Author Archive for Steve Landsburg

Double Standards

Published
by
Steve Landsburg
on August 1, 2013
in Current Events and Outrage
. 71 Comments

Remember last January, when the President said he wouldn’t negotiate with hostage-takers—like the Republican representatives who demanded spending cuts in exchange for raising the debt ceiling? His argument, as I understood it, was that:

  1. A failure to raise the debt ceiling would be unambiguously bad policy.
  2. It is irresponsible to threaten to implement a bad policy just to gain concessions on the spending front.

It’s an argument I expect we’ll hear again, next time the debt ceiling comes up.

And what’s the President up to in the meantime? He’s demanding a new round of spending increases in exchange for corporate tax reform. Now, since pretty much every sentient being in the Universe agrees that we’re long overdue for corporate tax reform (and in particular for lower rates), I think it’s fair to characterize the President’s position as a threat to retain a bad corporate tax policy just to gain concessions on the spending front.

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Non-Hansonian Prediction Markets

Published
by
Steve Landsburg
on July 22, 2013
in Humor, Miscellaneous and Snark
. 61 Comments

Having a baby? Want to predict its gender? Amazon.com offers just the product:

Does it work? Well, check out the distribution of customer reviews:

A delighted hat tip to our reader Mark Westling of Inuvi.com, who remarks that

The most interesting comments are along the lines of “It was wrong so I only gave it three stars”.

and then goes on to propose a business model:

Offer baby sex prediction over the web, charge $75 (so consumers know it’s good), and offer a full refund if you’re wrong (upon review of relevant documents).

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Unclear on the Concept

Published
by
Steve Landsburg
on July 18, 2013
in Humor, Oddities and Snark
. 56 Comments

Mike Rizzo at The Unbroken Window reports spotting these two bumper stickers next to each other — on the same car.

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A Bayesian Solution

Published
by
Steve Landsburg
on July 16, 2013
in Puzzles
. 198 Comments

There were many excellent comments on yesterday’s Bayesian Riddle. Here’s what I believe is the simplest and most natural analysis.

First, let’s recall the problem:

A murder has been committed. The suspects are:

  • Bob, a male smoker.
  • Carol, a female smoker.
  • Ted, another male smoker.
  • Alice, a female non-smoker.

You are quite sure that one (and only one) of these suspects is the culprit. Moreover, after carefully examining the evidence, you’ve concluded that the odds are 2-to-1 that the culprit is a smoker.

Now your crack investigative team, in which you have total confidence, reports that, on the basis of new evidence, they’ve determined that the culprit is definitely female.

Who’s the most likely culprit, and with what probability?

Notice that if you considered all the suspects equally likely, your estimate would have been three to one for a smoker. Since you estimated only 2-to-1, you must have believed that the individual smokers were less likely than average to be guilty. So when you find out the culprit is female, it’s the female non-smoker — that is, Alice — who is now your prime suspect.

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A Bayesian Riddle

Published
by
Steve Landsburg
on July 15, 2013
in Puzzles
. 80 Comments

A murder has been committed. The suspects are:

  • Bob, a male smoker.
  • Carol, a female smoker.
  • Ted, another male smoker.
  • Alice, a female non-smoker.

You are quite sure that one (and only one) of these suspects is the culprit. Moreover, after carefully examining the evidence, you’ve concluded that the odds are 2-to-1 that the culprit is a smoker.

Now your crack investigative team, in which you have total confidence, reports that, on the basis of new evidence, they’ve determined that the culprit is definitely female.

Who’s the most likely culprit, and with what probability?

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Fortune Comes a-Crawlin’

Published
by
Steve Landsburg
on July 11, 2013
in Blogging, Oddities, Personal and Religion
. 21 Comments


With great humility, I am honored to inform you that Eric Crampton of Offsetting Behavior has nominated me for sainthood.

Riffing off yesterday’s Acta Sanctorum post, Eric is asking for your help in making this a reality:

So, here’s the campaign for Saint Steven.

  1. Any of you who have any kind of illness at all pray to Steven Landsburg for intervention.
  2. If you do not receive divine Landsburgean intervention, don’t tell me about it.
  3. If you do receive divine Landsburgean intervention, please leave a record of such in the comments. Preferably with a link to a doctor’s note saying that your recovery was unexpected and pretty remarkable. This should happen in maybe 1% of cases.
  4. We submit the documented evidence of the successes, while ignoring the failures. Ta-dah! Saint Steven.

