V. Is God probable?

And are we? Statistics has been (ab)used to argue both for and against God. Can it be justified? What about statistical inference about miracles or studies on the efficacy of prayer? What about Intelligent Design?

Miracles and Statistics

If you tested your new pain killer on 1000 people, but only 724 of them reported that it worked, how sure can you be that it is effective, and that the people didn’t just get better all by themselves? And if no one reported adverse symptoms, can you really conclude that it has no side effects? How would this change if you had doubled the sample size? Although science generates useful data, statistics turns this data into meaningful information. The way you go from 100 experiments in a lab to a report describing how sure you are about your results is called statistical inference – drawing conclusions about what you observed in a rigorous, honest, and transparent way. It is a fascinating field, and often counter-intuitive one – one of those fields where you should only trust someone over 60. Experts regularly falter; “the mistakes are all there – waiting to be made” as chess grandmaster Tartakower observed.

So what about when you aren’t studying pain killers, but the reports of a formerly dead man walking around? How sure can you be that a miracle had happened? How many witnesses do you need to conclude that it was more probable than not that a miracle occurred? David Hume (a famous dead guy himself) said that it would always be more probable that the witnesses were mistaken or lying, than that a miracle had really occurred. There can never be enough witnesses according to Hume. Mathematician Charles Babbage (yet another FDG) took exception to this, and by applying the rigor of mathematical statistics to the question of miracles, proceeded to correct Hume’s fallacious thinking. In the late eighties W.H. Kruskall, chairman of the American Statistical Association, also entered the fray and tried to overturn Babbage’s conclusion. The saga continues, and even of such eminent intellects it may be said that often statistics is used the way a drunk man uses a lamppost; more for support than illumination.

Enter the statisticians

A fascinating paper presented by D.J. Bartholemew to the Royal Statistical Society [1], catalogues various areas where statistics have been brought to bear on theological questions: historiography and miracles, the anthropic principle and physics, studies of Biblical authorship, the efficacy of prayer, and the philosophy of conditional probability. The paper itself isn’t as interesting as the responses it invited from the audience. Many of the big names in statistics were there – for all their pomp the Brits are brilliant statisticians. But could statistics offer any help in the end? The rigour required by statistics certainly does aid clear thinking on these questions, and Bartholomew noted that. But when properly applied he is forced to conclude that

Although one may feel a certain sense of intellectual exhilaration in applying elementary probability ideas on the grand scale it is clear that the results which they yield are meagre. The most that one can claim is that some clarification and assessment of the strengths of competing arguments can be given.

In other words, the conclusions reached by the application of statistics are either so self-evident as to not require statistics, or else so opaque as not to be meaningful. In an incisive comment by R.N. Curnow during the vote of thanks, he observed that

Perhaps an argument for the existence of a supreme being is that, as Professor Bartholomew has shown, nobody except a supreme being could have made it so difficult to decide whether or not there was a supreme being! More seriously for me, the lack of randomness, except as a descriptive tool, forces me to concentrate on questions of purpose and therefore to questions not about the existence of a supreme being, but about the definition, nature, and purpose of that being… I shall continue to take refuge in the complex but easier areas of molecular evolution.

Of course much good, secular academic work has been done since 1988, especially by Intelligent Design proponent William Dembski. Some of it concerns design and the probability of the universe being the way it is [2], and some of the arguments concern semiotics. But Bartholomew’s paper serves a warning that applying inferential statistics to the question of a supernatural being yields ‘meagre’ results, i.e. it doesn’t tell you anything you don’t already (want to) know [3] Intelligent Design arguments are good and necessary, and some people have been convinced by them – Anthony Flew, who was one of the world’s most famous atheist philosophers was one of them. But as noted philosopher Richard Swinburne found when he tried to use formal Bayesian statistics to argue for God, most peoples’ assessment of God’s probability comes down to their prior commitments, not the evidence.

So, is he probable or not?

Statisticians use p-values to demonstrate how sure they are about an answer. Simply put, the p-value is the probability of getting the result you observed in an experiment, had the outcome been completely random. So in our painkiller experiment, the p-value would indicate chances of people getting better all by themselves, the pills having nothing to do with it. If God were probable, at what p-value would you start trusting him? The question is absurd. In one sense, God is probable as the best explanation for the vast improbability of us. We would expect nothing less if he created the whole show, and there are some fine arguments out there. Most show what is actually quite obvious. As Paul noted long ago, his invisible attributes, namely, his eternal power and divine nature, have been clearly perceived, ever since the creation of the world, in the things that have been made. But on the other hand, if you are looking for a probable God, you are missing the point. In a far more significant existential sense, God isn’t probable; he’s not that kind of thing, in the same way that he isn’t round or square. We Westerners get all hung up about these questions, but they are the wrong questions to ask. We are trapped within this bubble which most people think of as ‘enlightened’ or ‘modern and scientific’. But our science has no category for this kind of thing God is, which means that our usual modes of knowing – through experiment, proof, etc., are like insisting that God is a nail because we only know how to use a hammer. Statistician Andrew Vickers notes that [4]:

On the subject of tools, let me tell you that I own both a screwdriver, which I use a lot, and a crowbar, which I have used once or twice. If anyone told me that they used the crowbar a lot and the screwdriver rarely, I’d start looking around for a police officer.

We are the guys with the crowbars, trying to force God into the proof-boxes we can open. But knowing God and proving God are two very different things. Unfortunately for some people, he seems to be more interested in the former than in the latter, and there may be good reason for this. When you look around you at the way people behave, and at all the evil in the world, you realise that our problem is not a lack of information. Most people don’t believe the things they believe, and act the way they do, because God is too improbable. Frederick Beuchner said it beautifully:

We all want to be certain, we all want proof, but the kind of proof we tend to want-scientifically or philosophically demonstrable proof that would silence all doubts once and for all-would not in the long run, I think, answer the fearful depths of our need at all.  For what we need to know, of course, is not just that God exists, not just that beyond the steely brightness of the stars there is a cosmic intelligence of some kind that keeps the whole show going, but that there is a God right here in the thick of our day-by-day lives who may not be writing messages about himself in the stars but who in one way or another is trying to get messages through our blindness as we move around down here knee-deep in the fragrant muck and misery and marvel of the world.  It is not objective proof of God’s existence that we want but, whether we use religious language for it or not, the experience of God’s presence. That is the miracle that we are really after.  And that is also, I think, the miracle that we really get.

[1] D.J. Bartholomew. Probability, Statistics and Theology in Journal of the Royal Statistical Society Vol. 151, No. 1, 1988 pp.137-178.

[2] The Design Inference: Eliminating Chance Through Small Probabilities, Cambridge University Press

[3] Bartholomew has written some books as well, and I’d be interested to read them. God of chance  and God, Chance and Purpose.

[4] So, what’s a p-value anyway? Andrew Vickers