Wednesday, May 10, 2006

...And back to Greek

Can someone please explain this?!

Given these basic aspects of Epicurean physics:
1) Things are not divisable into infinity.
2) Things are made up of indivisable minima. All larger magnitudes, including atoms themselves, consist of a finite number of these minima.
3) Any perceived magnitude can be analysed into an exact number of minima, i.e. a minimum is an exact submultiple of any larger magnitude (there cannot be "bits" of minima leftover).
4) Minima are never in motion, only the magnitudes they make up move because minima are indivisable and cannot be "traversing" from point A to B - it is either in A or in B since it has no "parts".

SO, how is THIS evident?: "One further consequence should be the falsity of conventional geometry. If, for example, the perfect geometrical square could exist, its side and diagonal would be incommensurable - incompatibly with the theory of minima, in which, as we have seen, all magnitidues share a common submultiple. there is good historical evidence that Epicurus accepted this consequence, but none that he worked out in detail an alternative geometry." (Long and Sedley, The Hellenistic Philsophers, vol. 1)

Why please? I have a vague notion that this has something to do with the Pythagorean theorem, e.g. sides = 1, diagonal = Root 2... And has anyone worked out an alternative geometry?


Tengu said...

i think you are right. The length of the diagonal of a square is root2 of the side. Root2 is irrational, meaning there is no representation of root2 in the form a/b (where a and b are integers and b is not zero). However, this is a contradiction to epicurean physics as ALL magnitudes MUST be equally divisible by some number of minima (that is the diagonal MUST be able to be expressed in a/b).

marianevans said...

That makes sense. When I read "Root 2 is irrational" I had forgotten that "rational" and "irrational" were terms for numbers. I thought, What an interesting way to think of numbers, and then I remembered my math... but then it struck me that "rational" has always meant more, even as a mathematical term.

How often we separate "hard sciences" from philosphy, theology, metaphysics, etc. But my foray into Epicurean physics shows me that mathetmatics is just as much a part of the human imagination - another philosophy that says, "Reality is such and such, and works in this way." Epicurus proposed the "swerve principle" for moving particles - which he related to free will, and this is now confirmed by quantum physics. Wild.