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To return to cell division, 3 billion years = 1,095,000,000,000 days. Using your figure, we're talking about 12,975,750,000,000,000,000,000,000,000,000,000 cell divisions, and we're being conservative in our estimate. To produce 2.3 billion base pairs of information, we need roughly 1 in every 5,641,630,434,782,610,000,000,000 cell divisions to produce 1 base pair change.

Richard Dawkins in The Ancestor's Tale says the mystery isn't that there isn't enough time to evolve all the phenotypes we see around us, but that there is too much time to evolve all the phenotypes. IOW, he says it's a mystery why there aren't more species rather than how did all the species evolve in the time available.

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