Thursday, January 31, 2008

Tuesday, January 29, 2008

Probability, and a stupid error by me

In case anyone is reading this who doesn't know the background, I was engaged in a lengthy discussion concerning statistics and the types of inferences that were or were not valid from them. During this discussion, another person proposed a simple probability problem, and I made an error in evaluating the answer. I think we disputed on this in well over a hundred posts before I realized the mistake I made. It wasn’t the first time, and I have been on the correct side of such exchanges more often the wrong side, historically. That’s about all I expect.

Recently when referring back to this discussion, the other poster said I had made a specific kind of error. Since I had made a completely different error, I thought I should be correct about the type of oversight I had made. Rather than possibly do another hundred posts on probability in a message board actually devoted to the Utah Jazz (JazzFanz), I decided to bring that discussion over here.

The problem: your partner flips two coins in secret, and you choose one at random and it is heads. What is the probability the other one is heads?

My incorrect reasoning: there were four possible outcomes from the flip: TT, HT, TH, and HH. All four outcomes were equally likely. However, you know that TT did not occur. Therefore, among the three remaining possible flips, two of them would have tails, and one would have heads, so it is twice as likely the other coins is tails as heads. The probability is 1/3. Yes, it was stupid of me.

His (correct) reasoning: we have information only about one coin, and no information about the other. The probability is 1/2.

However, he seems to believe the problem was with my methodology, rather than the implementation of that methodology, so I want to be clear that the correct methodology is this: you have to adjust by the probability that heads would be shown for each type of flip. I did that for TT, by saying it was not possible, but I did not do so for the HT or TH groups. In each case, the odds of revealing heads at random (H) is 1/2, so you have to adjust for that in the calculation of the probabilities. Basically, you are twice as likely to get a head from a HH combination as from HT or TH. In terms of odds, it's [1/2 * P(HT) + 1/2 * P(TH)] : 1 * P(HH), or 1:1, making the probability 1/2.

If his method is easier, why did I use mine? Habit, I suppose. Looking at all the possibilities lets you answer a deeper range of questions than a mere comparison of knowledge method. For example, you can use it to evaluate the following question.

You get an offer to play a game. The rules are you flip two coins. You must reveal one coin, and it must be head if you have one. If the other player guesses the value of the second coin, he gets $1. For the game to be fair, how much should you get when he is wrong?

Edited to remove vertical bars and for clarification.
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Thursday, January 24, 2008

Mom's pants

You'd think that I'd have remembered from back when I was a teen, but no such luck. Yesterday my second son (14) wore a pair of his mother's pants. Not the first pair I gave him, mind you. I told him the first pair actually was his mother's pants, so of course he refused to wear them. I gave him another pair (only things clean) and told him they were his brother's, that was OK. Back when I was that age, it never would have been acceptable for me to wear Mom's pants, but you forget these things sometimes.

Of course, his older brother (15) has had occasion to wear Mom's pants from time to time too. He doesn't mind. Sometimes you keep busy reminding yourself of all the these he does mind, of the things he needs to keep his life in balance, you don't notice the things he accepts with a peep that would annoy any other youth. Amid keeping a ready supply of eggs and toast, making sure the french toast is not late, etc., you don't even realize that he doesn't care if he's wearing Mom's pants to school.
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Wednesday, January 23, 2008

The Price is Right for science

I just saw a game called “Pathfinder” on The Price is Right. You move from square to square, trying to make educated guesses about the next digit in the price of a car, based upon what you know of the car. When you get it wrong, you try to get another chance to make a new guess. That’s not too different from what scientists seems to do, they try to make good guesses, advance a square, and their prediction turns out to be right or wrong. Being right is always better, but even being wrong just makes it easier to be right next time.

Now, compare that to Intelligent Design/Creationism. They already have decided the path, so they say the price of the car has to change to match the path they see. They keep going on to the same squares, over and over. Not much like science at all, it seems to me.
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Friday, January 18, 2008

78th Skeptics' Circle

I have been remiss in not linking this earlier. The 78th Skeptics' circle has convened, including my very first post. I actually did feel honored.
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Robert Fischer, In Memorium

Bobby Fischer has died.

When I was a kid, I studied his games, especially the match against Spassky. The US press give him the golden-boy treatment, of course. Those of us who played with passion admired him. Looking back, though, it is any different than admiring Allen Iverson or Russell Wallace today? Good players, but also cases of being less than they could have been.

He took himself from being a force to being irrelevant in 1975, and played on the fond memories and patriotism of our country to help fund a re-match in 1992 with Spassky, where the chess was decidedly not up to current GM play. Yet to the end, he apparently thought he was still a great player.

Rest in peace, Fischer.
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Wednesday, January 16, 2008

Beat the Nuggets!

