Thinking and Doing

The Maverick Philosopher has an aphorism here, that I will quote:

The thinker, because he is a thinker, cannot naively live his life of thought, but must be tormented by doubts regarding it.  The doer, because he is not a thinker, can naively live his life of action.

And which is the philosopher? The doer or the thinker? The philosopher is neither; the philosopher is the man who unites thought and deed; the one who "understands the abstract concretely." (Kierkegaard) At least he was once understood thus.

The ancient philosophers were not tormented by doubts about their lives, because they had not yet separated thought and deed in the modern fashion. For the ancient philosopher, thought was a deed, which was why the Socratic cross-examination was a fruitful method of philosophical investigation. To force a man into a contradiction was to force a change in his life, because men lived immediately in their thought. Today, we are not bothered by contradictions, since our thought bears no necessary connection to our lives. The intellectual,  the man who manages to live serenely while advocating an array of bizarre and self-contradictory doctrines, is a peculiarly modern phenomena.

Philosophy is held in such ill-repute today because, once the separation between thought and life is made, the penalty of contradiction disappears. The critics are then quite justified in dismissing philosophy as a gassy exchange of opinions from which nothing decisive can emerge. If philosophy is to be renewed, it will only be by thought and life being reunited.

Douthat on Shrek

Ross Douthat has a review of the latest Shrek film in the June 21 National Review that reassures me that I'm not just a lone, crazy voice in the wilderness when it comes to this series, which I've hated from the get-go. He nails it exactly right:

What Sex and the City did for the love story, Shrek has done for the fairy tale: It's taken a classic genre and purged it of any trace of innocence, substituting raunch, cynicism, and a self-congratulatory knowingness instead, and then tying up the jaded narrative with a happily-ever-after bow.

Our culture robs children of their innocence as early as it can; and it is only in that innocence that the real meaning of fairy tales can be perceived. I believe this is one of the primary truths we learn from G.K. Chesterton. When we are older, we cannot but assume a critical distance from what we read. The child is still in the process of forming his self; what he reads (or is read to him) becomes a part of him in a way it never can again. For Chesterton, every truth worth knowing he learned in the nursery.

It is bad enough our children are exposed to things that destroy their innocence early on, and make the appreciation of fairy tales more difficult. Now, in the Shrek series, the fairy tale tradition itself is subverted. This constitutes a kind of inoculation against the power of fairy tales. Douthat is as depressed about this as I am:

I have a horrible feeling that the Shrek franchise offers millions of kids their first exposure - and worse, their last - to the Brothers Grimm and Charles Perrault.

The result is the sort of impertinent, self-satisfied young adults whom I encounter among my children's peers. They are not exactly insolent; but they are already jaded at age 17 and unselfconscious in their conviction that the world offers nothing before which they should bow. The notion that there might be something out there that might be more grand, significant and awesome than themselves is something that can't occur to them; they've been inoculated against it as they might have been inoculated against small pox. That such youths are somewhat unpleasant is not the major point. It is that they have been robbed of the virtue of humility that is the prerequisite for eros, the deep and mysterious longing in the soul for it knows not what. To draw on Chesterton one more time, we can perceive the gigantic only to the extent that we are small.  This is one of the primary lessons of fairy tales, a lesson our children can no longer learn... at least as long as Shrek and its ilk is available to them.

Making Money from Tuesday's Child

Here's a way to make money from the Tuesday's Child problem, assuming you can convince people that John Derbyshire is right and the probability in question is 13/27 (or 0.48, nearly even odds).

First, we need to convince seven of your neighbors of Derb's analysis, to wit, that the probability in question is 13/27. Then we need to find a large number of fathers with two children, at least one of whom is a boy. It doesn't matter on what days they were born. Have them bring the birth certificates. I hope you will agree with me that the probability that any father in this group has two boys is 1/3 (or 0.333, not 0.48).

