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The Improbability of Richard Dawkins

Although it's been out now for 13 years, The God Delusion    by Richard Dawkins still sets the standard for 21st century atheist polemics. Both lionized by atheists and demonized by some believers, he is deserving, I think, of neither. I've followed Dawkins for a while, mostly because of his particular pronouncements on the "improbability" of God. This thought intrigued me, because as someone  who has studied advanced probability (all right, I took a senior level math course in college), I was curious how that improbability was determined, and the methodology behind it. Dawkins's argument appears in Chapter 4, and reduces to this: 1. The origin of life is an extremely improbable event. (on that we all agree). 2. The history of life has been an inexorable progression from simple to complex. (conceded by most, except for young earth creationists). 3. Darwinian evolution is the one thing we know that builds increasing complexity over time. (highly tendentious