edition of Mysterium Cosmo­ the solar system, and graphicum in 7596. The five Platonic solids are in harmony with the planetary spheres. both remain true, de­ spite their formal differ­ The birds, which with light fe athers strike the air, ences. Neither of them is a "model" in today's sense of the The fish, which swim through rivers and through seas, term; each is a different expression of the universal process of Over all these by thy command he rules the development of nature. We see these harmonies, because By his dominion and his strong right hand. they carry the process of life, like a "little flag," just as does the visible Golden Section in the five petals of a flower. Great God, Creator of the Universe, Until his death, Kepler always looked upon the Mysterium And our eternal power, how great thy fa me Cosmographicum as the cornerstone of all of his work because In every corner of the whole wide world ! it expressed the character of his thinking and the character of the physical lawfu lness of nature. In this sense, Kepler says in The Mysterium and Kepler's life's Work his work Tertius Intervenies: "It is thus one of my ideas, In conclusion, we ask how Kepler's first work is to be un­ whether all of nature and all heavenly adornment is not sym­ derstood in the context of his life's work in general. Thorough bol ized in geometry." For, after all, he says, "As God played historians do point out how much Kepler's ideas are supposed the Creator, He also taught nature to play as His image, and, to have developed over the course of his life. The shift to ellip­ indeed, the very game which He played." tical orbits, especially, in contrast to the circular orbits about Author's Notes ------which Kepler speaks in the Mysterium, is taken to prove, that 1. This note was included in the first· edition. 2. This note was induded in the first edition. Kepler was still bound to "Aristotelian" thinking. Attention is 3. The English is reprinted with permission from A.M. Duncan's translation of also called to the fact that in the World Harmony, Kepler the Mys terium Cosmographicum (New York: Abaris Books, 1981), p. 225.

34 Winter 1995-1 996 21st CENTURY , FIRST. 'ENGLISH TRANSLATION Riem.ann�s Pllilosephieal Fragrlte'rtls

FOREWORD Riemann Refutes Euler' by Lyndon H. LaRouche, Jr.

TRANSLATION

. Philos�phic�l frag�ents ' by Be��haFd Riemallln

Introduction to the Second German Edition by Heinrich Weber 50,

Translator's Note ' 50 I. On Psychology and Metaphysics 51 II. Epistemological Issues 55 III. Natural I?,�ilosophy , SUPPLEMENTARY MATERIAL On the Hypotheses Which lie at the Foundations of Geometry [excerpts] by Bernhard Riemann

Riemann in English Translation 47 Euler's Lying Attack on Leibniz 48 Herbart on the Thc;)Ught Process 52

21 st CENTURY Winter 1995-1 996 35 Riemann Refutes Euler

Libraryof Congress Library of Congress Bernhard Riemann (1826-1866) Leonhard Euler (1707- 1783)

by Lyndon H. LaRouche, Jr.

n the fo llowing pages, 21st Century presents the first known main, into physics.s That statement plants Riemann, like his publication in English translation, of a group of posthu­ sponsor Karl Gauss before him, fu lly within the domain of I mously published early writi ngs of the famous physicist physics, rather than the virtual reality which one associates Bernhard Riemann (1826-1 866).' These have the special sig­ with the influence of Bertrand Russell and the Bourbaki nificance of providing some relatively indispensable back­ golem upon much of today's teaching of mathematics. The ground for understanding how Riemann came to develop his posthumously published papers presented in English transla­ earthshaking discoveries of 1853-1 854.2 tion here, bear directly on Riemann's development of his ap­ The special relevance of these pieces, pertains to the fact, proach to that issue. that there can be no competent appraisal of Riemann's work, which does not treat his writings as, like those of Karl Weier­ Riemann and Economics strass, a devastating refutation of Leonhard Euler's savage at­ 21 st Century's attention to Riemann reflects my own origi­ tacks on Gottfried Leibniz.3 The formal issue is the question, nal work in a branch of physical science founded by Leibniz, cloaked in a discussion of mathematical series, whether or known as physical economy. My discoveries in this field sup­ not mathematical discontinuities exist.4 The relevant substan­ plied the principal impetus for the mid-1970s fo unding of the tive issue behind these attacks on Leibniz by the 18th century Fusion Energy Foundation, which ricocheted into the later Newtonians, Dr. Samuel Clarke and Leonard Euler, is, much fou nding of 21st Century magazine. Although the principal more today than during Riemann's time, whether physics is a part of my discoveries were not prompted by Riemann's branch of mathematics, or mathematics a branch of physics. work, the approach adopted for solving the mathematical As in the concluding sentence of his famous 1854 habilita­ problems posed by those discoveries was prompted almost tion dissertation, Riemann demonstrated that, to settle the entirely by Riemann's habilitation dissertation, leading to the underlying issues of mathematics, one must depart that do- designation of "LaRouche-Riemann Method."6

36 Winter 1995-1 996 21 st CENTURY To introduce Riemann's posthumously published papers, I suggests. We must add non-space-time "dimensions," such as indicate the features of his dissertation which are most rele­ the notions of "mass," "charge," and so forth, to derive a vant to the problems of physical economy. To that end, con­ mathematics which agrees with our measurement of the mo­ sider, first, the place which mathematical discontinuities oc­ tions which are reflected, from physical space-time, upon that cupy in Riemann's discovery, and then, the significance of imaginary mirror known as simple space-time.8 Riemann's emphasis on what he terms Geistesmassen in the Thus, in place of a four-dimensional space-time of the posthumously published papers. imagination, the attempt to explore physical space-time pre­ First, to define the significance of mathematical discontinu­ sents us with a physical-space-time manifold of many more ities, I restate Riemann's point of departure in his dissertation dimensions than the four dimensions of naive space-time. We in my own words. call these added factors "dimensions," because they can be The origin of modern mathematics lies in what is com­ scaled, according to the ordering-principle of "greater than" monly identified as a "Euclidean" notion of simple space­ and "less than," as we do the dimensions of naive space-time. time. This idea of space-time pretends to represent the real Instead of saying n + 4 dimensions, we include the four in universe, which it does not represent. It is an idea which is our count of n; we speak, thus, of a "physical-space-time not a creation of the senses, but, rather, of the naive imagina­ manifold of n dimensions." Then, commonly, we attempt to tion. We merely imagine that space is defined by three senses portray motion within that physical-space-time, of n dimen­ of direction (backward-forward, up-down, side-to-side), and sions, in terms of its imaginary reflection upon a four-fold imagine that these might be extended without limit, and in space-time. perfectly uninterrupted continuity. We imagine that time is a In each case, the addition of a validatable new "dimen­ single, limitless dimension of perfect continuity: backward­ sion" to the physical-space-time manifold of reference, corre­ forward. Taken together, these presumptions of the imagina­ sponds to a change in measurement, a change in the yard­ tion define a four-dimensional space-time manifold, or, in stick we must employ to measure the relevant motion, or other words, a quadruply extended space-time manifold. analogous form of action. For example, Eratosthenes esti­ The naive imagination attempts to locate perceptible bod­ mated that the Earth was a spheroid of about 7,850 miles, ies and their motions within such a quadruply extended man­ from pole to pole (not a bad estimate for the time}.9 This ifold. It may be said fairly, that our imaginary space-time meant, that to measure motion along the surface of the Earth, manifold is used as a kind of mental mirror, upon which we we must use a yardstick of spherical trigonometry, rather than attempt to project reflections of motion of bodies in space­ one appropriate to a simple Euclidean plane. Similarly, once time. The result of such projections is a simple "Euclidean" Ole R0mer had demonstrated, in 1676, that the radiation of sort of algebraic mathematics, which, we soon discover, is light was governed by a principle of retarded potential, Chris­ not a mathematics of the real universe. tiaan Huygens, in 1677, generalized principles of reflection Classical experiments, typified by the measurement of the and refraction accordingly,lO and, Jean Bernoulli and Leibniz curvature of the Earth's surface by the ancient Eratosthenes of demonstrated that the mathematics of the transcendental do­ Plato's Academy at Athens/ supply measurable demonstra­ main's special relativity must supersede the algebraic meth­ tion that the motion of bodies in physical space-time does not ods of Galileo, Descartes, and Newton.1 1 correspond to what a naive, algebraic notion of space-time The validation of the necessary addition of such an added

1. See Bernhard Riemann's Gesammelte Mathematische Werke, Heinrich what became known as Leibniz's calculus was actually developed during Weber, ed. (New York: Dover Publications reprint, 1953), "Fragmente 1672-1676, in Paris, at Jean-Baptiste Colbert's Royal Academy of Sci­ philosophischen Inhalts," pp. 507-538. A more recent reprint of the same, ence. Leibniz's first paper, presenting the discovery, was submitted for Heinrich Weber's second edition (Stuttgart: B.G. Teubner, 1902), is publication, in Paris, in 1676, immediately prior to his return to Germany. Vaduz, Liechtenstein: Saendig Reprint Verlag Hans R. Wohlwnend. Here­ Isaac Newton's international reputation, and the Newton-Clarke attack on inafter, this is identified as Riemann Werke. Leibniz, was created by Venice's Paris-based Abbot Antonio Conti (1677- 2. See Bernhard Riemann, "Ober die Hypothesen, welche der Geometrie zu 1749), who sponsored a network of salons throughout Europe, a network Grunde liegen" ("On the Hypotheses Which Underlie Geometry"), Rie­ devoted to the principal mission of seeking to discredit Leibniz, and build mann Werke, pp. 272-287. This is the famous June 10, 1854, habilitation up Newton's reputation. Dr. Samuel Clarke was an agent of Conti, as dissertation, to which Albert Einstein referred, in identifying Riemann's were the Berlin circles of Maupertuis and Euler. work as a root of General RelatiVity. On the dating of the work embodied 5. "Es fiihrt dies hiniiber in das Gebiet einer andern Wissenschaft, in das in this dissertation, 1853-1854, see H. Weber's reference to Riemann's Gebiet der Physik, welches wohl die Natur der heutigen Veranlassung note, which dates the discovery underlying the paper to "March 1, 1853": nicht zu betreten erlaubt." ('This leads into the domain of another science, Werke, p. 508. the realm of physics, which the nature of today's occasion does not permit. 3. On Euler's attack on Leibniz, see Lyndon H. LaRouche, Jr., The Science us to enter.") Habilitation dissertation, Riemann Werke, p. 286. of Christian Economy (Washington: Schiller Institute, 1991), Appendix XI, 6. See Lyndon H. LaRouche, Jr., "Why Most Nobel Prize Economists are "Euler's Fallacies on the Subjects of Infinite Divisibility and Leibniz's Mon­ Quacks," Executive Intelligence Review, July 28, 1995, and Lyndon H. ads," pp. 407-425. That appendix includes the sections of Euler's Letters LaRouche, Jr., "Non-Newtonian Mathematics for Economists," Executive to a German Princess (dated by him May 5, 1761) in which his second ex­ Intelligence Review, Aug. 11, 1995. plicit attack on Leibniz is made. The first occurred as his role in the scan­ 7. See "How Eratosthenes Measured the Unseen" (Figure 2), in Lyndon H. dalous case of Pierre-Louis Maupertuis, whose exposed fraud on the sub­ LaRouche, Jr., "Kenneth Arrow Runs Out of Ideas, But Not Words," 21st ject of "least action" led to Maupertuis's 1753 ouster from direction of the Century, Fall 1995, p. 34-53. Berlin Academy; Euler was the prinCipal accomplice of Maupertuis in per­ 8. This image is an accurate representation of the intent of Plato's reference petrating that hoax. We emphasize the primary coincidence between Rie­ to shadows which reality casts upon the imagination, as if these shadows mann and Weierstrass here, not their secondary differences in approach. were reflections on the wall of a cave's firelit interior. 4. See the ·Leibniz-Clarke correspondence on the subject of the relationship 9. Greek Mathematical Works, 1980. Ivor Thomas, trans., 2 vols. (Cam­ between infinite series and the differential calculus. (G.W. Leibniz, Philo­ bridge, Mass.: Harvard University Press), Vol. II, p. 273, note c. sophical Papers and Letters, edited by Leroy E. Loemker, 2nd edition 10. Christiaan Huygens, A Treatise on Light (New York: Dover Publications [Dordrecht: D. Reidel, 1969, reprinted Boston: Kluwer Academic, 1989], reprint, 1962). pp. 675-721.) Although Leibniz's development of the differential calculus 11. The "brachystochrone problem": Jean Bernoulli (1696). The equivalence had roots in some of his earlier activities, the archival evidence is, that of least time to least action.

21st CENTURY Winter 1995-1 996 37 physical dimension, by measurement, implies the challenge science, whether by Plato and his academy after him, or from to be considered here. Each such addition signifies, that in­ moderns such as Leibniz or Riemann, fills such positivists stead of an n-fold physical-space-time manifold, n is super­ with an obscene, irrationalist rage, akin in spirit and rational­ seded by (n+ 1). This gives us a generalized term of topology, ity to that of Marat's or Danton's Jacobin mob. which we might express symbolically by (n+ 1)/n. The series This deeper of the two levels of axiomatic issues, underlies of changes, from n to n + 1 dimensions, is associated with a the assignment of Abbot Antonio Conti's agent, Dr. Samuel series of changes in the choice of the yardstick which we Clarke, for the attacks upon Leibniz. Th is is the issue underly­ must employ to measure the relevant physical action.12 ing the savage, posthumous attacks upon Leibniz by the Conti This is al so the problem which confronts us, in physical salon's Euler. This was also the basis for the hyena-like attack, economy, as one may attempt to define the correspondence led by the devotees of Ernst Mach, upon Max Planck, during between scientific and technological progress, on the one the period of World War 1.14 side, and, on the other side, a general, resulting increase in Once we acknowledge the primary historical fact of mathe­ the productive powers of labor, per capita, per household, matical-physical knowledge, that each of those discoveries of and per square kilometer. For that case, the type of yardstick physical principle which is validated by the appropriate mea­ used is termed potential relative population-density; that surement, presents mathematics with a topological challenge yardstick changes its sca le (per capita, per square kilometer) of the indicated (n+ 7)/n form, mathematical formalism is as the level of applied scientific and technological progress stripped of that attributed, god-like authority which the devo­ advances. tees of Euler and the Bourbaki cult defend so fa natica/fy. 15 Like Leibniz before him, Riemann's discovery demonstrates Science and Metaphor that formal mathematical-physics schemes do not embody All of the issues posed by Riemann's habilitation disserta­ the potentiality of a truth-doctrine. To find truth, we must de­ tion, while most profound, are so elementary that they might part the domain of mathematics, and go over into another do­ be understood at the level of a good secondary school's grad­ main, the realm of experimental physics. uate. Once we accept his intention in that location, that pa­ per is among the most lucid pieces of prose ever supplied to the literature of fundamental scientific discoveries. Admit­ "Like Leibniz before him, Riemann's discovery tedly, most of the classroom's putatively authoritative com­ mentators have conveyed a contrary, confused view of this demonstrates that formal mathematical-physics work. The fa ilure of all such commentaries examined, is that schemes do not embody the potentiality of a the commentators, by refusing to accept the fact of what Rie­ truth-doctrine. To find truth, we must depart the mann is saying, project upon him an intention which is ax­ domain of mathematics, and go over into iomatically contrary to his own. The axiomatic failures of such authoritative commentators another domain, the realm of experimental occur on two levels. physics." Closer to the surface, they have sought to defend such post- 1815 authorities in taught mathematics as Newton, Eu ler, Au­ gustin Cauchy, et aI., from the devastating refutation provided The key to all among these, and derived fo rmal issues of by Riemann's discovery. This centers around Eu ler's argu­ mathematical physic s, is the connection between the erro­ ment against Leibniz. That relatively more superficial ax­ neous insistence, that, ultimately, no discontinuities exist in iomatic assertion, is the hysterical insistence of the positivists, mathematics, and the deeper assumption (also false), as that, ultimately, mathematical discontinuities do not exist.13 among the fo llowers of the Bourbaki dogma, that mathemat­ On the deeper level, there is a more devastating issue, ics can be a truth-doctrine. which the opponents of Leibniz and Riemann refuse to de­ It is admissible to state, that any consistent mathematical bate. physics of a specific, n-fo ld physical-space-time manifold, The radical positivists of the Bourbaki cult exemplify this can be read as if it were a fo rmal, deductive theorem-lattice. deeper issue. The peculiar, Ockhamite deism of such posi­ In this interpretation, it appears that every theorem of that lat­ tivist ideologues, is the dogma, that all questions of science tice has the qualifying attribute of being a proposition which must be settled by mathematical proofs del ivered upon a has been shown to be not-inconsistent with whatever set of blackboard, or, by a modern digital-computer system. Every axioms and postulates underlie that lattice in its entirety.16 demonstration that mathematical formalism is not the god of Such a set of axioms and postulates is identified by both Plato

12. This does not justify the presumptions of some popularized notions of a Niels Bohr and other accomplices of Bertrand Russell, during the period differential geometry. The basis for that word of warning will be made of the famous 1920's Solvay Conference sessions. clearer below. 15. This is literally an ancient issue. This topological challenge is the same 13. Formally, Euler's assertion was a defense of the purely arbitrary assump­ ontological paradox, of the "One" and "Many," posed by Plato's Par­ tion of the naive Euclidean imagination, that linear extension is perfectly menides. continuous without limit. Since Euler's supposed proof of that assertion 16. For example: What Euler defends, by means of a rather silly tautology, in depends absolutely upon the assertion of that axiom which it purports to his 1761 attack upon Leibniz, is the naive, Euclidean, axiomatic assump.. prove, Euler's famous tautology proves nothing at all. Euler's folly on this tion of the perfect persistence of linearization indefinitely, into the very point is the hereditary origin, via Lagrange and Laplace, of Cauchy's large and very small. bowdlerization of Gottfried Leibniz's version of a calculus. 17. Riemann Werke, p. 525: "Das Wort Hypothese hat jetzt eine etwas an­ 14. That attack upon Planck, first from within the German-speaking scientific dere Bedeutung als bei Newton. Man pflegt jetzt unter Hypothese Alles zu communify of the World War I interval, was continued in the savagery of Erscheinungen Hinzugedachte zu verstehen."

