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Spring 2002 Issue 21st CENTURY SCIENCE & TECHNOLOGY \' Spring 2002 Features News SPECIAL REPORT 12 Alexander von Humboldt: 58 Why There Really Are A Republican Scientist in the Tradition of Franklin No Limits to Growth Timothy Rush Ralf Schauerhammer The most renowned scientist worldwide in the first half of the 19th PEDAGOGY Century, Humboldt is barely known today in the country of his 66 Gauss's Declaration of greatest philosophical affinities, the United States. Independence: The Fundamental Theorem of Algebra 31 Ibero-America Needs a Space Agency! Bruce Director Marsha Freeman NUCLEAR REPORT It's time for all the nations of Ibero-America to put forward bold 70 INTERVIEW WITH WALTER SIMON plans for space exploration, and for the developed nations to stop General Atomics Reactor sabotaging such projects, under the guise of non-proliferation. In Russia To Burn Weapons Plutonium 74 PBMR Moves Ahead In South Africa RESEARCH FRONTIERS 75 GROWING FOOD IN AIR A Second Green Revolution Caroline Hartmann and Elisabeth Pascali 76 INTERVIEW WITH DR. GIANCARLO COSTA Out-of-Soil Farming Produces A Superior Product at Less Cost SPACE 78 INTERVIEW WITH ACADEMICIAN NIKOLAI ANFIMOV Inside Russia's Unique Space Science Institute Departments EDITORIAL 2 Teach Gauss's 1799 Proof of the Fundamental Th e increasing prominence of skeptical environmentalist Bjorn Lomborg Theorem of Algebra was too much fo r Scientific American, which devoted 77 pages in its Laurence Hecht January 2002 issue to a hit-and-run attack on Lomborg, written by leading 3 LETTERS Malthusian scientists. The Special Report by Ralf Schauerhammer, "Why 8 NEWS BRIEFS There Really Are No Limits to Growth, " examines the fa ulty premises of 10 VI EWPOI NT both the Malthusians and Lomborg and his free market supporters. Back to the Moon, Then On to Mars! Or. Wendell W Mendell On the cover: Top left, Peruvian-born astronaut Carlos Noriega on a space walk (courtesy of NASA); lower left, artist's conception of the Argentine satellite SAC­ 55 2001 INDEX C, fully deployed in orbit (courtesy of CONAE); lower right, Brazil's VLS rocket 83 BOOKS (courtesy of Space Agency of Brazil). Cover design by Alan Vue. EDITORIAL EDITORIAL STAFF Edltor-In-Chief Teach Gauss's 1799 Proof Of the Fundamental Ma�orie Mazel Hecht Associate Editors' Elijah C. Boyd Theorem of Algebra David Cherry Marsha Freeman Colin M. Low(Y e have all heard the frequent point, from among that second category Gregory B. Murphy Wlaments among our co-thinkers and of subjects, I have seen the light bulb go 'ElisabethPascali professional colleagues at the sadly on rather quickly in a few cases. From Charles B. Stevens reduced state of science and mathematics the technically educated category, I Books education in our nation. As in all such have most often encountered a furious David Cherry matters, after the righteous indignation spurt of calculating and sketching, to no Art bi;ector and hand-wringing, is over, one must ask good end, sometimes followed by resig­ Alan Vue oneself the realistic question: Are you part nation. But, with persistence, these too Advertising Manager of the problem, or part of the solution? will solve it. The exercise of constructing Marsha Freeman If you are not sure, we have a propos­ the square and rectangular numbers, as SCIENTIFIC ADVISORY BOARD al for you. To introduce it, I ask you to Theaetetus describes it in Plato's dia­ Francesco Ceiani, Ph.D. perform the fo llowing experiment. logue of that name, can serve as a usefu l Hugh W. Eilsaesser,Ph.D. STEP 1: As a suitable subject, locate flank on the mental block encountered. Bertha Farfan,M.D. any person who has attended high An Induced Mental Block James Frazer,Ph.D. school within the last SO or so years. You What is the problem? No student of John Grauerholz, M.D. Emmanuel Grenier may include yourself. Now, politely ask the classical method of education, which Lyndon H. LaRouche, Jr. that person, if he or she would please has been around for at least the past Wolfgang Liilge, M.D. construct fo r you a square root. 2,500 years, could ever have any prob­ Ramtanu Maitra "What do you mean construct a square lem with this simple exercise. The men­ Thomas E.Phipps, Jr.,Ph.D. root? I know what a square root is, but tal block which arises here is perfect­ B.A. Soldano, Ph:D: the Jonathan Tennenbaum,Ph.D. what do you mean "construct' it?" is a typ­ ly lawful result of the absurd and preva­ 21 st'CenturyScience a. Technqlogy ical answer from one sort of person. lent modern"c;lay teaching that number (ISSN 0895;6820) is published 4 titnes ai "I was never good