From: Johnicholas Hines (johnicholas.hines@gmail.com)
Date: Sun Feb 15 2009 - 09:58:15 MST
On Sun, Feb 15, 2009 at 8:45 AM, Petter Wingren-Rasmussen
<petterwr@gmail.com> wrote:
> One of the things that really fascinates me about axioms is that although
> they cant be proved, their extrapolations have been used to put man on the
> moon.
> Could completely different axioms lead to the same result?
Zermelo-Frankel set theory with the Axiom of Choice is certainly not
crucial for spaceflight. :)
If you were thinking of Newton's laws of motion and gravity, those
aren't really axioms; they have justifications (not proofs, but
experimental evidence). Alternatives to Newton... You might use
Einstein's general theory directly instead. Or possibly there's a way
to use symbolic dynamics and topology of dynamical systems to pilot a
spacecraft without using Newton's laws explicitly.
Alternative laws that lead to the same result cannot be completely
different. If the alternative laws are approximating the same reality,
they can also be viewed as approximating each other.
Of course, you don't have to do math or science at all. Evolution (in
biology) and tinkering (in technology) can achieve results without
theorizing about them. It seems to take more experiments (failed trips
to the moon), but you can get amazing results.
Completely different axioms could certainly get us to the moon.
Somewhat different laws could probably get us to the moon. You don't
need axioms or laws at all to get to the moon.
Johnicholas
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