On Nov 25, 2013, at 2:51 PM, Joe Niederberger <firstname.lastname@example.org> wrote:
> R Hansen says: >> And, if we take that the smallest actual "point" on a drawn line would be represented by the centers of the molecules or atoms of the ink/lead, then I would suspect that those locations are all at irrational distances from the end (transcendental in fact). > > Really? You think physical distances are truly all irrational? And then what distance could ever be demarcated as 1?
Not only irrational, but transcendental (not algebraic). I am talking about the actual positions of the molecules and atoms, although they are moving, but you know what I mean. The argument is not much different than what you said about the improbability (impossibility) of a ray of light ever hitting a particular number. I am saying that said ray will not even hit any algebraic number. We know the ray of light will hit a number, I am saying that number will always be transcendental. But don't ask me for a formal proof.:)