bookmark_borderTheists, like Math Students, Need to Show Their Work

In my recent debate with Kevin Vandergriff, Vandergriff argued that biological evolution is evidence for theism. In support, he referred to the probability estimate of evolutionary biologist Francisco Ayala. According to Ayala, it is fantastically improbable that intelligent life on Earth is the result of unguided evolution.
Since I have a background in probability theory, I was most interested in learning how Ayala arrived at this conclusion and, more important, how he arrived at his precise quantitative value. While researching that estimate, I came across a 2007 paper by Frank Tipler which mentions this same probability estimate. Here’s an excerpt:

The well-known evolutionist Francisco Ayala has recently made this argument quantitative. He estimates that the probability of an intelligent species evolving on an Earthlike planet upon which one-cell organisms have appeared is less than 10 to the minus one million power! This number is so tiny that the evolution of intelligent life is exceedingly unlikely to have occurred even once. Ayala’s number is not contradicted by the fact that intelligent life exists on Earth. It is just exceedingly improbable that it exists anywhere in the universe (at least if the universe is finite in spatial size, as I shall argue in Section IV that it is). Ayala’s number depends on the assumption that gene changes upon which natural selection operates are essentially random. Evolution has no foresight. Mayr has emphasized that intelligence on earth is limited to the chordate lineage, so, he argues that if the chordates never appeared on Earth, neither would intelligence. But chordates first evolved more than half a billion years ago. These animals did not know that they had to evolve so that Homo sapiens would eventually appear. Natural selection can only operate during an animal’s lifetime. It cannot select a genome with the intent of using the genome a billion yeas later.

Tipler’s article provides no citation for the source of the Ayala probability calculation, however. Therefore, I emailed Ayala and asked him the following question.

… I understand the quotation accurately represents your view and that you took natural selection into account when making an estimate. My question, however, is this: where can I read the details of how you arrived at your estimate? So far, I’ve been unable to locate a book or article which goes into detail on the math used to derive this estimate.

Unfortunately I haven’t received a response from Ayala. If and when I do, I’ll post an update.
The moral of the story is this: when anyone quotes a scientist’s estimate of the probability of something, don’t be afraid to ask for the mathematical model used to produce that estimate. If the mathematical model isn’t published anywhere, you have the right to be skeptical of that estimate unless and until it can be independently reviewed.