By showing that mathematics can be used to model and thus explain and predict nature, Pythagoras (ca. 580–500 B.C.) has had as significant an influence on Western thought as perhaps anyone. Pythagoras postulated that the basic explanation (the logos; as in logical structure) for everything in the universe was found in numbers and in numerical relationships (ratios; as in rationality). He noted that the square of the hypotenuse of a right-angle triangle is exactly equal to the sum of the squares of its other two sides. Although this came to be called the Pythagorean theorem, it had probably been known to the Babylonians previously. Pythagoras also observed that a harmonious blending of tone results when one string on a lyre is exactly twice as long as another. This observation that strings of a lyre must bear certain relationships with one another to produce pleasant, harmonious sounds was, perhaps, psychology’s first psychophysical law. Indeed, physi- cal events (relationships between strings on musical instruments) were demonstrated to be systematically related to psychological events (perceived pleasantness of sounds). And, the Pythagoreans expressed this psy- chophysical relationship in mathematical terms.
According to the Pythagoreans, numbers and numerical relationships, although abstract, were nonetheless real and exerted an influence on the we would be aware only of objects and events that change from moment to moment. It is for this rea- son that empiricists are said to be concerned with the process of becoming rather than with being. Being implies permanence and thus at least the pos- sibility of certain knowledge, whereas a knowledge of empirical events (because they are becoming) can be only probabilistic at best. Throughout psychol- ogy’s history, those claiming that there are certain permanent and, therefore, knowable things about the universe or about humans have tended to be rationalists. Those saying that everything in the uni- verse, including humans, is constantly changing and thus incapable of being known with certainty tend to be empiricists.