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Science and Mathematics in Greece and China

The greatest of all Greek scientific discoveries was the discovery — or rather, as philosopher Geoffrey Lloyd put it, the invention — of nature itself. The Greeks defined nature as the universe minus human beings and their culture. Although this seems to us to be the most obvious sort of distinction, no other civilization came upon it. A plausible account of how the Greeks happened to invent nature is that they came to make a distinction between the external, objective world and the internal, subjective one. And this distinction came about because the Greeks, unlike everyone else, had a clear understanding of subjectivity arising from the tradition of debate. It makes no sense for you to try to persuade me of something unless you believe that there is a reality out there that you apprehend better than I do. You may be able to coerce me into doing what you want and even into saying that I believe what you do. But you will not persuade me until I believe that your subjective interpretation of some state of affairs is superior to mine.

So, in effect, objectivity arose from subjectivity — the recognition that two minds could have different representations of the world and that the world has an existence independent of either representation. This recognition was probably aided for the Greeks because, due to their position as a trading center, they regularly encountered people with utterly different notions about the world. In contrast, Chinese culture was unified early on and it would have been relatively rare to encounter people having radically different metaphysical and religious views.

The Greeks' discovery of nature made possible the invention of science. China's failure to develop science can be attributed in part to lack of curiosity, but the absence of a concept of nature would have blocked the development of science in any case. As philosopher Yu-lan Fung observes, "Why" questions are hard to ask if there is no clear recognition that there are mental concepts that somehow correspond to aspects of nature, but which are not identical to them.

The Greeks' focus on the salient object and its attributes led to their failure to understand the fundamental nature of causality. Aristotle explained that a stone falling through the air is due to the stone having the property of "gravity." But of course a piece of wood tossed into water floats instead of sinking. This phenomenon Aristotle explained as being due to the wood having the property of "levity"! In both cases the focus is exclusively on the object, with no attention paid to the possibility that some force outside the object might be relevant. But the Chinese saw the world as consisting of continuously interacting substances, so their attempts to understand it caused them to be oriented toward the complexities of the entire "field," that is, the context or environment as a whole. The notion that events always occur in a field of forces would have been completely intuitive to the Chinese. The Chinese therefore had a kind of recognition of the principle of "action at a distance" two thousand years before Galileo articulated it. They had knowledge of magnetism and acoustic resonance, for example, and believed it was the movement of the moon that caused the tides, a fact thateluded even Galileo.

In the desert of western China are buried bodies of tall, red-haired people, astonishingly well preserved, of Caucasian appearance. They found their way to that part of the world some thousands of years ago. Aside from the way they look, they are different from the peoples who lived in the area in another interesting respect. Many of them show clear signs of having been operated on surgically. In all of Chinese history, surgery has been a great rarity.

The reluctance of the Chinese to perform surgery is completely understandable in light of their views about harmony and relationships. Health was dependent on the balance of forces in the body and the relationships between its parts. And there were, and are for many East Asians today, relationships between every part of the body and almost every other part. To get a feel for this vast web of interconnections, look at a modern acupuncturist's view of the relations between the surface of the ear and the epidermis and skeleton. An equally complex network describes the relations between the ear and each of the internal organs. The notion that the removal of a malfunctioning or diseased part of the body could be beneficial, without attending to its relations to other parts of the body, would have been too simple-minded for the Chinese to contemplate. In contrast, surgery has been practiced in many different Western societies for thousands of years.

The Chinese tendency to focus on relationships in a complex, interconnected field is exemplified by the practice of feng shui, still continued in the East. When someone wishes to build a building, it is essential to call in a feng shui master. This person takes account of a seemingly limitless number of factors such as altitude, prevailing wind, orientation toward the compass, proximity to various bodies of water, and gives advice on where to locate the structure. This practice has had no real counterpart in the West, but the most modern skyscraper in Hong Kong will have had its feng shui workup before being built.

The Chinese conviction about the fundamental relatedness of all things made it obvious to them that objects are altered by context. Thus any attempt to categorize objects with precision would not have seemed to be of much help in comprehending events. The world was simply too complex and interactive for categories and rules to be helpful for understanding objects or controlling them.

The Chinese were right about the importance of the field to an understanding of the behavior of the object and they were right about complexity, but their lack of interest in categories prevented them from discovering laws that really were capable of explaining classes of events. And for all that the Greeks tended to oversimplify and to be satisfied by pseudo-explanations involving nonexistent properties of objects, they correctly understood that it was necessary to categorize objects in order to be able to apply rules to them. Since rules are useful to the extent that they apply to the widest possible array of objects, there was a constant "upward press" to generalize to high levels of abstraction so that rules would be maximally applicable. This drive toward abstraction was sometimes — though not always — useful.

The Greek faith in categories had scientific payoffs, immediately as well as later, for their intellectual heirs. Only the Greeks made classifications of the natural world sufficiently rigorous to permit a move from the sorts of folk-biological schemes that other peoples constructed to a single classification system that ultimately could result in theories with real explanatory power.

