It's an interesting "few glasses of wine" discussion topic; one
of the things I love about the Internet, it's like that great
cocktail party (or beer keg or college pot smoking session -
pick your social lubricant) discussion, but at any time and any
place and without the puking or hallucinations... well,
youtubepoop nonwithstanding :P I want to believe in Many Worlds
or Copenhagen - either one would be quite nice.* But here's
where I think an example of the sticky thing is: optical
illusions. In particular, the diagonal line. As humans, we find
quantizing the / into x + y particularly confounding; a2 + b2 =
c2... or in an opposite direction, square root of 2 - a
never-ending ax-cut into the number system itself that pushes
fractions deeper and deeper into the abyss with no end in sight.
Or Pi - the attempt to cut a circle and turn it into a line and
coming up with this number that makes us go "woah". And I
believe it is a fundamental limitation of human perception that
extends and becomes deeply embedded into our way of thinking in
so many ways. Why do I mention optical illusions?* Look how
easily our visual system is confused by the wireframe 3D box.*
It's just a hexagon with lines through it; and yet it appears to
jump out and push back simultaneously; our visual system can't
process it.* No matter how we retrain ourselves, for at least a
brief moment, it works. We are mystified by examples of purely 3
dimensions.* Cantor's Sets leading to infinities of different
kinds; running that diagonal - easily resolvable by flipping the
set "up" into a 3rd dimension instead of a grid; the infinity is
perfectly containable in a higher dimension. But we're mystified
by it.* It goes someplace that seems improbable... because it's
something we can't visualize with our mental systems entirely
well... and this lack of ability based on our biological
limitations extends into the very theories we use to describe
the Universe. I'm not against many worlds, or wave-particle
duality - or any stories that fuel the human imagination and
take us to fantastic places - and systems that describe such
fantastic places in detail; whether it be through literature or
through mathematics... or art.. or music or movies. And I'm not
discounting that numbers are practical; not at all; but I don't
believe the Universe is mathematical; rather the system of
mathematics describes the Universe very well; to a greater and
greater degree of precision. But, to steal from a Buddhist
concept (I'm not Buddhist but I like some of their stuff): do
not mistake the finger that points to the moon for the moon
itself. It's a tool; useful; practical; we're going to continue
to make amazing things by it.* But I don't think its necessary
to believe that numbers have an existence beyond the humans that
use them, in order to continue doing what we do with numbers. I
don't know if this makes any sense or if it's just babble :P
