Paying back debts

Suppose a charismatic anti-debt crusader (maybe Ron Paul) persuaded everyone in the world to pay pack all of his debts. This includes the U.S. treasury, all private banks, corporations, and all individuals (but not central banks, e.g. the Federal Reserve System banks, since their debts are represented by the currency itself). This includes all depository institutions, which would be required to send actual dollar bills to their depositors, and zero out the deposit accounts (since “deposits” are really just debts owed by the banks to the depositors).

Question: How many dollar bills would be in circulation (i.e. would exist and be owned by entities other than Federal Reserve System banks)?

I believe I know the answer, but I want to finish reading this before I say definitively.

Another question: is there any substantive reason the U.S. Treasury needs to be separate from the Federal Reserve, or is the separation motivated by the desire to have transparency and to encourage responsible governance?

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Getting your money back

Harold Camping and his organization, Family Radio, were proved wrong this weekend when the world did not end. NPR reports that Tom Evans, a board member of Family Radio, “hopes the organization will repay people who gave their money to the cause. But at this point he can’t guarantee it.” I have heard other calls for compensation to Camping’s followers as well. I wonder when leaders of other religious organizations that make very highly dubious claims (e.g. that the earth was created some time in the last ~10,000 years) will say that they hope to compensate their misled donors.

I actually think Camping should feel less guilty about misleading his followers than a lot of other religious leaders: he seems to have truly believed what he said. In contrast to most other religious leaders, he was willing to bet his reputation on a falsifiable claim, and thus was, all else equal, less likely to be lying. Other religious leaders tend to profess astounding levels of certainty about various beliefs, none of which, conveniently, are falsifiable.

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Another $20 Brainteaser

Update Saturday 1am: I am not totally satisfied with this puzzle as it feels a bit contrived. I think I can make it both more realistic and not that much more convoluted. I am going to try to do that and repost within a couple weeks. However, I will not retract my $20 offer, as I do not want to cause anyone’s Friday night to have been spent in vain.

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You are in a city with a grid-based system of streets. You need to walk to a destination separated from you by N East/West streets and M North/South streets. There is a stoplight at every intersection. Each time you arrive at an intersection, there is

a) a 40% chance you can cross the North/South street with no wait, but that you’d have to wait 1 minute to cross the East/West street

b) a 40% chance you can cross the East/West street with no wait, but that you’d have to wait a minute to cross the North/South street

c) a 20% chance you can cross the street of your choosing, but that once you cross that street, you’d have to wait a minute to cross the street in the other direction

In a and b (as well as c), after you cross in one direction, you’d have to wait 1 minute before crossing in the other direction (this not a perfectly realistic model of how it works in the real world, since it takes time to cross the street, but it is the assumption for this puzzle), otherwise you can continue walking in the same direction to the next crossing (assuming that will get you closer to the destination).

By assumption it takes 2 minutes to walk the distance between any 2 adjacent streets, and it takes no time to actually cross a street.

If you follow the optimal strategy, what is the expected time it will take you to reach your destination?

$20 to the first person who provides the correct solution.

Maximum payout to any individual person for puzzle answers is $20.

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Mirror Image Puzzle

Below is a puzzle I have come across on two different occasions, the latest one being when reading the introduction to Gary Drescher’s book “Good and Real: Demystifying Paradoxes from Physics to Ethics” (which I did not come close to finishing due to boredom, although I may return to it). Based on the amount of exposure I get to puzzles and brainteasers, I’d expect to have come across this one more than twice, as it is a good one. You need no special education at all to understand the question, so no one can claim exemption due to their major or specialty in life!

Puzzle: Why does a mirror reverse the left and right directions, but not the up and down directions? (In other words: Your mirror image wears his watch on his right hand. Why doesn’t he wear his shoes on his head?)

No monetary reward for the solution to this one, as there is (still unclaimed!) for the last one.

Update Tues 7pm: Recommended way of answering: post the answer in the comments, but in a foreign language (ideally one with an alphabet different from English’s), in order to allow readers to browse the comments, and decipher only the answers they’re interested in (you can use an online translator both to encode and to decipher the answers).

