Re: SUO: Re: Proposed SUO Content Outline
Pat,
That is essentially what I do by assuming that the coordinate
space is Euclidean 4-space. We can use a 4-tuple:
>Actually it occurs to me that we could insist that a coordinate be a
>finite n-tuple of values each of which must be from some totally
>ordered set. This would give a natural notion of dimension, and it
>would allow 'spaces' to be things like discrete pixellated surfaces
>as well as smooth manifolds. It would even allow things like the word
>count in a text to be a kind of dimension; but it would not be
>completely vacuous.
And please note that Section 2 on continuous processes
is followed by Section 3 on discrete processes:
>John, I think your requirement of differentiability is too strong.
>There are nondifferentiable surfaces even in geography, for example.
>Why do you need this? In fact, why do you even need to assume
>continuity? After all, computer screens have coordinate systems
>without continuity. If you relax these requirements I bet that one
>could apply dimensions even to mereology.
Any adequate theory must be able to support both differentiable
functions (such as the electromagnetic fields, QED fields, etc.)
and discrete approximations, such as the ones that you mention
here and I mention in Section 3 of the causality paper.
You need both. I approach the problem by showing that you
can approximate any continuous system to any desired degree
of granularity by a discrete system. Then the remainder of
my paper is based on describing discrete processes.
Bottom line: You need both, and you also need to be able
to move back and forth from one to the other.
John