« Saturday Gumpagraph | Main | Today's Bush Joke »

## March 18, 2006

Bad Math | Science/Technology |

Via Pharyngula, I've discovered an interesting new blog, Good Math, Bad Math, in which a computer scientist named Mark Chu-Carroll looks at ways that people — creationists, especially — misuse mathematics in their arguments. Several recent posts of his debunk an argument one hears all the time. It's an argument that happens also to be a pet peeve of mine, and I think it's worth looking at.

The argument allegedly proves that life is too improbable to have arisen without a designer. It goes something like this. Proteins are constructed by chaining together amino acids (of which there are 20). Consider a relatively simple protein that consists of 100 amino acids. At each of the 100 positions in the chain, there are 20 possible choices, so the number of ways of constructing a 100-amino-acid protein is 20 to the 100th power, which is about 10 to the 130th power. So the probability of chaining together randomly selected amino acids and getting the given protein is 1 divided by 10 to the 130th power. Now 10 to the 130th power is a BIG number, MUCH bigger than the number of particles in the known universe, for example, so the construction of a protein is clearly too improbable (so the argument goes) to have happened by chance. QED

There are a number of problems with this argument. For one thing, the geometry of amino acids is such that not all chains are possible. But let's leave that aside. Let's stipulate that the probability of constructing our 100-amino-acid protein is 1 divided by 10 to the 130th power. Does the extreme improbability of that construction prove anything?

As you might have guessed, the answer is no. As Chu-Carroll points out, if you take two distinguishable decks of cards and shuffle them together, the number of possible shufflings is about 10 to the 160th power. So the probability of any given outcome when the decks are shuffled is about a million trillion trillion times *less* likely than the construction of our protein. It's a million trillion trillion times more miraculous, you might say. But that obviously doesn't mean that it's impossible to shuffle two decks of cards. The probability of a given outcome when shuffling is very, very small, but the probability of getting *some* outcome is 100%.

The fallacy in the protein argument is the implied assumption that life requires exactly *that* protein for it to work. Trying to create exactly *that* protein by random chance is like shuffling the decks and trying to get a specific outcome. Almost impossible. But organisms can function with lots of possible protein configurations. There is nothing unique about the protein configurations that have arisen. Lots of others would do. You can't look at the one that happened to arise and declare that its improbability proves that it couldn't have happened randomly, any more than you can look at the particular outcome of card shuffling and say that it proves that card shuffling is an impossible act. In either case, you're taking the result that happened to have occurred and working backwards. You're placing a constraint on the outcome that wasn't there when you were doing the shuffling in the first place.

What do you suppose happens when creationists play cards? Do they just sit there stumped, waiting for God to shuffle?

**Update:** [3/19 2:01PM] If you found that interesting, check out this two-part post from last year that looks at the fallacious use of probability arguments against evolution from a different angle.

Posted by Jonathan at March 18, 2006 08:01 PM

## Comments

Maybe creationists think of Homo sapiens current configuration as perfect. Oh, wait, the bible accounts for sin, I'm sorry.

Posted by: Jeff at March 18, 2006 10:41 PM