My hope is to beat John Paul II’s record of two reported cures, plus the toppling of one Evil Empire, or, at a minimum, the National Endowment for the Arts. Oh, and while I’m at it I have a couple of other worldly improvements in mind. Watch your step, Paul Krugman!

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Acta Sanctorum

Published
by
Steve Landsburg
on July 10, 2013
in Bad Reasoning, Current Events and Religion
. 24 Comments

So if I have this right, it is now the official position of the Catholic church that:

  1. The late Pope John Paul II has the ongoing power to cure brain aneurysms.
  2. As far as we know, he has chosen to employ this power exactly once. (He also once cured a case of Parkinson’s.)
  3. While hundreds of thousands of others have suffered and/or died from brain aneurysms, John Paul has not been moved to intervene.
  4. The one victim he troubled himself to save was selected not because she was particularly deserving or particularly valuable to society, but because she chose the right guy to pray to — sort of like having to suck up to the teacher to get a good grade.
  5. All of this makes John Paul II particularly fit for veneration.

For God’s sake (you should pardon the expression), if you’re looking to make the case that John Paul II was capable of performing (or at least catalyzing) genuine miracles, isn’t the defeat of Soviet Communism good enough? That right there makes him a saint in my book — though if I ever come to believe that he can cure aneurysms and has been holding out on us, I might have to retract my endorsement.

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The Road Not Taken

Published
by
Steve Landsburg
on July 8, 2013
in Bad Reasoning, Blogging, Outrage and Paul Krugman
. 82 Comments

Paul Krugman, having apparently received another of his divine revelations, proclaims that if we demand (somewhat) better working conditions in Third World countries (backed up, presumably, with boycott threats), “we can achieve an improvement in workers’ lives … And we should go ahead and do it.”

Don’t ask how he knows; the ways of the Oracle are mysterious and beyond human ken.

Look. A well designed policy of boycotts and boycott threats can certainly improve working conditions in the Third World. It can also lower either wages, employment or both. Whether or not that package amounts to “an improvement in worker’s lives”, as Krugman puts it, is an interesting and important question, and well worth thinking about. But apparently the last thing Krugman wants you to do is think about it, since he’s already told you the answer, and seems to presume you won’t have the slightest interest in where it came from.

Now, among the many differences between me and Paul Krugman, there are probably some that redound to his credit. But his propensity to hide all of his reasoning (if any) is not one of them. Compare, for example, my blog post of a few years ago on working conditions in 1911 New York City, when the Triangle Shirtwaist fire claimed 146 lives, most of them young women, partly because the fire exits were blocked to prevent pilfering. Would workers in 1911 have wanted safer working conditions (including unblocked fire exits)? This was my answer:

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Hi, Mom!

Published
by
Steve Landsburg
on July 8, 2013
in Math, Personal and Puzzles
. 23 Comments

MomMy mother, who reads this blog, reports that she’s lost a few nights’ sleep lately, tormented by thoughts of Knights, Knaves and Crazies. Serves her right. Once when she and I were very young, she tormented me with a geometry puzzler that I now know she must have gotten (either directly or indirectly) from Lewis Carroll; you can find it here. If she remembers the solution, she should be able to sleep tonight.

Herewith, a proof that a right angle can equal an obtuse angle. The puzzle, of course, is to figure out where I cheated.

But wait! Let’s do this as a video, since I’m starting to fool around with this technology and could use the practice. Consider this more or less a first effort. If you prefer the old ways, you can skip the video and read the (identical) step-by-step proof below the fold.

Or, if you prefer to skip the video, start here:

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Hard and Harder

Published
by
Steve Landsburg
on July 5, 2013
in Logic and Puzzles
. 14 Comments

If you failed to solve Wednesday’s problem on Knights, Knaves and Crazies, take comfort from the fact that this has circulated among philosophers under the title “The Hardest Logic Problem Ever”. MIT philosopher George Boolos discussed it in the Harvard Review of Philosophy back in 1996. In that version, Crazies are never silent. But Oxford philosopher Gabriel Uzquiano soon observed that this can’t be the hardest logic problem ever, because it gets harder if the Crazies can be silent. Uzquiano’s new “hardest logic problem ever” was solved by the philosophers Gregory Wheeler and Pedro Barahona — and then solved again, substantially more elegantly, I think, in Wednesday’s comments section right here.

