From: scerir (scerir@libero.it)
Date: Tue Feb 05 2002 - 02:41:53 MST
Eliezer:
> The term "dissect" is also misleading. The pieces here cannot be created
> by any number of cuts, no matter how large. The sets of points do not
> have analytic boundaries. You can't create them by "cutting", even with a
> curved knife.
Yes, these piezes are not 'measurable'.
> Furthermore, you cannot cut up any object composed of a finite number of
> atoms. This isn't, as sometimes stated, because atoms are "too large".
> Even if the object were composed of an infinite but countable number of
> atoms, it wouldn't be enough.
...... thinking about the 'tesselation' of the quantum field. The introduction of cellular
automata in theoretical physics (Wolfram et al.) initiated several speculations
concerning their applicability to field theory (atomization of a continuous field
function into some discrete lattice of locally - or even nonlocally - connected array
elements, evolving in a discrete time). The amount of information per unit volume of
this discrete space-time lattice would be finite. The field function takes on a
countable number of states. The lattice representation is equivalent to a cellular
automaton. But I do not know if this has something to do with Banach & Tarski.
s.
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