A group of mathematicians associated with Pythagoras is said to have thrown a man overboard because it was discovered that he had revealed the scandal of irrational numbers, such as the square root of 2, which just goes on and on without a predictable pattern: 1.4142135.... Whether this story is apocryphal or not, it is certainly the case that most Greek mathematicians did not regard irrational numbers as real numbers at all. The Greeks lived in a world of discrete particles and the continuous and unending nature of irrational numbers was so implausible that mathematicians could not take them seriously.

On the other hand, the Greeks were probably pleased by how it was they came to know that the square root of 2 is irrational, namely via a proof from contradiction. One posits two whole numbers, n and m, such that the square root of 2 = n/m and shows that this leads to a contradiction.

The Greeks were focused on, you might even say obsessed by, the concept of contradiction. If one proposition was seen to be in a contradictory relation with another, then one of the propositions had to be rejected. The principle of noncontradiction lies at the base of propositional logic. The general explanation given for why the Greeks, rather than some other people, invented logic, is that a society in which debate plays a prominent role will begin to recognize which arguments are flawed by definition because their structure results in a contradiction. The basic rules of logic, including syllogisms, were worked out by Aristotle. He is said to have invented logic because he was annoyed at hearing bad arguments in the political assembly and in the agora! Notice that logical analysis is a kind of continuation of the Greek tendency to decontextualize. Logic is applied by stripping away the meaning of statements and leaving only their formal structure intact. This makes it easier to see whether an argument is valid or not. Of course, as modern East Asians are fond of pointing out, that sort of decontextualization is not without its dangers. Like the ancient Chinese, they strive to be reasonable, not rational. The injunction to avoid extremes can be as useful a principle as the requirement to avoid contradictions.

Chinese philosopher Mo-tzu made serious strides in the direction of logical thought in the fifth century B.C., but he never formalized his system and logic died an early death in China. Except for that brief interlude, the Chinese lacked not only logic, but even a principle of contradiction. India did have a strong logical tradition, but the Chinese translations of Indian texts were full of errors and misunderstandings. Although the Chinese made substantial advances in algebra and arithmetic, they made little progress in geometry because proofs rely on formal logic, especially the notion of contradiction. (Algebra did not become deductive until Descartes. Our educational system retains the memory trace of their separation by teaching algebra and geometry as separate subjects.)

The Greeks were deeply concerned with foundational arguments in mathematics. Other peoples had recipes; only the Greeks had derivations. On the other hand, Greek logic and foundational concern may have presented as many obstacles as opportunities. The Greeks never developed the concept of zero, which is required both for algebra and for an Arabic-style place number system. Zero was considered by the Greeks, but rejected on the grounds that it represented a contradiction. Zero equals nonbeing and nonbeing cannot be! An understanding of zero, as well as of infinity and infinitesimals, ultimately had to be imported from the East.

In place of logic, the Chinese developed a type of dialecticism. This is not quite the same as the Hegelian dialectic in which thesis is followed by antithesis, which is resolved by synthesis, and which is "aggressive" in the sense that the ultimate goal of reasoning is to resolve contradiction. The Chinese dialectic instead uses contradiction to understand relations among objects or events, to transcend or integrate apparent oppositions, or even to embrace clashing but instructive viewpoints. In the Chinese intellectual tradition there is no necessary incompatibility between the belief that A is the case and the belief that not-A is the case. On the contrary, in the spirit of the Tao or yin-yang principle, A can actually imply that not-A is also the case, or at any rate soon will be the case. Dialectical thought is in some ways the opposite of logical thought. It seeks not to decontextualize but to see things in their appropriate contexts: Events do not occur in isolation from other events, but are always embedded in a meaningful whole in which the elements are constantly changing and rearranging themselves. To think about an object or event in isolation and apply abstract rules to it is to invite extreme and mistaken conclusions. It is the Middle Way that is the goal of reasoning.

Why should the ancient Greeks and Chinese have differed so much in their habits of thought or, at any rate, why should this be true of the intelligentsia, who are the only ancient peoples whose mental life is known to us at all? And why should there be such "resonance" between the social forms and self-understandings on the one hand and the philosophical assumptions and scientific approaches on the other? Answers to these questions have implications for understanding the differences between Eastern and Western thought that exist today.

Copyright © 2003 by Richard Nisbett

Tags: Psychology & Psychiatry

About the Author

Richard E. Nisbett, Ph.D., has taught psychology at Yale University and the University of Michigan, where he is the Theodore M. Newcomb Distinguished University Professor. He has received the Distinguished Scientific Contribution Award of the American Psychological Association, the William James Fellow Award of the American Psychological Society, and a Guggenheim Fellowship. In 2002, he became the first social psychologist in a generation to be elected to the National Academy of Sciences. The coauthor of Culture of Honor and numerous other books and articles, he lives in Ann Arbor, Michigan.