My intuition is there's some fundamental equivalence between time and some information-theoretic concept unknown to me. McTaggart might have been right to recognize the importance of change, but the card exercise is also fundamentally representational, and therefore informatic, in nature. A different card exercise that's maybe more realistic is one where you have an infinite number of cards, randomly shuffled, and are tasked with sorting them in order. Is that even possible? It seems to me the possibility of that versus impossibility of that is related to the nature of time.
