I’m pretty darn Christian, and I think this is totally spot on. I have an entire speech I can give (and have, in my old home fellowship from my church) about how God does not seem to be in the business of routinely violating the laws of nature.
Now, I believe that prayer can actually work, but just working yourself up into a state of self-induced belief is good for just about nothing.
I have a friend who has lived her entire life according to this plan. She never thinks anything through. She has no reasoning skills at all.
She starts college and then changes her mind and quits (she is one or two semesters shy of a teaching degree (decided she didn’t like working with kids that much), she has 2 years of nursing school (decided nursing was too gross), she finished cosmetology school (didn’t like the gossipy atmosphere of beauty shops), went to cooking school for a year and a half (decided she just didn’t like it), and has done every shop-at-home thing (Avon, etc.) out there. She’s re-started college or technical school several times, but always drops out.
She pays bills late constantly. She’s always amazed when she comes home and either the cable or the phone or the electricity has been turned off.
She doesn’t understand the connection between not making car payments and having your car repossessed. She’s actually indignant that someone would come and “take” her car.
She’s one of those people who meets a guy, a week later is madly in love, two weeks later is engaged, three weeks later moves in with him, starts planning a wedding, and within a couple of months the whole thing disintegrates, and she’s devastated. Till she meets another guy and the whole cycle starts all over again.
"John is passing the time by flipping a quarter. Which of the following outcomes is more likely:
A) The first time, the quarter comes up heads
B) The first time, the quarter comes up heads, and the second time it’s tails.
It’s OBVIOUS that A is more likely, right? Only ONE condition has to be fulfilled for A to be true, whereas that same condition and ANOTHER condition must both be fulfilled for statement B to be true.
Well, go back to John the Limbaugh fan. If John is a janitor, statement A is automatically true… but statement B is NOT necessarily true. Oh, it may seem very likely, but the mere fact that there’s a second condition means that statement B is less likely to be true than statement A.
Now, that SHOULD be obvious to anyone using logic. Problem is, most of us DON’T employ logic. When I first encountered a variation on that brain-teaser (20+ years ago, when I was in high school), I got it wrong, myself. Our preconceived notions sometimes trump our abilities to use logic!
I gotta admit, Algernon, that even as I typed in this example, I felt somewhat queasy about it. I’m not suprised to find a rebuttal such as yours. Thanks for the statistics lecture!
Yes, I agree with all that if you are solving a brain teaser.
My reasoning was that the thread was about examples of poor reasoning in real life, particularly in conversation.
Suppose you were at a party, and A described John, then added “Oh, and I think he’s a janitor.”
B chimes in “Not only is he a janitor, but I think he opposes abortion.”
They both look at you and A says “Which of us is right?”
Now there is an additional implication - that A thinks John doesn’t oppose abortion.
I know this is not present in the puzzle version, but it certainly is there in conversation (else A would say “I’m not disagreeing, I just have no idea what his abortion position is.”)
One of my students turned in a paper on secondhand smoke with a passage something like this:
“Secondhand smoke has 4,000 chemicals in it. Therefore, you have a 0.15 chance of getting lung cancer with every breath. So if you take 100 breaths of secondhand smoke in your life, you have a 15% chance of dying of lung cancer.”
He was rather surprised when I told him that if his reasoning were accurate, EVERYBODY would be dead.
My own case of stupid reasoning:
I went to a “Cheap Red Wine” party, and ended up with one bottle being drunk by only me. After I had partaken of a sizeable portion of said bottle, I thought to myself, “I don’t feel very good. I should hurry up and finish the bottle so that I can start recovering.”
Thank god we don’t have a smiley which displays what I felt like next.
A friend asked me about nuclear weapons and that eventually got us on the topic of Albert Einstein. We were discussing how intelligent he was and she said, “Isn’t it funny that his name happened to be Einstein??”
I said, “Um…you mean…because he ended up so smart?” She said, “Yeah!”
Ho’boy. Then I had to explain to her that the association between intelligence and the name Einstein came after Albert.
Could you clarify your reasoning here? Because right now, it sounds exactly like the gambler’s fallacy. By what mechanism is the player’s performance in the previous year related to his performance this year? The ones I can think of include: accumulation of injuries and age (which would encourage worse play), and greater experience (which might encourage better play). But you don’t seem to be thinking of these because you say “a players ability is not going to change substantially over time.”
It seems like your logic could be used to argue that a fair coin that just gave 10 heads in a row should next give a tail. To paraphrase your argument: “Without some outside influence, the ratio of heads to tails is not going to change substantially over time. It will bounce around, both above and below the average, and year to year variation will generally be towards the average.” But to conclude from this that 10 head in a row increases the likelihood that the next flip will be a tail is exactly the gambler’s fallacy.
I think that there is something unfair in accusing those who do not correctly answer this puzzle of having poor logic skills or poor reading comprehension. Those of us who have been trained in logic may have a hard time remembering that the syntax encoded in modern formal logic is, to a great extant, arbitrary. Natural languages, such as the conversational English that the test-takers knew, may sometimes use a different syntax.
