It's not really clear what you mean by the brain accumulating noise. An analog computer can suffer from compounding imprecision, because error bars carry forwar

It's not really clear what you mean by the brain accumulating noise. An analog computer can suffer from compounding imprecision, because error bars carry forward. We are analog computers in a vague sense, but as humans we aren't imprecisely crunching numbers all day such that our results are out of whack by nightfall... You could say sleep is like a reset for the brain, but that doesn't say much. Sleep is complex and relates to most everything else about an organism in complex ways.