38 Winter 1995-1 996 21st CENTURY . .. HOW ERATOSTHENES Parallel rays , . �' 'MEASURED' THE EARTH'S � . from the sun CIRCUMFERENCE Eratosthenes, a member of the Platonic Academy in Athens and the � head of the library at Alexandria in the third century B.C., devised a / method of measuring the curvature of the Earth without seeing what he was measuring-but "seeing" an anomaly in sense perception. His � method fo cussed on the difference fo und between the shadows cast on two identical sundials at different latitudes at the same hour. At noon on the day of the summer solstice, two hemispherical sundials were placed, one at Alexandria and the other at Syene (A swan) in Egypt. The gnomon in the center of each sundial pointed to the center of the Earth. The gnomon cast no.shadow at Syene, but it cast a shadow of 7.20 at Alexandria. By knowing the dis­ ta nce between the two cities (about 490 miles), Era tosthenes calculated the Earth's circumference to be about 24,500 miles, which is accu­ rate to about 50 miles.

and Riemann as an hypothesis, in contrast to the illiterate's Riemann adopts a view of mathematical physics based misuse of the same term in Newton's famous "et hypotheses upon the succession of advances in those discoveries of phys­ non fi ngo."l ? ical principle which have been validated crucially by relevant The literate usage of "hypothesis," is mandatory in reading measurement, such as Eratosthenes' estimate for curvature of even the title of Riemann's June 1854 dissertation, even be­ the Earth typifies that principle of measurement. Riemann's fore proceeding to the body of the text. The key to a literate view of this topological transformation underlying mathemati­ read ing of Riemann's dissertation, is that a topological trans­ cal physics' progress, thus defines progress in mathematical formation typified by the transition from a mathematically physics in terms of a sequence of absolute mathematical dis­ n-fo ld physical-space-time manifold, to an manifold of (n+ 1) conti nu ities with in a formal ist readi ng of mathematical dimensions, is a transformation in the set of axioms and pos­ physics itself. It defines Newton, Euler, and Cauchy, for ex­ tu lates underlying mathematical physics. ample, as victims of their own scientific illiteracy, victims of Consequently, the history of those discoveries of physical an ontological paradox, of the "One"/"Many" form, which principle which, like Eratosthenes' discovery of an estimated they could neither solve, nor comprehend-and, apparently, curvature of the Earth, are validated by the relevant measure­ did not wish to comprehend. ment, presents us with a succession of topological changes In each case, one formal theorem-lattice is distinguished within mathematical physics, a series of changes which has from another by any change in the axiomatic content, from the form of the "One"/"Many" paradox of Plato's Pare that of the hypothesis underlying one, to that of the hypothe­ menides. In this instance, the "Many" are represented by a sis underlying the other; every theorem of the second lattice series of hypotheses; the challenge is to discover a higher is formally inconsistent with any theorem of the first. The dif­ principle, a higher hypothesis, a "One," which defines a gen­ ference between the two hypotheses, is a true, and relatively erative principle by means of which the series of hypotheses, absolute mathematical discontinuity. Such a "discontinuity" the "Many," is ordered "transfinitely." If Riemann's disserta­ has the same significance in mathematical physics as the tion is read in any different sense than this Platonic one, the proper understanding of the term "metaphor" in Classical resulting commentary upon the text is a scientifically illiterate forms of poetry or drama. What "discontinuity" signifies re­ one, no matter what the putative classroom authority of the specting the formalities of a consistent mathematical physics, commentator. is precisely what "metaphor" signifies for a Classical poem or

21st CENTURY Winter 1995-1 996 39 Library of Congress American Institute of Physics Isaac Newton (7642-1726) Augustin Cauchy (7789- 1857)

The pantheon of accepted classroom mathematics. Wh en the in his Parmenides and other late dialogues,23 physical world didn 't fi t their Procrustean bed, they cut In the successful Classical poem, efficiently illustrated as accordingly. to form by Goethe's simple Mailied,24 the strophes represent a succession of metaphors, which march, one after the other, drama.18 The understanding of this relationship between toward a conclusion. The metaphorical attribution of each of metaphor and mathematical discontinuity, is the key to the those strophes is generated by ironies, to such effect that no first of the posthumously published documents, "On Psychol­ proper attribution of either a confining literal or a symbolic ogy and Metaphysics," presented in the following pages. meaning for that strophe is to be permitted. The concluding In physics, a mathematical discontinuity appears as a mere metaphor, especially its final couplet, changes radically the mark. The magnitude of this mark is of transinfinitesimal metaphorical attribution-for example, the "meaning"-of small ness, so small that no calculable arithmetic magnitude the poem as a whole. It is that concluding, subsuming can measure it, yet it exists, nonetheless, as a phenomenon: metaphor, which identifies the idea of the poem taken in its apparently as a mark of separation of all magnitudes which entirety. are less, from all magnitudes which are greater.19 This mark The literate reading of such a poem, or its Classical song­ signifies the functional presence, outside the realm of mathe­ setting, demands a repeated review of the completed poem, matical fo rmal ities, of the mathematical-physical form of until the point is reached that two conditions are satisfied: what we recognize in Classical poetry as a metaphor. first, that the idea of the completed poem as a whole is clear; second, that the relationship of each step of progress within Riemann's 'Geistesmassen' the poem, to the reaching of the conclusion, is clear.2s The The fact that all true metaphors are singularities, is the key satisfaction of that requirement establishes the idea of the to an accurate understanding of Riemann's use of Geistes­ poem as a whole, in the mind, as the product of a tension be­ massen, translated here as "thought masses," in the first of tween two, literally Platon ic qualities of idea. The first, is the the posthumously publ ished papers, "On Psychology and idea of the completed poem in its entirety; this idea remains Metaphysics." As an illustration of the principle involved, ·unchanged, from prior to the re-read ing of the first line, to the consider the case of metaphor in either a Classical form of momentary silence following the reading of the last line. The strophic poem, or a song-setting of such a poem by a second idea, is the successive metamorphoses which the idea Mozart,20 Beethoven, Schubert, Schumann, or Brahms.21 of the poem undergoes, in proceeding from the begi nning to This case, of the Classical strophic poem, and its musical set­ the end. In Plato, that latter quality of idea is identified as the ting according to principles of motivic thorough-composi­ Becoming. It is the tension between the fixed conception, the tion, is key for understanding the mental processes by means idea of the completed poem as a whole, and the metamorphi­ of which a validatable discovery of new scientific principle is cal character of the process of Becoming, by which the per­ generated.22 This is also an example of the conception posed fected idea is reached, which is the "energy" of the poem. by Plato's treatment of the "One/Many" ontological paradox The same requirement applies to the performance of any

40 Winter 1995-1 996 21st CENTURY American Institute of Physics Courtesy ofAcademia Fran,aise Rudolf Cla usius (7822- 7 882) Pierre Louis Moreau de Maupertuis (7698-7759)

Classical musical composition. In the simplest case of such a of the point corresponding to the Sun, to the Earth. Thus, musical performance, it is the performer's memory of reach­ Eratosthenes gave a reasonable estimation of the Earth's cur­ ing the peliected (completed) composition, which creates the vature, approximately 22 centuries before any person saw tension of reenacting the performance of the metamorphosis, that curvature. the tension between the perfected idea of the composition, These examples, from poetry, music, and the work of Plato's and the moment of development in mid-performance. Academy of Athens, are each and all examples of Platonic The singularity in question is generated by the diffe rence in ideas, the quality of ideas to which Riemann assigns the term direction of time-sense-backwards versus forwards-of the Ceistesmassen. In physical science generally, such ideas have two, interacting ideas respecting the poem or musical compo­ initially the apparent character of ideas arising from vicious in­ sition in mid-performance. consistencies within observations made by aid of sense-per­ The same principle characterizes Eratosthenes' estimate of ception, inconsistencies which mock both naive sense-cer­ the curvature of the Earth's surface: the principle of develop­ tainty and generally accepted scientific opinion. Relatively ment uncovered, by re-experiencing the mutually contradic­ often, that mockery occurs in the most cruelly devastating way. tory individual readings of the midday sundials, to locate a Those ideas which purport to identify the generating principle generating principle of change which is consistent with the responsible for this paradox, and which are validated by rele­ final result. For Eratosthenes, the key to the generating princi­ vant modes of measurement, represent valid discoveries of ple becomes the re lationship between the perimeter of a cir­ physical principle. Those qualities of proven principle are clas­ cle and a pencil of lines, from a momentarily fixed position sically identified as Platonic ideas. Each and all of the validated

18. The relevant problem is that, many miseducated readers with advanced Sigerson and Kathy Wolfe, eds. (Washington, D.C.: Schiller Institute, degrees in arts have the same difficulty in coping with the term 1992), Chapter 11, pp. 199-228. "metaphor," which radical positivists experience with the term "mathemat­ 21 . Op. cit., pp. 220-221. Note the reference to Gustav Jenner, Johannes ical discontinuity." Beginning the early 17th century, the empiricists, such Brahms als Mensch, Lehrer und Kunst/er: Studien und Erlebnisse (Mar­ as Thomas Hobbes, launched a vile, energetic, and persisting campaign burg an der Lahn: N.G. Elwert'sche Verlagsbuchhandlung, 1930). Jen­ to eradicate the use of metaphor and the subjunctive mood from English­ ner's account of Brahms's instruction to him on composing a song for a language usage. The recent emergence of that radical-existentialist strophic poem, is directly relevant to the point being developed at this decadence known as the "deconstruction ism" of Professor Jacques Der­ point in the text, above. rida, et aI., is the outgrowth of a centuries-long campaign by the empiri­ 22. See Lyndon H. LaRouche, Jr., "Musical Memory and Thorough-composi­ cists and logical positivists, and related linguistics specialists, to locate tion," Executive Intelligence Review, Sept. 1, 1995, pp. 50-63. the origin of written language, even Classical poetry, in "texf' as such, 23. Plato's Parmenides is to be considered as a kind of prefatory piece for all rather than the irony-rich domain of speech. of his later dialogues. In it, he poses the challenge, the ontological para­ 19. In the extremely small, discontinuities are compared in respect to their dox, which is the subject addressed in its various aspects by all of the mathematical cardinality, not as arithmetic values. Hence, with deference other late dialogues. to Georg Cantor, this distinction is designated here by the usage of 24. LaRouche, "Musical Memory and Thorough-composition," p. 55. See note "transinfinitesimally small." 22. 20. After Mozart's first song composed in the new mode of motivic thorough­ 25. See Jenner's account of his instructions from Brahms, on memorizing a composition, his setting of Johann Goethe's "Das Veilchen" ("The Vio­ poem with sufficient thoroughness to satisfy those requirements, before let"). See A Manual on the Rudiments of Tuning and Registration, John undertaking to provide a song-setting for it. See note 21 .

21st CENTURY Winter 1995-1 996 41 American Institute of Physics Libraryof Congress Leonhard Euler (1707- 1 783) and (right) Immanuel Kant (1724-1804) both attacked Leibniz's not-entropic view of man and the universe and counterposed a world tHat was axiomatically linearized in the small and in the large.

ideas of "dimensionality" in an n-fold physical-space-time secondly, in the mental processes of the scientist, or the artist. manifold, have this quality of Platonic idea. It exists, thirdly, within the sovereign mental processes of Thus, all such ideas have the form of paradoxical singulari­ those members of the audience who have responded Socrati­ ties r�lative to the pre-existing mathematical domain of refer­ cally to the mark of the singularity, by generating in their own ence. The character of these ideas as singularities arises from mind a replication of the idea which has imposed its mark the way in which their existence is generated subjectively: by upon the medium of communication. the same kind of processes underlying the reading and com­ In mathematical physics, the validation of the ideas corre­ position of a valid Classical strophic poem. The quality of sponding to such marks occurs commonly through measure­ "singularity," and the associated form of mathematical dis­ ments which demonstrate, that those ideas correspond effi ­ continuity, arises from the opposing senses of time associated ciently to an effect which is not in correspondence with the with the interplay of perfected ideas with the process of their old ideas which the new ideas profess to supersede. development. 26 There is a most notable illustration of this point in the case These metaphors can never be deduced from the mathe­ of Riemann's paper, published in 1860, "On the Propagation matics, or other form of language employed. Within the lan­ of Plane Air Waves of Finite Amplitude."27 The fact that ac­ guage itself, they appear merely in the reflected form of sin­ celeration toward speeds above the speed of sound generates gularities, such as either mathematical discontinuities or other a singularity, was recognized by Riemann as showing the ex­ paradoxical adumbrati"ons reflected into the language­ istence of the transsonic phenomena studied by such fo llow­ medium. The ontological existence of the singularity lies out­ ers as Ludwig Prandtl and Adolf Busemann. It was this princi­ side the form of generation of the relevant mark within the ple of Riemann's which resulted, through the mediation of a domain of the language itself. German aerospace specialist, in the first successful powered, Thus, every theorem which claims to deny the existence of post-World War II, supersonic fl ight by a U.S. aircraft. This discontinuities within mathematics, such as Euler's, is based was in contrast to the fa iled contrary opinion expressed by upon the tautological fa llacy of composition, of using con­ such frequent adversaries of Riemann's work as Hermann structions premised axiomatically on linearization, to prove Helmholtz, Lord Rayleigh, and Theodor von Karman.28 the utterly irrelevant point, that any construction of this type In the relatively more obvious type of case, such as the is incapable of acknowledging any mathematical existence cited Eratosthenes case, the empirical validation of such a which is not linear! singularity is accomplished by measurements which lie The relevant formal mathematical discontinuity, or literary within the domain of arithmetic magnitudes. However, this is paradox, is merely the mark which the metaphor imposes, as not the only primary form of empirical proof of a Platonic its footprint, upon the formally defined medium of language. idea. As Riemann's referenced paper on shock-waves illus­ The actual metaphor, which the adumbrated mark, or para­ trates the point, in some cases, it is the existence of a non­ dox reflects, exists only outside the medium. It lies within arithmetic singularity, which has precise cardinality, but not three locations. It lies, first, in the substance of the process arithmetic magnitude, which presents us the mathematical which the language is attempting to describe. It also lies, form of the required proof. Riemann's success in forecasting

42 Winter 1995-1 996 21 st CENTURY eign mental processes of the individual which are impenetra­ ble by symbolic communications-media, such as a formal LETTERS OF EULER mathematics. Yet, despite the ethereal quality one might be tempted to attribute wrongly to such mental processes, the re­ ON DIFJ'Ka&NT aDaUCTII 1M' sult of such ideas is an increase of the human species' physi­ NATURAL PHILOSOPHY. cal power to command nature in general. In this respect, these papers of Riemann turn our attention A GERMAN PRINCESS. back to Leibniz's notion of a Universal Characteristic, which subsumes, commonly, non-living, living, and cognitive WITH NOT.a, ARD A LIFa or KULKa. processes with in our universe. This is the topical area ad­ DAVID ·BREWSTER, LL.D. dressed in the first two of the posthumously published papers: ra.s.� WHD. DD ED. "I. On Psychology and Metaphysics," and "II. Epistemological COnA.UnlfQ ... OLOISJ.1tY OJ' SCIENTIrIC TO •• Issues." After the writing of these papers, Riemann's pub­ WITH APDITIONAL NOTIS. lished work does not refer explicitly again to such. epistemo­ BY JOJ:i N GRISCOM, LL.Il logical underpinnings of science. From 1854 on, his pub­ lished work limits itself essentially to mathematical physics, IN TWO VOLUMES. with some impingement upon biophysics,29 although he VOL. II. clearly did not abandon that personal standpoint in his think­ ing about mathematical-physics matters. Therein lies some of the special importance of the posthumously published papers for identifying the deeper implications of Riemann's work as NEW-YORK: a whole. HARPKR

26. The proper notions of topology are derived from this consideration. this Riemann Fortpflanzung paper in that connection. It was at a subse­ 27. 'O ber die Fortplanzung ebener Luftwellen von endlicher Schwing­ quent, "report back" meeting that same year, that LaRouche underlined ungsweite," Riemann Werke, pp. 156-175. This was published in an Eng­ the application of the same paper to physical-economic modelling, and lish translation by Uwe Henke and Steven Bardwell, in the Fusion Energy presented the set of inequalities used to create the highly successful Foundation's International Journal of Fusion Energy, Vol. 2, No. 3, 1980, 1980-1983 U.S. Quarterly Economic Forecast of the Executive Intelli­ pp. 1-23. gence Revie w (EIR) newsweekly. 28. There is a relevant story behind the Fusion Energy Foundation's publica­ 29. For example, the brilliantly confirmed analysis provided within his tion of that translation. During the middle to late 1970s, the Fusion Energy Mechanik des Ohres (Mechanics of the Ear): Riemann Werke, pp. 338- Foundation (FEF) gained an international reputation for its important work 350. in promoting inertial confinement fusion. As a consequence of this, in 30. As noted, repeatedly, in other locations, this reporter has found it desir­ 1978, two representatives of the FEF, Mr. Charles B. Stevens, Jr., and Dr. able to apportion all physical science among four functionally distin­ Steven Bardwell, were invited to the Soviet Union to participate in an in­ guished domains of inquiry. Two areas, astrophysics and microphysics, temational scientific conference on inertial confinement. Prior to their de­ are domains in which the scale of phenomena is either too large, or too parture, these two FEF representatives met with LaRouche and others, at small, to be addressed directly by the senses. In a third area, biopHYSics, a Bronx location, to obtain LaRouche's list of requirements for that we deal with the principled distinction between processes, such as or­ Moscow visit. laRouche requested that they ask Soviet scientists for un­ ganic compounds, which, in one instant are functioning as part of a living classified documents pertaining to the use of Riemann's work on isen­ process, and, in another instant, not. This also defies simple sense-per­ tropic compression as a basis for the original development of thermonu­ ception. Those three domains, leave, as residue, the domain of macro­ clear ignition. Such unclassified documentation was obtained, identifying physics, in which sense-perception plays a larger immediate role.

21st CENTURY Winter 1995-1 996 43 ergy" to "energy of the system" must not decrease, despite frastructure." Physical economy recognizes a required func­ the accompanying requirement of rising per capita and per­ tional relationship between the level of these market-baskets square-kilometer values of capital-intensity and power-in­ and the productive powers of labor, as measured in terms of tensity. This desired result is realized, typically, by the fos­ both production and consumption of the content of these tering of increase of the (physical) productive powers of market-baskets.32 labor through investment in scientific and technological That yields an implied differential expression : What level of progress. input (consumption) is required to maintain a certain rate of Consider the fo llowing summary of the relevant argument output of necessary products for consumption? Without yet elaborated in other locations.31 knowing the exact answer to that question at any given point, Physical economy identifies the primary phenomena of the idea of the question is clear. This idea is expressed conve­ economic processes in terms of market-baskets of both neces­ niently as the notion of potential relative population­ sary physical consumption and certain crucial classes of ser­ density. 33 vices, limited essentially (in modern society) to education, The levels of combined market-basket consumption which health care, and science and technology as such. These market­ are required to maintain not less than some constant rate of baskets are defined per capita (of labor-force), per household, potential relative population-density, are compared to the no­ and per square kilometer of relevant land-area employed. tion of "energy of the system." Output of market-basket con­ The market-baskets are defined for personal consumption, tent in excess of those required levels, is compared to "free for the processes of production, and for those improvements energy." The "free energy" is considered "not wasted," on the in land-area used which we class under "basic economic in- condition that it is consumed in market-basket forms, for both

On the Hypotl1eses Which Lie �t the FoundatiQns of Ge·ometry

by Bernhard Riemann

These excerpts fro m Riemann's 1854 habilitation paper is, in such a way that every point goes over into a definite are from the translation by Henry S. White i'h A Source point of the other, then will all the modes of determination Book in Mathematics, edited by David Eugene Smith (New thus obtained form a doubly extended manifold ....If York: Dover Puplications, 1959), pp. 411-425. one considers his object of thought as variable instead of regarding the concept as determinable, then this construc­ Notions of quantity are possible only where there exists tion can be characterized as a synthesis of a va�iability of already a general .concept which allows various modes of n + 1 dimensions out of a variability of n dimensions and determination. According as there is or is ,not fqund among a variability of one dimension .. these modes of determination a continuous transition from one to another, they form a GontiAuous or a discrete mani­ * * * fo ld; ... . [T] here subsists an essential difference between mere Determi nate parts,of a manifold, distinguished by a mar.k relations of extension aAd those of measurement: in the for­ or by a boundary, are called quanta. Their comparison as mer, where the possible cases form a discrete manifold the to quantity comes in discrete magnitudes by counting, in declarations of experience are indeed never quite sure, but continuous magnitude by measurement. Measuring consists they are not lacking in exactness; while in the latter, where in superposition of the magnitudes to be compared; . possible cases torm a continuum, every determination based on experience remains always inexact, be the proba­ * * '" bility that it is nearly correct ever sci great. This antithesis In a concept whose various modes of determi nation be.comes important when these empirical determinations form a continuous manifold, if one passes in a definite are extended beyond the limits of observation into the im­ ) wa'y from one mode of determination to another, the measurably great. and the immeasurably small; for the sec­ modes of determination which are traversed constitute a ond kind of .relations obviously might become ever more simply extended manifold and its essential mark is this, inexact, beyond the bounds of observation, but not so the that in it a continuous progress is possible from any point first kind. only in two directions, forward or backward. If now one When constructions in space are extended into the im­ forms the thought of this manifold again passing over into measurably great, unlimitedness must be distinguished another entirely diffe rent, here again in a 'definite way, that from infiniteness; the one belongs to relations of extension,

