On 4/21/2013 11:06 AM, WM wrote: > On 21 Apr., 16:56, netzweltler <reinhard_fisc...@arcor.de> wrote: >> On 21 Apr., 16:03, WM <mueck...@rz.fh-augsburg.de> wrote: >> >> >> >> >> >>> On 21 Apr., 12:22, netzweltler <reinhard_fisc...@arcor.de> wrote: >> >>>> On 21 Apr., 11:07, WM <mueck...@rz.fh-augsburg.de> wrote: >> >>>>> On 21 Apr., 10:02, netzweltler <reinhard_fisc...@arcor.de> wrote: >> >>>>>> On 20 Apr., 19:03, WM <mueck...@rz.fh-augsburg.de> wrote: >> >>>>>>> All atoms of the accessible universe and all positions they can take >>>>>>> belong to a finite set. >> >>>>>> How do we prove, that the number of possible positions an atom can >>>>>> take along a line of 1 cm is finite? >> >>>>> By accepting quantum mechanics and excluding theology (these >>>>> assumptions taken as axioms for those who believe (as an axiom) to >>>>> need axioms) a proof is given here:http://arxiv.org/ftp/arxiv/papers/0709/0709.4102.pdf >>>>> pages 2-3. >> >>>>> Regards, WM >> >>>> What about a position between two quanta? Should there be no decimal >>>> fraction for a position between two adjacent quanta along this line of >>>> 1 cm?- >> >>> Quantum theory tells us, contrary to Einsteins's false beliefs, that >>> unmeasurable events do not exist. The electron or photon does not >>> simultaneously have fixed position and momentum (that would contradict >>> some results of interference experiments). >> >> 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.
This is why negation and identity relate to the modern mathematics of boundaries. What mathematics would that be?
> "What St. Thomas affirms on this point > about angels or intelligences ('that > here every individual is a lowest > species') is true of all substances, > provided one takes the specific > difference in the way that geometers > take it with regard to their figures." > > Leibniz > > > > "If m_1, m_2, ..., m_v, ... is any > countable infinite set of elements > of [the linear point manifold] M of > such a nature that [for closed > intervals given by a positive > distance]: > > lim [m_(v+u), m_v] = 0 for v=oo > > then there is always one and only one > element m of M such that > > lim [m_(v+u), m_v] = 0 for v=oo" > > Cantor to Dedekind >
To have parts, one must have limits delineating parts.
The interval when a body is at rest is different from the interval when a body is in motion. There is a boundary.
Associated with macroscopic objects will be an acceleration. Thus, there will be a force.
Impulse is force applied over time. As noted in the link,
If one considers the family of bell curves having the an area equal to a given impulse, but with decreasing intervals of time, one obtains the Dirac delta which can be used to model impulse as noted in the link