A few more thoughts, on the problem, its solution, and how to make it harder:

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Knights, Knaves and Crazies

Published
by
Steve Landsburg
on July 3, 2013
in Logic and Puzzles
. 97 Comments

SmullyanThe best dozen or so puzzle books ever written are, without a doubt, the works of Raymond Smullyan. If you’ve never encountered these, stop right now and order yourself a copy of What is the Name of This Book?, which is brilliant on multiple levels. On the surface, it’s a book of particularly amusing little brain teasers. One level down, those brain teasers contain a proof of Godel’s Incompleteness Theorem — solve all the riddles and you’ll have painlessly understood the proof!

Smullyan’s books are heavily populated by Knights who always tell the truth, Knaves who always lie, and bewildered travelers trying to distinguish one from the other via their cryptic utterances. Today’s puzzle is Smullyan-like in its set-up but considerably more difficult than most. It’s been proposed and discussed in philosophy journals, but I’m suppressing the sources (and rewording the problem) to make it a little harder to Google. I’ll of course pay appropriate homage to the authors when I post solutions in the near future. Meanwhile, if you’ve seen this before, or if you’ve found the answer on line, please restrain yourself from posting spoilers. But do post whatever you manage to come up with on your own.

And now to the puzzle:

Continue reading ‘Knights, Knaves and Crazies’

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A Queer Bit of Reasoning

Published
by
Steve Landsburg
on June 26, 2013
in Bad Reasoning and Current Events
. 110 Comments

Here is Justice Anthony Scalia, dissenting from the Supreme Court ruling striking down the Defense of Marriage Act:

It is enough to say that the Constitution neither requires nor forbids our society to approve of same-sex marriage, much as it neither requires nor forbids us to approve of no-fault divorce, polygamy, or the consumption of alcohol.

I don’t get it. The Consitution neither requires nor forbids our society to approve of the Atlantic Monthly, but it still requires us to tolerate the Atlantic Monthly. Or does Justice Scalia disagree?

(Note to potential commenters: This is not a post about whether we as a society either should or should not approve of same-sex marriage, or for that matter whether there’s any meaningful sense in which a “society” is capable of approving anything at all. It’s also not a post about what our policy should be toward same-sex marriage. It’s a post about Justice Scalia’s odd notion of what this case was about. Please stay on topic.)

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Multiple Comments

Published
by
Steve Landsburg
on June 26, 2013
in Bad Reasoning, Economics and Paul Krugman
. 80 Comments

Following up on yesterday’s Keynesian Cross post:

  1. The point, for those who missed it, is that using exactly the same reasoning that we find in Eco 101 textbooks to derive the Keynesian multiplier, we can conclude that sending all your money to me will make everyone rich. The conclusion is absurd; therefore the reasoning is invalid. And reasoning that’s invalid in one context is also invalid in another.
  2. Some commenters thought that my version of the Keynesian cross argument was an unfair caricature. I invite those commenters to peruse some actual Eco 101 textbooks. For example, they might browse through the section labeled “The Income-Expenditure Model” in a widely used textbook called Macroeconomics. The authors are Robin Wells and Paul Krugman.
  3. Let’s review the logic of that model. (See yesterday’s post for explanations of the notation.)

    Step I: Start with an accounting identity (in this case C+I+G).
    Step II: Throw in an empirical regularity (in this case C=.8Y).
    Step III: Combine the two equations to get a third equation (Y=5(I+G).)
    Step IV: Do a thought experiment involving a policy change (e.g. an increase in G) and predict the outcome by assuming that your equations will continue to hold after the policy change.

    By contrast, my alternative model starts with an accounting identity (Y=L+E), throws in an empirical regularity (Y=.999999E), combines these equations to get a third (Y=1000000L) and then predicts the outcome of a thought experiment (send me your money!) by assuming that the equations will continue to hold. In other words, yes, exactly the same logic.

