On Monday, April 1, 2013 11:38:05 AM UTC-7, Dan wrote:
> Falsifiability only comes into consideration when you have something > apparently 'external' against which to test your mathematical models .
Precisely. The "external" reality underlying mathematics is computation.
A very good way of thinking about this stuff is to think of the computer as the mathematicians' microscope which helps mathematicians peer into the world of computation, and then mathematics itself is the science that studies the phenomena observed in that world of computation. The "science of phenomena observable in the world of computation" includes all of the mathematics that helps us reason about the real world.
> What's so hard to understand?
What's hard to understand is why you ... oh, never mind.