QUANTUM METAPHYSICS - E-thesis

proposed by Pythagoras 42 (ca. 572-497 B.C.). It is here that the notion that mathematics, i.e. that
mathematical order is the basic principle whereby the multiplicity of phenomena can be
accounted for, is said to have originated. In the Pythagorean doctrine, mathematics and numbers
took a position similar to that of basic matter for the Milesians. The ultimate basis of all Being
was no longer envisaged as a material that could be sensed – such as water in the philosophy of
Thales – but as an ideal principle of form. In addition to matter the Pythagoreans added the
notions of order, proportion and measure. The most essential feature of creatures was the
numerical organization and form arising in them, which were governed by numbers, and the
colourful multiplicity of phenomena could be understood by recognising in them unitary
principles of forms, which could be expressed in the language of mathematics. If different
geometric figures represented different qualitative characteristics, the only quality that needed to
be attributed to matter was the capability of taking a geometric shape. 43
By numbers, Pythagoras apparently did not simply refer to whole numbers, but also to numerical
ratios and proportions. For him, both forms and numbers represented a deeper order, harmony,
hidden behind visible phenomena. Pythagoras is said to have made the famous discovery that
vibrating strings under equal tension sound together in harmony if their lengths are in a simple
numerical ratio. The harmonious concord of two strings does indeed yield a beautiful sound, and
it was certainly one of the momentous discoveries in the history of mankind that mathematical
structure, in this case numerical ratio, was a source of harmony and beauty. It is somewhat ironic
that the theorem 44 which carries the name of Pythagoras was experienced in ancient Greece as a
blow against the idea that numbers could be used as a general basis for explanation. The ability
to deal with irrational numbers through geometry did however exist, and this is thought to have
laid emphasis on the concept of form in later Greek thinking. 45
In ancient times, Pythagoras was regarded as both a religious and a scientific figure. The
discovery by Pythagoras that the length of a string and its resulting pitch when struck were in
numerical ratio to each other was regarded as both a religious revelation and a sign of the
fundamental harmony in nature. Students of his esoteric school believed mathematics to be the
41
Heisenberg 2000, 72.
42
Pythagoras was born on the island of Samos off Miletus. He later moved to the western Greek colony of Croton
in Italy where he founded an esoteric school in which mystery religions and mathematics were linked.
43
Guthrie 1950, 39-40. Stenius 1953, 47, 51. Heisenberg 1985, 58.
44
Pythagoras’ theorem about the ratio of the sides in a rectangular triangle was known to the Babylonians at least
one thousand years earlier.
45
Thesleff and Sihvola 1994, 39-40. Heisenberg 1985, 57. Stenius 1953, 45-49.
30