  4. The problem with the Landsburg multiplier story is that after you send me your money, the equation Y=.999999E is not likely to remain true. The problem with the Keynesian multiplier story is that after you increase government spending, the equality C=.8Y is not likely to remain true. Why not? Well, for one thing, if the government buys you a bowl of Wheaties, you’re correspondingly less likely to go out and buy a bowl of Wheaties for yourself. For another, if the government spends wastefully, you, as a taxpayer, are going to end up poorer, which means you’ll probably consume less. The exact nature of the change depends on the exact nature of the government spending. But there’s surely no reason to buy into the model’s assumption that there will be no change at all.

    5. Continue reading ‘Multiple Comments’

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The Landsburg Multiplier: How to Make Everyone Rich

Published
by
Steve Landsburg
on June 25, 2013
in Economics
. 59 Comments

Today’s lesson is about the Keynesian multiplier.

If you studied economics from one of the classic textbooks (like Samuelson) you might remember how this goes. We start with an accounting identity, which nobody can deny:

Y = C + I + G

Here Y represents the value of everything produced in (say) a given month, which in turn is equal to the total income generated in that month (because producing a $20 radio allows you — or perhaps you and your boss jointly — to earn $20 worth of income). C (which stands for consumption) is the value of the output that ends up in households; I (which stands for investment) is the value of the output that ends up at firms, and G (which stands for government spending) is the value of the output that ends up in the hands of the government. Since all output ends up somewhere, and since households, firms and government exhaust the possibilities, this equation must be true.

Next, we notice that people tend to spend, oh, say about 80 percent of their incomes. What they spend is equal to the value of what ends up in their households, which we’ve already called C. So we have

C = .8Y

Now we use a little algebra to combine our two equations and quickly derive a new equation:

Y = 5(I+G)

That 5 is the famous Keynesian multiplier. In this case, it tells you that if you increase government spending by one dollar, then economy-wide output (and hence economy-wide income) will increase by a whopping five dollars. What a deal!

Now, though I cannot seem to find a reference, I have a vague memory that it was Murray Rothbard who observed that the really neat thing about this argument is that you can do exactly the same thing with any accounting identity. Let’s start with this one:

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Judgment Calls

Published
by
Steve Landsburg
on June 23, 2013
in Current Events, Law and Policy
. 69 Comments

If you need further proof that a human being is a close cousin to a chimpanzee, you need look no farther than the design of the American justice system.

Debra Nelson, the judge in the George Zimmerman murder case, has disallowed testimony from audio experts about whether that’s Zimmerman or the deceased Trayvon Martin who can be heard screaming on the 911 tape. That matters, because much of what’s in dispute here is the question of who attacked whom.

One prosecution expert was prepared to testify that the screams are Martin’s, and another that they are at least not Zimmerman’s. Defense experts were prepared to dispute those claims. They made their arguments in front of the judge for several days, whereupon she ruled that the jury won’t be allowed to hear any of it.

The judge’s concern was that there is no good evidence that the experts’ techniques are reliable. That might be true. But who should be making that call — the judge or the jury?

There is, I think, an excellent case to be made that juries are, by and large, incompetent (or at least less competent than judges) to determine what constitutes a plausible argument by an audio expert. But if you buy that argument, I think you’ll be pretty much forced to conclude that the jury is also incompetent to reach a verdict. If that’s your view, we shouldn’t have juries in the first place.

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Hate Crimes in Black and White

Published
by
Steve Landsburg
on June 17, 2013
in Bad Reasoning and Policy
. 109 Comments

Which should the law treat more severely: Killing a guy because he cut you off in traffic or killing a guy because you don’t like his race?

Elsewhere on the web (link omitted because the source is the invitation-only blog of a personal friend), I read the following:

In the former case, you’re a danger to the person who wronged you. In the latter, you’re a danger to tens of millions of people, and that’s just in the US.

Hate crimes are different because the perp’s target list is vastly larger, with the built-in implication of recidivism.

There’s so much wrong with this I’m not sure where to begin. First of all, when a guy kills another guy for cutting him off in traffic, I’m inclined to think the likelihood of recidivism is pretty high. It’s not like nobody’s ever going to piss him off again. Second of all, I’d think that severity of punishment should be tied primarily to its effectiveness as a deterrent to others, not as a deterrent to recidivism. We can deal with recidivism partly by keeping an eye on past offenders, but when it comes to deterring unknown others, punishment is all we’ve got.