44 Winter 1995-1 996 21 st CENTURY expanding the scale of the economy, and increasing the po­ to bring the entire system to a higher state of organization; tential relative population-density. In the latter case; the capi­ Vernadsky's argument typifies the line of thought which is tal-intensity ("energy of the system" per capita, per household, otherwise encountered in various locations, including Leib­ and per square kilometer) must increase, and the power-den­ niz's notion of a Universal Characteristic, and also the refer­ sity must also increase. The requirement is, that the ratio of enced portions of Riemann's posthumously published papers. apparent "free energy" to "energy of the system" must not de­ Wiener made a mess of everything, with the popularization crease, despite a rising relative value of "energy of the system" of his wretched insistence that "negative entropy," for which per capita, per household, and per square kilometer. he employed the neologism "negentropy," was no more than The increase of potential relative population-density, under a reversal of the statistical entropy described by Ludwig the condition that those constraints are satisfied, is treated as Boltzmann's H-theorem. Contrary to Wiener's mechanistic the economic-process analog for what is expressed as "nega­ schemes, if we account for mankind and mankind's activity tive-entropic" evolutionary self-development of the biosphere as part of the planetary. system, man's increased power over in biology and in the terms of reference supplied by the Aca­ nature, typified by the increase of mankind's potential relative demician V.1. Vernadsky's notion of biogeochemistry. To population-density,34 is actually an increase of the relative avoid confusion with the "information theory's" popularized "negative entropy," or, "not-entropy," of the planetary system misuse of the term "negative entropy," the term "not-entropy" as a whole. In other words, mankind's development supplies is employed instead. an evolutionary upward impulse to the totality of the system In the field of what Academician V.1. Vernadsky defined as with which mankind interacts. biogeochemistry, this requires the evolution of the biosphere, In this view of the matter, human cognition has developed within the domain of living proce·sses, but those ecological characteristics of the human species which are entirely due to cognition, place mankind absolutely apart from and above all . the other to those of measure. That space is al'l unlimited, other living species. Thus, our universe subsumes the interac­ triply extended manifold is an assumptie>n applied in every tion among three distinguishable types of processes: non­ conception of the external world; ...From this, however, living, living, and cognitive. The commonly subsuming prin­ fo llows in no wise its infin iteness/but on the contrary ciple governing such a universe, is Leibniz's notion of a Uni­ space would necessarily be fin ite, if one assumes that bod­ versal Characteristic. ies are independent of situation and so ascribes to space a For today's conventional classroom opinion, what we constant measure of curvature, provided this meaSl!Jre 0f have just stated poses the question: "Is it not necessarily the 'curvature had any positive value however small. case, that if the 'not-entropy' of society increases, that this must occur at the price of increasing the entropy of the uni­ * * * verse with which society is interacting?" In other words, is [T) he empirical notions on which spatial measure­ the relationship of society to the remainder of the universe ments are based appear to 10se their validity wl:1en applied not what von Neumann's devotees term "a zero-sum game"? to the indefinitely small, namely the concept of a fixed The crux of the issue, is that the idea of "universal entropy" body and that of a light-ray; accordingly it is entirely con­ is not a product of scientific discovery, but of the reckless ap­ ceivable that in the indefinitely small the spatial relations plication of an axiomatically linear, mechanistic world-view, of size are not in accord with the postulates of geometry, upon the interpretation of the evidence of kinematic models and one· would indeed be forced to this assumption as of gases; on this account, there is an amusing ambiguity in soon as it would permit a simpler explanation of the phe­ the ironical meaning Norbert Wiener's work supplies to the nomena. term "gas theory." The question of the validity of the postulates of geometry The absurdity of the popular version of doctrines of "uni­ in the indefinitely small is involved in the question concern­ versal law of entropy," is suggested by the fact, that every ra­ ing the ultimate basis of relations of size in space. In con­ tional effort to describe the universe in the large, is an evolu­ nection with this question, which may well be assigned to tionary model, in which development is vectored as progress the philosophy of space, the above remark is applicable, to relatively higher states of organization. In mathematical namely that while in a discrete manifold the principle of terms, this progress to higher states of organization is indi­ metric relations is implicit in the notion of this manifold, it cated by the emergence of physical systems whose character­ must come from somewhere else in. the case of a c()ntinu­ istics cannot be identified without resort to the mathematics ous manifold. Either then the actual things forming the of successively higher cardinalities. The attempt to explain groundwork of a space must constitute a discrete manifold, or else the basis of metric relations must be sought for out­ 31. For example, Lyndon H. LaRouche, Jr., "Why Most Nobel Prize Econo­ mists Are Quacks," and "Non·Newtonian Mathematics for Economists." side that actuality, in colligating [binding together or unit­ See note 6. ing) forces that operate upon it. 32. For example, the case for household consumption was indicated by Gott­ fried Leibniz in Society and Economy (1671 ), which appears in English

* * * translation in Executive Intelligence Review, Jan. 4, 1991, pp. 12-13. 33. On "relative population-density," see Lyndon H. LaRouche, Jr., So, You This path leads out into the domain of another science, Wish to Learn All About Economics? (New York: New Benjamin Franklin into the realm of physics, into which the nature of this pre­ House, 1984). This introductory textbook has been published in various languages, including Russian, Ukrainian, and, most recently, Armenian. sent occasion forbids us to penetrate. 34. Per capita of labor-force, per household, and per square kilometer of rele­ vant land-area employed.

21st CENTURY Winter 1995-1 996 45 the efficient directedness of such a mathematics, is con­ such universalizing processes sidered as "proven" by all of of emergence of higher cardi­ the awesomely credulous nalities, renders absurd every professorial, head-nodding attempt to explain the exis­ dupes attending the relevant tence of matter itself in terms conference.36 of a mechanistic dogma of Once we recognize, that "building blocks." The evi­ such a mathematics consti­ dence is, that recognizably tutes no proof at all respect­ higher physical states of car­ ing the issues immediately at dinality, are accomplished by hand, the most generous transformations of the entire consideration which the ad­ system, not by accretions of vocates of the "Second Law" obj�cts of a mechanistically might require of rational fixed domain. people, is the famous Scots' The counterposing of the verd ict, "not proven." No developmental (for example, axiom of a mathematics is not-entropic) and Kant-like proven by the employment mechanistic views is noted of the formal mathematical by R-iemann, in the first of theorem-lattice whose exis­ the referenced papers. Cru­ tence depends upon that in­ cial is· t�e demonstration, cluded assumption. that, as irithe case of Euler's Those qualifying observa­ absurd 1761 attack on Leib­ tions stated, situate the mat­ niz's Monadology, the pre­ ter at hand. Now, turn di­ sumption of that Kant-like, rectly to the subject of mechanistic view, from Leibniz's Universal Charac­ which Rudolf Clausius, Lord teristic. Kelvin, and Hermann Grass­ The paradigmatic form of mann concocted their all increase in mankind's po­ Library of Congress chimerical "Second Law of tential relative population­ The Universal Characteristic described by Gottfried Wilhelm Thermodynamics,"35 is "ax­ density, from the several mil­ Leibniz (7646- 1716) corresponds to LaRouche's concept of iomatic linearization in the lions potential of a man-like not-en'tropy, or man's increasing power over the universe small." Create a mathemat­ higher ape, to the billions of through the use of reason, which is measured in the increase ics, in which all is subsumed today, is changes in social­ in society's potential re lative population-density. Riemann ex­ ynder the axiomatic assump­ productive behavior typified pressed this progress in knowledge topologically as an in­ tion, that everything in the by general application of the creasing density of singularities or discontinuities; that is, an universe is consistent with fruits of scientific and tech- increase of the fo rm (n + 1 Yin . the Euclidean blind fa ith in nological progressY t�e universality of perfectly Each of the transmitted continuous linear extension, even into the extremely great discoveries is known by means of the replication of that origi­ and the extremely small. The true believer then regards any nal act of discovery within the mind of the hearer. On the formulation which is inconsistent with such a mathematical condition that education of the young proceeds according to "proof," as "disproven," and everyth ing which must be as­ that latter principle, present-day knowledge is the accumula­ sumed to preserve consistency within the theorem-lattice of tion of all of those singularities which valid past discoveries

35. It was Kelvin who proposed to Clausius this radically mechanistic interpre­ implication of Lord Rayleigh's denunciation of Riemann's Fortpflanzung tation of Sadi Camot's work. In this case, as in all of his attacks upon paper, is the same: The root of the mechanistic world-view, which the em­ Bemharp Riemann, Clausius relied upon Hermann Grassmann for the piricist world-outlook of modern Britain acquired from its ancient master, mathematical side of his endeavors. See Riemann Werke, note on page Paolo Sarpi, is always the presumption of the universality of percussive 293. The crucial role which the axiomatic presumption of linearization in causality within a universe which is axiomatically linearized in the very the small played in Grassmann's work, including all of his work on the small. "SE!cond Law" and attacks upon Riemann, is reflected in his famous 1844 37. This progress in the human condition is not due only to scientific and tech­ work founding a relevant branch of modern vector analysis, the so-called nological progress. The metaphors which arise from Classical forms of Ausdehnungs/ehre. poetry, tragedy, and music have as crucial a role in increasing man's 36, During 1978, former FEF Director Morris Levitt dug out a document au­ power to exist as what we term conventionally "natural science." Nonethe­ thored by J. Clerk Maxwell which caused FEF much amusement at that less, as we have already indicated, valid fundamental scientific discover­ tirpe. In this document, Maxwell responded to the question: Why had ies merely typify the more general case for all forms of expression of the Maxwell failed to give credit to such predecessors as Wilhelm Weber and creative-mental powers of persons as metaphor: as the great English poet fliemann (and also, most crucially, the founder of electrodynamics, Am­ Percy Shelley expressed the pOint, within his "A Defense of Poetry" : the pere) for many of the discoveries which Maxwell tacitly presented as ei­ "power of communicating and receiving intense and impassioned concep­ ther the work of Michael Faraday, or his own? To this, Maxwell replied, tions respecting man and nature." What is stated above, here, should be that ''we,'' referring to the circles including Kelvin, et aI., had chosen to dis­ read with the understanding that the case for scientific ideas typifies the regard any work which relied upon geometries "different than our own." case for metaphor in general. The same point is made, in similar terms, in Maxwell's principal work. The

46 Winter 1995-1 996 21st CENTURY have conveyed to the use of the present generations: just as students today would be scientific illiterates, until they re-ex­ perience the original discoveries by the members of Plato's Riemann in English Academy at Athens in this way, from Plato, Eudoxus, and Theaetetus, through Eratosthenes. Without a Classical educa­ Translation tion of the young, in the great Classical works of poetry, tragedy, music, and natural science, going back to the foun­ The few works by Riemann that have previously ap­ dations of modern civilization over 2,500 years ago, there peared in English are these: cannot be a truly civil ized or even rational society, a cruel "On the Hypotheses Which Lie at the Foundations of fact we see enacted so brutishly on our streets and in our gov­ Geometry," in A Source Book in Mathematics edited by ernment and universities today. David Eugene Smith (New York: Dover Publications, Each valid such discovery invokes the principle we have 1959), pp. 41 1-425. This is Riemann's habilitation dis­ associated here with the topological symbol (n+ 7)/n. Each sertation. Excerpts of two other papers are also found in discovery is a singularity of that type. Progress in knowledge this volume under the title, "On Riemann's Surfaces and is an accumulation of such singularities. As Riemann empha­ Analysis Situs," pp. 404-410. sizes, within the texts provided below, that accumulation of "On the Propagation of Plane Air Waves of Finite Am­ knowledge is interactive, every new concept interacting with plitude," International journal of Fusion Energy, Vol. 2, every other accumulated within the same mind. Thus, with No. 3 (1980), pp. 1-23. every thought, this increase of singularities is reflected effi­ "The Mechanism of the Ear," Fusion Vol. 6, No. 3 ciently: In mathematical terms, the density of discontinuities (Sept.-Oct. 1984), p. 31-38. for any arbitrarily selected interval of human action, is in­ "A Contribution to Electrodynamics," International creased. It is this increase of "density of discontinuities" journal of Fusion Energy, Vol. 3, No. 1 Uan. 1985), pp. which typifies the form of "not-entropic" and the form of the 91-93. ' action which generates "not-entropy" in, for example, the "Gravity, Electricity, and Magnetism according to the form of increase of society's potential relative population­ Lectures of Bernhard Riemann, compiled by Karl Hat­ density. tendorf," in Energy Potential by Carol White (New York: The crucial fact is, that this increase of knowledge, as de­ Campaigner Publications, 1977), pp. 173-293. fined in this way, is consistently efficient. The universe obeys * * * the human creative-mental powers' command! Th us, as Gen­ A recent, two-part study of Riemann's method is: esis 1 prescribes, mankind exerts dominion over nature. Con­ "The Scientific Method of Bernhard Riemann" by Ralf versely, the universe is manifestly so constituted, that it is Schauerhammer and Jonathan Tennenbaum, 27st Cen­ prone to submit to the authority of that power of creative rea­ tury Science & Technology, Winter 1991 , pp. 34-42, son which is a potentiality peculiar to the individual human and Spring 1992, pp. 32-48. personality.

this way, is also an efficient approximation of Reason as it ex­ "The paradigmatic form of all increase in ists, ostensibly objectively, as an efficient principle pervading mankind's potential relative population­ the universe as a whole. What we recognize in the form o� "not-entropy," as in the density, from the several millions potential of increase of society's potential relative population-density, is a man-like higher ape, to the billions of the characteristic of Reason, both as it exists efficiently, "ob­ today, is changes in social-productive jectively" within the universe at large, and as we are able to behavior typified by general application adduce the principles of reason, "subjectively," through the efficiency of valid discoveries of principle in the domains of of the fruits of scientific and science and art. technological progress." Once that is acknowledged, then it is clear to us, that the universe is not linearized in the extremely small, or extremely large. It is "not-entropic," in the extremely small and ex­ By accumulating a reliving of the original valid acts of dis­ tremely large, alike. To see this more clearly, it was sufficient, covery of principle, which constitute the accumulation of hu­ to shift the emphasis in reading Riemann's contributions to man knowledge to the present date, we are enabled to recog­ mathematical physics, away from physics narrowly con­ nize the distinguishing features of that form of act of creative ceived, back to the vantage-point of Leibniz, the vantage­ reason, by means of which valid discoveries have been com­ point of physical economy, the vantage-point of the efficient monly achieved. That experience becomes known to us, as to relationship between valid human individual reason, and Johannes Kepler, as Reason, or, as for Gottfried Leibniz, as man's increased power over the universe. Thus, we may say, necessary and sufficient reason. Once we recognize, that that not-entropy, as reflected in type by Riemann's topologi­ mankind's cumulative development of knowledge represents cal expression (n+ 7)/n, corresponds to what Leibniz named a the power of the human will to command the universe ac­ Universal Characteristic. cording to the law embedded in that universe, we have Economist Lyndon H. LaRouche, jr., is a member of 21 st shown ourselves that reason as we define it subjectively in Century's scientific advisory board.

21st CENTURY Winter 1995-1996 47 Euler's Lying Attack on Leibniz .. ,J.'

Letters of Euler on Different Subjects in Physics and Philoso­ this class. What can be more shocking than to confound phy, Addressed to a German Princess was published in 1770 all spirits, and the Supreme Being among the rest, with the as part of a continuing campaign to discredit Leibniz and his minutest particles into which a body is divisible, and to collaborators. In this excerpt, Euler describes how the Berlin rank them in the same class with these particles, which it Academy was used as a center for the attack upon Leibniz:1 is not in the power of the learned term monad to enable? [Vol. I, pp. 353ff.] There was a time when the dispute respecting monads employed such general attention, and was conducted leibniz on Metaphysics with so much warmth, that it forced its way into company A comparison of Euler's attack with Leibniz's writings makes of every description, that of the guardroom not excepted. the fraud clear. The best known, perhaps, is Leibniz's essay There was scarce a lady at court who did not take a de­ "The Monadology" (1 714). His "Principles of Nature and cided part in favor of monads or against them. In a word, Grace, Based on Reason," written about the same time, pro­ all conversation was engrossed by monads, no other sub­ vides a beautiful exposition of his philosophy. Here Leibniz ject could find admission. wrote:2 The Royal Academy of Berlin took up the controversy, and being accustomed annually to propose a question So far we have just spoken as simple physicists; now for discussion and to bestow a gold medal of the value of we must rise to metaphysics, by making use of the great 50 ducats on the person who in the judgment of the principle, little used, commonly, that nothing takes place Academy has given the most ingenious solution, the without sufficient reason, that is, that nothing happens question respecting monads was selected for the year without it being possible for someone who knows enough 1748. A great variety of essays on the subject were ac­ things to give a reason sufficient to determine why it is so cordingly produced. The president, Mr. de Maupertuis, and not otherwise. Assuming this principle, the fi rst ques­ named a committee to examine them ....Up on the tion we have the right to ask will be, why is there some­ whole, it was found that those [arguments] which went thing ra ther than nothing? For nothing is simpler and eas­ to the establishment of their existence were so feeble, ier than something. Furthermore, assuming that things and so chimerical, that they tended to the subversion of must exist, we must be able to give a reason for why they all the principles of human knowledge. The question must exist in this way, and not otherwise. was, therefore determined in favor of the opposite opin­ This sufficient reason for the existence of the universe ion, and the prize adjudged to a Mr. Justi, whose piece cannot be found in the series of contingent things, that is, was deemed the most complete refutation of the in the series of bodies and their representations in souls; monadists. [Vol. 2, pp. 35-36] for, since matter is in itself indifferent to motion and rest, and to one motion rather than another, we cannot find in Euler's philosophical outlook is Aristotelian and Newtonian, matter the reason for motion, still less the reason for a giving primacy to sense-certainty over reasoned judgment, and particular motion. And although the present motion his discussion of the history of science is dishonest on all found in matter comes from the preceding motion, and essential questions. For example, he does not give credit to it, in turn, comes from a preceding motion, we will not Kepler for his discoveries. Similarly, in the case of the Principle make any progress in this way, however far back we go, of Least Action, Euler assigns Leibniz's discovery to de Mau­ for the same question always remains. Thus the sufficient pertu is. Leibn iz was clear that monads were simple sub­ reason, which needs no other reason, must be outside stances, without extension, of which all others were com­ this series of contingent things, and must be found in a pounded. Euler twists Leibniz's words to mean that monads substance which is its cause, and which is a necessary are infinitely small particles]. being, carrying the reason for its existence with itself. Otherwise, we would not yet have a sufficient reason A monad, then, is a substance destitute of all extension, where one could end the series. And this ultimate reason and on dividing a body, till you come to particles so for things is called God.... minute, as to be susceptible of no farther division, you It fo llows from the supreme perfection of God that he have got to the Wolffian monad [Christian Wolff was a chose the best possible plan in producing the universe, a disciple of Leibniz], which differs therefore, from the plan in which there is the greatest variety together with most subtle particle of dust, only in this, that the minutest the greatest order . . . the greatest effect produced by the particles of dust, are not perhaps, sufficiently small, and simplest means; . . . that a farther division is still necessary to obtain real And it is surprising that, by a consideration of efficient monads .... causes alone, or by a consideration of matter, we cannot The idea which I form of spirits, appears to me incom­ give the reason for the laws of motion discovered in our parably more noble than that of those who consider them time, some of which I myself have discovered. For I have as geometrical points, and who reduce God himself to found that we must have recourse to fi nal causes for this,

