Immortals, Irrationals

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Responding to a question on the Math History List, I wrote this:

| One reason why some Greeks had problems accepting irrationals
| is that the existence of intervals in irrational ratios to each
| other defeated the assurance that all cosmic cycles have a common
| unit and thus that all configurations of the cosmos recur eternally.
| Inasmuch as eternal recurrence guarantees a kind of immortality, the
| possibility of cosmic cycles starting out in a "Garden of Eden" state
| that never recurs means that the Pythagorean belief in the immortality
| of the soul can no longer be proven solely by way of arithemetic alone.

On being questioned about the source, I find that it may take some search.

Being that the Art is long and the attention span short,
I'll post my notes on this question here as I find them.

I read a lot of Plato and the Pre-Socratics in the 70's
and I know that Plato's Timaeus was a big influence on
me all through the 80's as I was using a quotation from
that as a constant epigraph on the programming work that
I did at the U of M Institute for Social Research (ISR) --
It made for many punny associations with the title of
one project I worked on, called the "Time Use Study".

Here is the epigram that I used at the time:

| These are the forms of time,
| which imitates eternity and
| revolves according to a law
| of number.

Plato, "Timaeus", Benjamin Jowett (trans.).
in Edith Hamilton and Huntington Cairns (ed.),
''The Collected Dialogues of Plato, Including
the Letters'', Bollingen Series LXXI, Pantheon,
New York, NY, 1961.  (p. 1167).

CC: Arisbe, Inquiry, Math History

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