From: Dan Fabulich (dfab@cinenet.net)
Date: Tue Jan 21 1997 - 19:18:14 MST
Eliezer Yudkowsky wrote:
> The question is: Can [1+1=3] *ever* appear *completely* consistent,
> cognitively, thanks to adaptation by the child... or will our built-in
> processes of visualization interfere?
It's not just our problems with visualization which get in the way, it's
the fundamental logical premise. 1 + 1 = 3 is not a strong enough
axiom upon which to build mathematics.
A first, try defining an associative and commutative property of
equality.
For example, simply given:
1 = 1
1 + 1 = 3
----------
1 + (1 + 1) = 1 + 3?
1 + 3 = 4? 5?
1 + 1 + 1 + 1 = (1 + 1) + (1 + 1) ?= 3 + 3 ?= 9?
1 + 1 + 1 + 1 ?= (1 + 1 + 1) + 1 = 4 + 1 = 5???
Even more complicated questions await us as we approach subtraction
problems like x - 1... What if I try to put three things together at
once? What happens when I try to take one away from that cluster?
Or, perhaps a better question, what possible use could this serve?
(Then again, isn't that what Mandelbrot said about fractals?)
-He who laughs last thinks slowest-
dAN
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