that time, unless we have colonized beyond the Solar System, mankind will long since have died out, extinguished along with our sun!
All of the Friedmann solutions have the feature that at some time in the past (between ten and twenty thousand million years ago) the distance between neighboring galaxies must have been zero. At that time, which we call the big bang, the density of the universe and the curvature of space-time would have been infinite. Because mathe- matics cannot really handle infinite numbers, this means that the general theory of relativity (on which FriedmannΓÇÖs solutions are based) predicts that there is a point in the universe where the theory itself breaks down. Such a point is an example of what mathematicians call a singularity. In fact, all our theories of science are formulated on
