Why should you never be 100% sure of anything?

Because if you are 100 percent sure, no evidence can ever change your mind, not even overwhelming evidence. That's the core of Cromwell's rule, a principle from Bayesian inference, the method of reasoning that treats beliefs as probabilities and updates them as new information comes in. In Bayes' theorem, your new belief is your old belief adjusted by the evidence. Start at exactly 0 or exactly 1, and the arithmetic locks you there forever.

The statistician Dennis Lindley named the rule after Oliver Cromwell, who in 1650, shortly before the Battle of Dunbar, wrote to the leaders of the Church of Scotland: "I beseech you, in the bowels of Christ, think it possible that you may be mistaken." Lindley's own example was more playful. You should leave a little probability, even one in a million, that the Moon is made of green cheese. Otherwise, if an army of astronauts came back carrying samples of the cheese, you would remain unmoved.

A coin puzzle shows what's at stake. A stranger has two fair coins and one with heads on both sides, and tosses one of them three times: heads, heads, heads. Tim assumes any coin could have been picked and calculates an 80 percent chance it's the trick coin. Susan is certain the stranger used a fair coin. However many heads follow, Tim's confidence keeps rising, while Susan's never budges, and they never come to agree. The only exceptions to the rule are things true or false by logic alone, like 2 + 2 = 4.