Something like 87% of Americans would readily admit that they don't understand science, they certainly admit ignorance of mathematics. What offends Americans about the Lynns and Franks is that they consider themselves intellectually superior to that 87% of Americans, when anyone with a pulse can see that they are manifestly not.

There is nothing scientific in their opposition to the teaching of 'intelligent design' in schools, their opposition is every bit as faith-based and religious in nature as is the position of those who insist that G-d created the Heaven and the Earth in six days and rested on the 7th.

I don't buy 'intelligent design' beyond some kind of uncaused first cause, but there are plenty of intelligent, intellectually rigorous and honest scientific types I know who do. Thus, for those who are interested in it, I don't see the harm in bringing it up.

Lynn trots himself out just like any self-appointed scold, and Republicans will always gain ground whenever he comes out against them. But there will be more opposition to this than just the Lynns or the Democrats. Krauthammer ran an artile this week urging social conservatives to be happy with the gains they have made with respect to religion and to not push for an ID school agenda. ID is clearly not science, even many conservatives are in agreement with that.

Fundamentalists have clearly not taken over the country, you'd better redo your headcount.

bart:

Yes, the funny thing is the 13% who claim they do.

Robert:

Yup, that Jewish psychiatrist lobby has always had a lot of sway in middle America.

the libertarian blogs have their panties in a royal twist about this, they almost seem leftist in the venom they spit. poor glenn reynolds is under heavy porn sedation.

Give the libertarians some free pot or free guns or free male prostitutes, and they will be happy.

bart, name one.

Professor Reynolds made the righteous point that a true federalist would have said that it was an issue for local school boards, and, in his confused way, Bush sort of did that.

Orrin may be right on the politics, although in the long term deciding issues of natural science by a vote of people who have spent their lives avoiding knowing anything about natural science may prove unhelpful. It has in the past.

If he'd been honest, Bush would have said, 'I don't have a freakin' clue about whether there's a controversy here or not. I couldn't summarize what "intelligent design" is supposed to mean if you locked me up in a library all weekend.'

Harry:

Most folks ignore science and thereby avoid getting their hearts broken every time it changes. 8th grade science class tells you as much as you need to know to realize it's just a faith with a more strident claim to truth. Sadly, you invested so much in Darwinism its eclipse is unbalancing you.

Harry,

Easy. I'll give you three. One is a retired professor of Physics at Wake Forest University, named Tom Taylor, who was the first person ever to tell me about Intelligent Design. Another is a friend who is a successful pediatrician in Mississippi, Mary Crocker, who inter alia graduated from Johns Hopkins Medical School and another is my cousin's husband who is the Revlon Professor of Reproductive Endocrinology at Cornell Medical School and the author of the lead Gynecology textbook used in English language medical schools around the world. If you travel to places like BYU or meet a fair number of Orthodox Jewish scientists, you'll meet people interested in ID.

I'm not saying I agree with it, but I don't know enough to pooh-pooh it out of hand, as I would have when I was much younger. And it's not just the OJs of the world who buy into it, so there must be some substance to it.

Harry, I absolutely agree with you that scientific matters cannot be decided by a vote. If I tell a class that 2+2=4, we don't have a vote to see if they agree. But, when matters are legitimately in dispute, we can't be doctrinaire about them either. An example of this from mathematics is the Monty Hall game. You are given the choice of 3 doors to choose, one of which has the grand prize. You choose a door. Then, Monty and the lovely Carol Merrill open a door that is not the prize. Monty then offers you the chance to change or stick with your original answer. What do you do and why?

you change your choice, every time, and end up winning 2/3 of the time. you have been given more information. it's amazing how counter-intuitive this is and how much people resist accepting it.

bart:

All 2 + 2 = 4 represents is a consensus.

But enough of a 'consensus' to bet your life on it, especially when the alternative is usually 2 + 2 = 3.9 (or 5, or 2x10E17, or whatever).

It's like surgery - the organ is in there, but each one is slightly different. That doesn't negate anything, but it does provide for repeatability.

cjm,

Really?

Considering that you now have a choice of two doors, aren't you really only left with a 50/50 split? You were making a choice of 3 doors, now you have a second choice, it is as if the first choice no longer exists. You have no more information about the remaining doors than you had before. Another version is that you always switch because it is a 50/50 choice, whereas your earlier choice was only one in three.

The arguments go round and round. It's not a bad argument to have with friends after some heavy drinking or a good game of Risk.

OJ,

It's the rules. If you can show me a circumstance where that is not the case, I'll be impressed.

bart:

Exactly. It's about rulemaking, not reality.

It's actually about Bayesian filtering, and it's a settled argument. Wikipedia's explanation is in this case quite good. The key is the constraints that are placed on the game-show host (he has to open a door, and he has to open a door with a booby prize, so he has to know which doors are which.) Those constraints have the effect that the player partakes of the host's knowledge after the initial choice has been made.

