Have you ever wondered whether our universe could just have existed forever? Perhaps you have wondered about the possibility of infinitely old civilisations passing traditions down from the unending past? I was at a conference recently (Bonn international workshop on ordinal computation). At this conference we were talking about various sorts of infinite computation (this is what my PhD degree is on). One of these types of infinite computation (which a fellow researcher and I dreamt up) was a form of computer that has always been running and always will be running.
So this is a rough model for the idea of a universe that has existed forever and will exist forever. So what I'm going to tell you are some of the astonishing results that we came up with (In everyday not mathematical terms).
Firstly we needed to define how such universes are to be understood. It was obvious that not every universe makes sense as something that has always existed. The best example of this is a universe that always expands (at a steady rate). Clearly at some stage in the past the stuff in the universe must all have been in one place and there could not have been a time before that. Also expressing some rules that the universe must follow does not uniquely define a universe if that universe may have existed forever (even if you know how the universe looks now that can be the case). You might have a universe with only a ball in it and your rule of physics might be that the size of the ball increases by 2 times every second and then decreases by 2 times the next second in a cycle. Such a universe is not fully defined (we don't know how big the ball is when its contracted!).
So we specify that the rules of the universe must be written in such a way that there is only one possible time history of the universe. To do this we have to allow ourselves to relabel the year 0 in the universe but this is no problem. We also have to rule out silly universes in which nothing at all happens or in which events are cyclic. Once we've done this an amazing thing happens. The very existence of a universe that satisfies some finite list of rules tells us fundamental truths about mathematics. For any statement about whole numbers there is a description of a universe that has a possible history only if that statement is true! And for any such statement there is a set of rules so that from within a universe following those rules you can tell whether that statement is true or not.
So its like finding an ancient civilisation on an old planet somewhere. They've been around forever, performing these rituals. Just knowing that tells you fundamental truths about rational thought. In fact this researcher and I figured out exactly what sort of questions you could hope to answer but here the details don't translate across very well to philosophy. Nevertheless I hope you found this interesting!