48 Winter 1995-1 996 21st CENTURY along a straight line. Thus the Calculus of Varia­ tions was born. Then Johann Bernoulli and Leibniz extended their investigation to discover the characteristics of families of brachystochrones. What, for in­ stance, would be the curve formed by connecting simulta­ neous positions of heavy parti­ cles which had been released from a given point at the same instant, but which travelled in different directions. This curve they called the synchrone, and it turned out to be an orthogo­ nal trajectory identical to the se­ ries of wave fronts connected to a ray of light. This was, in turn, only the be­ ginning of a new series of inves­ tigations of the behavior of other fa milies of curves. It was also the starting point for Euler's examination of partial differen- Museo di Storia della Scienza, Florence tial equations and variationa I An 18th century brachystochrone. principles, although in his pub­ and that these laws do not depend upon the principle of lished work he failed to give credit to Leibniz and the necessity, as do logical, arithmetical, and geometrical Bernoullis. truths, but upon the principles of fitness, that is, upon the Leibniz later wrote a philosophical essay that reflected his choice of wisdom. And this is one of the most effective earlier studies, the "Tentamen Anagogicum: An Anagogical and most evident proofs of the existence of God for those Essay on the Investigation of Causes." Here he wrote:3 who can delve deeply into these matters .... As for rational soul, or mind, there is something more The most beautiful thing about this [metaphysical view in it than in monads, or even in the simple souls. It is not applied to physics] seems to me to be that the principle of only a mirror of the universe of created things, but also perfection is not limited to the general but descends also an image of the divinity. The mind not only has a per­ to the particulars of things and of phenomena and that in ception of God's works, but it is even capable of produc­ this respect it closely resembles the method of optimal ing something that resembles them, although on a small fo rms, that is to say, of forms which provide a maximum scale .... or minimum, as the case may be-a method which I have introduced into geometry in addition to the ancient The Brachystochrone method of maximal and minimal quantities. For in these Leibniz's philosophy and his scientific method were one forms or figures the optimum is found not only in the and the same. In 1696, Leibniz and Johann Bernoulli began whole but also in each part, and it would not even suffice studying the brachystochrone, the path of quickest descent of in the whole without this. For example, if in the case of a moving body between any two points on a vertical plane. the curve of shortest descent between two given points, Although Leibniz was able to solve this problem using an ex­ we choose any two points on this curve at will, the part of tension of his differential calculus by mapping the relation­ the line intercepted between them is also necessarily the ship between neighboring points of two nearly identical, line of shortest descent with regard to them. It is in this possible trajectories of the body, and then determining an in­ way that the smallest parts of the universe are ruled in ac­ finitesimal difference to represent this, this was not the pur­ cordance with the order of greatest perfection; otherwise pose of the study. Leibniz and Bernoulli were able to show the whole would not be so ruled. that the brachystochrone curve could be determined by mapping the problem of motion in a gravitational field, to Notes ------the propagation of light waves through media of infinitesi­ 1. The edition of Letters of Euler used here is the Henry Hunter translation, 2nd edition, London, 1802. mally changing density. 2. Excerpted from G.W. Leibniz, Philosophical Essays, edited and translated Both the propagation of light waves and the propagation of by Roger Ariew and Daniel Garber (Cambridge, Mass., and Indianapolis: a moving body were determined by least action functions. The Hackett Publishing Co., 1989), pp. 209-21 1. All rights reserved. 3. Excerpted from G.W. Leibniz, Philosophical Papers and Letters, edited by brachystochrone was found to be a cycloid-the trajectory of a Leroy E. Loemker, 2nd edition (Dordrecht: D. Reidel, 1969, reprinted fixed point on the circumference of a circle, as the circle rolls Boston: Kluwer Academic, 1989), p. 478. All rights reserved.

21 st CENTURY Winter 1995-1996 49 Philosophical Fragments by Bernhard Riemann

Introduction to the Second German Edition

The philosophical speculations whose results-in so far as Euler's, and-on the other hand-Herbart's works. Concerning they can be assembled from his literary remains-are here the latter, I could concur almost completely with Herbart's communicated, concerned Riemann throughout the greater earliest investigations, whose results are expressed in his gradu­ part of his life. Anything definite concerning the time at which ation and habilitation theses (of Oct. 22 and 23, 1802), but I these individual fragments were written can hardly be deter­ had to diverge from the later' course of his speculation on an mined. The drafts here are far from being coherent essays ready essential point. I differ with him in regard to natural philosophy for publication, even if many passages indicate that Riemann and those propositions in psychology which concern their con­ had at certain times intended such a publication; they suffice, nection to natural philosophy." in any case, to characterize Riemann's orientation to questions Further along, in another place, we find a more exact descrip­ of psychology and natural philosophy in general and to indicate tion of this standpoint: the course taken by his investigations; unfortunately, however, "The author is a Herbartian in psychology and epistemology ' almost every exposition is lacking in detail. The value that (methodology and the theory of perception); he cannot, howev­ Riemann himself placed on these labors can be seen from the er, for the most part, agree with Herbart's natural philosophy fol lowing note: and the related disciplines (ontology and the study of con-, "The tasks that principally concern me now are: tinua)." "1 . To introduce the imaginary into the theory of other tran­ The three fragments unified under the common title "III. scendental functions, in a manner similar to the way this has Natural Philosophy" have been rearranged in this second edi­ already been done with such great success for algebraic func­ tion. Number 2 of the first ed ition has been exchanged with tions, the exponential and cyclical functions, and the elliptical number 3. According to a conjecture of Dr. Isenkrahe in Bonn and Abel ian functions. To that end, I have supplied the most which is well supported by internal evidence, it is the essay necessary general preparations in my inaugural dissertation. titled "Gravitation and Light" which is referred to in the passage , ' ! ' (S�e article 20 of this dissertation.) of Riemann's letter of Dec. 28, 1853� that is cited in the bio­ "2. In connection with this, new methods exist for integration graphical sketch [pp. 539-558 of his Collected Works], accord­ of partial differential equations, which I have already applied ing to which Riemann had in view a publication of these investi­ to several physical subjects with success. gations. The essay, "New Mathematical Principles of Natural ' '' 3. My principal task concerns a new conception of known Philosophy," with the observation, "Discovered on March 1, natural laws-the expression of these laws by means of other 1853," which is concerned with an entirely different set of fundamental concepts-through which it becomes possible to ideas, is therefore of an earlier origin, and the bold hypothesis use experimental data on the reciprocal action of heat, light, expressed in that essay of the disappearance of matter was not magnetism, and electricity in order to investigate their relations. further pursued by Riemann. I was led to this principally through the study of Newton's, -Heinrich Weber (7892)

Translator's Note This is the first English translation of various sketches left by York) issued such a reprint in 1953, with the title The Collected Works Riemann at his death in 1866. They were compiled under the title of Bernhard Riemann, although the only English content was a brief Fragmente philosophischen Inhalts (Phiiosophical Fragments), and new introduction by Hans Lewy on Riemann's career and thought. first appeared in the 1876 first edition of Bernhard Riemann's Gesam­ In the German edition of the fragments translated here, the individ­ melte Mathematische Werke und Wissenschaftlicher Nachlass (Bern­ ual pieces are apparently separated by the short, centered rules that hard Riemann's Collected Mathematical Works and Scientific Re­ have been carried over in this translation. All emphases and ellipses mains), published by B.G. Teubner. The volume was edited by Hein­ are in the original. Words or phrases in square brackets have been rich Weber, who later compiled and published Partial Differential supplied by the translator. Riemann's own footnotes are indicated Equations in Mathematical Physics from Riemann's Lectures. by asterisks and daggers, while the translator'S notes are numbered Teubner published a more complete second edition of Riemann's and appear at the end. collected works in 1892, also prepared by Weber, and a supplement The translation owes its inspiration to Lyndon H. LaRouche, and of additional materials (Nachtrage) appeared separately in 1902, was done under the supervision of Carol White. Thanks go to William edited by M. Noether and W. Wirtinger. These two volumes were F. Wertz, Jr. and Renee Sigerson for their abundant help. later reprinted by various publishers as one. Dover Publications (New -David Cherry

50 Winter 1995-1 996 21st CENTURY I. On Psychology and Metaphysics

Do not scornfu lly reject the gifts I have devotedly marshalled for you, before you have understood them. -Lucretius

ith each simple act of thinking, something durable, sub­ Wstantial, enters our mind. This substance appears to us, in fact, as a unity, but it appears (insofar as it is the expression of space and time extension) as comprising a subsumed mani­ fo ld; I name this a "thought mass."! To this effect, all thinking is the development of new thought masses. The thought masses entering into the mind appear to us to be images; their varying internal states determine how they differ qualitatively. As they are fo rming, the thought masses blend; or are folded together, or connect to one another and also to older thought masses, in a precisely determined manner. The character and strength of these connections depend upon causes which were only partially recognized by Herbart, but which I shall fill out in what follows. They rest primari ly on the internal relationships among the thought masses. The mind is a compact, multiply connected thought mass with internal connections of the most intimate kind. It grows continuously as new thought masses enter it, and this is the means by which it continues to develop. Thought masses once formed, are imperishable; and their connections cannot be dissolved; only the relative strength of these connections is altered by the addition of new thought masses. Bernhard Riemann (1826-7 866) Thought masses need no material carrier for their continued existence, and exert no lasting effect upon the physical world. weaker degree according to the diminished amount and in­ Therefore they are not related to any portion of matter, and creased distance of their connections. have no position ·in space. The most general and simplest expression of the effectiveness On the other hand, a material carrier is required for every of older thought masses is in their reproduction, which occurs entry, generation, every formation of new thought masses, and when an active thought mass strives to reproduce one similar for their unification. Thus all thinking does occur at a defi­ to itself. nite place. The formation of new thought masses is based partly on the (It is not the retention of our experience but only thinking, combined effect of older thought masses, partly on material which is strenuous; and this exertion of effort, in so far as we causes; and these, working together, are retarded or advanced can estimate it, is proportional to the mental activity.) according to the internal dissimilarity orsimilarity of the thought Every thought mass which enters the mind, stimulates all masses whose reproduction is sought. thought mass to which it is related, and does so the more strongly the less the dissimilarity between the internal states (quality). The form of the developing thought mass (or the quality Of This stimulation is not confined, however, merely to related the image which accompanies its formation) depends upon the 2 thought masses, but also extends, through mediation, to those relative form of the motion of the matter in which it is shaped, . that are linked with them (that is, connected by previous so that a given form of motion of the matter, causes a like form thought processes). Thus if among the related thought masses, of the thought mass shaped within it; and conversely, whatever a portion is linked, these will be stimulated not merely directly the form of the thought mass, it presupposes a like form of but also through mediation, and therefore will be stimulated motion of the matter in which it is shaped. proportionally more strongly than the rest. All thought masses simultaneously being formed (in our The reciprocal action of two thought masses being formed cerebro-spinal system) are connected in consequence of a at the same time, is conditioned by a material process between physical (chemical-electrical) process between the sites where the places where they are both being formed. Likewise, for they are formed. material reasons, all thought masses being formed enter into Each thought mass strives to reproduce a thought mass of unmediated interaction with those formed immediately before; like form. It therefore tries to recreate the form of motion of however, through mediation, all older thought masses linked the matter in which it is formed. to these will also be stimulated into activity, although to a The assumption of mind as a unified carrier for that which

21st CENTURY Winter 1995-1996 51 is enduring-produced by individual acts of mental life (im­ ages)-is based upon the following: 1. On the close connection and mutual interpenetration of Herbart on the all images. In order to explain the linking of a particular new image with others, it is however, not sufficient to simply assume . Thought Process a unified carrier; rather the cause as to why the given image enters into just such particular connections, with just such Johann Friedrich Her­ particular strengths, must be sought in the images to which it bart, German ph i loso­ binds itself. Once these causes are given, however, it then pher and educational becomes superfluous to make the assumption of a unified carri­ theorist, was the domi­ er for all of the images .... nant influence on Amer­ ican ed ucation in the 1890s, until his classical Let us now apply these laws of mental processes, to which theory was attacked by the explanation of our own inner perception leads, to explain radical empiricist John what we perceive to be purposefulness on earth, i.e., to an Dewey in 1896. explanation of existence and historical development. The fo llowing passage For the explanation of our mental life, it was necessary to from his seminal work, assume that the thought masses which were produced in our Outlines of Educational nervous system endure as part of our mind; that their internal Doctrine (translated by relations persist without alteration, and that they are subjected Alexis F. Lange, New Johann Friedrich Herbart to alteration only in so far as they enter into connection with York: Macmillan, 1911) (1776- 784 7) other thought masses. is typical of those upon which Riemann drew in formu­ It is a direct consequence of these principles of explanation, lating his theory of the process of creative discovery in that the minds of organic beings-i.e., the compact thought terms of an elaboration of successively higher-dimen­ masses arising during their lives-also continue to exist after sional, multiply connected manifolds. their death. (Their isolated continuance is not sufficient.) In Herbart writes (page 19): order to explain the systematic development of organic nature, however-in which previously gathered experiences obviously Each body of ideas is made up of complications serve as the foundation for subsequent creations-we must of ideas, which, if the union is perfect, come and assume that these thought masses enter into a greater compact go in consciousness as undivided wholes, and of thought mass, the biosphere,) and there serve a higher mental series, together with their interiacings, whose mem­ life, according to the same laws as those which operate when bers unfold successively, one by one, provided they we reproduce thought masses in our nervous system to serve are not checked. The closer the union of parts our own mental life. within these complications and series, the more ab­ Take as an example, the case in which we see a red surface. solute the laws according to which ideas act in The thought masses produced in an aggregate of individual consciousness, the stronger is the resistance against primitive fibers is bound into a single, compact, thought mass, everything opposing their movement; hence the dif­ which enters into our thinking at once. In the same way, the ficulty of acting upon them through instruction. thought masses produced in various individuals of a species They admit, however, of additions and recombina­ of plant, which enter the biosphere from a region of the earth's tions, and so may in the course of time undergo es­ surface which is not very diverse climatically, will be combined sential changes; up to a certain point they even into a single impression. Just as various sense perceptions of change of themselves if repeatedly called into con­ the same object are united in our mind into one image of the sciousness by dissimilar occasions, e.g., by the fre­ object, so all plants of one part of the earth's surface will give quent delivery of the same lecture before different the biosphere a picture, worked out in the finest detail, of its audiences. climatic and chemical condition. In this manner, the way in -David Cherry which the plan for later creations evolved from the earlier life of the earth, can be explained. But, according to our principles of explanation, the contin­ Accordingly, the only remaining assumption is that the pon­ ued existence of thought masses once present, requires no derable masses within the rigid crust of the earth are the carrier material carrier; yet all of the interconnections, at least every for the mental life of the earth. connection between thought masses of different kinds, can only Are these masses suitable for this purpose? What are the occur by means of ofthe production of newer thought masses external conditions necessary for the life process? We can estab­ by a common process of the nervous system. lish the fou ndation for an answer only empirically, on the basis For reasons to be developed later, we can seek the carrier of the living processes that are accessible to our observation; fo r a mental activity only in ponderable matter. but only insofar as we succeed in explaining them, can we Now it is a fact,. that the rigid crust of the earth, along with draw conclusions from them which are also applicable to other everything ponderable above it, does not serve a common classes of phenomena. "mental" process; we can only explain the movement of these Empirically, the external conditions of living processes in ponderable substances by other causes. the range of phenomena accessible to us are:

52 Winter 1995-1 996 21st CENTURY 1. The higher and more completely developed the life­ pounds could not exist. process, the more it is necessary to protect its carrier from We must therefore assume that these conditions are valid external causes of motion which strive to change the relative only for the life process under the present relationships on the position of its parts. surface of the earth, and only in so far as we are successful in 2. The physical processes (changes in matter) known to us explaining these, can we judge from them the possibility of that serve as a means for the thought process: the life process governed by different relationships. (a) absorption of gas by liquids Why, therefore, are only the four organic elements universal (b) osmosis inward through a cell wall carriers of the life process? The reason can only be sought in (c) formation and decomposition of chemical compounds properties by which these fo ur elements are distinguished from (d) Galvanic currents. all others. 3. The substance of organisms has no recognizable crystal­ 1. One such general property of these four elements consists line structure; it is partly solid (only slightly brittle), partly gelati­ in the fact that they and their compounds are the most difficult nous, partly liquid or gaseous, but always porous, that is! mark­ to condense of all materials, and, some of them have not yet edly penetrable by gases. been condensed at all. 4. Among all chemical elements, only the four so-called 2. Another property which they share is the great multiplicity organic elements are general carriers for the life process, and of their compounds and the ease with which they decompose. again, quite definite compounds of these, the so-called organiz­ This property, however, could just as well be the consequence ing compounds, are components of organic bodies (protein, of their use in living processes as its cause. cellulose, etc.). However, the former property, that of being difficult to con­ 5. Organic compounds exist only to a definite upper temper­ dense, is what makes these fo ur elements preeminently suited ature limit, and can be carriers of life only to a definite low­ to serve life processes. To a certain extent this is directly ex­ er one. plainable from the conditions of the life process enumerated ad. 1. Changes in the relative position of the parts of a body under 2. and 3.,6 but even more if we attempt to trace the are caused by the fo llowing (in decreasing stepwise order of phenomena found in the condensation of gases to liquids and their effect): mechanical forces, changes in temperature, light solids, back to their causes .... radiation; accordingly, we can order the facts-of which our proposition is the general expression-as fo llows: 1.The propagation of lower organisms through division. The Zend-Avesta is in fact a life-giving word, * which creates new gradually decreasing reproductive capacity of higher animal or­ life for our mind, in knowledge as in faith. For like many a ganisms. thought, which indeed was at one time powerfully effective in 2. The parts of plants are the more sensitive to changes in the course of development of mankind, but is now only pre­ temperature, the more intensive and the more highly developed served for us through tradition, Zend-Avesta arises now, all at the life process is in them. In the higher animal organisms, an once, from its apparent death, into a purer form of new life, almost constant temperature governs, especially in their most and reveals new life in nature. Now as the life of nature­ vital parts. previously only manifest on the surface of the earth-is immea­ 3. The parts of the nervous system which serve independent surably extended before our eyes, it appears inexpressibly more thinking are protected against all these influences as much sublime. What we considered as the seat of forces working as possible. senselessly and unconsciously, now appears as the workplace Obviously, the foundation for the fact first presented4 is that, of the highest spiritual activity. What our great poet has por­ the more the relative position of the parts can be determined trayed with prescient inspiration as the goal, which hovered by processes occurring within the interior of the matter, the before the mind of the investigator, is now fulfilled in a won­ less will it be determined by external motion. This indepen­ drous way. dence from external sources of motion, however, occurs to a Just as Fechner in his Nanna seeks to demonstrate that plants far higher degree inside the crust of the earth, than for organic possess the characteristics of mind/ so the point of departure beings on the outside. for his reflections in Zend-A vesta is the teaching that stars share In the context of the following facts, taken together, those characteristics of mind. His method is not to abstract general placed under 4. and 5. [above] are apparently contrary to our laws through induction in order to apply and confirm these in assumption; they would be so, in fact, if absolute validity were the explanation of nature, but rather to reason by analogy. He to be ascribed to those conditions perceived by us for the compares the earth to our own organism, which we know possibil ity of a life process, rather than a merely relative val idity has a mind. He does not merely one-sidedly investigate the within the limits of our experience. The fo llowing reasons go similarities, but also does as much justice to the dissimilarities. against their absolute validity, however: In this way he obtains the result that all the similarities indicate 1. All of nature, with the exception of the surface of the that the earth is a being possessing characteristics of a mind, earth, would then have to be considered dead, since on all and that all of the dissimilarities indicate that it is a being with other celestial bodies, temperature and pressure relations pre­ a mind of a far higher order than our own. The persuasive dominate under which organic compounds cannot exist. power of this presentation lies in its many-sided, detailed expo­ 2. It is absurd to assume that the organic arose from the sition. The total impression of the picture unfurled for us, of i, norganic on the rigid crust of the earth. In order to explain the life of the earth, provides evidence for his view, and com­ the origin of the lowest organisms on the earth's crust, some pensates for that which the individual conclusions lack in rigor. organizing principle must be assumed, and thus a thought

processs must exist under conditions in which organic com- • Compare Fechner, Zend-Avesta, Vol. 1, Preface, page V.

