Originally Posted by
Malintent
Yea, I get that... Math, as a model, can do more than the universe can do. While precision can reach into infinity, there is an upper limit of what is USEFUL.
I am a wood worker. Precise cuts (especially in very hard woods) is very important. Do I need an electron microscope attached to my table saw to get my cuts "perfect". Of course not. I ARBITRARILY choose an upper limit of precision... down to maybe a 32nd of an inch, at best.
1/32 of an inch, in my thought experiment, would cause an error greater than the width of our solar system (galaxy?, sector?,... a lot).
I arbitrarily chose the plank length as the smallest distance... the chosen degree of precision for this experiment. I also arbitrarily chose the diameter of the universe for the chosen magnitude.
I understand that using a mathematical model allows us to divide angles and distances infinitely, but lets just say we are galactic woodworkers that only really care about useful measurements... forget my statement of "the most" precise, or any notion of "maximum describable using any tool", imagined or real. I apologize if that caused confusion. For this thought experiment, 27.4 billion is the largest number and 1 plank is the smallest. That is the range of numbers that exist in this imaginary universe.