But I mention those issues only in passing on my way to what I think is the really interesting question, namely: Which is more harmful? Targeting a specific individual for death or targeting a randomly chosen representative of some race?

And while we’re at it: Which is more harmful? Targeting someone for being black, or for being white?

Some thoughts:

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Basic Confusion

Published
by
Steve Landsburg
on June 14, 2013
in Oddities and Personal
. 13 Comments

Andre Weil was a towering figure in 20th century mathematics, his book on Basic Number Theory being just one of his many immortal contributions. (The title is something of a joke; this is a pathbreaking treatise at a very advanced level.)

None of which explains why today, fifteen years after Weil’s death, I received an email from the mathematical publisher Springer-Verlag that reads:

Dear Andre Weil,

We are writing today regarding your book *Basic Number Theory (ISBN: 978-3-662-05980-7), and to let you know about our plans
for an electronic archive, the Springer Book Archives.

…

Your author benefits at a glance:

– Your book will be digitized and become an eBook, published on SpringerLink, our online platform, and for e-reading devices such as the Kindle or iPad.

– Your book can never go ‘out-of-print’ and will be preserved for future generations of scientists.

– You will be provided with free access to the electronic version of your book once it is included in the archive.

– You will receive royalties, or can choose to waive them in support of charitable organizations such as INASP or Research4Life,
that help provide the developing world with access to scientific research.

Please go to the following website and select your preferred royalty option.

[URL deleted]

Yours sincerely,

[Etc.]

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Cato Unbound: The Political Economy of Recycling

Published
by
Steve Landsburg
on June 12, 2013
in Economics, Policy and Self-Promotion
. 75 Comments

Here’s why recycling poses a policy dilemma: To keep people from dumping their trash on their neighbor’s lawns (or, when they burn it, in their neighbor’s lungs), we have to keep the price of landfill space artificially low. But once you’ve made landfill space cheap, you weaken the incentive to recycle, so arguably we get too little recycling. One solution is to pump up that incentive by casting recycling as a moral imperative. Unfortunately, once people believe recycling is a moral obligation, we’re liable to get too much of it.

This month’s issue of Cato Unbound is titled “The Political Economy of Recycling”, with a lead essay by Michael Munger of Duke University expanding on these and related points, with responses by Edward Humes, Melissa Walsh Innes and myself.

Over the course of the next month or so, we’ll be posting responses and re-responses to each others’ essays, as the mood strikes us. The best of your comments here might well find their way into some of my posted responses there.

Below the fold, a brief teaser from my essay:

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The Story Darkens

Published
by
Steve Landsburg
on June 10, 2013
in Current Events, Outrage, Paul Krugman, Politics and Truthseeking
. 65 Comments

It turns out that last week’s tag-team smear of a young Heritage Foundation economist, executed by Senator Sheldon Whitehouse of Rhode Island and his lackey Paul Krugman of the New York Times, was even worse than we knew.

As you’ll recall, Salim Furth of the Heritage Foundation testified before the Senate Budget Committee, accurately presenting data on economic policy changes in various countries for the years 2007-2012. Then Senator Whitehouse, cheered on by Paul Krugman, spent eight minutes excoriating Furth for inventing those numbers — the sort of accusation which, if it were taken seriously, would surely destroy Furth’s career. (As well it ought to, if it had contained a grain of truth.)

And what was Senator Whitehouse’s evidence for Furth’s “meretriciousness”, as he put it? Well, it was the fact that Whitehouse had gone to Furth’s source, looked for the numbers, and found them to be entirely different.

What Senator Whitehouse didn’t tell you was that he was “refuting” Furth’s accurate report of the historical record with projected numbers, which is to say pie-in-the-sky promises by politicians about what they’re going to do in the year 2016. It was, as I said last week, as if I’d announced plans to lose 30 pounds and then promptly gained 10. When Furth accurately reports my recent weight gain, Whitehouse calls him a liar because a 10 pound gain is not a 30 pound loss.

Paul Krugman, who must know better, cheered on this mendacity when he wrote:

a Heritage Foundation economist has been accused of presenting false, deliberately misleading data and analysis to the Senate Budget Committee.