Then we segregate the fathers into seven groups according to what day of the week the boy was born on. If the father has two boys born on different days of the week, have him flip a coin and join son #1's group if heads, son #2's group if tails.

Have the group with a boy born on Tuesday line up, and then repeatedly knock on neighbor #1's door and say:

"I have two children. At least one is a boy. He was born on Tuesday. Two dollars will get you three if I have two boys."

Hopefully neighbor #1 will take the bet, having been convinced that he's getting good odds. He's getting a 3:2 payout on a bet that he thinks is approximately 1:1.

Have the group with a boy born on Wednesday line up, and then repeatedly knock on neighbor #2's door and say:

"I have two children. At least one is a boy. He was born on Wednesday. Two dollars will get you three if I have two boys."

Do this with the groups for the remaining days of the week and remaining neighbors. As far as we are concerned, we are paying out at 3:2 a bet that is actually 2:1! (A fair payout would be four dollars for every two dollars bet. We are paying out as though the odds were 2/5 or 0.40. Our advantage is 7%, better than the house advantage in a typical casino game. ) 

As far as any single neighbor is concerned, he's simply seen a repetition of the Tuesday Child problem. Everybody who knocks on his door says the same day of the week. Once you've got all their money, they might get suspicious, but you've got the birth certificates to back it up... and the (bogus) mathematical analysis. Some people are just lucky, you will tell them.

The Tuesday's Child Game

In this post I discussed the so-called Tuesday's Child problem in probability theory. The theory (with which I disagree) is that the probability of that the speaker has two boys is 13/27. I think the probability is actually 1/3. I've made a crude Java applet, the Tuesday's Child Game, to demonstrate the point.

Since the theory claims the odds are approximately even that the speaker has two boys, if I give you anything better than even odds, you are probabilistically ahead of the game. The applet pays off at 3:2 so,
according to the theory, you should win a lot of money.

If you are still interested in this problem, and can get $100 before going broke, let me know.

Tuesday's Child

Here is a post at the corner concerning a probability question. It leads to a number of other posts and to Derbyshire's analysis here. If you follow the chain of posts back, it leads to other sites and considerable debate over the interpretation of this problem.

The analysis is tricky only if the problem is interpreted in something other than its straightforward, plain meaning. The statement of the problem is:

"I have two children. One is a boy born on a Tuesday. What is the probability I have two boys?"

Now the problems all come from that "born on a Tuesday" clause in the middle sentence. Take that out, and everyone agrees on the answer:

"I have two children. One is a boy. What is the probability I have two boys?"

This is the classic coin-flip enumeration problem. Having children is like flipping a coin, with heads = boys and tails = girls. The possible outcomes for two consecutive coin flips are:

Heads - Heads
Heads - Tails
Tails - Heads
Tails - Tails

or, in the boy girl terms:

Boy - Boy
Boy - Girl
Girl - Boy
Girl - Girl

Since we know that at least one of the children is a boy, the last case is ruled out and the probability that the speaker has two boys is one in three.

Returning to the original problem, the analysts all seem to think the phrase "born on a Tuesday" is very significant, but they can't agree on its significance. I don't think it adds anything to the problem at all. In the straightforward, obvious interpretation, it is only a statement after the fact of birth concerning the day of birth. It's like saying the boy was 8 lbs at birth, or was born with blue eyes. It doesn't say anything about the prior possibilities of weight or birthdays; it is only a statement about what in fact occurred. It doesn't say that one or both boys couldn't have been born on a Wednesday. If that had happened, the consequence would be that the problem would say:

"I have two children. One is a boy born on a Wednesday. What is the probability I have two boys?"

The answer to this question is the same as the answer to the Tuesday question and to the simpler question that does not refer to a day at all: 1/3.

