I spent the last few days at the National Science Foundation reviewing grants. Truth be told - you know you're nerdy when you walk into a restaurant after having forgotten to remove one's NSF temporary ID badge reading "Hello, my name is experimentaholic." and are reminded of this fact by an attractive yet not-so-nerdy restaurant hostess. Reviewing grant applications, in and of itself, in not very much fun, because I simply don't like being the one who decides who gets funded and who doesn't. I think everyone should get funded, myself included! But this is not the state of affairs - only some get funded, others get the apology letter. And I've gotten my share of those thin ones.
Which brings me to the topic of the probable and the possible. What does probability mean? For instance, these people who wrote grants submit them, and there is a certain probability that they will get funded, which is based on how much money NSF has to dish out. They also have a certain expectation of the probability that their grant will get funded, which may differ from that which is actually possible given the availability of funds.
But what does it mean to expect an event with a certain probability? Like dying on a plane crash. The probability of this event is quite low - something on the order of one in eight million. So we get on the plane, and most of the time, get off the plane. But when you get on that one plane that explodes, and you ARE that one in eight million, the probability is not quite 1 but certainly close to it. But what does uncertainty mean, at least at the level of a psychological construct?
I know that there is a lot of evidence on this - and most of it points to the fact that people are particularly bad at assessing probabilities and changing their behaviors based upon these assessments. People drove after 9/11 out of fear of flying, and this increase of traffic and the resulting accidents that ensued killed more people than had died on the planes of 9/11. True! I buy a lottery ticket when the powerball is in the hundreds of millions, realizing full well that the probability of actually winning is the same as correctly guessing a random a number between zero and 120,526,770.
I am at the moment in a coffee shop, it is a Friday night, and two students next to me are discussing Spinoza, and specifically free will. This makes me wonder about our free will in relation to our assessment - and flawed assessments - of probabilities. I have always dreaded flying, even knowing that the probability of dying is the same probability of guessing a number correctly between zero and eight million. But what if I am just lucky (or unlucky) that day? Everyone who has ever died in a plane crash has gotten on that plane imagining that the probability of a crash was one in eight million. Which is fine, if you're a member of that elite group of eight million. But if you're not, not.
One way to think about it perhaps is actuarially. When you get on a plane, you have to think of the degree to which taking this trip will actually reduce your life. A related situation is when you buy a lottery ticket. A lottery ticket is really worth what you paid for it, plus whatever the probability of winning the ticket multiplied by the reward. Imagine the senario of the powerball. The ticket costs $1. The jackpot is 100 million But the real value of the ticket is $1 + $100,000,000 X 1/120,526,770. Which is $1.82. Of course, afterwards, any given ticket is either worth $0 or $100,000,000...but in the seconds before the balls drop, it is worth $1.82. What about one's life? The probability of dying in a plane crash is 1 in 8 million. As a thirty year old, I expect (or I should say hope) to live another 30 years at least. More would be better. 30 years comes out to 946,080,000 seconds. But by getting on that plane I am reducing my life by 946,080,000 seconds X 1/8000000 or 118.26 seconds. Of course, after the plane lands or crashes, that amount changes to 0 seconds or 946,080,000 seconds. Is it worth it? Does this way of looking at the problem solve the problem, or just create new ones?
Which brings me back to free will. Does the fact that we live in uncertain world make it such that our free will is compromised? I don't know. How does our inability to reason about probabilities affect our decisions? Probably in some domains, probably not in others. Some people are notoriously bad at making comparative judgments of probabilities and possibilities - those who drove rather than fly after 9/11, who are now in the grave or scattered to the winds because their dread risk overcame their rational capacities.
In this sense, statistical probability and mental probabilities must be related, but they are not homologies. Keyes wrote something about this, on personal probability, but I confess I haven't read it, yet. Perhaps I'll read it someday. It's both possible and probable.