What’s so shocking? Not the false, misleading data and analysis — that’s SOP at Heritage. … What’s shocking is that they got called on it, in real time.

Now it turns out that Senator Whitehouse’s numbers were even farther off base. Not only was were the numbers invented to begin with; he took those numbers for various years and added them up, even though they were already cumulative. It’s as if I’d announced plans to lose 30 pounds in 2013 and another 20 in 2014 — a total of 50 over two years. What Senator Whitehouse did was the equivalent of adding the initial 30 to the total of 50, and then announcing that my projected weight loss is 80 pounds. And then calling Furth a 90-pound liar for accurately reporting my 10 pound weight gain.

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Lies and Lying Liars

Published
by
Steve Landsburg
on June 7, 2013
in Current Events, Outrage, Paul Krugman, Politics and Truthseeking
. 35 Comments

When a politician misleads the public with distorted or flat-out fictional data, or uses eight minutes of national TV time to smear the character of the careful scholar who dared to report an inconvenient set of facts, you can always count on Paul Krugman of the New York Times to leap to the defense of truth and honesty — or, alternatively, to jump on the bandwagon if the politician happens to be a Democrat.

Here, you see, is what happened this week: Salim Furth, an economist at the Heritage Foundation (and a graduate of the University of Rochester, where I knew him to be a thoughtful and honest researcher) testified before the Senate budget committee, where he presented data from the Organisation for Economic Cooperation and Development (OECD) showing that most European governments have recently increased their spending. (This isn’t surprising for several reasons, one of which is that governments often spend more in recessionary times.)

Enter Senator Sheldon Whitehouse of Rhode Island, who spent eight excruciating televised minutes lambasting Furth and questioning his honesty, by reading out OECD numbers that differed dramatically from what Furth had reported. Some choice comments:

Dr. Furth, I am very concerned about your testimony….

When I look at the graph, for instance, which you source to the OECD — did you actually look at what the OECD says?….

They’ve actually written what the numbers are. And here’s what the numbers actually are, according to the OECD….

I am concerned that your testimony to this committee has been meretricious…I am contesting whether you have given us fair and accurate information.

And then there’s another eight minutes of reading out numbers that are, Senator Whitehouse keeps reminding us actually from the OECD, as opposed to these other numbers reported by Furth, which Furth claims are from the OECD, but obviously can’t be, because Whitehouse has the actual OECD numbers right here, and look how different they are — all of this interspersed with a barrage of attacks on Furth’s character and integrity. (See the video below, if you have the stomach for it.)

Now here’s the thing: There are a couple of legitimate reasons why Furth’s and Whitehouse’s numbers don’t agree. The first is that they’re for different time periods. Furth’s are for the years 2007-2012, while Senator Whitehouse’s are for the years 2009-2016. That’s right, 2016. Which brings us to the other reason these numbers differ: Furth’s come from the historical record, while Senator Whitehouse’s come from somebody’s ass.

Continue reading ‘Lies and Lying Liars’

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Keep Them Coming

Published
by
Steve Landsburg
on June 6, 2013
in Blogging
. 0 Comments

The extremely interesting boxcar discussion is now up to 233 comments, many of them extremely insightful. This morning, comments were briefly closed, but this was a glitch and it’s now fixed. (Thanks to Ken B. for alerting me.) Keep those comments coming!

Comments are turned off on this post because I want to keep the discussion all in one place. I’ll soon be back with more content, not all of it boxcar-related.

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I Too Have Riddled Boxcars Boxcars Boxcars

Published
by
Steve Landsburg
on May 23, 2013
in Physics and Puzzles
. 0 Comments

Okay, Tuesday’s boxcar problem has gotten pretty interesting. I thought I knew the answer, but the comments on Wednesday’s followup post have sowed major seeds of doubt. There are a lot of excellent comments there.

I am thankful that I acknowledged in advance (at the bottom of Wednesday’s post) that I’m less sure of this one than I am of many others. I’d cheerfully bet $1000 (subject to agreement on a suitable referee) that I’m right about this relativity puzzle. (My answer is here.) And as far this old chestnut goes, my answer is here and I hereby cheerfully renew my offer to bet up to $15,000 on the outcome of a computer simulation. (Or any other amount, as long as it’s over $1000, to make this worthwhile.) Email me if you’re interested.

