The Universe and everything

So I know that there have been a lot of new theories about the beginning of the Universe since I learned about the Big Bang, but that's the oh-so-ancient premise I'll start my post on. Paul said in class on Monday that at some point the universe was computable - there were few enough particles and little enough space, I suppose, that you could follow what happened from microsecond to microsecond. My question is this: when did it stop being computable? Where was the breaking point? What emerged from this fledgling universe for the first or millionth time (depending on whether you believe in the Big Crunch or not) that eliminated all possibility of an ordered world? Was it humanity? Was it life? I can imagine being able to compute the doings of a single-celled organism: while (alive == TRUE){ if(hungry == TRUE) {find(food);} else {find(mate);} } When did it simply become too complex? It seems to me that "computable" is a term not dissimilar to "ordered" (but I'm willing to hear arguments against that semblance). And perhaps I'm falsely correlating things, but as the universe has gotten older and less computable, it has also...expanded. Thinking about all this, I suddenly came to a realization: What if, as the universe expands, it is moving away from order and closer to the entropy of complete non-computability? Is that even possible?