Modern science, for reasons that are only dimly understood, appears to have had its origins in Europe and the Middle East although it is now totally international in character. It is surely Europe's most enduring and universal contribution to world culture--more than any of our religions, our arts, our music, our political systems, or even our languages. In the history of western thought it looms as perhaps the largest theme.

Nothing like the scientific revolution of the European Renaissance occurred anywhere else at any time, a cause for much baffled scratching of the head and a puzzle to which I want to return at the end of my remarks when I will say a little about what people have learned in studying comparisons between the history of science and technology in Europe and in China.

Einstein was once asked his opinion on why modern science began in Europe instead of in China or India. He said that this wasn't the real question. The real question is how it is that so arduous and unlikely an undertaking as science arose anywhere, not why it failed to be developed somewhere in particular. It is arduous and unlikely and the long story of its tortured development is one of the most interesting histories I know. There is nothing obvious or linear or inevitable or upward about the tale. It has produced some extremely strange and unexpected concepts. One of these is the concept of "The Laws of Nature".

To sophisticated thinkers such as the Chinese encountering the Jesuit missionaries in the 17th and 18th centuries, the idea that "Nature" had "Laws" was incomprehensible. The missionaries tried to prove the existence of God using the traditional argument that there must be a Creator since the universe shows so wonderful a regularity and that it must be governed by divine laws--hence the existence of God, creator and law giver. To those Chinese this whole argument was meaningless and it is interesting now to read their description just how absurd it seemed to them. It would take us too far a field to look into that right now.

What I would like to do in the short time that I have is to try to emphasize the oddness of the very idea of "The Laws of Nature" and give a little flavor of the enduringly weird character of those laws that have been discovered.

The ideas and the questions which were being persistently asked in the Greek Ionian city states in the sixth century BC are surely older, but that century was a time of astonishing ferment and speculation not only in the Mediterranean but all over the parts of the world for which we have written history of that time. It was the century of the Gautama Buddha, Confucius, Lao Tse, Zoraster, and of the group that have come to be known as the Pre-Socratic Ionian philosophers. If ever there was an inappropriate and unjust label, this is it. Socrates disapproved of much that these so-called Pre-Socratics stood for so there is more than a little irony in their being named for their eventual critic and repudiator.

For us, as we do a quick survey of the development of the idea of Laws of Nature, the questions they asked are interesting. They wondered how to reconcile the notion of the unity and regularity of nature, which they could see evidenced in the motions of the stars and planets, with the equally evident observations of ceaseless change and variety. They believed with considerable tenacity that there was a unity, that this unity was material and not mystical, and that mankind had the ability to know it. Brash. Unwarranted. It's almost as if these Ionian philosophers had the list of forbidden questions which are enumerated by the voice in the whirlwind in the Book of Job and proceeded to throw them back defiantly at that discouraging speaker.

With many of these philosophers, their way of trying to imagine how, behind the shifting facades of change and seeming chaos, there could nonetheless be a deeper unity was to argue that everything was made of water. They had euphonious names and startling hypotheses: Anaximander taught that all is Air; Heraclitus the Obscure taught a paradoxical doctrine in which change itself was somehow the unity; Heraclitus of Ephesus opted for fire as the fundamental substance; Empedocles believed in four elements--Earth, Air, Fire, and Water; and about a century later Democritus was to teach that all was composed of atoms and the void. None, or practically none, of any of this was based on any evidence whatsoever. The idea that controlled experiment might be involved in efforts to answer questions about the world hadn't yet become part of such speculations. I have left out one of the most peculiar of the speculators, and in the end one of the most prescient: Pythagoras. Pythagoras taught that everything was made of numbers, almost literally of numbers. The arguments were vague, mystical, and much influenced by the discovery of the relationship between the length of lyre strings and heard harmony. Pythagoras taught the wonderful doctrine of the music of the spheres whereby the planets and stars in their motions emit beautiful sounds, sounds which we no longer hear because we have been bathed in them from birth. The nature--harmony--numbers--mathematics metaphor or idea was to haunt thought for thousands of years and to prove to be astonishingly fruitful.