(This is on my mind because I’ve just had a very unpleasant encounter with a troll in another venue, who, like other trolls, is happy to bluster but runs away when you offer to put money on the line.)

For the first time ever, I am turning off comments on this post, because I don’t want to dilute yesterday’s interesting discussion by allowing it to take place half over there and half over here. Go there to participate. Many thanks to the commenters who have forced me to think harder about this, and thanks to anyone else who can help resolve the controversy.

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About That Boxcar

Published
by
Steve Landsburg
on May 22, 2013
in Physics and Puzzles
. 348 Comments

Yesterday’s puzzle was this: A boxcar filled with water sits on a frictionless train track. A mouse gnaws a small hole in the bottom of the boxcar, near what we’ll call the right-hand end. What happens to the boxcar?

(Spoiler warning!)

Continue reading ‘About That Boxcar’

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Boxcar Willie

Published
by
Steve Landsburg
on May 21, 2013
in Physics and Puzzles
. 37 Comments

I’ve just been pointed to this notice of a conference in honor of the topologist Tom Goodwillie‘s 60th birthday.

This reminded me of several things, not all of them related to the relentless march of time.

For example, once a very long time ago (though it sure doesn’t seem that way) Tom asked me a simple physics question that troubled me far more than I now think it ought to have:

A boxcar full of water sits on a frictionless train track. A mouse gnaws a hole through the bottom of the boxcar, in the location indicated here:

The water, of course, comes gushing out. What happens to the boxcar?

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News From The Math World

Published
by
Steve Landsburg
on May 20, 2013
in Math
. 5 Comments

Big news from the math world:

One of the oldest problems in number theory is the twin primes problem: Are there or are there not infinitely many ways to write the number 2 as a difference of two primes? You can, for example, write 2 = 5 -3, or 2 = 7 – 5, or 2 = 13 – 11. Does or does not this list go on forever? There are very strong reasons to believe the answer is yes, but many a great mathematician has tried and failed to find a proof.

Here’s a related problem: Are there or are there not infinitely many ways to write the number 4 as a difference of two primes? What about the number 6? Or 8? Or any even number you care to think about? It seems likely that the answer is yes in every case, though no proof is known in any case. But….

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What’s a Bitcoin Worth? (Wonkish)

Published
by
Steve Landsburg
on May 13, 2013
in Economics
. 71 Comments

This might be one of those questions I’ll eventually be embarrassed for asking, but…..

Imagine a future in which Bitcoins (or some other non-governmental currency) are widely accepted and easily substitutable for dollars, at an exchange rate of (say) $X per Bitcoin.

Then if there are M dollars and B bitcoins in circulation, the money supply (measured in dollars) is effectively M + X B .

Money demand is presumably P D, where P is the general price level and D depends on things like the volume of transactions and the payment habits of the community. (If it helps, we can write D = T/V where T is the volume of transactions and V is the velocity of money.)

Equilibrium in the money market requires that supply equals demand, so

M + X B = P D

Now M is determined by the monetary authorities; B is determined by the Bitcoin algorithm, and D, as noted above, is determined outside the money market.

That leaves me with two variables (X and P) but only one equation. What pins down the values of these variables?

Continue reading ‘What’s a Bitcoin Worth? (Wonkish)’

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Seven Trees in One

Published
by
Steve Landsburg
on May 9, 2013
in Math
. 31 Comments

When you met the late Armen Alchian on the street, he used to greet you not with “Hello” or “How ya doin’?”, but with “What did you learn today?” Today I learned that there are contexts in which the most ludicrous reasoning is guaranteed to lead you to a correct conclusion. This is too cool not to share.

But first a little context. The first part is a little less cool, but it’s still fun and it will only take a minute.

First, I have to tell you what a tree is. A tree is something that has a root, and then either zero or two branches growing out of that root, and then either zero or two branches (a “left branch” and a “right branch”) growing out of each branch end, and then either zero or two branches growing out of each of those branch ends, and so on. Here are some trees. (The little red dots are the branch ends and the big black dot is the root; these trees grow upside down.)

A pair of trees is, as you might guess, two trees — a first and a second.

