UC San Diego SIO Reference Title Our Modern Idol: Mathematical Science Permalink https://escholarship.org/uc/item/4db41867 Author Eckart, Carl Publication Date 1984 eScholarship.org Powered by the California Digital Library University of California by Carl Eckart The Author Carl Eckart was an eminent mathematical physicist. He was a professor at the Univer- sity of Chicago and later at the University of California at San Diego. His earliest well-known achievement was in quantum mechanics where he established unifying re- lationships between the matrix and wave mechanical formulations. After leaving his mark on quantum mechanics he turned to classical physics and developed some of the fundamentals of irreversible thermodynam- ics. Subsequently his interest shifted to the physics of oceanography, in particular to acoustics and hydrodynamics. He published a number of papers on these subjects as well as a book Hydrodynamics of Oceans and Atmospheres. During this period he also served as Director of the Scripps Institution of Oceanography. He died in 1973 at the age of 71. OUR MODERN IDOL: MATHEMATICAL SCIENCE CARL ECKART SCRIPPS INSTITUTION OF OCEANOGRAPHY UNIVERSITY OF CALIFORNIA LA JOLLA, CALIFORNIA 92093 1984 SIO REF. 84-27 Preface At the time of the author's death this book was in the form of an unpublished manuscript. The manuscript consists of seven loose-leaf notebooks, handwritten in pencil, on lined notebook paper. Each page is carefully numbered and dated. It appears that it is a first draft, yet the initial wording is precise, with almost no after-thoughts. The title Our Modern Idol: Mathematical Science belies its con- tent. Although the author was an eminent mathematical physicist the book is not mathematical in nature; there are no mathematical equations or derivations. The few mathematical expressions are simple and the book is clearly intended for the non-mathematical reader. It does not appear to have a definitive, coherent theme; rather it is a collection of eclectic essays connected historically or sociologically. In short, this book is about people, ancient and recent, as individuals and in society. It was the opinion of several commercial publishers to whom this manuscript was submitted that this would not be a commer- cially viable book without extensive editing. Their proposals required condensation of the whole and the addition and deletion of material so that the theme could be more clearly developed. Upon consultation with friends and colleagues of the author, it was decided to publish the manuscript privately as written, without sub- stantive editing. In this endeavor I was ably assisted by Maureen Perry and Laurie Nord who carefully read the manuscript and made necessary but minor editorial changes. In addition Ms. Perry set the entire manuscript in type using the University of California computing facilities. Their knowledgeable contributions and persistent efforts made private publication possible. Leonard Liebermann Professor of Physics Table of Contents Introduction ....................................................................................... 1 The Failure of Universal Education ....................................................... 4 The Brandywine Valley and Similar Experiences ...................................... 7 Town and Country ............................ ..................................................... 15 The Aristocratic Fallacy ......................... .............................................. 18 Solon and the Aristocracy of Wealth ......................................................... 24 The Silver of Mount Lauriam ............................................................... 28 Pericles and the Athenian Empire .......................... ............................ 30 The Structure of Modern Western Society ...................... ................ 33 Intelligence Quotients and Career Counseling ..................................... 37 The Nature of a Plan ..................... ....................................................... 41 The Revolutions of the Eighteenth Century .......................................... 45 Fiction. Theory. and Social Change .......................................................... 48 Recent Planning by the Scientific Communities ..................................... 54 The Changing Public Images of Science and Technology ......................... 60 The Planning Process in the Federal Government ................................. 64 The Invention of the Steam Engine ............................ .. ......................... 66 The Beginning of the Scientific Revolution ............................. .. ......... 71 The Optical Industry in the Nineteenth Century ..................................... 75 The Emergence of the Engineering Communities .................................. 80 The Instrument Makers and Technicians ......................... ................. 84 The Scientific Revolution in the twentieth Century U.S. ...................... 87 Our Numerical Society .............................. ............................................. 92 The Anthropology of Whole Numbers ............................ ..................... 95 Counting. Memoranda. and Arithmetic .......................... .............. 101 Seals. Numerals. and Writing .................................... ... .............................. The Abacus: History and Conjecture ................................... .... .................. The Egyptian Mathematical Texts ............................................................ The Mesopotamian Numeral Systems .................................................... The Land of the Alphabets ................................................................... The Greek Alphabet and Numerals .......................................................... Human Language and Inhuman Logic ...................................................... Archimedes. Buddha. and the Uncountable ............................................ How the Decimal Numbers Came to Europe .......................................... Fractions. Equity. and Higher Education ................................................. The Decimal Point and Long Division ................................................... Epidemics. Square Roots. and Elementary Education .............................. The Perception of Space .............................................................................. The Rules of the Cord ............................................................................... Plato and Eucleides of Megara ................................................................. Plato and the Academy ............................................................................... The Dialogue Timaeus and Greek Cosmology ........................................... Pythagoras and the Pythagorean Theorem ................................................ Ideals and the Technology of Triangles ..................................................... Euclid of Alexandria and the Elements ................................................... Aristotle and the Axioms .......................................................................... Aristotelianism and Christianity ................................................................. Pythagoreanism becomes Rationalism ........................................ ............... The Intellectual Problems of the Seventeenth Century ............................ The Rise and Decline of the Axioms ........................................................ Pacifism and the Elements of Logic .......................................................... Atoms. Evolution. and Ethics .................................................................... Greek Religion and Mythology ........................ ....................................... The Influence of Democritus in Recent Centuries ....................... ..... Laplace's Mechanical Man ...................... ............................................... Chance. Gambling. and Insurance .......................................................... Atoms. Causality. and Politics ................................................................. 346 Man is an Animal. but not an Ape ...................................................... 350 The Changing Beliefs of Physical Scientists ............................ ........... 354 Some Conclusions .......................................................................................360 One hears it said that, for the first time, man now has the power to determine his own future, if only people will be sensible. This is a popular summary of a number of serious books, none of which are quite so incautious. Still, their authors are enthusiastic about the achievements of science and technology, and are con- vinced that others are coming; moreover that these achievements have improved the lives of people and will continue to do so. These achievements have been largely those of the physical and bio- logical sciences, and those in biology have come mainly after biolo- gists began to use the tools and methods of the physical scientists. Among these methods are the mathematical theories of physics and chemistry. Remarkably, those sciences that are specifically devoted to the study of people, sociology, psychology and political science, have made no corresponding achievements. This requires explanation. One facile explanation is widely accepted, especially by the scientific and technological communities. This is that these behavioral