Date: Apr 22, 2013 7:27 AM
Subject: Re: Matheology §252
On 21 Apr., 21:32, netzweltler <reinhard_fisc...@arcor.de> wrote:
> On 21 Apr., 18:06, WM <mueck...@rz.fh-augsburg.de> wrote:
> > On 21 Apr., 16:56, netzweltler <reinhard_fisc...@arcor.de> wrote:
> > > If non-measurable distances don't exist, don't we face another
> > > problem? Let's say, d is the smallest distance that can be measured.
> > > Distances below d don't exist. So, d/2 is a non-existing distance. Is
> > > it still valid, that d/2 + d/2 = d then? I mean, how can distance d
> > > exist, if it is composed of two non-existing distances d/2?-
> > The old problem of Aristotle: How can a resting body come to move?
> > There must be a point of time where rest and movement are
> > simultaneously realized. But that is impossible.
> > Concerning mathematics, there is d/2 even for d = 10^-1000000 fm.
> > Thats facilitated by invention of the system of fractions. But you had
> > asked for real atoms.
> Yes. I am still asking for _real_ distances.
> If there is a d/2 for any d, how can we say, that the number of
> positions of an atom is finite?
In reality there is not a d/2 for every d. The shortest possible wave
cannot be shortened and cannot be used to find a shorter d than its
wavelength or a finite fraction of it. Further, if the shortest
possible wave is created, there are no atoms marking a distance any
longer and no men to measure it, because all energy has been used to
create the wave.