A crucial development or invention in Greek, and hence "western" thought, was that of axiomatic geometry. The ancient Greeks became obsessed with mathematics, geometry in particular, and with chains of logical inference. This led to that shining body of thought called Euclidean geometry, named for the man who troubled himself to write down the work of many others. Though there was much sophistication of calculation and notation developed by the Babylonians, Egyptians, Indians, and Chinese there is no evidence that anyone other than the Greeks invented the chains of "theorem--proof, theorem--proof" that can seem, on the other hand, so barren, and on the other, so magical a way to discover eternal truths.

Inevitably the speculations of the Pre-Socratics and the preoccupations of the mathematical thinkers would become intertwined. Let me mention just two examples among many: one strange, eccentric, and almost clairvoyant; the other ambitious practical, and enormously productive.

The strange one is Plato's so-called dialogue called the Timaeus. This is a sort of a dream of an axiomatic theory of the entire universe full of mathematical apparatus and purporting to account for everything from the stars to fingernails and hair. Earth, Air, Fire, and Water are composed of a subset of the so-called Platonic solids, regular polyhedra bounded by isosceles triangles and squares which assemble and disassemble from the solids in a sort of snowstorm of change and unity.

It's a beautiful, poetic, and very obscure work. It was read in Europe right through the Dark Ages when most of Plato's other works were not known. It fired the imaginations of those who knew it. It fueled a fascination with numerology and the association of mathematics and natural phenomena.

The practical example is Ptolemaic Astronomy. This is the contraption, the imagined geometrical model mechanism involving crystalline spheres, epicycles and deferents which was able to account for and predict the motions of the sun and the planets against the majestically rotating celestial sphere of the fixed stars. It was a model that called on the full sophistication of ancient engineering and of Euclidean geometry. It worked, giving predicted positions of heavenly bodies precise enough for calendar making to use in civil and agricultural affairs as well as in astrology and its application to medicine. Eventually the model had to be abandoned as the observations became more accurate and the practical needs more demanding but it was, in its way, a success. Here is where the idea of the universe as a machine governed by mathematical rules comes from.

Note the word "governed". Gradually the notion of "law" became intertwined with the idea of the orderly unfolding and recurrences of nature. Scholars who study such matters point out that, as the Roman Empire became more far-reaching and diverse, the distinction between local customs and practices and the body of law that should apply to all people in the Empire led to the idea of "natural law"--the sort of law that applied to all. Also contributing to the notion of Laws of Nature were the teachings of the Stoics who urged their disciples to live according to the laws of nature so as to achieve serenity and balance in a basically hostile world. "Go along or be dragged". Thinking about the laws promulgated by imperial authority and the Stoic's laws of nature led, as Christianity developed, to the idea of God's laws and to the rather novel idea that His laws extended not just to mankind but to nature and nature's creatures as well. In the medieval imagination these laws of nature could be violated and the violators punished. In 1474 a cock was sentenced to be burned alive for the "heinous and unnatural crime" of laying an egg, at Basel.

These many ideas and strands of thought began to be gathered together as Europe began to be transformed by what we now call the Renaissance. Galileo discovered and publicized the power of controlled experiments. He also pointed out explicitly and bluntly that the book of nature was written in a mathematical language--God is a Geometer. Kepler, enthralled both by Platonic numerology and a reverence for carefully measured data, discovered regularities that came to be known as "Laws of Planetary Motion". The medieval idea that nature was a book (now in mathematical language) in which the Laws of Nature (and hence something of the character of God) could be learned by humans became a research agenda rather than a lovely metaphorical thought.

It was Newton, of course, who astonished the world with his translation of this book of nature. In what was to become the future pattern for scientific thought, he managed to summarize a wide variety of observation and experiment in the statement of a very few Laws (four) expressed in mathematical form from which, by mathematical deduction, a staggering list of new predictions could be made as well as the explanation, in the form of relating to the Laws and hence to one another of many previously apparently unrelated phenomena.

