Assuming a universe that will collapse in on itself, and repeat a big bang and collapse over and over...

All matter exists as a singularity. There is no way to differentiate between matter, as all matter is identical in form, energy and position.

When the big bang happened, there must have been a mathematical construct to define which bit of matter blew in what direction. Whether it was a perfectly even distribution, or perhaps something reminiscent of fractals.

This leads us to a couple fun thoughts:

1. Did I live my life, exactly as I am now, an infinite amount of times in the past, and doomed to live it an infinite amount of times in the future?

2. If we could see the whole of the universe, is there a pattern? Ie, are there several other mes with identical lives in far distant galaxies that are identical to our own?

3. Is my existence a mathematical tautology, and completely intrinsic to the universe's existence?