Real Life Answers

The Elegant Universe

I’ll do my best to minimize the nerdiness of this post, but I make no guarantees.

Something that always puzzled me was how two rational, intelligent people could take the same information and come to opposite conclusions. Two physicists observe a universe governed by an elegant set of rules, with parameters apparently minutely tuned to allow life to develop, and one sees a Creator and the other sees  a coincidence. Is one interpreting the data wrong? Is one being fooled by wishful thinking? Not necessarily. There’s no rule that says two people seeing the same data must come to the same conclusion. In fact, there is a rule–Bayes’ Rule–that says just the opposite: the conclusion you draw from observing data depends not only on the data itself but on the beliefs you had before observing the data. So two people can draw equally valid but different conclusions from the same data, depending on what prior beliefs they are bringing to the analysis.

Here is Bayes’ rule applied to the probability that God exists, given some data we observe about the universe. This data could be the fact that the physical world seems to obey an orderly set of rules, it could be a miraculous experience, or anything else that might affect our belief in God. The probability that God exists, given some data about the universe  is equal to the probability of observing that data if God did exist, multiplied by our prior probability that God exists (our belief before observing the data), divided by the overall probability of observing the data. In mathematical form, just to keep things clean:

Pr(God exists given data) = Pr(data given God exists) x Pr(God exists) / Pr(data).

So what does this mean? It means the higher somebody’s prior probability that God exists, the higher the probability they will assign to God existing even after observing the data, and vice versa, somebody with a very low prior probability of God existing will tend to give a lower probability to God existing, even after observing the same data. In fact, if you look carefully, somebody who has a zero prior probability of God existing (an Atheist) will continue to be an atheist, no matter how much evidence he or she is confronted with, since zero times anything is … zero!

So then how do dramatic conversions happen? Wouldn’t Saul from the New Testament (before he became Paul) have had a zero prior probability that Jesus is the Son of God? Or Alma the Younger from the Book of Mormon? Does this Bayes’ Rule framework not apply here? Actually, I think it applies perfectly. It’s true that if you multiply zero by anything (finite) you get zero, but when you divide zero by zero you can get anything! So if we take our formula seriously, the only way for a recalcitrant unbeliever to be converted is to somehow divide by zero–they need to have an experience that they would have considered to have zero probability of happening. In other words, an epiphany. Saul, in hearing the voice, and Alma, in seeing the Angel, observed “data” that they would have thought had zero probability of occurring, but there it was all the same, and the result of incorporating the experience into their beliefs was conversion.

One possible criticism of Bayes’ rule as a useful framework here is the critical role the prior beliefs play in the final conclusion. After all, it says nothing about where that prior probability comes from. It could just be the subjective probability that each person chooses or is just born with, or the product of upbringing, environment, etc. And worse still, for any potential piece of evidence or data you could confront me with having some bearing on whether God exists, I could generate any final (posterior) probability of God existing by just choosing a different prior probability. So if we’re free to choose our prior beliefs, then Bayesian analysis just perpetuates whatever initial prejudices we had, right? Is this just teched-up confirmation bias?

Not quite. True, we may start out with different prior probabilities that are functions of preferences, choices, upbringing, etc., but once we start observing data and updating our beliefs, as we incorporate more and more evidence into our beliefs, the importance of the initial prior belief fades away. Indeed, you can start from any initial beliefs about God (as long as the probability you assign initially is less than one and greater than zero–unless you’re counting on an epiphany!) and eventually your beliefs will converge on the truth with more and more certainty–no  matter what your starting point was, as long as the initial probability was greater than zero, even if ever so slightly.

So the only requirement to develop faith is to start out allowing at least a shred of possibility that God exists (or whatever the spiritual truth is we are seeking faith about), and then to actively and honestly seek out and incorporate evidence into our beliefs. Easier said than done, but if Bayes was right, it’s a mathematical fact you will get to the truth!

Thomas Bayes