“What was the Sherlock Holmes principle? ‘Once you have discounted the impossible, then whatever remains, however improbable, must be the truth.’”
“I reject that entirely,” said Dirk sharply. “The impossible often has a kind of integrity to it which the merely improbable lacks. How often have you been presented with an apparently rational explanation of something that works in all respects other than one, which is just that it is hopelessly improbable? Your instinct is to say, ‘Yes, but he or she simply wouldn’t do that.’”
“Well, it happened to me today, in fact,” replied Kate.
“Ah, yes,” said Dirk, slapping the table and making the glasses jump. “Your girl in the wheelchair—a perfect example. The idea that she is somehow receiving yesterday’s stock market prices apparently out of thin air is merely impossible, and therefore must be the case, because the idea that she is maintaining an immensely complex and laborious hoax of no benefit to herself is hopelessly improbable. The first idea merely supposes that there is something we don’t know about, and God knows there are enough of those. The second, however, runs contrary to something fundamental and human which we do know about. We should therefore be very suspicious of it and all its specious rationality.”
-- Douglas Adams. The Long Dark Tea-Time of the Soul (1988) p.169
I can’t find the quote easily (it’s somewhere in God, No!), but Penn Jillette has said that one aspect of magic tricks is the magician putting in more work to set them up than anyone sane would expect.
I’m moderately sure that he’s overestimating how clearly the vast majority of people think about what’s needed to make a magic trick work.
Make the secret a lot more trouble than the trick seems
worth. You will be fooled by a trick if it involves more
time, money and practice than you (or any other sane
onlooker) would be willing to invest. My partner, Penn,
and I once produced 500 live cockroaches from a top hat on
the desk of talk-show host David Letterman. To prepare
this took weeks. We hired an entomologist who provided
slow-moving, camera-friendly cockroaches (the kind from
under your stove don’t hang around for close-ups) and
taught us to pick the bugs up without screaming like
preadolescent girls. Then we built a secret compartment
out of foam-core (one of the few materials cockroaches
can’t cling to) and worked out a devious routine for
sneaking the compartment into the hat. More trouble than
the trick was worth? To you, probably. But not to
magicians.
Edit: That trick is 19 minutes and 50 seconds into this video.
Yes, exactly the same idea. Partial versions of your quote have been postedtwice in LW already, and might have inspired me to post the Chesterton prior version, but I liked seeing the context for the Adams one that you provide.
Out of context, the quote makes much less sense; the specific example illustrates the point much better than the abstract description does.
Just for fun, which of the following extremely improbable events do you think is more likely to happen first: 1) The winning Mega Millions jackpot combination is 1-2-3-4-5-6 (Note that there are 175,711,536 possible combinations, and drawings are held twice a week.) 2) The Pope makes a public statement announcing his conversion to Islam (and isn’t joking).
Assuming that the 123456 winning must occur by legit random drawing (not a prank or a bug of some kind that is biased towards such a simple result) then I’d go for the Pope story as ]more likely to happen any given day in the present. After all, there have been historically many examples of highly ranked members of groups who sincerely defect to opposing groups, starting with St. Paul. But I confess I’m not very sure about this, and I’m too sleepy to think about the problem rigorously.
In the form you posed the question (“which is more likely to happen first”) it is much more difficult to answer because I’d have to evaluate how likely are institutions such as the lottery and the Catholic Church to persist in their current form for centuries or millennia.
In the form you posed the question (“which is more likely to happen first”) it is much more difficult to answer because I’d have to evaluate how likely are institutions such as the lottery and the Catholic Church to persist in their current form for centuries or millennia.
It’d be even more fun if you replaced “1-2-3-4-5-6” with “14-17-26-51-55-36″. (Whenever I play lotteries I always choose combinations like 1-2-3-4-5-6, and I love to see the shocked faces of the people I tell, tell them that it’s no less likely than any other combination but it’s at least easier to remember, and see their perplexed faces for the couple seconds it takes them to realize I’m right. Someone told me that if such a combination ever won they’d immediately think of me. (Now that I think about it, choosing a Schelling point does have the disadvantage that should I win, I’d have to split the jackpot with more people, but I don’t think that’s ever gonna happen anyway.))
more likely to happen first
Dunno how you would count the (overwhelmingly likely) case where both Mega Millions and the papacy cease to exist without either of those events happening first, but let’s pretend you said “more likely to happen in the next 10 years”… Event 1 ought to happen 0.6 times per million years in average; I dunno about the probability per unit time for Event 2, but it’s likely about two orders of magnitude larger.
Aren’t you choosing an anti-Schelling point? It seems to me that people avoid playing low Kolmogorov-complexity lottery numbers because of a sense that they’re not random enough—exactly the fallacious intuition that prompts the shocked faces you enjoy.
Choosing something that’s “too obvious” out of a large search space can work if you’re playing against a small number of competitors, but when there are millions of people involved, not only are some of them going to un-ironically choose “1-2-3-4-5-6″, but more than one person will choose it for the same reason it appeals to you.