21st CENTURY Winter 1995-1 996 53 This evidence rests on the intuitive clarity of the image, and within the life of a single generation. Therefore, the cause of on its execution in the greatest possible detail. I would therefore their purposefulness is not to be sought in a simultaneously bel ieve myself to be doing harm to Fechner's view, were I to continuing process of thought. attempt to present here, in outli ne, the course he takes in his Apart from these aspects of (organic) purposefulness, there works. In the following discussion of Fechner's views, I will is still in man and animals, by common consent-and in plants ignore the form in which they are presented, and consider only in Fechner's view-a closed lattice of interpenetrating and vari­ the substance, and thus take as a basis the former method, the able relations of purpose and action; and this purposefulness abstraction of general laws by induction and their confirmation is explained by the existence of a unified "thought process" in the explanation of nature. within them. Let us ask first: From what do we conclude that something These conclusions which we draw from our principles are has a mind (the occurrence within it of a continuing, unified confirmed through our inner perception. thinking process)? We are directly aware of our own mind, According to the same principles, however, we must look and with others (human beings and animals), we infer it from for the reason behind the purposefulness which we perceive individual purposeful movements. in organisms in a unified thought process occurring in the earth, In general, wherever we trace a well-ordered purposefu lness on the fo llowing grounds: back to a cause, we seek this cause in a process of thought; (a) The relationships of purpose and action characteristic of we do not have another explanation. Thinking itself, however, organic life on earth cannot be separated into separate systems; I can only consider as a process which occurs within the interior on the contrary, everything is interlocked. They cannot there­ of ponderable matter. As is evident to anyone who tries to fore be explained as several particular thought processes, in analyze inner perception impartially, it is impossible to explain various parts of the earth. thinking on the basis of the motion of matter in space; however, (b) There is no basis, as far as our experience goes, for the abstract possibility of such an explanation may be conced­ seeking the reason for this purposefulness in a greater whole. ed here. All organisms are determined only for life on the earth. The No one will deny that purposefulness is perceived on the condition of the earth's crust contains, therefore, all the (exter­ earth. And so the question arises: Where are we to locate the nal) reasons needed to explain how they are organized. thought process that is the cause of this purposefulness? (c) Organisms fo und on earth are individual. According to The concern here is only with conditioned purposes (those everything that experience teaches, we must assume that they which take place within limited time and space); unconditional are not replicated on other celestial bodies. purposes find their explanation in an eternal Will (not produced (d) They do not persist throughout the life of the earth. In­ in a process of thought). The only purposefu lness whose cause stead, new, more perfect organisms are always appearing. We we perceive is that of our own actions. It originates in willing must therefore seek the cause in a thought process that is the end and reflecting upon means. simultaneously ascending to higher levels. If we find a body consisting of ponderable matter in which The assumption of a biosphere is therefore a hypothesis for a lattice of continuing, related purposes and actions are com­ explaining the existence and the historical development of the pletely realized, we can explain this purposefulness by means organic world, from the standpoint of exact natural science, of a continuing, unified thought process, and this hypothesis of a natural explanation from causes. will be the most probable if (1) the purp0sefulness is not com­ pleted merely in parts of the body and (2) no reason is present to seek the cause of that purposefulness in a larger whole of "When the body of the lower soul dies," Fechner says, "the which the body is a part. higher soul takes it up from its perceptual life into its life of If we apply this to the purposefulness which we perceive in memory." The souls of deceased creatures are thus said to form human beings, animals, and plants, then it follows that a part the elements for the soul-life of the earth. of this purposefulness is to be explained by a thought process The various processes of thought seem to be principally which occurs within these bodies; another part, however, the distinguished by their temporal rhythm. If plants possess minds, purposefulness of the organism itself, is to be explained by a so must hours and days be for them, what seconds are for us; process of thinking in a larger whole. the corresponding period of time for the earth mind encom­ The reasons for this are: passes many millennia, at least, for its outward activity. As far 1.The purposefulness of organisms does not find completion as the historical memory of mankind reaches, all movements in individual organisms. The reasons for the constitution of the of the inorganic crust of the earth are probably to be explained human organism are obviously to be sought in the constitution by mechanical laws. of the entire surface of the earth, with organic nature taken into account. 2. The organism'S activities repeat themselves innumerable Antinomies times, in part simultaneously in different individuals, partly successively in the life of an individual or a generation. For Thesis Antithesis the purposefulness which lies in them already per se, we need The finite, the representable. Infinite, conceptual systems not assume a special cause in each case, but rather a com­ which lie at the boundary of mon cause. the representable. 3. In the case of human beings and animals, their constitu­ I. tions undergo no further development within the lifetime of Finite time and space ele- The continuous. the single individual, nor (in the case of plants and embryos) ments.

54 Winter 1995-1 996 21st CENTURY II. a guide for the hearts and fate Freedom, i.e., not the capacity Determinism. of man; the concept of provi­ to begin absolutely, but rather dence must be supplemented to decide between two or and in part replaced by the more given possibilities. concept of the governance of the universe. So that decision through No one, when acting, can give choice be possible, despite up the conviction that the fu­ the existence of fully determi­ ture is partly determined by General Relationship between the Conceptual nate laws of the working of his action. Systems of Thesis and Antithesis images, one must assume that The method, which Newton used for founding the infinites­ the psychic mechanism itself imal calculus, and which, since the beginning of this century, has, or at least takes on, in its development, the characteris­ has been acknowledged by the best mathematicians as the tic of leading to the necessity only one which produces re liable results, is the method of of decision through choice. limits. The method consists in this, that instead of considering a continuous transition from one value of a magnitude to another, III. from one position to another, or in general, from one mode of A God who operates in time A timeless, personal, omni­ determination of a concept to another, one first considers a scient, omnipotent, all-good (governance of the universe). transition through a finite number of intermediate steps, and God (providence). then allows the number of these intermediate steps to grow, IV. so that the distance between two consecutive intermediate Immortality. A thing in itself, which is the steps decreases ad infinitum. basis of our transient exis­ Conceptual systems of antithesis are concepts indeed fi rmly tence, endowed with tran­ determined through negative predicates, but not positively rep­ scendental freedom, radical resentable. evil, intelligible character. Just because an exact and complete representation of these Freedom is entirely compati­ conceptual systems is impossible, they are not accessible to ble with the strict lawfu lness direct investigation and treatment by our reflection. But they of the course of nature. But can be considered to lie at the boundary of the representable, the concept of a timeless God i.e., one can form a conceptual system which lies within the is not tenable beside it. Rath­ representable, but which passes over into the given conceptual er, the limitation which om­ system through mere changes in the relative magnitudes. Apart nipotence and omniscience from the relative magnitudes, the conceptual system remains must suffe r through the free­ unchanged in the transition to the limit. In the limiting case dom of creatures, in the sense itself, however, some of the correlative concepts of the system established above, is removed lose their representability, in fact precisely those which mediate through the assumption of a the relationship will:! .other concepts. God operating in time, who is

II. Epistemological Issues

Attempt at a Theory of the Fundamental confirmation through experience. But if something takes place Concepts of Mathematics and Physics as the that is unexpected according our existing assumptions, i.e., Foundation for the Explanation of Nature that is impossible or improbable according to them, then the task arises of completing them or, if necessary, reworking the Natural science is the attempt to understand nature by means axioms, so that what is perceived ceases to be impossible or of exact concepts. improbable. The completion or improvement of the conceptual According to the concepts through which we comprehend system forms the "explanation" of the unexpected perception. nature, our perceptions are supplemented and filled in, not Our comprehension of nature gradually becomes more and simply at each moment, but also future perceptions are seen more complete and correct through this process, simultaneous­ as necessary. Or, to the degree that the conceptual system is ly penetrating more and more behind the surface of appear­ not fu lly sufficient, future perceptions are determined before­ ances. hand as probable; according to the concepts, what is "possible" The history of causal natural science, in so far as we can is determined (thus also what is "necessary," and conversely, trace it back, shows that this is, in fact, the way our knowledge impossible). And the degree of possibility (of "probability") of of nature advances. The conceptual systems that are now the each individual event which is seen as possible, in light of basis for the natural sciences, arose through a gradual transfor­ these concepts, can be mathematically determined, if the con­ mation of older conceptual systems, and the reasons that drove cepts are precise enough. us to new modes of explanation can always be traced back to To the extent that what is necessary or probable, according contradictions and improbabilities that emerged from the older to these concepts, takes place, then this confirms the concepts, modes of explanation. and the trust that we place in these concepts rests on this The formation of new concepts, in so far as this process is

21st CENTURY Winter 1995-1996 55 strongest reason for the latter conception is the demand to maintain as far as possible, the already proven concept of the existence of the thing in itself. Of course, it is not possible to actually represent such a transition through all intermediate steps, which, however, as noted, is valid, strictly speaking, for all concepts. At the same time, however, according to the concept of the thing in itself, formed earlier and proven by experience, the thing would remain what it is, unless something else intervened. This creates the impulse to seek a cause for every change.

I. When is our comprehension of the world true? "When the relations among our conceptions correspond to the relations of things." The elements of our picture of the world are completely distinct from the corresponding elements of the reality which they picture. They are something within us; the elements of reality are something outside of ourselves. But the connections among the elements in the picture, and among the elements Gustav Fechner (1801-1887) was an experimental psycholo­ of reality which they depict, must agree, if the picture is to gist and professor of physics at the University of Leipzig from be true. 1834 until 1839, when he resigned because of illness. His The truth of the picture is independent of its degree of fine­ work, however, continued to be very wide-ranging after his ness; it does not depend upon whether the elements of the subsequ�nt recovery. He is remembered today chiefly in con­ picture represent larger or smaller aggregates of reality. But, nection with Fechner's (or Weber's) law that stimuli are per­ the connections must correspond to one another; a direct action ceived by the mind with logarithmic compression: The inten­ of two elements upon each other may not be assumed in the sity of a sensation increases arithmetically if the intensity of picture, where only an indirect one occurs in reality. Otherwise the stimulus increases geometrically. the picture would be false and would need correction. If, how­ ever, an element of the picture is replaced by a group of finer elements, so that its properties emerge, partly from the simpler accessible to observation, therefore takes place in this way. properties of the finer elements, but partly from their connec­ Herbart furnished the proof that concepts that allow us to tions, and thus become in part comprehensible, then this in­ comprehend the world-those whose origin we can trace nei­ creases our insight into the connection of things, but without ther in history nor in our own development, because they the earlier understanding having to be declared false. are delivered to us unnoticed through our language-can be II. How do we find the relations among things? derived from this source, in so far as they are more than mere "From the connections of phenomena." forms combining simple sense images; and therefore these con­ The representation in determinate space-and-time relations cepts need not be derived from some special constitution of of things of the senses is something met with in deliberate the human mind which precedes all experience (such as reflection on nature or is given in that reflection. However, as Kant's categories). we we ll know, the quality of the characteristics of things of This proof of their origin in our ability to comprehend that the senses-color, sound, tone, smell, taste, heat or cold, is which is given to us by sense perception, is important for something merely derived from our own sensations and does us, because it is only in this way that their meaning can be not exist outside of ourselves. determined in a manner satisfactory fo r science.. .. The relations among th ings must therefore become known to us from quantitative relations, the spatial and temporal rela­ tions of things of the senses and the relative intensities of their After the concept of things existing in themselves has been characteristics and their qualitative differences. formed, then in reflecting on the process of change, which Knowledge of the connections among things must arise from contradicts the concept of things existing in themselves, the reflection on the observed relations of these relations of magni­ task arises of maintaining this already proven concept as far tudes. as possible. From this problem arise simultaneously the con­ cepts of continuous change and causality. All that is observed is the transition of a thing from one state Causality into another, or, to speak more generally, from one mode I. What an action strives to accomplish must be determined of determination to another, without a sudden jump being through the concept of the action; its acting cannot be depen­ perceived in the transition. In order to complete the observa­ dent upon anything else than the action's own being. tions, we can either assume that the transition occurs through II. This demand is satisfied when the action strives to main­ a very great, but finite, number of leaps imperceptible our ta in or restore itself. senses, or that the thing goes continuously through all of the III. Such an action is not conceivable, however, if the action intermediate steps, taking it from one state to the other. The is a thing, a being; but only if it is a state or a relationship. If a

56 Winter 1995-1 996 21st CENTURY striving exists, to maintain or restore something, then deviations himself compelled to assume that the concept of causality from this something must also be possible-and indeed in precedes all experience, this is tantamount to throwing the diffe rent degrees. And in so far as this striving conflicts with baby out with the bath; because this implies that the mind other strivings, it will in fact be maintained or restored only to wou ld be preconditioned to accept any perception, given by the extent possible. But there is no gradation of being; a differ­ experience, as a cause, if it could be connected to any other ence of degrees is conceivable only for states or relationships. arbitrary one as effect, according to a rule of mere sequence. If therefore, an action strives to maintain or restore itself, it (Of course, we must derive the relationships of causality from must be a state or a relationship. experience, but we must not dispense with correcting and IV. Obviously, such action can only occur in those things completing our comprehension of the data of experience that can assume such a state. But in which of these things it through reflection.) occurs, and whether it occurs in them at all cannot be deter­ mined from the concept of the action.* Kant quite rightly notes that we can neither discover the The word hypothesis now has a somewhat different meaning existence of a thing, nor that it is the cause of something else, than with Newton. We are now accustomed to understand by merely from analysis of the concept of the th ing; so that the hypothesis all that is added by thought to phenomena. concepts of bei ng and causality cannot be derived from analysis Newton was far from the absurd thought that the explanation but only from experience. When, however, he later believes of phenomena could be gained by abstraction from experience. Newton: [In Latin from the General Scholium of Principia

• These theses are valid only if the effect is to be ascribed to a simple real cause. Mathematical "And thus much concerning God; to discourse If two things a and b are connected through an external cause, then a of whom from the appearances of things, does certainly belong consequence e can be ascribed either to the connection, the process of being connected itself, or else to a change in the degree of the connection. The to natural philosophy. [ ...l But hitherto I have not been able simplest assumption is that the consequence ecan be ascribed to the process to discover the cause of those properties of gravity from phe­ of being connected. It is unnecessary to to take these considerations further. Their principle nomena, and I frame no hypotheses." consists in holding to the thesis: "What an action strives to effect must be Arago, Oeuvres Completes, Vol. 3, 505: determined from the concept of the action"; but this thesis must be applied, [In Frenchl "Once and once only did Laplace rise into the not as Leibniz or Spinoza did, to beings with a manifold of determinations, but rather to real causes of the greatest possible simplicity. realm of conjecture. His conception at that time was nothing less than a cosmogony." Laplace in response to Napoleon's question, why the name In German, one tends to translate "actio" as well as "effect us" by "Wirkung God did not occur in his Celestial Mechanics: [in Frenchl "Sire, [effect]." Since the word occurs in the latter sense more commonly, unclarity I have no need for that hypothesis." easily arises if it is used for "actio," as, for example, with the standard transla­ tion of "actio aequalis est reactioni [action and reaction are equal]," or "principi­ um actionis minimae [principle of least action]." Kant seeks to remedy this by adding the Latin expressions "actio" and "actio mutua" in parenthesis to The distinction that Newton makes between laws of motion, "Wirkung" and "Wechselwirkung [interaction]." One could perhaps write, "die Kraft is gleich der Gegenkraft [the force is equal to the opposing force]," "Satz or axioms, and hypotheses, does not seem tenable to me. The vom kleinsten Kraftaufwande [the principle of least expenditure of force]." law of inertia is the hypothesis: If a material point were present Since, in fact, we lack a simple expression for "agere," a striving directed toward something else, I may be permitted the use of the foreign word alone in the world and moved in space with a definite velocity, [agens, action]. then it would constantly mainta in this velocity.

III. Natural Philosophy

1. Molecular Mechanics d2XI XI ' tud es -- - - ... co IIectlve I y = 0, and they also take the dt 2 ml The free movement of a system of material points ml, m2 minimum value only then; for, were one of these magnitudes, ... with rectangular coordinates XI, YI , ZI ; X2, Y2 , Z2; ... , on d2x 1 X d2x I which forces Xl , Yt , ZI ; Xl i Y , Z ; ... act in parallel to the for example, ---"- not equal to 0, then __ could con- 2 2 dt 2 ml dt2 three axes, takes place according to the equations tinuously change so that the absolute value of this magnitude and consequently its square would decrease. The function (1 ) wou ld thus become smaller if all the other accelerations were simultaneously left unchanged . This function of the accelerations is distinguished from This law can also be expressed as follows: The accelerations are so determined that

becomes a minimum; for this function of the accelerations takes its smallest value 0 if the accelerations collectively are only by a constant, that is, by a magnitude independent of determined in accordance with equation (1), that is, the magni- the accelerations.