I really dislike the Nuggets (Denver, not chicken). I haven't liked Carmelo Anthony ever since he whined about Kirilenko being inthe All-Star game. I'm not fond of George Karl. I have respect for Iverson as a player, but on a personal level he represents so many things about professional athletes that show they often simply don't appreciate how lucky tehy are or the responsibilities that should go with that much acclaim. I never liked Camby either, and Martin always seemed like a bully (although if the Jazz had signed him, he would have been *our* bully). I don't know the Jazz will, or even can, win in Denver tonight, but this is one game I would really like for them to win.

Edit to add: oops, tomorrow night. :(
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Tuesday, January 15, 2008

Morality is bigger than that

Lot’s of people discuss on whether there morality is subjective or objective. I’ve been thinking lately that the entire argument is both too dismissive and irrelevant.

Regardless of from where you think morality comes, it’s a complex social structure made up of many parts. Some of these parts are close to universal, others vary considerably by culture. I have never heard of a culture that approves of random killings, rape, or stealing from your fellow tribesmen. Whether the reason is the need for a stable society or some putative God laying this down, I have no problem conceding that a few of these precepts could be labeled as objective. At the same time, most issues that deal with sexuality, slavery, and the right to make war on people not well known to you have had varying expressions in a wide variety of seeming stable, healthy cultures. I see no reason to consider morals in these matters to be anything other than subjective. Any basis for morals perforce will be the product of arbitrarily chosen principles. Trying to force the whole concept of morality into one place or the other is unworthy of a topic rich in context and subtlety.

Also, in the final matter, it is of no consequence whether the morals of your culture are subjective or objective. If you believe they come from some putative supernatural revelation, you’re going to follow your source for the most part. If you see them coming from other principles, you’ll still be following those principles. Either way, when you violate the standards of your own morals, you’ll feel the guilt, and when you violate the standards of your culture, you’ll risk facing punishment. Whether they are subjective or objective makes little difference there.
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Monday, January 7, 2008


Lucky is how we felt from the time he was born. Our first child was healthy, happy, and very independent for a baby. He would amuse himself for a couple of hours, needing no attention at all except when he ate or needed a diaper change. He was so beautiful that, when he was eight, we had an agent come to us inside a grocery store and ask to represent him as a model.

Of course, that was not going to happen. He couldn't stand being touched by strangers, or having a constantly changing routine. His language skills were well below age level. When he got upset, he would bang things repeatedly. It was autism, exactly, certainly not Aspberger's nor Childhood Disintegrative Disorder. It's Pervasive Developmental Disorder-Not Otherwise Specified, in the autism spectrum.

Still, we never had to buy him a bicycle helmet to keep him from damaging his head. He was a little sensitive to loud noises and to smells, but not overly so. We had a fairly normal life. We were lucky, compared to many.

Today he plays the trumpet in the high school concert band. He washes dishes on occasion, rakes the yard, and plays Yu-Gi-Oh! with his brother and his brothers friends. Of course, he has no friends of his own, and doesn't seem to particularly want any. He's quite content with Word Searches and SoDoKu (he needs some help with the three-star puzzles). He wants to have his own apartment when he grows up (although I think a group home is more likely). In many ways he's more reliable and helpful than many of the kids I grew up with. We still feel lucky to have him, every day (well, almost every day).
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Sunday, January 6, 2008

Logic: everywhere or nowhere?

I just finished digesting Dr. Victor Repperts article, "The Argument from Reason", over at and was disappointed with one aspect in particular. Dr. Reppert describes how a formal system works in one paragraph, and them much later disregards the same properties when discussing a different formal system.

On the other hand, if I am playing chess, and I am missing a pawn, I can get a penny, a button, a half-eaten carrot, or just about anything else to play the role of a pawn. This is because unlike the frisbee[sic], the pawn's role is purely symbolic, determined by convention.
That seems clear, and I agree. Chess is one type of formal system, basically a instantiation of rules and procedures. Formal systems can be applied to a variety of objects with no change tot he structure of the system. They form a sort of model. Dr. Reppert seems to forget this in a later paragraph, though.

But principles like the laws of non-contradiction apply universally. Contradictions cannot be true in Phoenix, in Houston, in Antarctica, on Venus, in the Virgo cluster, in the furthest nebulae, or even in Southern California. From what particular experience could our knowledge of this have come?
Equally true would be, "But principles like the diagonal movement of bishops apply universally. Bishops cannot move orthogonally in Phoenix, in Houston, in Antarctica, on Venus, in the Virgo cluster, in the furthest nebulae, or even in Southern California. From what particular experience could our knowledge of this have come?" Of course, the obviously true answer would be that we set up the rules of chess the same everywhere, otherwise it's not chess. The same reasoning applies to logic. Any time you set up a system where you only accept two logical values (true or false) and only allow each statement to have one of those values, you get a formal system where the law of non-contradiction obtains. There is no experience this comes from, any more that there is an experience of a real-life bishop that never walks forward straightly. It's a feature that we built into the system, not one innate in the universe.
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