>>13487785/shrug. Physical or metaphysical, theories that are built of first order logic should at least attempt to be internally consistent. How far do you mentally fractal zoom on the line you represent with the sqrt(2) before you give up and pretend you got there?
In addition the Wiki states
>In addition to measuring distance, real numbers can be used to measure quantities such as time, mass, energy, velocity, and many moreHow quickly do our imprecise definitions make for shaky foundations in our physics.
The Babylonions, with their obsession with exact numerals (you get less '...' numbers in base 60 btw) highlights that we have something to learn from reexamining the foundations of our thought.
Doesn't it make sense too? we are about 30 years into the internet age. The Descartes, Euclids, Ramanujans got perhaps a handful of books, now we get the best of 1000's of thinkers at our finger tips, I say we dare to think we can build a better foundation, so that we can build higher the areas we have been stuck in for the past 40 or 50 years