21st CENTURY Winter 1995-1 996 57 If the forces between points result only from attraction and additionally, an action which strives to keep the magnitude repulsion, which are functions of distance, and the tth point - P as small as possible. and the t'th point at a distance r repulse one another with a The latter action can be analyzed into efforts to keep the force (,,(r) or attract one another with the force - (,,(r) then, as individual terms of the sum L,F1" ,(rl,I') as small as possible, that is known, the components of the forces can be expressed 1,1' is, into attractions and repulsions between any two points, and through the partial derivatives of a function of the coordinates this would lead us back to the customary explanation of the of all the points laws of motion from the law of inertia and of attraction and repulsion; but it can also lead us back, for all natural fo rces P = L,F" " (r",, ), l,l' known to us, to the forces that act between contiguous spatial elements, as will be explained in the following article on gravi­ where F" ,,(r) is a function with derivative (,,(r), and for t and t' tation. two different indices are set for each. If these value� of the components 2. New Mathematical Principles of ap ap Natural Philosophy* = X' = -a x, ' Z' -a z, Although the title of this essay will hardly create a favorable are substituted into the above function of the accelerations and impression on most readers, it nonetheless seems to me to best express the overall direction of the essay. Its purpose is to are multiplied by C:'through which the positions of their maxi­ penetrate beyond the fo undations of astronomy and physics laid by Galilei and Newton, into the interior of nature. For ma and minima are not changed, then we obtain an expression astronomy, certainly these speculations cannot immediately which is distinguished from have any practical use, but I hope that this circumstance will not cause any diminution of interest in the eyes of thereaders of this publication .... The foundation for those general laws of the motion of pon­ derable bodies that are presented at the beginning of Newton's Principia lies in the internal state ofthese bodies. Let us attempt only by a magnitude which is independent of the accelerations. to form an analogy between these and our own inner mode If the position and the velocities of the points at time tare of perception. New image masses constantly arise in us and given, then this position is determined at time t dt such that + very rapidly disappear again from our consciousness. We ob­ this magnitude becomes as small as possible. Accordingly, serve a constant activity of our mind. Every mental act is based there is a striving for this magnitude to become a minimum. upon something enduring, which is manifest (through memory) This law can be explained on the basis of actions which on certain occasions, without exerting a lasting influence on strive to make the individual terms of this expression as sm all the phenomena. Thus (with every act of thinking) something as possible if we assume that the strivings working against one enduring continually enters our mind, which does not however, another are so equalized that the sum of the magnitudes which exert a lasting influence upon the world of phenomena. Every the individ ual actions strive to maintain at a minimum, be­ mental act, therefore, is based upon something enduring, which comes itself a minimum. enters our mind with the act, but at the samemoment complete­ If we assume that the masses of the points m1, m , ..., mn 2 ly disappears from the world of phenomena. behave like the whole numbers k1 , klt ... , knt so that m, = Guided by this fact, I form the hypothesis that there is a k,ll, then the expression, which becomes as small as possible, kind of space-filling substance which continually flows into consists of the sum of the magnitudes ponderable atoms and there disappears from the world of phe­ nomena (the corporeal world).B 2 2 2 d2X, dy. dz , Both hypotheses can be replaced by the one, that in all !:!: ((d ) (d ) (d ) ) 4 dt + dt + dt ponderable atoms, substance from the corporeal world contin­ uously enters into the world of mind. The reason the substance disappears there is to be sought in the thought matter which for the totality of material particles Il and of magnitude - Pt +dt • was formed in the immediately preceding period; and the pon­ If we therefore, with Gauss, consider the magnitude derable bodies are accordingly the place where the world of mind engages the corporeai world.t 2 2 2 2 d Xl dy. dZI The effect of universal gravitation, the first thing to be ex­ (d ) (d ) (d ) dt + dt + dt plained by this hypothesis, is well known to be fu lly determined for every part of space, if the potential function Pof all pondera­ ble mass for this part of space be given, or, which is the same as the measure of the deviation of the state of motion of mass Il at time t dt from its state of motion at time t, then the + • Discovered on March 1, 1853. analysis of the total action in relation to each mass yields an t At every instant, a definite quantity of substance, proportional to the gravita­ action which strives to make the deviation of its state of motion tional force, enters into every ponderable atom, and disappears there. It is a consequence of the psychology based on Herbart's work, that at time t dt as small as possible relative to its state of motion + substantiality accrues not to the mind but to every individual image formed at time t, or an effort to preserve its state of motion, and, within it.

58 Winter 1995-1 996 21st CENTURY 2 2 2 thing, there is a function of position P, such that the ponderable ds = dx + dy + dz = dS1 + dsj + ds j . ap masses contained within the closed surface 5, are J..- a dS . 41t P The magnitudes C, - 1, C2 - 1, C) - 1 then signify the major I deformations for the particle of substance at in the transition If we now assume that the substance that fills space is an 0, from the former form to the latter. I indicate them by A" 1. , A). incompressible homogeneous fluid, without inertia, and that 2 Now I assume that a force results from the difference between an amount proportional to the mass of any given atom flows the earlier forms of the particle of substance and its form at into it during equal times, then obviously, the pressure exerted time t, which strives to change it; and, other th ings being equal, on the ponderable atom (will be proportional to the velocity of the substance at the site of the atom(?))9 that the influence of an earlier form will become the less the Thus the effect of universal gravitation on a ponderable atom longer the time prior to twhen it occurred. Thus there is a limit can be expressed through (and thought of as dependent upon) before which all earlier fo rms can be ignored. I further assume the pressure of this space-filling substance in the immed iate that those states that still manifest a detectable influence differ neighborhood of the atom. so slightly from the state at time t, that the deformati.9ns may It ,n ecessarily fo llows from our hypothesis that the space­ be regarded as infin itely small. The forces that strive to make fi lling substance must propagate the vibrations that we perceive A" Av A) small can then be regarded as linear functions of A" as light and heat. 1.2, A); and indeed, because of the homogeneity of the aether If we consider a simple polarized beam, and designate as x for the total moment of these forces (the force which strives to the distance of an indeterminate point of this beam from a make A, small must be a function of A" 1.2, A), which remains fixed origin, and y its displacement at a time t, then the fo llow­ unchanged when we exchange 1.2 with A), and the remaining ing equation must be at least very nearly satisfied, since the forces must follow from it, when 1.2 is exchanged with A" and velocity of propagation of the vibrations in space free of ponder­ A) with A,) we obtain the following expression: able atoms is under all conditions very nearly constant (= a): 01.,(aI., + bA2 + bAll + 01.2 (bA, + aA2 + bAll + oA)(bA, + bA + aA)) y = f(x + at) +

For it to be strictly satisfied, or with a somewhat changed meaning of the constants:

oA, a(A, + 1.2 + A)) + bA, + oA a(A, + 1.2 + A)) + bA2 a a 2 ( ) l ) = aa d't a� t a; + oAl a(A, + 1.2 + A)) + bA) 2 I = � o(a(A, + 1.2 + 1.)) + b(A1 + Al + An) . would have to apply; obviously, however, for the sake of experi­ ment, we can be satisfied with the equation Now the moment of the force that strives to change the form of the infin itely small particle of substance at 0, can be regarded a as resulting from forces that strive to change the length of the = aa (t - 't) d't a� t aa2;

while How then must the functions \jI and

21st CENTURY Winter 1995-1 996 59 gravitation, light, and radiant heat may be propagation through mass-point and directly proportional to its gravitational force.t the substance of space? The cause, determined according to magnitude and direction (accelerating gravitational force), which, according to 3., is found at every point in space, I seek in the form of motion of The effects of ponderable matter upon ponderable matter a substance that is continuously spread through all infinite are: space, and, indeed, I assume that the direction of the motion (1 ) Attractive and repulsive forces inversely proportional to is equal to the direction of the force from which it is to be the square of the distance. explained, and the velocity is proportional to the magnitude (2) Light and radiant heat. of the force. This substance can therefore be represented as a Both classes of phenomena can be explained if we assume physical space whose points move in geometrical space. that the entirety of infinite space be filled with a homogeneous According to this assumption, all effects caused by pondera­ substance and that every particle of that substance acts directly ble bodies on ponderable bodies through empty space must ' only upon its immediate neighborhood. be propagated by this substance. Therefore also the forms of The mathematical law in accordance with which this occurs motion of which light and heat consist, which celestial bodies can be thought of as divided into transmit to one another, must be forms of motion of this sub­ (1 ) the resistance of a particle of substance to a change in stance. These two phenomena, however, gravitation and the volume, and motion of light through empty space, are the only ones that must (2) the resistance of a physical line element to a change be explained purely by means of the motions of this substance. in length. Now I assume that the actual motion of the substance in Upon the first part are founded gravitation and electrostatic empty space is combined from the motion which must be attraction and repulsion; upon the second, the propagation assumed for explanation of gravitation and that which must be of light and heat, and electrodynamic or magnetic attraction assumed for the explanation of light. and repu lsion. The further development of this hypothesis can be divided into two parts in that the fo llowing are to be sought: 1. The laws of motion of the substance which must be as­ 3. Gravitation and Light sumed for the explanation of the phenomena. 2. The causes by means of which these motions can be ex­ The Newtonian explanation of gravitational motion and the plained . motions of celestial bodies consists in the assumption of the The first subject is mathematical, the second, metaphysical. fo llowing causes: In reference to the latter, I note in advance that the goal will 1. There exists an infinite space with the properties which not be considered to be any explanation on the basis of causes are assigned to it by geometry, and there exist ponderable that strive to change the distance between two points of the bodies which change their positions within this space only con­ substance. This method of explanation by means of attractive tinuously. and repulsive forces owes its general application in physics 2. At every mass-point, there is at every moment a cause not to any direct evidence (or specific conformity to reason), determined by magnitude and direction, by virtue of which nor, apart from electricity and gravity, to its particular facility, cause the mass-point has a determinate motion (matter in a but on the contrary, to the circumstance that the Newtonian determinate state of motion). The measure of this cause is ve­ law of attraction, in contradiction to the opinion of its discover­ locity.* er, has so far been considered to need no further explanation.§ The phenomena to be explained here do not yet lead to the assumption of different masses for ponderable bodies. I. Laws of motion of the substance that, 3. At every point of space, there exists at every moment according to our assumption, causes the a cause (accelerating force), determined by magnitude and phenomena of gravitation and light. direction, which communicates a determinate motion to every mass point present, and indeed, the same motion to each, Expressing the position of a point in space by means of which combines geometrically with the motion that it al­ rectilinear coordinates Xl, Xv X), I designate the velocity compo­ ready has. nents-parallel to the coordinates at time t-of the motion that

4. At every mass-point in space, there exists a cause (absolute causes the gravitational phenomena as Ul , Uz, U), and those of gravity) determined by magnitude, which combines geometri­ the motion that causes the phenomena of light as WI , Wz , W) , cally with all other accelerating forces present there. By virtue and those of the actual motion as VI, Vz, V) , so that V = U + of th is cause, at every point of space an accelerating force exists, w. As will emerge from the laws of motion themselves, the inversely proportional to the square of its distance from this substance, if it is everywhere equally dense at one point in time, maintains this same density everywhere at all times. I * Every material body, if alone in space, would either not change its position in space or would move in a straight line with constant velocity. will therefore assume this to be everywhere equal to 1 at time t. This law of motion cannot be explained by means of the Principle of Sufficient Reason: That the body continues its motion, must have a cause, which can only be sought in the internal state of the matter. § [In English] Newton says: "That gravity should be innate, inherent, and essen· t The same mass point would undergo changes in motion between two points, tial to matter, so that one body may act upon another at a distance through whose directions coincide with the directions of the forces and whose magni· a vacuum, without the mediation of anything else, by and through which their tudes are proportional to the forces. action and force may be conveyed from one to another, is to me so great The force divided by the change in motion, therefore, always gives the an absurdity, that I believe no man who has in philosophical matters a same quotient for the same mass'point. This quotient is different for different competent faculty of thinking can ever fall into it." See the third letter to mass· points and is called their mass. Bentley.

60 Winter 1995-1 996 21st CENTURY a. Motion That Causes Only which arises the differential dU = ul dxl + U2dx2 + U3dx3 and Gravitational Phenomena. thus the derivatives U , and the others then yield U = V  = The gravitational force is determined at every point by + constant. * the potential function V, whose partial derivatives av av av b. Motion that causes only light phenomena. are the components of the gravitational force, aXI ' aX2 ' aX3 and this V is in turn determined through the fo llowing condi­ The motion that must be assumed in empty space for the tions (disregarding an additional constant): explanation of the phenomena of light can be considered (fol­ a2 v a 2 v a 2 v lowing a theorem) as composed of plane waves, that is, of such 1. dXI dxz dX3 (- + - + - ) outside the attracting a XI2 aX2 aX32 motions where the form of motion is constant along each plane 2 of a family of parallel planes (wave planes). Each of these wave body 0, and has for every ponderable material element a = systems consists then (in accord with observation) of motions constant value. This is the product of-4n in the absolute magni­ parallel to the wave plane that are propagated perpendicular tude of the attractive force, which according to the theory of to the wave plane with a constant velocity e that is the same attraction must be assigned to it, and will be designated as dm. for all forms of motion (types of light). 2. If all attracting bodies are within a finite space, If SI' S I S3 are the rectangular coordinates of a point in space av av . av . .. · 2 r - ,r- ,r- at an Inf· In ·Ite d·Is tance r f rom a pOint In t h IS for such a system of waves, the first being perpendicular, the a XI a X a X3 2 others parallel to the wave plane, and 0)1, 0) , 0)3are the compo­ space are infinitely small. 2 nents of velocity at this point parallel to the coordinates at time Now according to our hypothesis,  = U and consequently t, then we have aO) aO) 0, aS z = aS3 = o. This includes the conditions According to observation, first

(1 )

second, the movement is composed of motions with velocity (2) e, one propagating from the positive side of the wave plane, and one propagating from the negative side. If the velocity " components of the first are 0)' and that of the latter are 0) , then ru ru3 r 00. ' (3) rUI = 0, 2 = 0, = 0, for = the 0) remain unchanged if t increases by dt and SI increases " by edt, and the 0) are unchanged, if t increases by dt and SI Conversely, the magnitudes u, if they satisfy these conditions, ' " by -edt, and we have 0) = 0) + 0) . From this it follows that are equal to the components of the gravitational force. Since the conditions (1 ) contain the possibility of a function U from aO)' aO)' ( + e ) dt = 0, at aSI * This function U is therefore given through observation (from relative motions) by means of the general laws of motion, but only without taking account of a linear function of the coordinates, because we can only observe relative mo­ tions. The determination of this function is based on the following mathematical theorem: A function Vof position is determined within a finite space (ignoring a constant) if it is not said to be discontinuous along a surface, and for all and thus . · a a a ·· af I ts I t e emen s (-'v + -'v + -'v) dx, d dx, h I X3 at t e Imlt, elth er V or its axl axl ax! derivative is given for an inward change of position, perpendicular to the limit. Of which it should be noted:

1. If this derivative at the bounding element ds is designated by , then  These equations give the fo llowing symmetrical results: V in the latter case J I a'v dx, dx, dX3 must be eqUal to - � ds through the ax J up entire space because of 'its bound; otherwise, in both cases, all of the deter­ mining elements can be taken arbitrarily and are therefore necessary to the determination. a 2. For a spatial element where I 'vbecomes infinitely large, the product ax' olthe two is to be substituted by -J  ds in relation to the limit of this element. which, expressed in the original coordinate system, become a 3. If I 'v has a value other than zero only within a finite space, then equations of the same form, that is, ax the boundary' condition can be substituted by the statement that at an infinite distance R of a paint in this space R  becomes infinitely small. (1 )

21st CENTURY Winter 1995-1 996 61 (2)

d. Common expression for the laws of motion of the These equations are valid for every plane wave passing through substance and the effect of gravity on the motion of the point (x), Xv X3) at time t and consequently also for the ponderable bodies. combined motion of all such plane waves. The laws of these phenomena can be summed up by the c. Motion that causes both types of phenomena. condition that the variation of the integral

From the conditions established for u and w, the following conditions fo llow for vor laws of motion of the substance in empty space:

av) aV2 aV3 _ (I) + + - 0 , ax) aX2 aX3

2 2 2 2 (a t - cc (a x) + a X2 + a x3)) (�::- �::)= 0 2 2 2 2 2 (II) (a t - cc (a x) + a X2 + a x3)) (�:�- �::)= 0 + 2n f dm L (a�') dt

a2t - cc (a2x) + a 2X + a 2x3) - = 0, ( 2 ) (�:; �:�) becomes zero under appropriate boundary conditions. In this expression, the first two integrals extend over the entire as is easily derived if the operations are carried out. geometrical space, the latter over all elements of ponderable These equations show that the motion of a point of the bodies, but the coordinates of every element of ponderable substance only depends on motions in contiguous regions of bodies are to be so determined as functions of time, and 11 ), space and time, and their (complete) causes can be sought in 112, 113, Vas functions of x), Xv X3 and t, that a variation satisfying the effects in their neighborhood. their boundary conditions produces only a variation of the Equation (I) proves our earlier assertion that the density of second order of the integral. the substance remains unchanged during its motion; since Then the quantities a;:(=v ) are equal to the velocity compo­ nents of the motion of the substance and V is equal to the potential at time t at point (x), X2, X3)'

Translator's Notes ------which as a result of this equation is equal to 0, expresses the mass of the substance which flows into the spatial element dx) 1. The German expression is Geistesmasse. It had earlier appeared in the correspondence between Schiller and Goethe (personal communication of dX dX3 in time element dt, and the mass of the substance 2 George Gregory). contained in it therefore remains constant. 2. The expression form of motion (Bewegungsform), which begins to appear Conditions (II) are identical with the condition that here early in the fragments, appears as "forms of motion (types of light)" in one late occurrence in which the subject is electromagnetic radiation. This suggests that form of motion refers to wavelength or frequency. 3. In the fragments on psychology and metaphysics, Riemann refers to the Erdseele. The literal translation is earth mind or earth soul. We have instead used the expression biosphere. It will be helpful to the reader to keep in mind all the possibilities suggested by biosphere, earth mind, and earth be equal to a complete differential dW. Now soul, in the four instances where biosphere appears in the translation. The German Seele (soul or mind) is the equivalent of the Greek psyche. The Greek word also carries the meaning, that which enables fife. In his Harmonices Mundi, Kepler used anima-the nearest Latin equivalent of psyche-as a metaphor for universal graVitation. The translator thanks George Gregory for these observations on the Greek and Latin terms and their use. and consequently 4. See the first of the three paragraphs marked "1 " immediately preceding, which begins "1 . The higher ..." 5. The German word is Denkprocess. 6. Not the paragraphs 2. and 3. immediately preceding, but the earlier pair dW = a 2t - cc (a2x) + a 2X + a 2x3) (u)dx) + U dx + U3dx3 ) ( 2 ) 2 2 following the paragraph that reads, "Empirically, the external conditions of living processes in the range of phenomena accessible to us are:" Beseeltheil. 2 2 2 2 7. "Characteristics of mind" is used for = (a t - cc (a x) + a X2 + a X3) )dV 8. Here Riemann addresses the question of the space-filling substance, which he also calls '1he aether" in one instance. In this translation, it is also referred to in the expression "particle of substance,' and sometimes as simply "sub­ stance," after the concept of space-filling substance has been introduced. These expressions for space-filling substance are thus distinct from "ponder­ able atoms," "ponderable mass," or "ponderable bodies." 9. The question mark and both pairs of parentheses appear in the German without explanation. Are they Riemann's marks, or do they indicate an uncertain reading of the manuscript?

