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 Finally (and fortunately for the future of Western science) Plato did return to Athens. He taught philosophy just as his mentor had done. One of his students, Euclid, wrote Elements of Geometry, the foundation of geometry for the next twenty-two centuries. Another student, Aristotle, taught Alexander the Great, who fostered the spread of Hellenic science throughout his new empire. The seeds sown by Alexander in Asia flowered throughout Europe more than a thousand years later, catalyzing the ‘birth’ of the modern scientific method.

Why do I begin this brief history of scientific methods with the death of Socrates and with Plato’s response? From Pythagoras to Ptolemy, many individuals built Hellenic science. Yet the heart of this development may be the remarkable mentor-student chain of Socrates-Plato-Aristotle-Alexander. The focal point was not a panorama of historic events, but the response of an individual, Plato, when faced with a choice: should I follow the example of Socrates or should I react against the injustice of society?

Science and the scientific method were not born in Greece. Two criteria for the existence of science -- scientific observation and the collection of facts -- thrived in several pre-Hellenic cultures. Ancient astronomy is the most obvious example: the Mesopotamians in about 3500 B.C., as well as other agricultural cultures at other times, gradually evolved from star-gazing to using the stars and sun for predicting the seasons and eclipses. If technology implies science, should we trace science back to the first use of fire or the first use of tools?

A remarkable number of the key ingredients of scientific methodology were discovered during the Hellenic period:
 * Pythagoras, and later Plato, advocated what has become the fundamental axiom of science: the universe is intrinsically ordered and can be understood through the use of reason. Socrates stressed that human intelligence and reason can discover the logical patterns and causal relationships underlying this order. This axiom cannot be proved; we accept it because it is so successful (Killeffer,1969). Previously, most cultures had interpreted order and law as human concepts that were largely inapplicable to nature.
 * Pythagoras identified the relationship between musical notes and mathematics. The Pythagoreans educed that mathematical laws could describe the functioning of nature and the cosmos. Although they did invent geometry, they were unable to develop the mathematical techniques needed to exploit this insight.
 * The Hellenic culture, founded on intellectual freedom and love of nature, created a science both contemplative and freer from religious dogma than the preceding and following millennia. The systematic Hellenic investigation of nature, as seen in their geometry, mathematics, astronomy, geography, medicine, and art, may be responsible for our modern Western perception that science had its roots in ancient Greek civilization (Goldstein, 1988). Then, as now, science tested the limits of intellectual freedom. The death of Socrates is proof.
 * Aristotle firmly steered Greek science towards rational thought and classification. He honed the blunt tool of deductive logic into the incisive instrument of syllogism. Aristotle also attempted to classify and systematize biological samples that Alexander sent back to him.
 * Aristotle also fostered the development of induction, the inference of generalizations from observation: “Now art arises when from many notions gained by experience one universal judgement about a class of objects is produced.” [Aristotle, 384-322 B.C.]