at math. I'm not a can exist independent of any physically 2000, 21 year in every third month, by st Cen­ math person," is the usual form of the other determining principle. This is the ivory­ tury Science Associates, 60 Sycolin Road, Suite 203, Leesburg, Va. 20H5. Telt(703)'h type response. Curiously, I have fo und that tower view of mathematics, which holds 777-7473. it is from this category of respondents that sway from grade school to university, Aadress ail correspondence to 21st Cen­ tury, P. O. Box 16285; Washington, D.C. the correct solution is more I ikely to appear and reaches up like a hand from the 20041. " rapidly. In either case, some degree of grave, even into the peer review process Second-class postage is paid at Lees­ resistance, tempered by a natural curiosity, governing what can be reported as the burg, Va. and additional mailing offices. ' 21st centuryis dedicated to the promo­ is most often encountered at this point. results of experimental physics. tion of unending scientific progress, all STEP 2: Remain calm, but resolute. This was the view that the young Carl directed to serve the proper commcm aims of mankind. Draw a square on a piece of paper, and Friedrich Gauss so devastatingly attacked Opinions expressed in articles are not nec­ ask the question again. "Here is a square, in his 1799 "Proof of the Fundamental 21 essarily those of st Century Science.Asso­ please show me the square root." Theorem of Algebra,"l submitted as his ciates or tha SCientific adviSOry board .. We are not responsible for unsolicited Among the technically educated, it is doctoral thesis to the University of manuscripts. very common, next, to see the diagonal Helmstedt. That every algebraic equation Subscriptions by mail are,,$25 for 6 issues or $48 for 12 issues in the USA and Canada. of the square appear, often with the label of degree m, where m is a positive integer, Airmail subscriptions to other countries are �2 attached. As this has nothing whatso­ will have m roots, was a matter usually $50 6 $5 for issues. Back issues are each ever to do with the solution, I have learned as a truism in any high school­ ($6 foreign). Payments must be in U.S: cur­ rency. • found it most effective to point out in level advanced algebra course, at least POSTMASTER: Send address changes such cases, that the problem is really until the recent bad times. The proof of to 21 st Century: P. O. Box 1,6285, Washing- . ton, D.C. 20041-0285. much simpler than that. No knowledge the assertion was not a matter one usually Copyright © 2002 of the Pythagorean Theorem, nor any addressed. However, one has to take the 21st CenturyScience Associates higher mathematics, is required. student no further than the simple illustra­ Printed in the USA ISSN 0895-682 A discussion of what is meant by a tive case x2 + 1 = 0 to cause a recogni­ www.21 stcenturysciencetech_�om square root may now prove useful. I tion of the essential paradox involved. mean a very simple discussion. At this In the usual training, one is taught to 2 Spring 2002 21 st CENTURY EDITORIAL write ±"'-1 as the two solutions. be accepted as true in mathematics, which "What is the square roa t af minus 1 ?" da es na t correspand to. a principle of phys­ "Ahem, that's com plicated; we may ical actia n. "It works," ar "it is ca nsistent address that later." with aur defined set af allawable apera­ Mathematicians have knawn af this tions and pracedures," is, therefare, nat problem since at least 1545. In that year, acceptable. By accepting such shartcuts, Letters Girolamo.Cardano published a delightful first truth is destroyed, then science, then account in Chapter XI af his Ars Magna. eca nam ies and wha le natians. Here Cardan solves the problem "find A New Curriculum twa numbers whase sum is 10 and Our prapasal, suggested by Scientific Fermat's Principle whase product is 40." After showing us Advisary Board member Lynda n H. To the Editor: that the solutians must make use of the LaRauche, Jr., is this. Let the mastery af I read with interest ya ur editarial an square ra ats af -1 5, Cardan exam ines Gauss's fundamental thea rem as devel­ Ferm at's principle ["Why You Don't what such a thing might be. Ask yourself: aped in his revalutionary 1799 proaf, Believe in Fermat's Principle," Fall If a square roa t is the length af a side of serve as a ca rnerstane af a new curricu­ 2001 , p. 2). I have na t seen ya ur view­ a certain square number, what is the area lum fa r seca ndary and university under­ pa int expressed elsewhere. I think there af the square, the length of whose sides graduate students.
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