62 Winter 1995-1 996 21 st CENTURY FUSION REPORT Tokamak Plasma Advances Made, But Budget Cuts Threaten Program

by Mark Wilsey

ecent experiments with the two large Ru.s. tokamaks have produced marked improvements in plasma confine­ Central ment and plasma densities-the kinds of solenoid developments that could have a signifi­ magnet cant impact on the size and cost of future fusion power plants. However, a short­ sighted Congress has threatened any fur­ ther progress in fusion by slashing the fu­ sion budget by 30 percent and cancelling the next-generation fusion device, the Poloidal field TPX, or Tokamak Physics Experiment. magnet Scientists have striven for decades to harness fusion energy as an economi­ cal, plentiful energy source. But al­ though fusion energy powers the Sun and stars, creating the same conditions Toroidal field magnet here on Earth has been an elusive goal. The experiments with the General Atomics Doublet tokamak, the 0111-0 Figure 1 (pronounced "dee-three-dee") in San SCHEMATIC OF THE TOKAMAK Diego and with the Tokamak Fusion Under extremely high temperatures and pressure, the isotopes of hydrogen, Test Reactor (TFTR) at the Princeton deuterium and tritium, fu se and release a burst of energy. Confining and Plasma Physics Laboratory in New Jer­ maintaining the stability of this fu sion plasma are key concerns in the pro­ sey have now given us a glimpse of a duction of fusion energy. Tokamak fusion devices use magnetic fields to con­ new physics regime. tain the hot plasma. The externalmagnetic coils produce a toroidal magnetic Reversed Shear field, which tra vels the long way along the torus. The poloidal coils generate The technique used at Princeton and a second magnetic field, which tra vels the short way around the torus. General Atomics to improve confine­ Source: PPPL ment and plasma stability is called re­ versed shear. In both tokamaks, reversed shear was achieved by adjusting the brute-fo rce collisional approach­ groups have submitted papers to Physi­ magnetic fields to maximize the electri­ adopted by Princeton-in the form of cal Review Letters. cal current density profile of the plasma, scaling up the tokamak. Ironically, scien­ Charles Kessel, a physicist at Prince­ off-center. In typical tokamak operations, tists there have now "discovered" the ton whose theoretical work aided the the peak is at the center of the plasma. kind of self-organized geometry that was success there, notes how reversed shear The result of this off-center peak is, in ef­ central in the work of such scientists as yields distinct improvements: The parti­ fect, a partitioning of the plasma into a Winston Bostick, Daniel Wells, and tion acts to suppress particle and energy highly stable "core" region and a sur­ Bruno Coppi. transport out of the plasma; this im­ rounding "mantle." At Princeton, in tests run in spring proves confinement, which then leads to Magnetic fusion research in the 1970s 1995 on the TFTR, particle confinement higher densities and temperatures in the included a broad range of experimental improved by a factor of 40, with core core. In addition, the current induced in approaches designed to utilize the nat­ plasma density boosted by a factor of 3 the plasma reinforces the current gener­ ural geometries of plasmas in order to over conventional operations. At Gen­ ated by the plasma itself. With the TFTR, promote the conditions necessary for fu­ eral Atomics, experiments conducted in it can generate as much as 80 to 90 per­ sion. As the overall fusion budget was 1994 on the 0111-0 showed a marked cent of its own current. cut, the funds for these alternative pro­ improvement in plasma confinement The self-generated current in the grams were cannibalized in favor of the and plasma densities. Both research plasma is called the "bootstrap current,"

21 st CENTURY Winter 1995-1 996 63 proaches to tokamak power plant de­ Major radius sign. The approach taken at General Figure 2 Atomics has been to use reversed shear TOKAMAK MAGNETIC to change the current profi le in the FIELD GEOMETRY plasma to improve what is called the The combination of the beta limit. toroidal and poloidal mag­ Beta is the ratio of the plasma pressure netic fields produces a heli­ at the center to the magnetic pressure cal field that tra vels the long being applied to the tokamak, and can way around the torus. The be thought of as a measure of how well pitch of the helix varies the device is able to confine the plasma. along the minor axis. This As the pressure builds up, instabilities change with respect to ra dial occur in the plasma that let the pressure distance is called shear. out. Hence, the plasma reaches its sta­ Resultant helical field bility limit, or beta limit. The achievement of higher densities and fusion researchers are hopefu l that it ning, but that the United States will not leads to increased fusion reactivity. Re­ can be employed in future fusion de­ have scientists and engineers capable of searchers at Princeton are confident that vices to extend experiments for several continuing the quest for fusion energy. it may now be possible to double minutes, or perhaps indefinitely,. Now, The Beta limit TFTR's output, from 10 megawatts, its machines can operate only in pulses of a It was in part out of the design studies record set in 1994, to 20 MW or higher, few seconds at best. for the now-cancelled TPX that Charles using deuterium-tritium fuel. So far, ex­ The Budget Axe Kessel and his Princeton colleagues be­ periments have been conducted only Reversed shear, as well as other ad­ gan investigating the reversed shear ap­ with deuterium. vanced tokamak concepts, can be com­ proach for tokamak operations. The TPX Tokamak Physics pletely demonstrated only in a continu­ was planned to operate in steady-state Tokamaks are toruses, that is, shaped ous operation, steady-state machine. mode for pulse lengths of up to 1,000 like donuts (Figure 1). External mag­ This was the role that TPX was to have seconds. netic coils placed around the tokamak played in the u.s. fusion program. But General Atomics came to investigate produce a toroidal magnetic field, now this next-generation device has reversed shear as part of a range of ad­ which travels the long way along the been slashed out of the budget. vanced tokamak physics concepts being torus. The toroidal field induces a cur­ The fusion fu nding provision for fiscal explored on the 0111-0. Tony Taylor, a rent in the plasma which, in turn, gen­ year 1996 passed by Congress is $244 scientist at General Atomics who has erates a second magnetic field, the million-a sharp reduction from this been involved in this work since 1991 , poloidal field, which rotates about the year's $349 million and more than 33 explained that the object is to use the centerline of the torus. Still other mag­ percent below the $366 million re­ best physics we know to bring new ap- nets are used to augment and control quested by the administra- this current. The combina­ tion. tion of the toroidal and TFTR was to have been Direction of poloidal fields defines the increasing shear, shut down this year to make from edge inward magnetic fields inside the way fo r TPX. But with the and from center plasma; these are helical in outward cancellation of TPX and the shape, going around the reduced funding, Princeton length of the torus (Figure 2). has been forced to lay off a The tw ist of the helix third of its fusion staff, some changes within the plasma 240 employees, and it is not /(/\ as a result of the increasing clear whether TFTR will be strength of the poloidal field allowed to operate next toward the centerline of the � torus. The helix tends to be­ Edge of plasma year. Indeed, the continued Mantle operation of other fusion fa­ come more tightly twisted cilities is also threatened by toward the center. The such reduced funds. change in its twist (pitch) as Unless the low funding one moves inward along the levels are reversed, it seems Region of maximum shear; q is at its minimum. minor axis is called "shear." unlikely that the United In reversed shear, the field States will be able to main­ Figure 3 lines increase in twist up to a tain a fusion program. Of REVERSED SHEAR IN THE PLASMA CROSS SECTION point, and then decrease. In real concern is not simply In the reversed shear mode, the magnetic shear within the the TFTR, that point was that the nation will no longer plasma increases fr om the edge inward, as well as fro m found roughly one-third of invest the funds to keep its the center outward. The core region is highly stable. the way out from the center. present fusion machines run- This is the point at which the

64 Winter 1995-1 996 21 st CENTURY FUSION REPORT plasma is divided into the core and man­ tle regions (Figure 3). 6 The beta limit is expected to increase in this process. As Tony Taylor explains 5 it, normally the magnetic fields within CT the plasma are crossed, as the twist c5 changes toward the center. Then as the U 4 � pressure is increased, these fields are � pushed out from the core and start to CD Cii 3 line up, at which point, the plasma be­ CJ) comes unstable. With reversed shear, however, the field lines are crossed in 2 such a way that they do not line up again, thus avoiding instabilities and in­ 1.5 2.0 2.5 3.0 3.5 creasing the beta. Radius (m) Another way to look at it, is in terms of what is called the safety factor, or q, Figure 4 which measures the magnetic twist by SAFETY FACTOR, q, PROFILE FOR THE TFTR the number of laps that the field lines The two curves show safety fa ctor, q, profiles fo r TFTR at two different times make around the torus the long way be­ during an experiment. The q profile evolves with time as the current diffuses fore they make one turn the short way. A into the plasma. The center of core is at approximately 2.65 meters on the lower q means a higher twist, showing major ra dius. Th e two low points of the W-shaped curve are where the shear that it takes fewer laps around the torus reverses. to make one twist. A plot of the safety factor, q, versus Source: Levinton et aJ.lPPPL distance along the radius for a reversed shear mode will show a characteristic in "high mode," or "H-mode," meaning a future fusion power plant. The design W- shaped curve (Figure 4). The peak of that the conditions at the edge of the work on TPX supported the idea that a the W is in the center of the core. The plasma tend to also reduce transport, steady-state reactor would be fo ur times low points on either side of the core are and thus improve confinement. smaller in size than a pulsed reactor, the points at which the shear reverses, To date, neither TFTR nor 0111-0 has base on current designs. Kessel has changing directions. By contrast, in the actually shown marked improvements in found that when the reversed shear is more typical tokamak operation, the q beta (the ratio of plasma pressure to appl ied to the operations of a steady­ profile would be more U-shaped toward magnetic pressure) in these reversed state reactor, the size and cost of plant is the center; that is, the q constantly de­ shear experiments. A doubling of the reduced yet another 50 percent. creases, or the twist of the magnetic field beta values over conventional opera­ constantly increases. tions is the payoff that the researchers The W- shaped q profi le is accom­ are looking for. Taylor thinks that the plished by ramping up the current in the broader plasma pressure profile of the H­ LaRouche plasma while simultanously heating the mode reversed shear may be a more Campaign core. Continuously changing the current productive route to higher beta values. in the magnetic field coils induces a Implications Is On the current in the plasma. The current in the GA's Tony Taylor cautioned against Internet! plasma tends to start at the edge and overestimating the importance of these Lyndon laRouche's Democratic presidential diffuse toward the center. The time that reversed shear results. While he is ex­ primary campaign has established a World it takes for the current to diffuse is a cited by them, he realizes that there is Wide Web site on the Internet. The "home function of the plasma temperature. So, still much work ahead to prove out this page" brings you recent policy statements by heating the plasma, using neutral approach. Still, these results do demon­ by the candidate as well as a brief beams, that time can be stretched out. strate that there is a great deal of interest­ biographical resume. The heating of the plasma retards the ing physics to be explored. WI.iMU;:- the laRouche page current penetration to produce an off­ Princeton has shown on paper that 1 __.iI .IfI ..Ii. II ••Ii. II. I_ 1 on the Internet: center peak. based on a reversed shear mode, re­ http://www.clark.netllarouche/ Princeton and General Atomics use searchers shou Id be able to at least welcome.html similar approaches for reversed shear ex­ double the output of TFTR, and per­ periments, except that the 0111-0 has a haps even achieve breakeven. This WI.iMUQ:- the cam�aign by .. .. . O-shaped cross-section, while the TFTR's would mean achieving very high beta 1 __.iI .IfI Ii. iIIIi. II. I_ 1 electrOnIc mall: cross-section is circular. GA researchers values, which remains a significant [email protected]

have also achieved reversed shear in challenge. Paid for by Committee to three different operating modes with the Looking farther into the future, Prince­ Reverse the Accelerating Global Economic and Strategic Crisis: 0111-0, one of which is very similar to ton's Charles Kessel has begun to exam­ A LaRouche Exploratory Committee. that of the TFTR, and two others that are ine what reversed shear could mean for

FUSION REPORT 21 st CENTURY Winter 1995-1 996 65 GEOMETRY

li-, .1, IN THE FOOTSTEPS OF KEPLER A Master Polyhedra Builder Demonstrates H is Art by Charles B. Stevens

ne of the world's leading construc­ tors of polyhedra, Father Magnus J. OWenninger, visited 27st Century in Au­ gust to display some of the models (shown here and on the covers) and talk about the method of construction. Wen­ ninger is a Benedictine monk and a re­ tired high school mathematics teacher, who has written the three leading works on construction of polyhedral models: Polyhedron Models, Spherical Models, and Dual Models. All are published by Cambridge University Press. Wenninger was the first to construct models of the set of 75 uniform polyhe­ dra-solids that had been derived from Kepler's specifications for expanding the set of regular and semiregular solids­ Elijah C. Boyd . ,!, ." , , and the first to discover and construct Fa ther Magnus }. Wenninger (right) with Charles Stevens (left) and Rogelio Maduro, the complete set of their duals. His surveying some of the polyhedral models Wenninger presented to 21 st Century. method appears in his book Dual Mod­ els, published in 1983. polyhedral stellations and duals. Stella­ fam ily although it is not itself formally a Father Wenninger's visit was well tions, according to Kepler, derive from star polyhedron.) timed-1 996 is the 400th anniversary of the extension out into space of the face Further developing the geometric the publication of Kepler's first major planes of the original solid, which are methods exhibited with the stella octan­ work, Mysterium Cosmographicum, and star-like in shape. Duals are determined gula, Kepler elaborated the stellations of his work is a direct continuation of Ke­ by placing a point in the center of each the dodecahed ron. This provided the pier's study of geometry.1 face of a polyhedron and connecting basis for extending the series of regular Stellations and Duals them to form a new solid. The tetrahe­ Platonic solids; that is, incorporating As Father Wenninger indicated in his dron, for example is its own dual, while star polygons amang the set of regular presentations, the ancient texts were lost the cube and the octahedran are duals. polygans leads to seven new regular and, therefore, Johannes Kepler was the Kepler's stella octangula involves both star polyhedra. And, in fact, Kepler was fi rst to present a complete description of concepts. It is the figure comprised of the first ta construct two new regular the 5 regular Platonic solids and the 13 the two tetrahedra that are seen within a polyhedra, each having 12 star penta­ semiregular Archimedean solids, which cube and share its eight vertices. These gram faces: the small and great stellated he did in his Harmonices Mundi (1 61 9). two tetrahedra are duals of each other. dodecahedra. Kepler also significantly extended the Also, the total configuration is the first­ Applying the same methods to the concept of regular and semiregular and last-stellation of the octahedron. semiregular Archimedean polyhedra solids, and generated two new families The stella octangula is also the begin­ leads ta 53 new polyhedra that have of solids based on stellation and creation ning of an entirely new fam ily of polyhe­ faces consisting of a combination of reg­ of dual solids. dra-star polyhedra-that have interpen­ ular and star polygons. The fu ll set of He was the first to rigorously develop etrating faces. (It can be called the regu lar and semiregular polyhedra are the concepts of how to generate these zero'th star polyhedron; it generates the today called the uniform polyhedra.

66 Winter 1995-1 996 21st CENTURY GEOMETRY In the 1930s, geometers, led by H.M.5. Coxeter, elaborated the set of 59 icosahedral stellations that maintained the fu ll rotational degrees of freedom of the dodecahedron. It was not until the 1950s, that a fu ll set of uniform polyhedra, based on Kep­ ler's original specifications, was found. Wenninger was the first to construct models of this full set of these uniform polyhedra. He then discovered and con­ structed their duals. Figure 1 Toward New Regular Polyhedra Figure 2 KEPLER'S STELLA OCTANGULA Wenninger is continuing to explore OCTAHEDRON CORE OF THE As elaborated by Father We nn­ these basic geometric methods of Kepler STELLA OCTANGULA inger, most of the conceptual The removal of the eight tetrahe­ by extending the notion of regular poly­ fra mework fo r the stellation and hedra. He is doing this primarily by fur­ dral cells of the stella octangula dual-generating processes is con­ ther elaborating the stellation process. to reveal the octahedron core of ta ined in Kepler's construction of Besides stel lating the regular Platonic the stellation. his stella octangula, literally a solids, it is also possible to stellate the stella ted octahedron, as shown semiregular Archimedeans and their du­ here. als. Work on exploring these stellation The octahedron is the Platonic possibil ities is still only at a preliminary solid with eight triangle fa ces, and stage. Research on this has led to new it is also the dual of the cube. That types of regular polyhedra. is, if we place a point in the cen­ For example, some stellations of ter of each fa ce of the octahedron Archimedean duals have features in and connect them to fo rm a new common with regular polyhedra: All ver­ solid, we will have the eight-cor­ tices are the same and the solid is made nered cube. In the same way, we with all the same kinds of polygonal could place a point in the center face. But, the polygon face is no longer a of each of the six squares of the regu lar polygon, and it is not necessarily cube and connect them to gener­ two-sided-that is, the polygon face can ate the octahedron. Kepler's stella be "crossed" and one-sided like a Moe­ octangula is both a stellation of bius strip. the octahedron and a representa­ Figure 3 This new type of regular polyhedron tion of two dual tetrahedra. STELLATION NET OF THE has significant implications for advanced OCTAHEDRON applications to topology, elliptic modu­ The six intersections of fa ce lar functions, and analytic number the­ Despite the deep mathematical impli­ planes to fo rm the stellation net ory. cations of Father Wenninger's work, he of the octahedron. Perfect Polyhedra has always carried out his work in a A second new class of polyhedra de­ form that is accessible to high school riving from this research is the perfect students. will be published early next year. It has polyhedra. These have arisen out of the Collaboration with Wenninger and his also been determined recently that the research on uniform polyhedra. Many of colleagues has already led to major new star polyedra lead to a set of 12 regular the uniform polyhedra have casings in discoveries in the nested Platonic solids polyhedra. wh ich the vertices are the same as one model for the atomic nucleus created by When constructing the vertices for the of the 13 Archimedeans. (The casing of a the late Dr. Robert Moon of the Univer­ duals of Archimedean and uniform poly­ solid is another solid made by connect­ sity of Chicago, and discoveries in the hedra, which have more than one face ing the vertices of the first.) In some field of polyhedra.2 type, the face center must be inverted cases the vertices are slightly distorted. For example, Christine Tuveson, a with respect to the sphere circumscrib­ For example, what would be the vertices leading collaborator of Wenninger, has ing the original polyhedron. of a square become the vertices of a rec­ discovered that the Moon Model specifi­ Constructing Stellations tangle, in terms of the casing. cation already contains a compound of One way to construct the stella oct­ These casings represent examples of 20 cubes and the Gauss Golden Penta­ angula is to take eight tetrahedra-the "perfect" polyhedra. The polygons used gramma Mirificum. The 20-cube com­ Platonic solids with four triangle faces­ to make them are no longer regular in pound is a focus of Wenninger's current and place each on the face of an octa­ that they use more than one edge length, research and is at the forefront of poly­ hedron. This generates eight star points, usually two different lengths that are in hedral research in general. A book on as seen in Figure 1. The eight tetrahedra golden proportion to one another. the 20 cubes, titled Symmetry Orbits, have been removed to reveal the octa-

GEOMETRY 21 st CENTURY Winter 1995-1996 67 hedron core of the stella octangula in Figure 2. Many people before Kepler had tried to generate new polyhedra by adding ar­ bitrary pyramids to the Platonic and Archimedean solids, but Kepler was the first to rigorously specify how stellations are generated from the original base polyhedron. The stellations, according to Kepler, derive from the extension out into space of the face planes of the origi­ nal solid. For example, there are three faces adjacent to one face on an octahe­ dron. If we extend the planes of these three faces over the one face, they will lIustrations on the Covers intersect to generate a three-faced pyra­ Front cover: mid, which, together with the one face, forms a closed cell. (a) An example of a perfect polyhedron with the vertices of the Archimedean In this case, the closed cell is actually icosadodecahedron, which has 30 rectangular fa ces and 20 perfect hexa­ a small tetrahedron. When this is done gons. With it is a small stellated dodecahedron. for each of the eight faces of the octahe­ Back cover: dron, eight cells (eight tetrahedra) are (b) Kepler's stella octangula, which is both the first and last stellation of the generated, and the stellation is the stella octahedron and a compound of two tetrahedra. octangula. (c) The small stellated dodecahedron. For sol ids with more faces than the (d) The ninth stellation of the icosahedron is the dual of two different polyhe­ octahedron, like the dodecahed ron, dra-with hidden vertices: the medial triambic icosahedron and the great tri­ more than one layer of closed cells in ambic icosahedron. space can be generated by the extension (e) The icosahedron. of the solid's face planes. (For the dodec­ ahedron, three cell layers are generated, (f) The small rhombicuboctahedron is a perfect version of the Archimedean each of which in turn constitutes a stella­ solid. It has 72 rectangles and 6 squares, together with 8 triangles, instead of tion of the dodecahedron.) 78 squares and 8 triangles in the regular version. The Stellation Net For constructing a model of a stella­ generate the stel lation net. This is actu­ inscribed within a pentagram. Outside of tion, the crucial thing to know is the ally a cross section of the nesting of cells the original pentagonal face of the do­ number and shape of all of the facets generated by the extension of the solid's decahed ron, there are th ree layers of that appear on the outside of the stella­ face planes through space. That is, we cells. Can you find them? tion. To obtain this information, we must look at how all the solid's face planes in­ For polyhedra with more faces (and tersect one particular face plane. therefore more face planes to intersect in Take an octahedron and place it face space), the stellation nets become quite V(3) down on a piece of paper. If we use a complex. And the number of possible stiff piece of cardboard, we can extend stellations grows to astronomically large the planes of six of the seven remaining numbers-for example, more than all triangle faces of the octahedron to see the electrons currently thought to exist in V(3)...---...... ,----:;l,,----..,,.V( 3) how they intersect the piece of paper. the universe. (The seventh face is parallel to the During Wenniger's visit to 27st Cen­ eighth one on the paper, so its extension tury, a new method for generating stella­ never intersects the paper.) tion nets was discovered, one which The six lines of intersection of face makes use of the pentagram method of planes with the face on the paper are Leonardo da Vinci and Kepler. In out­ shown in Figure 3. This is the stellation line, the method derives all stel lation V(3) V(3) net of the octahedron, an equilateral nets from the pentagram net of the do­ triangle inscribed in an equilateral tri­ decahedron through the use of Jacob Figure 4 angle. The inner triangle is the face of Steiner's synthetic geometry. STELLATION NET OF THE the octahedron. To make the stella oct­ DODECAHEDRON Notes ------angula, one must make the three outer 1. A feature article on Kepler's Mystery of the The stellation net of the dodeca­ triangles eight times, or 24 triangles Universe appears on page 22. hedron from which all stellation in all. 2. For more on the Moon model, see Laurence nets can be synthetically derived. Hecht, "Mysterium Microcosmicum: The Geo­ Figure 4 shows the stellation net for metric Basis for the Periodicity of the Ele­ the dodecahedron, which is a pentagram ments," 21st Century, May·June 1988, p. 18.

