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Numbers to Pythagoras
Pythagoras founded the Pythagorean Society in Crotone around 518 BC, on the eastern coast of Italy, a place of relative peace and safe, as a religious, philosophical and scientific society (known also as Pythagorean School)
Pythagoras himself was the head of the society which had an inner circle of followers known as the mathematikoi and an outer circle known as the akousmatics.
The mathematikoi lived permanently with the Society, had no possessions and were vegetarians. They were taught by Pythagoras himself and obeyed strict rules. They were obedient and silent, abstained from food.
The akousmatics lived in their own houses, only coming to the Society during the day. They were allowed their own possessions and were not required to be vegetarians.
Members were not allowed to discuss information of the disciplines with others outside the society. Information was transferred through word of mouth instead of written accounts to ensure this secrecy. By law, women were not allowed to attend public meetings but they were admitted to the Master's lectures. It was their belief that the soul of a person is immortal and could inhabit the body of another person or animal.
Here are some of the rules:
*To abstain from beans. *Not to pick up what has fallen. *Not to touch a white cock. *Not to stir the fire with iron. *Do not look in a mirror beside a light. *Men and women are equal.
Property was communal even mathematical discoveries
What has this to do with numbers?
Pythagorean conception of number is magnitude. It is a symbol of an innermost mystical and universal harmony. A harmony between Soul and World which is manifested musically. This music is divine because the opposites (like equality/inequality, identity/difference) are in continuous relationship. So "number" expresses universal harmony through music that we don't hear because we are accustomed to it since birth.
Numbers in metaphysical sense are expressions and realization of the divine. They are not mathematical (i.e. for computation and calculation) but rather conceptualized in its matter as an esoteric symbol of divine truths.
Its worth to note that numbers represented as pebbles and points on sands. So they are seen as solid figures that occupy space and have magnitude as indicated previously.
A person living at the time of Pythagoras had no interest or any need to represent numbers arithmetically. Numbers are studied on a quite different aspect far from our scientific needs of quantitative results. So they dealt mainly with whole and rational numbers ignoring numbers as irrationals.
