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Human Life Is a Statistical Improbability

In A Short History of Nearly Everything, Bill Bryson marvels at what makes up human life:

No one really knows, but there may be as many as a million types of protein in the human body, and each one is a little miracle. By all the laws of probability proteins shouldn't exist. To make a protein you need to assemble amino acids…in a particular order, in much the same way that you assemble letters in a particular order to spell a word. [For example, to make collagen,] you need to arrange 1,055 amino acids in precisely the right sequence….
The chances of a 1,055-sequence molecule like collagen spontaneously self-assembling are, frankly, nil. It just isn't going to happen. To grasp what a long shot its existence is, visualize a standard Las Vegas slot machine but broadened greatly—to about ninety feet, to be precise—to accommodate 1,055 spinning wheels instead of the usual three or four, and with twenty symbols on each wheel (one for each common amino acid). How long would you have to pull the handle before all 1,055 symbols came up in the right order? Effectively forever. Even if you reduced the number of spinning wheels to two hundred, which is actually a more typical number of amino acids for a protein, the odds against all two hundred coming up in a prescribed sequence are 1 in 10 to 260 (that is 1 followed by 260 zeros). That in itself is a larger number than all the atoms in the universe….
Yet we are talking about several hundred thousand types of protein, perhaps a million, each unique and each, as far as we know, vital to the maintenance of a sound and happy you.

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