From: Anton Sherwood (dasher@netcom.com)
Date: Wed Nov 05 1997 - 20:29:47 MST
Anders Sandberg wrote:
: > No. The amount of radiation you get from a star decreases with the
: > square of the distance. But the number of stars grows with the square
: > of the distance, so the total radiation from a given distance is
: > approximately constant.
Greg Butler writes
: I don't understand how one can compare one infinite number with
: another (such as an infinite volume of space and an infinite number of
: stars). If there is an infinite space per star, it seems possible that
: it won't get filled. One infinite amount does not necessarily equal
: another. For instance, how big is an infinite amount of space squared?
: Is it bigger than a "regular" infinite amount?
Imagine an infinite row of identical stars, equally spaced along a
line. From any point in space, this would look exactly the same as
one star between two infinite parallel mirrors.
Now imagine an infinite cubic lattice of stars: this is equivalent
to one star in a mirrored cube. Where's the infinite space for it
to dump its light?
The cubic lattice is obviously a simplification, but your infinite
homogeneous universe is qualitatively no different.
There is a way out: Mandelbrot suggests that the distribution of stars
is a fractal dust with dimension less than 3 - which means that the
number of stars within a given radius increases more slowly than the
volume of the sphere. As you go out, you find ever-bigger empty spaces.
Anton Sherwood *\\* +1 415 267 0685 *\\* DASher@netcom.com
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