So whether this choice is Schelling or anti-Schelling depends on reference sets that are quite fuzzy on the specified information, to wit, the set of non-random-seeming selections and (the proportion of players in) the set of people who play them.
I still think many more people pick any given low Kolmogorov-complexity combination than any given high Kolmogorov-complexity combination, if anything because there are fewer of the former. If 0.1% of the people picked 01-02-03-04-05 / 06 and 99.9% of the people picked a combination from http://www.random.org/quick-pick/ (and discarded it should it look ‘not random enough’), there’d still be 175 thousand times as many people picking 01-02-03-04-05 / 06 as 33-39-50-54-58 / 23. (Likewise, the fact that the most common password is password doesn’t necessarily mean that there are lots of idiots: it could mean that 0.01% of the people pick it and 99.99% pick one of more than 9,999 more complicated passwords. Not that I’m actually that optimistic.)
(Now that I think about it, choosing a Schelling point does have the disadvantage that should I win, I’d have to split the jackpot with more people, but I don’t think that’s ever gonna happen anyway.))
With this in mind I think I would choose combinations that match the pattern /[3-9][0-9][3-9][0-9][1-6][0-9]/. Six digit numbers look too much like dates!
1-2-3-4-5-6 is a Schelling point for overt tampering with a lottery. That makes it considerably more likely to be reported as the outcome to a lottery, even if it’s not more likely to be the outcome of a stochastic method of selecting numbers.
After seeing quite a few examples, I’ve recently become very sensitive to comparisons of an abstract idea of something with an objective something, as if they were on equal footing. Your question explicitly says the Pope conversion is a legitimate non-shenanigans event, while not making the same claim of the lottery result. Was that intentional?
After seeing quite a few examples, I’ve recently become very sensitive to comparisons of an abstract idea of something with an objective something, as if they were on equal footing. Your question explicitly says the Pope conversion is a legitimate non-shenanigans event, while not making the same claim of the lottery result. Was that intentional?
No, I just didn’t think of it. (Assume that I meant that, if someone happens to have bought a 1-2-3-4-5-6 ticket, they would indeed be able to claim the top prize.)
You said that the Pope was definitely not joking, (or replaced by a prankster in a pope suit), but left it open as to whether the lottery result was actually a legitimate sequence of numbers drawn randomly from a lottery machine, or somehow engineered to happen.
In that sense, you’re comparing a very definite unlikely event (the Pope actually converting to Islam) to a nominally unlikely event (1-2-3-4-5-6 coming up as the lottery results, for some reason that may or may not be a legitimate random draw). Was that intentional?
No, but if someone successfully manages to rig the lottery to come up 1-2-3-4-5-6, and doesn’t get caught, I’d count that as an instance. Similarly, if the reason the Pope issued the public statement was that his brother was being held hostage or something, and he recants after he’s rescued, that’s good enough, too; I just wanted to rule out things like April Fools jokes, or off-the-cuff sarcastic remarks.
1-2-3-4-5-6 is a Schelling point for overt tampering with a lottery.
I don’t think that’s true. If you were going to tamper with the lottery, isn’t your most likely motive that you want to win it? Why, then, set it up in such a way that you have to share the prize with the thousands of other people who play those numbers?
I specified “overt tampering” rather than “covert tampering”. If you wanted to choose a result that would draw suspicion, 1-2-3-4-5-6 strikes me as the most obvious candidate.
-- Douglas Adams. The Long Dark Tea-Time of the Soul (1988) p.169
I can’t find the quote easily (it’s somewhere in God, No!), but Penn Jillette has said that one aspect of magic tricks is the magician putting in more work to set them up than anyone sane would expect.
I’m moderately sure that he’s overestimating how clearly the vast majority of people think about what’s needed to make a magic trick work.
His partner Teller says the same thing here:
Edit: That trick is 19 minutes and 50 seconds into this video.
It’s not clear to me that clear thought on the part of the audience is necessary to make that statement true.
Yes, exactly the same idea. Partial versions of your quote have been posted twice in LW already, and might have inspired me to post the Chesterton prior version, but I liked seeing the context for the Adams one that you provide.
Out of context, the quote makes much less sense; the specific example illustrates the point much better than the abstract description does.
Just for fun, which of the following extremely improbable events do you think is more likely to happen first:
1) The winning Mega Millions jackpot combination is 1-2-3-4-5-6 (Note that there are 175,711,536 possible combinations, and drawings are held twice a week.)
2) The Pope makes a public statement announcing his conversion to Islam (and isn’t joking).
Assuming that the 123456 winning must occur by legit random drawing (not a prank or a bug of some kind that is biased towards such a simple result) then I’d go for the Pope story as ]more likely to happen any given day in the present. After all, there have been historically many examples of highly ranked members of groups who sincerely defect to opposing groups, starting with St. Paul. But I confess I’m not very sure about this, and I’m too sleepy to think about the problem rigorously.
