Laws of Nature

I'm not as comfortable as are some with the phrase "laws of nature."

One way of framing the issue of "physicalism" versus various non-physicalist or dualist views of the world is to ask whether humans or something about human nature constitutes an exception to the laws of nature. If the ansawer is "no" then (runs this line of thought) you are a physicalist.

Not so fast! I have to say. The phrase "laws of nature" implies something ironclad, and this biases whatever constitutes the "physicalism" thus defined. For all we know, though, every 'law of nature' may be probabilistic. That almost certainly is the case with the second law of thermodynamics, for example. The reason heat disperses is that there are lots and lots of molecules moving about and the law of "large numbers" applies. If there is a small group of fast-moving molecules that start off as a tight knot (a hot spot, in macro terms) and a surrounding group of slower-moving molecules, (cooler surroundings) then the fast ones will disperse into the slower ones, even though some specific fast-moving molecules will be moving toward one another some of the time. At a macro level, that won't matter.

I'm out of my debt there and shouldn't go any further, but the bottom line is that the famous 2d law is a statement of probability, which at the macro level looks like an inevitability.

Suppose every law of nature, even gravity, turns out to be probabilistic. This means that we will be in a position to accept something like ideas of free will as applied to human nature without making of the human mind an "empire inside the empire." This line of thought, as you can see, points us toward Penrose, quantum computing, etc.

The Monty Hall Puzzle, continued

Most people, when confronted with the story in yesterday's entry, will answer that there is no reason to change, that the contestant might as well stick with curtain A. After all, there are two unopened curtains. The big prize is behind one of them. The odds that it is behind curtain number one are, then, 0.50, or 1:2, so the rational contestant is indifferent as between one curtain and the other.

Conditional probability theory, though, looks carefully at what Monty Hall's own actions have already told us. When the contestant made her first choice her odds of having picked the right curtain were: one out of three. The chance that she had made the wrong choice then, was: two out of three. What Mr. Hall has told us hasn't changed the chance that her initial choice was wrong at all—it has concentrated that chance—which is now embodied, so to speak, by curtain B. Why? Because Mr. Hall knows where the $1 million is, and surely wouldn't have opened curtain three if he knew it was there. So his choice to open the one that he did was non-random.

At any rate, conditional probability theory says that given the fact that Monty now has eliminated curtain C the rational contestant will pick curtain B, giving herself a two-thirds chance of winning. Don't be surprised if this is counter-intuitive and even disorienting. It has that effect on a lot of people. As a psychological matter, if she picked curtain A, and Monty opened curtain C, she might well take that as a confirming event ("so far, what has happened is consistent with my initial guess") which would make her likely to dig in her heels and stick with it, theory be damned!

I mention it because conditional probability theory has important consequences in the world of finance and may have something to tell us about last year's credit crunch. But I'll give the connection some thought before pontificating further,

The Monty Hall puzzle

Suppose you're on the old quiz show, "Let's Make a Deal." For those of you who are too young to remember it -- don't worry, you'll catch on as we go along. Quiz shows are quiz shows through every generation.

The host, Monty Hall, shows you three curtains: A, B, and C. Behind one of these curtains is a fabulous prize. Behind each of the other two is some absurd gag gift.

At random you say, "I'll take what's behind curtain A, Monty."

Monty replies, "Before we pull back A, let's pull back C, just for fun."

His beautiful assistant gracefully pulls back curtain C revealing ... a mound of shaving cream.

Then Monty turns back to you and asks: "Do you want to stay with A, or change your guess?"

Well ... do you? Does it matter one way or the other for your chances whether you do?