"Revlon Professor of Reproductive Endocrinology"

The mind reels.

your first choice has a 1/3 chance of being right, and that can never change as long as the prize isn't moved. that means the other two doors have a combined chance of 2/3 of holding the prize.

after the "empty" door is opened, the other door (you didn't choose initially) now has that 2/3 chance all to itself.

anyone who would like to play against me for money, is welcome to get in touch :)

also, anyone who thinks i am wrong on this please make yourself known so i can ignore anything you ever have to say, that involves logic of numbers.

aog, bart, back me up on this, please :)

Robert, you can visit the website. He is also, according to the NY Post, the third highest paid faculty member of any American university, coming in at about $2.5 million.

cjm,

The problem I have is that the decision to stick or move is another choice, independent of the earlier decision.

bart: as long as the prize isn't moved in between moves, the probabilities don't change, and the initial pick can not vary from 1/3. people either see this problem or they don't, no amount of discussion will sway them.

bart:

Marilyn vos Savant once got a series of columns out of this scenario, in which she insisted that the odds were 2/3 and other people, including Ivy League mathematicians, insisted that it was 1/2. I understand that this has been scientifically tested via computer models and Ms. vos Savant was correct.

It's counterintuitive and I admit that I don't really understand it, but unless my information is faulty the controversy is settled.

Remarkable, eh?

I guess the logic is that if you get to open two doors the odds remain at 2/3 no matter what.

i took a combinatorics class three times so i guess i know what i am talking about :)

There is a confusion here over the probability of any individual action, and of a series of actions.

Say that one rolls an ordinary six-sided die.
The probability that the number "6" will appear is one in six.
Further, say that one rolls the die 1,000 times, and "6" never comes up. That is a highly improbable sequence, and so "6" is "due", i.e., there should be a sequence of rolls in which "6" appears MORE frequently than one out of six times, as the number of appearances by any side of the die reverts back to the mean.
However, even though it's highly improbable that "6" will fail to appear again, the odds of roll # 1,001 showing a "6" are STILL ONLY ONE IN SIX.
Each individual roll is a separate event, independent of the outcome of every other roll.

Thus, bart and joe shropshire are correct. It's the ability to choose whether or not to switch doors that makes the odds 50/50.

Without the ability to make a choice, then cjm and Matt Murphy are correct, your initial choice still only has a 1/3 chance of being correct, even though you now have additional info, since you cannot act on it. (Note that this is NOT the same as saying that the unchosen, unopened door has a 2/3 chance of being the prize door; that probability is still 50/50).

This is the kind of thing that makes gamblers lose all of their money playing a "system".

Bart: Passed it the third time, eh? You and me both, brother. But this isn't a combinatorial problem, it's a conditional.

Michael: cjm is correct, switching wins 2/3s of the time in a game with three doors. In general, switching wins (n -1 ) / n of the time in a game with n doors. Sorry, should have been more explicit about that. The key is that this is a game with two players, one of whom knows what is behind all the doors in advance. That knowledge on the second player's part conditions his behavior ( he has to open all the not-picked doors exept one, and he can't open a door with the real prize. ) In other words: a dice game consisting of ten rolls of one die is a game with ten independent events. The odds of rolling a two on all ten throws is simply (1/6)**10 = not too likely. The Monte Hall game, regardless of how many doors it's played with, is a game with three conditional events, as follows:

(1) player 1 chooses a door. This separates the doors into two groups, picked and not picked. The probability P that the prize is in the picked group is 1/n where n is the number of doors. The probability that it is in the not picked group is 1 - P = 1 - (1/n) = (n - 1)/ n, for example 2/3 , 9/10, 99/100. This probability does not change for the rest of the game.

(2) player 2 opens all the doors except one in the not picked group. At this point player 2, who knows what is behind all the doors, finds that his behavior depends on the prior behavior of player 1, as follows. If player 1 has chosen the door with the real prize then player 2 opens (n - 2) doors at random. The probability that any given door out of the not picked group stays closed is (n - 2)/(n -1). In a game with three doors that's your 1/2, and it's a red herring, a monte, since none of those doors pays off. On the other hand if player 1 chose a door that does not have the real prize there's just one way player 2 can behave: he has to open the n - 2 doors he knows don't have the prize behind them. The odds of this happening overall are (1 - 1 /n )*1.0000, since player 1 has only a 1/n chance of choosing the right door to begin with, but once he does the next step is completely determined. Say it another way: in a game with ten doors, player 1 has a nine in ten chance of forcing player 2 to show him where the real prize is! But he can only take advantage of that if he switches. In a game with 3 doors that chance drops to 2 out of 3.

(3) Player 2 stays or switches. If he's studied his Bayes Theorem he switches.

Gacch. Sorry Bart, meant cjm.

Bart, Joe correct.

As explained by Joe above, lets start with 1000 doors with the initial choice being 1 out of 1000. Practically nil probability for our purposes. Monte then opens 998 empty doors and allows you to switch. I suggest you switch Cjm.

Gacch. Step 2 should have read as follows: "...player 1 has only a 1/n chance of choosing the right door to begin with, and if he doesn't the next step is completely determined..." 'Twas late.

Not only did vos Savant explain the logic, she did it in that difficult, abstruse publication Parade magazine.

Orrin is a Feyerabendian, another instance of his Christian heterodoxy. All major theologians have thought differently.

Harry:

No, the point is that such things are true irrationally, not rationally.

cjm;

You're completely correct about the Monty Hall problem. As someone else noted, not switching means you win if you guessed right on your first choice. Switching means you win if you guessed wrong on your first choice. With three doors, this means 1/3 vs. 2/3. In other words, switching means you effectively get to pick two doors instead of one, the one Monty opens and the one you didn't pick initially.

aog: i knew a fellow cs'r would come through :)