Tuesday, May 24, 2005

Pascal's Wager and Gambler's Ruin

Blaise Pascal was undoubtedly one of the more influential figures in the history of science and mathematics. I have been continually professionally and recreationally indebted to him, so to speak, for his work in probability, especially for the optimality of bold play when the game is less than favorable.

Bold play, for those who don't want to wade through the equations at the link (but should, especially if they have friends who go to casinos) is a strategy in which the gambler a) has a goal, and b) bets either his entire fortune, or the difference in his fortune + the goal and his fortune at each trial. It can be shown (see references above) that, compared to timid play (a gambler betting one unit of a fortune until his target is reached) bold play works much better. In fact, timid play is a disaster.

This in real life produces some amusing experiences in casinos when practiced: if you go into a casino with $200, and look to make $20 (the cost of the real cheap meal for 2 at these places generally), you'll spend about 15 minutes or so in the casino until you win that little amount most of the time, or you'll lose $200 a small percentage of the time. (But you will of course lose that money eventually. It's an unfair game after all.)

Pascal is also famous for saying that philosophy is "not worth an hour's trouble," which brings him even nearer to my heart. But, unfortunately, sometimes he didn't take his own advice, and at one such time, cooked up Pascal's Wager.


And so Joe Carter plays with Pascal's Wager today.

Now the main criticism I, and many others have with Pascal's Wager is its inherent insincerity and appeal to selfishness: even if you have grave doubts about the existence of a (Christian) deity, you should pretend that you don't have those doubts because it's in your selfish interest to do so.

Unlike gambling in a casino (where there is no pretense that it is anything other than a quid pro quo for your time and money versus a likelihood that you might win some money sometimes if you're not a degenerate gambler) this is not recreational, but is theoretically to inform the interstices of the most subtle aspects of your entire life. So the gambling metaphor falls apart unless you realize that the stakes are pretty important.

Which gets me back to Carter:

But how can we determine what is more likely when applied to an issue such as the ontological status of God? That is the question British theoretical physicist Stephen Urwin attempts to answer in his book, The Probability of God.

By applying Bayesian probabilities, a statistical method devised by 18th-century Presbyterian minister and mathematician Thomas Bayes, Urwin attempts to determine the probability of God’s existence. Since 50-50 represents “maximum ignorance”, Unwin begins with a 50 percent probability that God exists and then applies it to the following modified Bayesian theorem:

urwin formula.gif

The probability of God's existence after the evidence is considered is a function of the probability before times D ("Divine Indicator Scale"):

10 indicates the evidence is 10 times as likely to be produced if God exists
2 is two times as likely if God exists
1 is neutral
0.5 is moderately more likely if God does not exist
0.1 is much more likely if God does not exist

Unwin then uses the following lines of evidence and applies his own, admittedly subjective, figures for their likelihood:

Recognition of goodness (D = 10)
Existence of moral evil (D = 0.5)
Existence of natural evil (D = 0.1)
Intra-natural miracles (e.g., a friend recovers from an illness after you have prayed for him) (D = 2)
Extra-natural miracles (e.g., someone who is dead is brought back to life) (D = 1)
Religious experiences (D = 2)

Plugging these figures into the above formula (in sequence, where the P after figure for the first computation is used for the P before figure in the second computation, and so on for all six Ds), Unwin arrives at the conclusion that the probability that God exists is 67%.

Another problem I have with this is how it has, um, left out a few things.


a = altruistic behavior observed in other beings who are not monotheists (= 0.02)

b= bad behavior and an absence of
metanoia (“repentance” or a true turning away) seen in followers of a given monotheistic religion for which there is an apologetic. (= 0.1)

W= alternative explanations for the world as seen by Buddhists, Taoists, Jains, naturalists, behaviorists, and any permutation of positions thereof which dilutes a given apologetic explanation (= 0.00001)

Then subsuming these values into D above gives a value "for the probability of God existing" that is rather small. Which is what we expect: there's no lifeboat coming to save us. Even Pascal's look at the stars at night told him he was alone, and that exercises like this were to no avail. His solution: stupefy yourselves and "take holy water." Plunge into the Catholic faith, he advised. Apologetics was bunk.

So, in this bit of exercise on my ability to use Blogger to post in Symbol font (not entirely a useless exercise therefore) we've shown why Pascal's Wager doesn't really work. It is a useful tool, though to illustrate dukkha, precisely because of its ultimate impotence. Oh, and Firefox doesn't do Symbol fonts by default for some odd reason...

To a Buddhist, therefore, this illustrates its own insufficiency and our own discomfort. And, (2nd Noble Truth) there's a reason for that: we are attached to the idea that somehow we're entitled to know what happens after death, and furthermore, we're somehow entitled to game the system (I so rarely get a chance to use that metaphor) in such a way as to get something of infinite value after we die. But of course, once we become nonattached to the notion of what happens after we die and what magic words we need to say or deeds we need to do to prevent the rot and decay of our physical bodies from impeding a soul's transit to some happy place, we can actually begin to do something useful.

And so it is with this post: there's garbage to take out before my zazen.

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