Update Thurs 11am: Spoilers in comments

Good and Real: Demystifying Paradoxes from Physics to Ethics

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NY Times admits to basing its linguistic decisions on U.S. government diktat

(UPDATED Monday 2pm: last paragraph changed based on feedback from my friend Adam)

The New York Times’ ombudsman has a column on the Times’ practice of not (generally) using the word “torture” when describing the way the Bush administration dealt with War on Terror detainees. He concludes by saying the Times should change this practice, and use the word “torture” to describe this behavior. The Times’ rationale for not using the word “torture” before was as follows:

The Bush administration offered formal legal opinions that the “enhanced interrogation techniques” it authorized were not torture under United States law. The Times adopted the view that labeling these as “torture” in news articles could create the appearance of taking sides.

Thus, the Times did not use the word “torture” since the U.S. government said it was not an appropriate word. So we can immediately dispense with the notion that the Times is “unbiased” (whatever that means) — they are biased in favor of the U.S. government. If a reporter were writing an article on the treatment of U.S. PoW’s by the Japanese during WWII, and he wanted to use the word “torture,” would the Times be in the slightest bit interested to know how the Japanese government referred to the treatment? (Even if they were, they wouldn’t be able to find anything useful, since the Japanese use the Japanese language rather than English, and thus wouldn’t have used the English word “torture” in official decisions, even if they believed that to be the appropriate English word.)

The ombudsman confusingly points out that the New York Times’ decision was based on the desire not to appear to be “taking sides.” What does it mean to “take sides” as a reporter? A reporter should report a fact if that fact is clear with a very high probability, and if it is relevant to the reporter’s readers. That is probably an oversimplification, but what can be said for certain is that the issue of whether the reporter is “taking sides” should not be part of the calculus at all, and it is a meaningless notion. What could it mean to “take sides” when reporting a fact?

One possibility is that it means to report a fact that a lot of people do not believe to be true. If that were what the Times were trying to do, then they could never report anything meaningful at all, since they’d only report on things that everybody already knew. Another possibility is that it means to report a fact that a lot of people do not believe to be true, and will not be convinced of even after they’ve read the article. This is a possibility, but it is a dumb standard — who would want to read from a newspaper that only reported things that were guaranteed to generate no controversy. It appears in this case that the Times’ operational definition of “taking sides” is “reporting a fact that the U.S. government disagrees with.”  It is certainly true that the Times sometimes does “take sides” based on this definition of the term, so I am not saying that the Times has a consistent policy that forbids them from disagreeing with the government. But they have admitted to being swayed by a desire not to do so in this particular case. (And Bill Keller, the editor of the newspaper, was unashamed in explaining this policy of not wanting to “take sides.”)

Thanks to the ombudsman for telling the Times to remedy their behavior. He should have gone further, though, and pointed out that the desire not to “take sides” is at best nonsensical and at worst (and apparently) a desire to adhere to the judgments of the U.S. government. The Times should not defer to legal U.S. legal opinions when reporting the facts of our detainee treatment any more than they should defer to Japanese legal opinions when reporting about WWII. The Times can find plenty of good instruction on the English language without biasing themselves towards the desires of governments.

(update explanation: I originally wrote that the Times had “follow[ed] the orders of the U.S. government,” which, as Adam pointed out, is not exactly correct. The Times did not follow “orders,” but rather voluntarily strove to use language consistent with views of the government.)

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Word usage error in NY Times

Update (Sunday 8:30pm): link to article removed, since the Times modified the story (although there is no evidence that the modification was due to their having learned their lesson about word usage!)

New York Times, today:

“It was 10 minutes before its scheduled departure,” said Mr. Kelly, who could not immediately say whether Mr. Strauss-Kahn was traveling alone or how soon before the flight he had purchased a ticket.

Error: use of “soon”

“Shortly” should be used instead. “Soon” means “occurring a short while after [the reference time, e.g. the time when Strauss-Kahn purchased the ticket]”

“Shortly” means “occurring a short while either before or after [the reference time]”

This is a common error though, and the folks at the New York Times are still learning, so we should cut them some slack.

