[From Bill Powers (2006.05.25.1513 MDT)]
Fred Nickols (2006.05.25.0750)
> You can't say that a pair of dice either shows a seven or doesn't show a
> seven, making it sound as if there's a 50% chance of throwing a seven.
Hmm. I agree that you shouldn't say there's a 50% change of throwing a seven but I see nothing wrong with saying either of the following:
"I'm about to roll these dice. When done, they will or won't show a seven."
OR
"A pair of dice have just been rolled. They show a seven or they don't."
As a description after the fact, there's nothing wrong with that. But as a prediction, you can't leave out the probabilities. If you're willing to bet on the basis that they will or won't show a seven, then I'll be happy to give you odds or 2 to one: if they show a seven I pay you 2 dollars; if they don't, you pay me one dollar. The odds are actually close to 5 to 1 against rolling a seven, so if you keep playing, or if I can find a series of different people who will take those odds, I will clean up.
Science is about comparing prediction with reality, as a way of refining and revising theories and thus makiing better predictions. Even applied science needs to calculate the odds, as when a therapist starts seeing an individual and has to decide whether THIS person should be treated as a bulemic case. The scientist has his reputation to consider; the therapist, his track record of successes. Only the true dilettante doesn't care or keep track of how often his predictions are correct, being happy as long as they sound plausible enough over a few beers.
I'm not quibbling with your words here. I'm trying to get at something I've found important over the years. I call it "the basic binary split." When confronted with problems in the workplace, for example, I can take action or not. That's the basic binary split. If I elect to take action, I'm then confronted with or faced with working up some action options.
But what are the odds, in a given case, that taking action will pay off better than just waiting a while? When it comes to picking up the bill at lunch, no action may in the long run be less expensive than action. When it comes to watching the fire in the wastebasket get larger, action is probably better. In both cases you can only act or not act -- but that doesn't mean the choice is equal. You really need to calculate the odds if you're talking about general policies.
So, the dice do indeed show seven or not. If not, you have to ascertain what they do show. But, I still see nothing wrong with saying that they do or don't show a seven - which is quite different from saying that there's a 50% chance of throwing a seven.
The only difference I can see is that when you ignore the odds, the choice probably doesn't make any difference. The coin will land heads up or tails up, that's for sure (just about). So? If that's all you have to say about it, then who cares which way it lands? But if the cost to you of landing one way is enough greater than the cost of landing the other way, you will be well advised to learn the odds -- for example, after 10 heads in a row, you will be well advised not to bet more than even money that the next toss will be tails.
In cases like that of bulemia, there's an even more important complication (actually not all that complicated). Who says that bulemia even exists? Exactly how much does a person have to eat before throwing up to be called bulemic? One peanut? 100 pounds of peanuts? When you say a person either does or doesn't show the bulemic pattern, you're already in pattern-recognition trouble. There are plenty of cases where you just can't be sure that you're seeing the "real" or "typical" pattern, so in the end, most classifications in the middle of the bell-shaped curve are arbitrary. If they turn out to be wrong close to half the time, you'll be lucky, considering that it's actually possible that NOBODY "has bulemia."
Best,
Bill P.