Here is an example of natural language syntax that does not conform to that of formal logic: “All that glitters is not gold”. When people say this, they mean something like, “there are things that glitter even though they aren’t gold.” Parsed in accordance with modern logic, the phrase actually says that among those things that glitter, none are gold. In other words, if it’s gold, then it doesn’t glitter. Interpreted one way (the intended way) the phrase is true. Interpreted using the syntax of modern logic, it is false. To achieve the intended meaning, modern logic would have us word the phrase as “Not all that glitters is gold”. The only difference is where the “not” is placed. Formal logic has decreed that a negation operator, such as “not”, should always precede the entire statement being negated, including all quantifiers (the quantifier in my example is the word “all”).
But this is just syntactic convention. Another convention in formal logic is that the conjugation operator AND should be placed between the statements being conjugated, so that the conjugation of A with B is “A AND B”. This is not the only way to do it, though. In the logic of Lukasiewicz (upon whose system the “reverse polish notation” of HP calculators is based), the conjugation operator precedes both statements being conjugated, so that the conjugation of A with B may be expressed as AND(A,B). Which convention you use is an arbitrary choice. Both are consistent with correct reasoning.
Just like the “all that glitters…” example, the sentence used in ultrafilter’s puzzle may have a different interpretation from that given by formal logic when used in natural language,. Imagine that you are starting a job as a waiter in a restaurant. The manager is telling you, “If someone doesn’t have shoes, don’t serve them.” Then, remembering an additional rule, she adds, “Or if they don’t have a shirt, don’t serve them.” It would be more in accordance with formal logical syntax to phrase the rule as “If someone either doesn’t have shoes or doesn’t have a shirt, then don’t serve them.”
But the manager wasn’t speaking formal logic; she was speaking natural language. You may therefore validly infer from what she said that if someone comes in without shoes, then you don’t serve them.
I would not consider temporary landmarks (even multiple ones) examples of good reasoning. If you do, then I don’t know what to say. If there isn’t a big sign on the nearest light pole that has a big “D” on it or something similar, one might approximate how many cars you are in deep relative to a door or something. But saying “I’m between the blue honda and the red toyota, across from the vw bug…” at the mall is begging for you to wander about aimlessly unless you actually took note of some permanent features…
I don’t want to be a jerk, but since Mr Notametsfan’s logic seemed pretty good to me, I looked up the stats. First, Rickey Henderson’s batting averages:
Damn, he couldn’t have been more right if he was psychic! Actually he made perfect sense to say that they would probably revert to the form they had played at for several seasons rather than repeat an anomolous year.
The mechanism is that it’s the same player, and each player has some level of ability which usually doesn’t change much from year-to-year. So you would expect Barry Bonds to have a pretty good year at the plate because he’s Barry Bonds and he always has had good years at the plate. Similarly, you would expect Rey Ordonez to have a crappy year batting because he is Rey Ordonez and he never has been able to bat worth a damn. This is different from tossing a coin, because every coin is the same (with respect to head/tails probability) and every toss is independant.
I know a LOT of people confuse statistical relationships with perfect causality, and so they therefore think any evidence of a non-perfect relationship automatically refutes the claim.
Example: a study finds that children of smoking parents have higher incidence of bronchiolitis.
Along comes Joe Genius, who boldly proclaims that HIS parents smoked, yet HE never had bronchiolitis, therefore this study is crap. I’ve seen this logic brought up time and time again, and to my great shame a LOT of times on this board. It came up a lot in a thread about breastfeeding vs. formula. Sigh.
Granted, that is a mechanism for a relation. Perhaps I should have been more clear, but the sort of mechanism I was looking for was one that would justify the claim, quoted in the OP, that “past success in 1999 was a good indication of future failure.”
I assumed the OP was being flippant when he phrased it that way. The argument by Mr Notametsfan (if that is his name :D) was more that failure in 1997 and 1998 is a good indication of future failure, and that the success in 1999 was a fluke.
Manduck, thanks for handling Tyrrell’s questions with such elan. Your answers are better than what I would’ve come up with (especially the naming of Mr. Notametsfan. ~grin~). And thanks for looking up their batting averages. I was amazed to see that they both really did have outstanding seasons in 1999.
The reason why Variation to the Mean is different from the Gambler’s Fallacy is subtle.
Instead of baseball players, let’s to back to talking about dice. With a normal die, if six comes up ten times in a row, the gambler, falling victim to the Gambler’s Fallacy says “there is no way in hell that another six is going to turn up”, when in fact, the probability of another six is exactly the same as it was prior to the streak… one in six. The prior tosses are not any predictor to what the next toss will be.
With Variation to the Mean, think of the die as being weighted as follows:
a one turns up 4 percent of the time,
a two, 10 percent
a three, 70 percent
a four,10 percent
a five, 4 percent
a six, 2 percent
If on any toss of the die a six turns up, it is highly unlikely that another six will be thrown. It is much more likely that a three, or perhaps a two or four, will be thrown. While it is still true that the prior tosses are not any predictor of what the next toss will be, Variation to the Mean says that the most likely result is the one that has the highest probability of occuring.
With baseball, the batting average over the course of a year that is most likely to occur is the batter’s career average. It has a much higher probability of occuring than having a year where they exceed (or fall short) of their career average by a substantial margin.
The probability curve for batting averages is bell shaped centered around the mean, while the probability curve for throwing a normal die is flat.