Many of the details and basic features of Newton's world picture have been modified, abandoned, or superseded. His absolute space and time proved not to be adequate, his laws of mechanics and gravitation have had to be modified, his mechanical universe in which rigidly causal playing out of initial conditions (Laplace's Boast) has proved to be far from the experimentally discovered quantum nature of things. The boundary between order and chaos has been confused both by the biology of evolution through natural selection and by modern investigations of unadorned Newtonian mechanical systems themselves. The idea of the world as a mechanical contrivance has been challenged by the rise of field theories with Maxwell's synthesis of electricity, magnetism, and electromagnetic radiation leading the way.

Still the idea that one can fashion an axiomatic mathematical map of a wide variety of natural phenomena has proved to be very powerful indeed. Why the map should so appropriately be one which relates physical phenomena (out there) with that play thing of the human mind, mathematics (in here), remains a mystery. Why should mathematics be the uniquely suitable human tool for the study of nature?

An extremely striking feature of the actual laws of nature which have emerged is their elegant parsimony. Consider the world of "classical physics" a version of the laws of nature which reigned briefly about 100 years ago having to bow out with the advent of quantum mechanics and relativity and the new range of phenomena which they treat. Classical physics can be summarized in just 8 statements which, in the compact notion invented for the purpose of expressing them succinctly, appear as:

The first three represent Newton's three laws of motion; the second is his universal law of gravitation, and the last four encapsulate electricity, magnetism, and electromagnetic radiation. The process of mapping these mathematical statements and their symbols onto physical phenomena is, of course, not contained in these bare prescriptions and is also where most of the content lies. Still, as a starkly beautiful account of the action of the solar system, the world of light and color, electromagnetic technology, the foundation for much engineering, the rhythm of the tides, and the flow of fluids, it is astonishingly economical and extremely explicit in its manner of use.

I have talked very briefly about some of the familiar episodes in the epic called the history of science and tried to indicate just a little how unlikely and unusual this epic has been. I said at the outset that I would make a few remarks on the contrast between this European epic and the parallel and different experience of China.

Joseph Needham, a legendary scholar and scientist of this century, has spent a lifetime trying to understand why modern science developed only in the Western world. In particular he has been a great instructor to both East and West in what he has called the "...triumphs and poverties of the Chinese scientific tradition..." Why, he has repeatedly asked, did the scientific discoveries and inventions of the European Renaissance not occur in some way in China which for many centuries was far more technologically advanced than Europe; which had observed the heavens for just as long and with more precision and thoroughness than the Greeks, the Babylonians, Europeans, or the Arabs, and which never went through the collapse and recovery that Europe had to endure during the Dark Ages.

There is an intriguing parallelism between the astronomical, chemical, mechanical, and technological challenges that were being explored, often almost contemporaneously but in long lasting mutual isolation in China and in the West. This pair of histories present themselves as one of the rare cases when one can confront "if history" with two examples rather than the usual single and unique one. It is as if you had subsequent developments both for Caesar crossing and Caesar not crossing the Rubicon. Needham and others, in trying to understand why it might have been that science did arise in Europe but not in China, have come up with a wide variety of intriguing contrasts in society, government, language, religion, traditions of thought, economic considerations, social position of craftsmen and astronomers, and in legal theories.

To me, Needham's most convincing case rests on the observation that for some reason, the Chinese never developed an axiomatic mathematics such as Euclidean geometry, and their practical concern with human society and technological problems acted as a barrier to the sort of wildly impractical speculation that led to the construction of an imagined mechanical model of the heavens.

Confucius is often compared with Socrates as a thinker about human societies. The Pre-Socratics have had their anticipatory revenge on both Socrates and Confucius. Or maybe Socrates and Confucius, both of whom could be called profoundly anti-scientific, were wiser than we yet understand.

--B. Gale Dick, Ph.D.
Professor of Physics at the University of Utah