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This is what lying is (according to Whyte)

Here is a good example of a case where we should make someone bet money to prove how sure they are of something, an issue discussed in the previous post.

David Brooks writes:

But, remember, the debt-ceiling limit has to pass. If it doesn’t, there will be ruination for all involved. Moreover, if the two parties do come up with a compromise, the rewards would be enormous. President Obama would have averted a national catastrophe, put the government on a sustainable path and transformed the atmosphere in Washington. He’d surely win re-election in a walk. Boehner and McConnell would go down in history as the men who tamed the federal leviathan. The forces of fear and hope push powerfully toward a deal. [emphasis added]

Brooks is saying that Obama would surely win reelection if the debt-ceiling is passed. If this were true, Brooks could multiply his wealth by 1.7 by putting his money where his mouth is on Intrade. Is he going to do this? Probably not. Why? Because he is lying.

A more minor quibble: Brooks argues that all “the rewards would be enormous” for republican leaders as well as Obama if the debt-ceiling passes.  I disagree with reading of the political situation. If a political event seals Obama’s chances of winning the presidency, then surely there should be a good number of republicans who do not see that event as having brought “enormous rewards.” The republicans should at least get enough concessions from Obama on the debt-ceililng passage such that it would not seal his chances of victory in order for the passage to be declared as having brought such great rewards to the republicans themselves.

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What is Lying?

Jamie Whyte has a guest-post on Steve Landsburg’s blog arguing that we should force politicians to put their own money on the line when they make prognostications. E.g. we should have forced Tony Blair (Whyte is British) to place a bet, using his own money, on whether Saddam Hussein had WMD.

This certainly is a good idea, and it applies not only to politicians but to other blowhards as well.

In making his argument, Whyte defines “lying” as misrepresenting one’s degree of certainty about a factual claim:

Lying is not a matter of saying something you do not really believe. This is because, on matters subject to doubt, we believe “both sides of the debate”. For example, I believe that Osama Bin Laden is dead. But I am not certain of it. Or, in other words, I believe, to a small degree, that Bin Laden is alive. So, if I said “Bin Laden Lives!”, though I would be lying, this would not be because I do not believe it; I do believe it a little. I would be lying because I believe it with less confidence than my assertion suggests.

Once you see lying as misrepresenting your degree of belief, it is clear that politicians lie incessantly. They pretend to a level of confidence that they cannot really feel. Forcing them to bet material sums of money on their claims would encourage them to reveal their true confidence.

Whyte is playing with semantics here a little bit (“I believe, to a small degree, that Bin Laden is alive” is just an unconventional way of using the word “believe.”) But the substance of his argument is that you are lying any time you misrepresent your degree of certainty, not just when you say that you know something, when in fact you believe it is not true. Again, this argument is just about the definition of a word (“lying”) but it raises the question, why are we so quick to condemn those who say “I believe X” when in fact they do not believe X (“these people are liars!”) whereas we are not nearly as quick to condemn those who say “I know X” when in fact they merely believe X, with considerably less than 100% certainty.

It seems clear that it can be just as dangerous for someone to say “I know X” when really he is only 70% certainty of X, as for him to say “I believe X” when really he is 60% certain that X is not true.

This boils down to our gravitation towards incorporating the 50% threshold when defining words. We generally define lying as representing our certainty as being on one side of this threshold, when in reality it is on the other side of the threshold (this is a rough definition). Why don’t we instead define lying to refer to cases where our professed level of certainty differs from our actual level of certainty by, say, 10%? Probably because we hardly ever force people to actually indicate their level of certainty (as as percentage) about anything in the first place.

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Modification to IBM Puzzle

Modify this puzzle in the following way: Suppose that the encoding is in trinary, with 0’s, 1’s and 2’s, and that 0 represents white and 1 represents black (as in the original) and that 2 represents red. Suppose further that each digit is a 0 with probability 40%, 1 with probability 40%, and 2 with probability 20%. Then, the new question is: What is the expected number of digits between 2 adjacent non-white (i.e. red or black) bars, each with width at least 20 bits?

($20 to the anyone the first person who solves it)

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Who was the annoying person who wanted to snap a photo?

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