Olbers paradox

Anton Sherwood (dasher@netcom.com)
Wed, 5 Nov 1997 19:29:47 -0800 (PST)

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