Read the following text, paying particular attention to the highlighted words.
Time in History
In the life of politics the Greek language refers to the reign of justice by the term aosmos; but the life of nature is a kosmos too, and indeed this cosmic view of the universe begins with Anaximander's dictum. To him everything that happens in the natural world is rational through and through and subject to a rigid norm.
Emphasis on the role of time characterised the Pythagorean idea of the kosmos. According to Plutarch, when asked what Time (Chronos) was, Pythagoras (sixth century BC) replied that it was the "soul", or procreative element, of the universe. The extent to which Pythagoras and his followers may have been influenced by oriental ideas has long been a subject for argument. The Orphic idea of Chronos, which may have had an influence on Pythagoras, seems rather like the Iranian idea of Zurvan akarana. In particular, both were depicted as multi-headed winged serpents. Similarly, the dualism which played an important role in pythagorean philosophy appears to echo the Zoroastrian cosmic opposition of Ohrmazd and Ahriman, although these two ultimates were regarded as personal gods and not as abstract principles like the Pythagorean ten basic pairs of opposites, such as limit versus unlimited, good versus bad, male versus female, odd versus even. The most fruitful feature of Pythagorean teaching was the key idea that the essence of things is to be found in the concept of number, which was regarded as having spatial and also temporal significance. Numbers were represented figuratively by patterns similar to those still found on dominoes and dice. Although this led to Greek mathematics being dominated by geometry, time was no less an important element in early Pythagorean thought. Indeed, even spatial configurations were regarded as temporal by nature, as is indicated by the role of the gnomon. This was originally a timemeasuring instrument - a simple upright sundial. Later the same term was used to denote the geometrical figure that is formed when a smaller square is cut out of a larger square with two of its adjacent sides lying along two adjacent sides of the latter. Eventually, the term came to denote any number which, when added to a figurate number, generates the next higher number of the same shape (triangular numbers, square numbers, pentagonal numbers, and so on). The generation of numbers was regarded by the early pythagoreans as an actual physical operation occurring in space and time, and the basic cosmogonical process was identified with the generation of numbers from the initial unit, the Monad, which may have been a sophisticated version of the earlier Orphic idea of the primeval World-egg.
It is well known that Pythagoras' belief in the significance of numbers was supported by his alleged discovery, with the aid of a stringed instrument, that the concordant intervals of the musical scale correspond to simple numerical ratios. This led many later Greek thinkers to regard musical theory as a branch of mathematics (together with geometry, arithmetic, and astronomy it constituted what eventually came to be called the quadrivium), although this view was not universally accepted, the most influential of those who rejected it being Aristoxenus of Tarentum (fourth century BC). He emphasised, instead, the role of sensory experience. For him the criterion of musical phenomena was not mathematics but the ear.
Long before the time of Aristoxenus, some of the most acute Greek thinkers had found that the concept of time was difficult to reconcile with their idea of rationality. Indeed, parmenides, the founding father of logical disputation, argued that time cannot pertain to anything that is truly real. The essence of his difficulty was that time and change imply that the same thing can have contradictory properties - it can be, say, hot and cold, depending on the time - and this conflicted with the rule that nothing can possess incompatible attributes. His basic proposition was "That which is is, and it is impossible for it not to be." From this he argued that, since only the present "is", it follows that past and future are alike meaningless, the only time is a continual present time and what exists is both uncreated and imperishable. Parmenides drew a fundamental distinction between the world of appearance, characterised by time and change, and the world of reality which is unchanging and timeless. The former is revealed to us by our senses, but these are deceptive. The latter is revealed to us by reason and is the only true mode of existence.
(Time in History by G. J. Whitrow)
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