On 1/23/2020 5:22 PM, Lawrence Crowell wrote:
On Thursday, January 23, 2020 at 5:56:08 PM UTC-6, John Clark wrote:
On Thu, Jan 23, 2020 at 6:35 PM Bruce Kellett <[email protected]
<javascript:>> wrote:
/> You seem to have missed an important little word in Brent's
post: Brent talked about needing an infinite RANGE of
coordinate values for an infinite universe/
OK fine, so in a finite universe you'd only need a finite RANGE of
coordinate values printed on a finite number of labels for all the
finite number of points in that finite universe. But as I said, if
new points are constantly being made at an accelerating rate in
that "finite" universe then you're going to run out of those
finite labels.
> /nothing whatsoever about having only a finite set of
distinguishable labels....../
Nothing whatsoever? He specifically said a "range of coordinate
values to *label* all the points". And if a label isn't
distinguishablethen it isn't a label.
John K Clark
If you have a sphere that is expanding the coordinate grid comoves
with that. The spacing between coordinate points increases. The number
of points needed to specify things does not need to change.
But if "the spacing increases" means anything at all, it means the range
of coordinate values to define those points must increase.
Brent
The points on a space are not physical information. In some ways they
are just mathematical fantasies of sorts that happen to satisfy
requirements of a self-consistent axiomatic system called point-set
topology. If the sphere has constant curvature the only intrinsic
piece of information you need then is just one point, which you define
as your coordinate. All other coordinates can be derived.
If the 3-sphere has lots of hills and valleys then you do need to
specify more points. In this situation there is more real information.
If these hills and valleys becomes infinitely craggy in a fractal then
the amount of information required to specify this sphere has
unbounded Kolmogoroff complexity. But for a smooth sphere, and one
that is expanding so it becomes every smoother, does not at all
require added information to describe it as it expands.
LC
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