Derbyshire calculates the probability as 13/27. He can only get there by interpreting the "Tuesday clause" as affecting the prior probabilities of birth. In other words, the case of two boys born on Wednesday need not be included in our enumeration of cases because it wasn't possible for both boys to be born on Wednesday, since we know one was born on Tuesday! I hope everyone can see the post facto fallacy in this reasoning. Anyone who would buy this line of reasoning is playing the role of the father in the following comic scenario:

One day you get a letter from the town correcting your son's birth certificate. He was born two seconds after midnight so he was actually born on a Wednesday rather than a Tuesday. With a heavy heart, you sit your son down and tell him the unfortunate news: "I'm sorry to tell you this son, but I'm not your real father. My son could only have been born on a Tuesday, and I've just learned you were born on a Wednesday."

By the way, this problem is not comparable to the Monty Hall problem. The Monty Hall problem is a genuinely counter-intuitive probability result. The Tuesday's Child problem is more like a riddle or joke that depends on deceptive or ambiguous language.

Is Free Will a Contingent Possibility

With respect to this post at the Secular Right, Kierkegaard cannot be bettered:

Freedom is never possible. It is either actual or it is not at all.

Put another way... anyone who wonders if he is free (or even could possibly wonder if he is free) is already free.

Toy Story and Religion

I just saw the wonderful Toy Story 3 with my wife and daughter, and it put me in mind of an argument I read years ago at the Internet Infidels. I haven't been able to find the article (it was in the "Agora", which they no longer seem to have), but the gist of it was straightforward. Toy Story, the argument goes, is a parable of atheism. It is the story of Buzz Lightyear, a man living in a false world of imaginary Space Rangers and Evil Emperors, finally brought back to reality when his illusions are punctured. Buzz hangs on to his illusions as long as he can but, finally summoning the courage to find out the truth one way or the other, puts them to empirical test. One of his "special powers" is supposed to be an ability to fly, so he jumps off a second floor bannister in an attempt to prove it. Naturally, he falls to the floor, and is broken both physically and spiritually. But the story has a happy ending as Buzz is not only physically repaired, but learns to accept the non-dramatic and mundane truth that he is but a child's toy. Would that the Buzz Lightyears attending Mass every weekend could follow his example.

The argument is a good example of how atheist arguments can be perfectly sound but miss the target. The Christian can accept the argument in its entirety, and even applaud with the atheist Buzz's breakthrough to a true understanding of his nature. For it is not in his dreamworld as a Space Ranger battling Emperor Zurg that Buzz has found religion (or, at least, religion in the sense of a metaphysical religion like Christianity), but rather when he recognizes the true cause and source of his being; and that cause is a Creator who made him in light of a final cause: To be of service to a child in providing him joy in the form of a toy. And it is only when Buzz comes to terms with his destiny (a destiny created for him) that he can be truly happy.

Buzz Lightyear is no product of an atheist universe. If Toy Story were an atheist parable, then Buzz and the other toys would be the accidental result of a brute physical process. In those terms, their destiny as a child's plaything would have as much purchase as any other destiny; which is to say, none. Indeed, it would have no more purchase than Buzz's Space Ranger worldview. We can reimagine Toy Story in atheist terms in the following way: Finally tiring of Woody's attempts to "enlighten" him out of his Space Ranger fantasy, Buzz pulls Woody aside and lets him in on something. Of course, Buzz says, I know there is not an Emperor Zurg in the sense you think I think there is, and that I can't defy gravity. So what? Your insistence that I am "meant" to be a child's plaything is as much a fantasy as my Space Ranger worldview. The difference between us is that I know whatever purpose I give my life is purely of my own fantastic creation, while you are under the illusion that you "know" the "true meaning" of every toy's existence. You are, in a word, naive.

Why isn't the atheist version of Toy Story produced? It certainly isn't because Hollywood is afraid of offending religious believers. It's just because few people would want to see it. The story is boring. It's a story that can be told only once, and it was told long ago. It's the story of the discovery that, in the end, there isn't really anything worth discovering; a discovery that, if it puts an end to anything, it puts an end to storytelling.