PHILIP W. ANDERSON is a physicist at Princeton University. He is the author of Concepts in Solids.
Isn’t God very improbable? You can’t, in any logical system I can understand, disprove the existence of God—or prove it, for that matter. But in the probability calculus I use, he is very improbable.
There are a number of ways of making a formal probability theory which incorporate Ockham’s razor (the principle that one must not multiply hypotheses unnecessarily). Two of them are Bayesian probability theory and minimum entropy. If you have been taking data on something and the data are reasonably close to a straight line, these methods give us a definable procedure by which you can estimate the probability that the straight line is correct—not the polynomial that has as many parameters as there are points, or some intermediate complex curve. Ockham’s razor is expressed mathematically as the fact that there is a factor in the probability derived for a given hypothesis that decreases exponentially in the number n of parameters that describe your hypothesis. It is the inverse of the volume of parameter space. People who are trying to prove the existence of ESP (extrasensory perception), for example, abominate Bayesianism because it strongly favors the “null hypothesis” and beats them every time.
Well, now, imagine how big the parameter space is for God. He could have a long gray beard or not; be benevolent or malicious in a lot of different ways and over a wide range of values; have a variety of views on abortion and contraception; like or abominate human images; like or abominate music—and the range of dietary prejudices he has been credited with is as long as your arm. There is the Heaven-Hell dimension, the one-versus-three question, and I haven’t even mentioned polytheism. I think there are certainly as many parameters as sects, or more. If there is even a sliver of prior probability for the null hypothesis, the posterior probability of any particular God is pretty small.