Bah! My brain is flummoxed by a familiar but long forgotten problem: The tendency of some of the fundamental equations of cosmology to wrap around and eat themselves in a bewildering and irritating manner. It doesn’t help that the notation and conventions in the literature are rather flexible as well. There must be 50 different ways of writing down the Friedmann equation in equivalent but subtly different manners. Blah... My head’s tired. It’s Friday and it doesn’t want to be wrestling with cosmology.
But there it is. It needs to get done. I have a class on Tuesday, and I need to have both a new problem set and a set of lecture notes ready. So I will return to trying to find a clean and clear way to show that the Friedmann equation predicts a universe that evolves away from flatness with time. This is a well known result, that seems to be addressed in a unique way in every textbook and set of lecture notes I have access to. Worse, it seems that they all seem to suffer from a bad case of handwaving or “then a miracle happens” syndrome in the math: making a leap that seems altogether reasonable on first glance, but which doesn’t seem to follow directly upon close examination.
Ah well, that’s why they pay me the big bucks right? To make sense of the self-eating-snake equations map out their curves for all to see? Boldly going where students would otherwise fear to tread? Which, in self-eating style brings us back to flags and snakes. Or Pretzels. Something topologically complex that wraps around itself endlessly. Like a closed universe. See, again I can’t seem to escape. I seem to have become trapped inside a semantic event horizon, with no way out but to hope I can quantum tunnel through the barrier and Hawking radiate myself to another topic.
Or maybe just give up and get back to work.
But there it is. It needs to get done. I have a class on Tuesday, and I need to have both a new problem set and a set of lecture notes ready. So I will return to trying to find a clean and clear way to show that the Friedmann equation predicts a universe that evolves away from flatness with time. This is a well known result, that seems to be addressed in a unique way in every textbook and set of lecture notes I have access to. Worse, it seems that they all seem to suffer from a bad case of handwaving or “then a miracle happens” syndrome in the math: making a leap that seems altogether reasonable on first glance, but which doesn’t seem to follow directly upon close examination.
Ah well, that’s why they pay me the big bucks right? To make sense of the self-eating-snake equations map out their curves for all to see? Boldly going where students would otherwise fear to tread? Which, in self-eating style brings us back to flags and snakes. Or Pretzels. Something topologically complex that wraps around itself endlessly. Like a closed universe. See, again I can’t seem to escape. I seem to have become trapped inside a semantic event horizon, with no way out but to hope I can quantum tunnel through the barrier and Hawking radiate myself to another topic.
Or maybe just give up and get back to work.
1 comment:
Mind-boggling.
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