## Thursday, January 9, 2014

### ... against an algebraic formula taken for arithmetic

Video commented on:
Numberphile : ASTOUNDING: 1 + 2 + 3 + 4 + 5 + ... = -1/12
http://www.youtube.com/watch?v=w-I6XTVZXww
My comment:
• 1) answer to series:

"1 - 1 + 1 - 1 ..."

is NOT "1/2" BUT "1 OR 0"
• 2) in physics you do not measure infinities, correct - in a finite universe (as a Thomist considers the Created Universe to be) any series has an ectual, though of course arbitrary end.
• 3) If time after other physicians come up with "-1/12" for "1 + 2 + 3 ...." that implies something is misstated as compared to actual mathematical realities.

Let me give a very easy parallel to what I mean.

"(a - b) sqrd = a sqrd - 2ab + b sqrd", right?

Not really. It is more like "= a sqrd - ab - (ab - b sqrd)". The usual simple answer "a sqrd - 2ab + b sqrd" is a simplification of it, it is in nature algebraic rather than geometric. It goes for the simplest expression rather than the one reflecting what happens in physical geometry when for instance you take a square of paper size "a sqrd" and first cut off an "ab" and then an "ab - b sqrd".

This involves that "infinity" as in "infinite series" (or "infinite length" or ...) is a sham concept. It has its uses, but it is not really there in the mathematical reality which the mathematical expression is supposed to be about. Something else is, which can be expressed that way, no doubt, but not that itself.

Very unlike the case in which "3 = 1 + 1 + 1" per definition gives a clue to what a statement involving the number 3 means.