There are infinitely many trees, and infinitely many pairs of trees, and purely abstract considerations tell us that there’s got to be a one-one correspondence between these two infinities. But what if we ask for a simple, easily describable one-one correspondence? Well, here’s an attempt: Starting with a pair of trees, you can create a single tree by creating a root with two branches, and then sticking the two trees from the pair onto the ends of the two branches. Like so:

Continue reading ‘Seven Trees in One’

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To Hold You Over….

Published
by
Steve Landsburg
on May 3, 2013
in Bad Reasoning, Blogging, Current Events, Economics, Paul Krugman and Policy
. 77 Comments

Sorry to have been so silent this week; various deadlines have kept me away from this corner of the Internet. I’ll be back in force next week for sure. Meanwhile, if you’re looking for some good reading, this is the best thing I’ve seen all morning.

Edited to add: “Best all morning” was not intended as damning-by-faint-praise. It’s actually the best of many mornings.

Click here to comment or read others’ comments.

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A Sip of Monstrous Moonshine

Published
by
Steve Landsburg
on April 25, 2013
in Anecdotes, Game Theory, Math and Musings
. 58 Comments

You and a stranger have been instructed to meet up sometime tomorrow, somewhere in New York City. You (and the stranger) can decide for yourselves when and where to look for each other. But there can be no advance communication. Where do you go?

Me, I’d be at the front entrance to the Empire State Building at noon, possibly missing my counterpart, who might be under the clock at Grand Central Station. But, because there are only a small number of points in New York City that stand out as “extra-special”, we’ve at least got a chance to find each other.

A Schelling point is something that stands out from the background so sharply that we can expect people to coordinate around it. Schelling points are on my mind this week, because I’ve just heard David Friedman give a fascinating talk about the evolution of property rights, and Schelling points play a big role in his story. But that story is not the topic of this post.

Instead, I’m curious about the Schelling points that say, two mathematicians, or two economists, or two philosophers, or two poets, or two street hustlers might converge on. Suppose, for example, that you asked two mathematicians each to separately pick a number between 200 and 300, with a prize if their answers coincide. I’m guessing they both go for 256, the only power of two within range.

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Terror, Truth and Torture

Published
by
Steve Landsburg
on April 22, 2013
in Current Events, History, Policy and Truthseeking
. 39 Comments

Last week was not the first time the United States was transfixed by an act of terror. In 1964, three civil rights workers in Philadelphia, Mississippi were (quoting Wikipedia) “threatened, intimidated, beaten, shot, and buried by members of the Mississippi White Knights of the Ku Klux Klan, the Neshoba County Sheriff’s Office and the Philadelphia Police Department.” It took 44 days and an FBI-initiated act of torture to locate their bodies.

The FBI, in a nod to the theory of comparative advantage, subcontracted the torture to the Mafia, more specifically to the Colombo family associate Gregory Scarpa. Here’s the story as relayed by Selwyn Raab, the New York Times investigative reporter who covered the Mafia for 25 years:

[Scarpa] went down to Mississippi for the FBI and kidnapped a KKK guy agents were sure was involved in disposing of the bodies. The guy had an appliance store. Scarpa bought a TV and came back to the store to pick it up just as he was closing. The guy helps him carry the TV to his car parked in the back of the store. Scarpa knocks him out with a bop to the head, takes him off to the woods, beats him up, sticks a gun down his throat and says “I’m going to blow your head off”. The KKK guy realized he was Mafia and wasn’t kidding and told him where to look for the bodies.

(Source: Raab’s book Five Families, which is fascinating throughout. Raab says the story has been verified by “former law enforcement officials who asked for anonymity and lawyers who are aware of the circumstances”.)

The moral of the story is that torture sometimes works. Other times it doesn’t, eliciting either no information, or false information, or whatever “information” the victim believes the inquisitor wants to hear. I am almost 100% ignorant, and hence virtually 100% agnostic, about the relative frequency of these outcomes in those cases where the torturer is both skilled in his art and genuinely interested in eliciting the truth. I will be very glad if any educated reader can shed light on this question. I doubt that we’re likely to learn of any controlled experiments, but I’ll settle for sketchy data or even well-chosen anecdotes. Failing that, I’ll settle for plausibility arguments.

Continue reading ‘Terror, Truth and Torture’

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