In the form you posed the question (“which is more likely to happen first”) it is much more difficult to answer because I’d have to evaluate how likely are institutions such as the lottery and the Catholic Church to persist in their current form for centuries or millennia.
Good point.
It’d be even more fun if you replaced “1-2-3-4-5-6” with “14-17-26-51-55-36″. (Whenever I play lotteries I always choose combinations like 1-2-3-4-5-6, and I love to see the shocked faces of the people I tell, tell them that it’s no less likely than any other combination but it’s at least easier to remember, and see their perplexed faces for the couple seconds it takes them to realize I’m right. Someone told me that if such a combination ever won they’d immediately think of me. (Now that I think about it, choosing a Schelling point does have the disadvantage that should I win, I’d have to split the jackpot with more people, but I don’t think that’s ever gonna happen anyway.))
Dunno how you would count the (overwhelmingly likely) case where both Mega Millions and the papacy cease to exist without either of those events happening first, but let’s pretend you said “more likely to happen in the next 10 years”… Event 1 ought to happen 0.6 times per million years in average; I dunno about the probability per unit time for Event 2, but it’s likely about two orders of magnitude larger.
Aren’t you choosing an anti-Schelling point? It seems to me that people avoid playing low Kolmogorov-complexity lottery numbers because of a sense that they’re not random enough—exactly the fallacious intuition that prompts the shocked faces you enjoy.
Choosing something that’s “too obvious” out of a large search space can work if you’re playing against a small number of competitors, but when there are millions of people involved, not only are some of them going to un-ironically choose “1-2-3-4-5-6″, but more than one person will choose it for the same reason it appeals to you.
Thank you for that insightful observation.
Just to follow up, army1987′s actual choice is:
So whether this choice is Schelling or anti-Schelling depends on reference sets that are quite fuzzy on the specified information, to wit, the set of non-random-seeming selections and (the proportion of players in) the set of people who play them.
I still think many more people pick any given low Kolmogorov-complexity combination than any given high Kolmogorov-complexity combination, if anything because there are fewer of the former. If 0.1% of the people picked 01-02-03-04-05 / 06 and 99.9% of the people picked a combination from http://www.random.org/quick-pick/ (and discarded it should it look ‘not random enough’), there’d still be 175 thousand times as many people picking 01-02-03-04-05 / 06 as 33-39-50-54-58 / 23. (Likewise, the fact that the most common password is
passworddoesn’t necessarily mean that there are lots of idiots: it could mean that 0.01% of the people pick it and 99.99% pick one of more than 9,999 more complicated passwords. Not that I’m actually that optimistic.)With this in mind I think I would choose combinations that match the pattern /[3-9][0-9][3-9][0-9][1-6][0-9]/. Six digit numbers look too much like dates!
1-2-3-4-5-6 is a Schelling point for overt tampering with a lottery. That makes it considerably more likely to be reported as the outcome to a lottery, even if it’s not more likely to be the outcome of a stochastic method of selecting numbers.
After seeing quite a few examples, I’ve recently become very sensitive to comparisons of an abstract idea of something with an objective something, as if they were on equal footing. Your question explicitly says the Pope conversion is a legitimate non-shenanigans event, while not making the same claim of the lottery result. Was that intentional?
No, I just didn’t think of it. (Assume that I meant that, if someone happens to have bought a 1-2-3-4-5-6 ticket, they would indeed be able to claim the top prize.)
I might not have worded that very clearly.
You said that the Pope was definitely not joking, (or replaced by a prankster in a pope suit), but left it open as to whether the lottery result was actually a legitimate sequence of numbers drawn randomly from a lottery machine, or somehow engineered to happen.
In that sense, you’re comparing a very definite unlikely event (the Pope actually converting to Islam) to a nominally unlikely event (1-2-3-4-5-6 coming up as the lottery results, for some reason that may or may not be a legitimate random draw). Was that intentional?
No, but if someone successfully manages to rig the lottery to come up 1-2-3-4-5-6, and doesn’t get caught, I’d count that as an instance. Similarly, if the reason the Pope issued the public statement was that his brother was being held hostage or something, and he recants after he’s rescued, that’s good enough, too; I just wanted to rule out things like April Fools jokes, or off-the-cuff sarcastic remarks.
I don’t think that’s true. If you were going to tamper with the lottery, isn’t your most likely motive that you want to win it? Why, then, set it up in such a way that you have to share the prize with the thousands of other people who play those numbers?
I specified “overt tampering” rather than “covert tampering”. If you wanted to choose a result that would draw suspicion, 1-2-3-4-5-6 strikes me as the most obvious candidate.
Why would anyone want to do that? (I’m sure that any reason for that would be much more likely than 1 in 175 million, but still I can’t think of it.)
The three most obvious answers (to my mind) are:
1) to demonstrate your Big Angelic Powers
2) to discredit the lottery organisers
3) as a prank / because you can
The former will happen about every couple million years in average, so I’d say the latter is more likely by at least a factor of 100.