Pet Peeves

Fun with conditional probabilities

Yes, mathematics is sometimes hard to understand. Probability theory is a prime candidate where “common sense” might mislead you. And once you venture into conditional probabilities (“given A is true, what’s the probability of B being true as well?”) things get tricky.

A good example is the following statement: “The orbit of our earth so incredibly fine tuned to the requirements of intelligent life, that this is a strong indication that a higher being was involved.”

This may sound reasonable at first glance, but it’s completely wrong. Let me rephrase the statement to make this clear:

“What is the probability that the environment here on earth is suitable for the development of life, given the fact that this question is asked by a person whose species evolved here on this planet?”

The answer is 1 (100% probable).

Or in other words, if the environment here on earth were hostile to us, we wouldn’t be here to ask this question. And indeed, there are billions of planets, where nobody is asking this question.

So no, these considerations do not provide an argument regarding the existence of god.

(Btw, the same reasoning applies to arguments concerning the fundamental constants of this universe. In that case, you just need to assume an infinite number of universes with varying parameters, as a number of physicists postulate.)