68 Winter 1995-1 996 21 st CENTURY GEOMETRY BOOKS

SAVING THE OLIGARCHS The Real Agenda Behind the Greens

by Rogelio A. Madura

She describes the fundraiser as a stir­ Cloak of Green Elaine Dewar ring event. Paiakan vividly told of his Toronto: James Lorimer & CO.,1995 people's fight against the rapacious gold Paperback, 497 pages, U.S. $22.95 miners and timber barons who were try­ ing to rape the Amazon. The response loak of Green, by one of Canada's from the audience, mostly Yuppies, was leading investigative journalists, is a to crowd the large number of fundraising devastC ating expose of the shady finances tables and contribute to the cause. of the international environmental move­ Dewar became so interested in the is­ ment, its dirty operations, and, most im­ sue that she decided to fo llow it up by portant, the role of multinational corpo­ writing a series of articles. In July, she at­ rations and the European nobility in tended a Sierra Club International Con­ directing the actions of the movement. ference in Minnesota where Paiakan was The book demonstrates the interlocking receiving a prize for his work in preserv­ components of the international environ­ ing the rainforest. It was during this mental movement, and questions on meeting that the green propaganda fa­ whose behalf this network is operating. cade began to fall apart. Author Elaine Dewar spent more than It started when some in the audience five years amassing a mountain of evi­ confronted Paiakan with the fact that the dence, which she presents in a very Kayapo, the "Defenders of the Rainfor­ readable narrative, almost like a detec­ est," were actually selling gold mining tive novel. In her own way, Dewar cor­ and logging concessions to multinational roborates many of the charges made in corporations. Paiakan told Dewar that the October 1994 special report, "The that the charges were true, but that the Fall of the House of Windsor," published Kayapo's aim was to control the extent ucts holding company, which was in by the political weekly Executive Intelli­ of the exploitation! turn controlled by Brascan, a holding gence Review and written under the di­ Later, at a press conference, when Pai­ company prominent in the empire of rection of Lyndon H. LaRouche, Jr.* akan was asked for what the money be­ Sam Bronfman's nephews, Edward and Cloak of Green begins in November ing raised for the Kayapo by the Sierra Peter Bronfman." 1988 at a fundraiser "to save the Ama­ Club was being used, he said that he At the time, Brascan was considered zon ra i nforest," co-sponsored by the didn't know. The Kayapo had not seen the number one destroyer of the Ama­ World Wildlife Fund in Canada. More any of it, he replied. zon rainforest! than 2,000 people gathered to hear Two days later, Dewar met Paiakan in But Zimmerman was not the only Paulinho Paiakan, an Indian chief from Toronto, where he had been invited by magnate present. The heads of Canada's the Kayapo tribe in the Amazon. The Adam Zimmerman, chairman of the largest corporations had gathered to pay Brazilian government was planning to Canadian branch of Prince Philip's homage to Paiakan. "As the living room bu ild dozens of dams in the Amazon, World Wildlife Fund. Zimmerman gave filled with guests," she writes, "my note­ the public was told, plans that not only a reception for Paiakan at his home, book filled with the names of the rich, would destroy the Amazon but would where the Kayapo chief was staying. the powerfu l, and the well known." affect the global climate. This seemed odd, Dewar says, because Saving the Oligarchs Dewar attended the fund raiser be­ "Zimmerman was then president of No­ Why were some of the richest and cause she was "deeply worried" that randa Forest Products, which then con­ most powerful figures in the world sup­ "[fJ looding huge tracts of Amazon· rain­ trolled MacMillan Bloedel and other for­ porting this Amazon Indian's campaign? forest would be the atmospheric equiv­ est companies. Noranda Forest Products At this point, Dewar decided to uncover alent of the straw that broke the camel's was itself a subsidiary of Noranda, Inc., the real story. She traveled to Brazil, back." a multinational mining and forest prod- Continued on page 77

BOOKS 21 st CENTURY Winter 1995-1 996 69 Another Biased Account of Cold Fusion

by Dr. Edmund Storms

A Dialogue on Chemically Induced sen ted demonstrates that skeptics, in­ Nuclear Effects: A Guide for the cluding Hoffman, will bel ieve the most Perplexed about Cold Fusion unlikely possibilities in order to avoid Nate Hoffman believing the "cold fusion" effect. La Grange Park, III.: Explaining Away Tritium American Nuclear Society, 1995 Cloth, 223 pages, $30.00 Many examples of this phenomenon are provided, a few of which are espe­ cially outrageous. Hoffm an attempts to o a casual reader, N'ate Hoffman's explain away the claims for tritium pro­ Tbook might seem like an objective duction by adopting an amazing series of and balanced treatment of the controver­ assumptions. He first proposes that com­ sial phenomenon conventionally known mercial heavy water has been contami­ as cold fusion. Unfortu nately, this im­ nated with tritium, uranium-238, and pression is very wrong. lead-210 as a result of its being mixed not actually being produced in these Sadly, the book provides even more with heavy water previously used in nu­ cold fusion experiments. confusion than found in the other two clear reactors. According to Hoffman, And in case his explanations were not recent effo rts to kill the field: John this mixture can account fo r the ob­ sufficient to convince his readers, Hoff­ Huizenga's Cold Fusion: The Scientific served tritium (and neutrons as well-but man then applies his imagination with Fiasco of the Century and Gary Taubes's that is another story). even greater abandon. He assumes that Bad Science: The Short Life and Weird The high initial tritium levels could, in commercial palladium has been contam­ Times of Cold Fusion. At least each of Hoffman's view, be the source of the inated with tritium by being mixed with these two books leaves the reader with anomalous tritium found in some cold metal used during the atomic weapons no doubt about the author's bias! fusion experiments. Should this idea not program. Such mixing has been looked Everyone, skeptic and bel iever a:like, fly, Hoffman suggests that beta radiation for hundreds of times without any evi­ agrees that many questions need answers from Pb-210 decay might be mistaken dence being found. However, to be on and that experimental error exists in for tritium by careless experimenters. the safe side, cold fusion researchers use many studies. However, the public Never mind that all studies of tritium only "virgin" pal ladium, and most test for would be better served if skeptics used production in cold fusion experiments tritium before its use. the same respect for truth and logic that compare the beta activity before the ex­ In addition, palladium known to be they demand of those who support re­ periment to the activity resulting from the contaminated does not release its tritium search in the field of cold fusion. This re­ procedure and use only very-low-tritium in the same manner as observed when spect for truth is frequently absent in water. Tritium is only claimed when this anomalous tritium is made in the cold Hoffman's book. difference changes by a significant fusion experiments. All of these facts to­ Hoffman starts off well by giving a amount. tally discredit Hoffman's proposed expla­ good assessment of how the cold fusion Never mind that Pb-2 10 is an ex­ nation. field fe ll into such disrepute and by pro­ tremely rare isotope of lead, being pro­ Intellectual Honesty viding a wealth of unpublished experi­ duced at a maximum rate of about 3 Of course, an examination of all wild mental data. He also provides an under­ atoms per minute from 1 gram of U-238. ideas is necessary and appropriate if we standing of how the negative attitude Only a fraction of these atoms would de­ are to understand the amazing effect developed and was reinforced by the cay during a measurement because Pb- known as cold fusion. However, when leadership of the electric utilities' think 210 has a 21-year half-life. Most U-238 an idea turns out to be ridiculous, intel­ tank, the Electric Power Research Insti­ decays to Pb-214, which cannot be mis­ lectual honesty requires this realization tute (EPRI). As an example of this, EPRI's taken for tritium. Consequently, the de­ to be pointed out. Why must a reader of Thomas Schneider concludes in the cay rate and the total number of offend­ this book have to contact the suppliers of book's foreword that because neutrons ing atoms would be at least 15 orders of heavy water and palladium, or look up or other expected nuclear products are magnitude below these quantities when the decay chain of U-238 to learn the not observed in cold fusion experiments, observed during typical tritium measure­ missing facts? no energy production by nuclear means ments. Although some good information is to is possible; hence "cold fusion" cannot And finally, Hoffman ignores the fact be found within the nonsense in this be real. that commercial heavy water does not book, a reader would have to be more The rest of the book is designed to contain used nuclear reactor water or skilled than most to make a proper selec­ provide supporting evidence for the neg­ any U-238. tion. This is definitely not a "guide for ative viewpoint expressed by Schneider. All of these facts are easy to check­ the perplexed about cold fusion" as the Instead, however, the evidence pre- unless one wants to believe that tritium is subtitle promises.

70 Winter 1995-1 996 21 st CENTURY BOOKS sions, to build luxury air-conditioned vil­ tional measures and supranational insti­ The Real Green Agenda las with servants and to purchase the lat­ tutions to be resolved. Continued from page 69 est model luxury cars and planes. Dewar documents how the environ­ Breaking Up the Nation State mentalists, the United Nations, the Switzerland, and Washington, D.C., to Dewar concluded that the tightly run NGOs, and Schmidheiny's Business trace the money and uncover who was network she had uncovered had a clear, Council on Sustainable Development really behind the campaign to save the underlying agenda: to destroy the institu­ (representing the multinational corpora­ rainforests and why. tion of the nation state, break up sover­ tions) all want to destroy the nation Dewar discovered that the world of eign nations, and seize the natural re­ state for their own reasons. These are environmental groups and other non­ sources from the squabbling tribes that not competing interests. As Dewar governmental organizations (NGOs) is a inherit the land. shows, the publicly perceived adversar­ small, tightly linked network of individu­ Her discovery of "the agenda" came ial relationship between radical green als. This movement is funded by the in October 1990, at a series of events groups and multinational corporations world's most powerful families through during Rainforest Week in Toronto. As dissolves in the back rooms of the U.N. their fa mily foundations, such as the Dewar recounts it: apparatus in Geneva. These groups not Ford and Rockefeller Foundations, as Jason Clay of Cultural Survival, Inc. only are tied together, but very often are well as the world's largest multinational " ...laun ched into a treatise favouring composed of the same people! corporations. the rise of ethnic nationalism as opposed The Green Prince As Dewar found out, enormous to the nation state. . ..This thesis ex­ The World Wildlife Fund is at the cen­ amounts of money raised to save the pressed the real shared vision of those ter of Dewar's story. After discussing the ra inforest or fo r other environmental who toiled together in the network­ role of Prince Philip in setting up the causes, mysteriously disappeared or environmentalists, democrats, former World Wildlife Fund internationally, De­ were used for other purposes. Dewar's Maoists, government officials, corpora­ war describes some of the dirty WWF painstaking tracking of the movement of tions, and the politicians in power in operations as well as the secrecy that money through the foundations, corpo­ certa in countries. They did share a very surrounds the leadership: rations, and green groups, looked like an broad common Agenda ....[which] "There are only 300 true members of apparatus modeled after a drug money was far broader than a global attempt to WWF Canada. They are drawn from laundering operation, not a charitable get environmental issues into the centre three exclusive groups: the board; the 68 organization. of domestic pol itics ....The broad Canadian members of the 1001 Nature Dewar shows how the Canadian gov­ common Agenda aimed to remake the Trust; and a donor group called 200 ernment plays a major role in launder­ institutions of governance, to lever Canadians for Wildlife ....[T] he trust ing th is money, as well as providing its power up to large multilateral regional [is now] full, but if one were asked to own funding and direction to what she institutions while stripping it away from join, the price of entry had already calls "the network." She learned that the nation states. . . . climbed to u.s. $25,000." Canad ian International Development "His [Clay's] theme was: the nation As for the agenda of the WWF, Dewar Agency (ClDA), the Canadian embassy state is a corrupt idea with no remaining states: in Brazil, and other sources were giving political legitimacy. The nation state "The . . . World Wide Fund for Na­ large sums of money to a network of en­ should wither away, its functions re­ ture, is directed by members of aristo­ vironmental organizations and suppos­ placed by institutions of local and global cratic families, CEOs of major oil, gas, edly pol itically neutral NGOs. As she governance." transport, pharmaceutical, investment, spells out in detail, these same NGOs The green network, Dewar says, is tobacco, and banking interests with then use the money to finance political using the United Nations as a platform strong political connections. [WWF] parties as well as candidates for office, to sell the idea of a global environmen­ takes money from people with a need to including presidential campaigns. tal crisis as the basis to promote what In addition, many of the NGOs also she terms the Global Governance use the money to impose changes in in­ Agenda. The hidden aim of the Rio Did you miss... ternational policies through the United Summit in 1992, she says, was to ad­ Nations and through international insti­ vance the agenda by persuading na­ tutions like the World Bank. All this poli­ tional governments to cede jurisdiction "The Really Shocking ticking, of course, is carried out in the in key environmental areas to the U.N. name of saving the environment. bureaucracy. Royal Secret: British As for the "victims" of the exploita­ "By the year 2000," she writes, "there Crown Rul es the tion, Dewar discovered that the Kayapo would be few independent national enti­ were not concerned about preserving ties left capable of defending local com­ Greens" in 21st Century) the Amazon! They used the money munities" from exploitation by multina­ Winter 1994-1995? raised for them by the international tional corporations. The argument for green and anthropologist groups-that this one world government, as Dewar Back issues are available is, what was left of the money after the outlines it, is that environmental prob­ at $5 each. fu ndraisers took their share-and the lems like ozone depletion and global money from logging and mining conces- warming are global and require suprana-

BOOKS 21 st CENTURY Winter 1995-1996 71 � ------r------�� ��------� o Riema1mian Geometry--A Beginner's Guide, by Frank Morgan. Physically oriented; lacks philosophy. Jones and BEN FRANKLIN Bartlett hardcover, $29.95 o Measuring the UlI iverse--{;osmic Dimensions from Arls­ Booksellers 8LRecord Shop tarchus to Halley, by Albert van Heiden. U. of Chicago, $12.95 o The Librariall Who Measured the Earth, by Kathryn Lasky. A book about Eratosthenes fo r elementary school children. little, Brown hardcover, $16.95 o Tirion's Bright Star Atlas 2000. Willmann-Bell, $9.95 o Cloak of Green, by Elaine Dewar. Links between the Greens, government, and big business. LOrimer, $22.95 o Battling Wa U Street--The Kennedy Presidency, by Donald Gibson. A book every anti-Green should read. Environmentalism in context. Sheridan Sq. hardcover, $24.95

Ben Franklin Booksellers 107 South King Street Leesburg, Virginia 22075 Type ofcredit am (circle one); Mas[crCard Visa Discover AmEx Phone (703) 777-3661

Toll free (800) 453-4108 Credit card /I Fax (703) 777-8287 Exp. date

Name For shipping, add $3.50 fo r first book $.50 Address and for each additional book. For Canad, add S7 and S 1.30.

City TDtal book price $

State Zip Plus shipping $

Home phone Va. residems add 4.5% saJesr", $ Business phone Tetal enclosed $

buy political influence. [WWFj has hired Media Myths for people they'd covered ...." people who have worked fo r intelli­ How has this apparatus been able to Not only Pyle, but Ted Turner, her gence agencies. The objectives of the or­ control the environmental debate? De­ boss, played a key role in promoting all ganization can be interpreted as real war describes the role of the news media these operations, as Dewar outli nes in concern for the dangers facing human in creating the myths used by the envi­ detail. This was done both through the life or as attempts by managers and ronmental movement. For example, De­ creation of the Better World Society, owners of multinational corporations war notes the critical role in the rainfor­ whose goal is to implement the Global with considerable influence on Western est campaign played by David Suzuki, 2000 report, as well as through the film­ governments, to preserve areas likely to the superstar of the Canadian Broadcast­ ing and airing of dozens of biased, inac­ produce the riches of the future." ing Company, and Barbara Pyle, envi­ curate documentaries in the Turner ronment editor of CNN (Cable News Broadcasting Network. QED Coherence in Matter Network) and head of the documentary For those who are fighting fo r scien­ unit fo r Turner Broadcasting System tific and technological progress, this by Giuliano Preparata, U,j.i,',,·sity of Mil" n (TBS) in Atlanta. book is good background . And if you've Condensed matter is not an electrostatic erec­ Marveling at "the cohesion in a group been snookered into supporting the tor set! A new paradigm is emerging, which builds condensed matter through the long of such peculiar composition ..." as groups that raise money to prevent envi­ range quantum·electrodynamic interaction. that present at the reception noted ronmental doomsdays, this book just This interaction creates coherent configura­ above, Dewar points out that CNN's might help save your money for real tions of atoms and molecules, which. oscillate "Barbara Pyle had already made a film causes. in phase with a coherent macroscopic (and on Paiakan for TBS. She had attended classical) electromagnetic field that, through Notes ------­ the strong interaction with matter, remains Altamira. Now she was poised to run * Offprints of this 64-page report are available from ElR News Service, at each, P.O. Box trapped inside it. more fundraisers for Paiakan in the u.s. $10 17390, Washington, D.C. 20041-0390. Paperback, 252 pages, $67.00 This seemed to me an obvious conflict of interest for a media person. I'd never World Scientific heard of a television network that al­ 1060 Main Street · River Edge, N.J. 07661 lowed those who chose its news and 1-800-227·7562 To order these books. (24hrs. 365 days) documentary topics also to raise money "lense call (800) 96-Book-\ (Ext. 3800)

72 Winter 1995-1 996 21 st CENTURY BOOKS