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