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universe ruled by integers

Only not so fast there friend... I think what the gentlemen might have been discussing is the possibility of a universe where everything (at least in geometry) has an integral relationship. That would be most everything :) Consider that if it did there would be no real numbers. That's going to be bad for manifold reasons. Physics just got broken! As did things like compound interest. I am just a humble engineer, but I dont think life itself can exist without irrational numbers. I'll say NO, and throw in the fact that you meant to write "an irrational constant whose value is set exactly 3.14" ;) So there! take that and stuff.

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