I am interested in information on what is known about Pythagorean
number theory.  Specifically, I want to know exactly what the
Pythagorean derived from their number theory and how literally they
want the quote "everything is number" to be taken.  I would appreciate
an answer than is as close to Pythagoras' original intention as is
possible.

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Request for Question Clarification by pafalafa-ga on 20 Sep 2006 19:04 PDT

timbanky-ga,

Have you seen this write-up on Pythagoras?


http://en.wikipedia.org/wiki/Pythagoras


It's very well done and...given the limited amount of information
available on his works...it's hard to imagine posting a more complete
answer to your question.


Let me know if that link works for you.


pafalafa-ga

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Clarification of Question by timbanky-ga on 24 Sep 2006 13:34 PDT

I had read the wikipedia article, but I found the information on
'number' to be extreamly minimal.  I understand the information is
limited (as is the nature of fragmental work), but was really hoping
there was a resource that handled the issue of number theory.  It is
possible that my question cannot be answered, but i remain hopeful.  I
would be satisfied with anything that either examined the quote
"everything is number" seriously, or discussed the implication and
limitation of this pre-socratic number theory.

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Request for Question Clarification by pafalafa-ga on 24 Sep 2006 13:46 PDT

Allrighty, then.  Have a look at this paper [warning...slow download!]:


http://www.acmsonline.org/Stucki-Worship.pdf
Mathematics As Worship


The Pythagoreans represent the earliest systematic cult of number.
Prior to Pythagoras (6th century BC) there is little evidence of
numbers and mathematics being anything other than practical tools of
civilization. Some speculation has been made, however, that Pythagoras
was influenced by ancient Egyptian and Babylonian thinking (or even
Buddha) during his famous travels through Mesopotamia, Africa, and
Asia...


The Pythagoreans, who believed that everything is number, worshipped
number as deity. Pythagoras defined number as ?that which prior to all
things subsists in a divine intellect, by which and from which all
things are coordinated, and remain connumerated in an indissoluble
order.? (Taylor, 1816, p. 3) Each number was philosophically adorned
with various attributes ranging from physical to supernatural to
mythic to aesthetic to moral. For example, according to Nicomachus the
Pythagoreans described the tetrad (the number four) as ??the greatest
miracle, a God after another manner (than the triad), a manifold, or
rather, every divinity. It is also the fountain of natural effects,
and is the keybearer of nature...



Again, let me know how on/off target this is as an answer to your question.


paf