Monthly Archive for January, 2010

Weekend Roundup

Last weekend’s roundup triggered some lively back-and-forth regarding the Supreme Court and freedom of speech. Wednesday night’s Obama/Alito showdown was old hat to readers of The Big Questions, who had already been on top of this issue for a full four days.

With the start of the week proper, we had two more lively discussions, over relativity theory and capital taxation; never let it be said that this blog is narrowly focused. We also had a report on my collection of really bad animal books, and we saw pictures of a watermelon car.

Upcoming next week: A recap of the relativity controversy, a few words on how to think (and how not to think) about the national debt, and much more. See you Monday!

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Both Sides of the Aisle

Interviews with Democratic Representative Barney Frank and Republican Senator Richard Shelby are the final installments in BigThink’s series of video interviews on “What Went Wrong?” during the financial crisis. (You’ll also find links to all the previous installments.) If you have a taste for politics, you can comment here on what you thought of them.

If You Licked the Handle, Would a Car Grow Inside You?

While everyone else blogs the State of the Union, I prefer to bring you something a little more uplifting—like a watermelon car. I want one.

I first discovered this at ReflectionOf.Me, which houses a really quite extraordinary collection of beautiful oddities. You might want to mosey around there and take your mind off politics for a while. You’ll feel better.

A Quick Economics Lesson

I am opposed to all taxes on interest, dividends and other forms of capital income. Supporters of these taxes keep making the same fallacious argument. The purpose of this post is to shame those people out of ever making that argument again. (They are, of course, free to make other arguments.)

The fallacy I have in mind goes like this: First, economics teaches us that everything should be taxed at the same rate to avoid unnecessary distortions. Second, QED.

With appropriate caveats, the first part is true. The problem is with getting from there to the second part.

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Animania

animal-125Let me tell you about my collection of really bad animal question-and-answer books.

This is a genre that thrived back before the Internet (mostly between 1930 and 1960) when connoisseurs of weirdness and misinformation had only bound books to turn to. Its heroes include Osmond P. Breland (author of the classics “Animal Facts and Fallacies”, “Animal Friends and Foes”, and “Animal Life and Lore”) and Alan Devoe (who gave us “Speaking of Animals” and “This Fascinating Animal World”).

Here’s a six-question quiz I compiled from these books.

  1. Can a toad live for years sealed up in solid rock?
  2. Can a dog procreate with a skunk?
  3. Do snakes swallow their young to protect them from danger?
  4. Can salamanders live in fire?
  5. Is the rattlesnake a gentleman?
  6. Can male animals lay eggs?

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The Big Answers

trainLast week, I posed some brain teasers and a riddle about special relativity.

The brain teasers were all solved by multiple commenters; I’ll summarize their answers at the end of this post. The special relativity problem proved trickier; here it is again:

A circular train (front of the locomotive attached to the rear of the caboose) sits on a circular track. At some point, the train accelerates and starts traveling around the track. Because the train is moving, I (an observer stationary relative to the track) should see it shrink. But the track doesn’t shrink. So the train can’t stay on the track, and gets pulled inward, ending up inside the track. On the other hand, the passengers say the track has shrunk, so they should expect to get pushed outside the track. How can everyone be right?

Now to the answer.

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Weekend Roundup

Still reeling from the revelation that four Supreme Court Justices have withdrawn their support for the First Amendment to the United States Constitution, I am pulling myself together to bring you this week’s blog roundup. Or actually two weeks’ worth of blog roundup, since I skipped last week’s due to travel.

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Geek or Dork?

There are a bazillion alleged “paradoxes” in special relativity, all based on exactly the same fallacy, but I might have just invented a brand-new one—-where “invented” is shorthand for “confused the hell out of myself for a while”. When I finally got up and drew a picture (as opposed to lying in bed with my eyes closed doing something that felt like thinking), it became clear that, sure enough, it was the same old fallacy again (how could it not have been?), but in a new enough guise that someone reading this might find it amusing.

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Office Politics

While scanning Randy Cohen’s recent Ethicist columns for something to complain about, I found this query about allocating faculty offices:

I am a faculty member at a university undergoing major campus renovations, including new office spaces. Departments were asked to determine their own ways of assigning rooms, but the task is complicated by factors like seniority and rank — does someone with tenure deserve a better room? Some faculty members have greater teaching demands and might need larger rooms to meet with students. What is the most ethical way to allocate offices: seniority? Rank? Lottery?

True to form, Cohen has nothing interesting to say, and offers no rationale for his random suggestions. It never seems to have occurred to him that scarce resources tend to be allocated most efficiently by markets. If he’d done a little research, he might have found this charming account of how the economists at Arizona State solved the office allocation problem.

n Guilty Men

jury

Whenever I ask about the reasoning underlying some legal principle or another, my friend the law professor is always quick to remind me that “there is no such thing as legal reasoning”. So it is with William Blackstone’s famous doctrine that it’s better for ten guilty men to escape than for one innocent to suffer. Why ten? Because that’s the first number that happened to enter Blackstone’s head; that’s why.

Writing 200 years after Blackstone, Emory Law School professor Alexander Volokh surveyed the history of alternatives to “ten” in a charming essay called n Guilty Men. The bottom line is that a great many alternatives have been offered, almost never with anything approaching a justification.

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Trial by Ordeal

ordealPeter Leeson of George Mason University (currently visiting the University of Chicago) offers a new take on the medieval practice of “trial by ordeal”:

“For 400 years the most sophisticated persons in Europe decided difficult criminal cases by asking the defendant to thrust his arm into a cauldron of boiling water and fish out a ring. If his arm was unharmed, he was exonerated. If not, he was convicted.”

According to Leeson, this is less crazy than it sounds: As long as defendants believe (superstitiously) that ordeals yield accurate verdicts, guilty defendants always confess to avoid the ordeal. At the same time innocent defendants always opt for the ordeal—and are always acquitted, provided the priests cheat by (for example) substituting tepid for boiling water, or “sprinkling” a few gallons of cold holy water over the cauldron, or liberally redefining what counts as “unharmed”.

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Happy Holiday

Happy Martin Luther King Day. I’m still traveling, taking the holiday off from substantive posting, and planning to be back
tomorrow, or possibly Wednesday, after which we’ll resume our regular schedule.

Teasing Your Brain

brain2My travel schedule for the next several days will probably keep me from posting anything too substantial. So let me leave you with three lovely brain teasers to keep you occupied in the meantime.

1) (Hat tip to Ben Tilly): I have thought of two numbers, which I call A and B. You know nothing about how I came up with these numbers. I plan to flip a fair coin and then tell you the value of A if the coin comes up heads or B if the coin comes up tails. Your job is to guess whether the number I quote is the larger or the smaller of A and B. Devise a strategy that guarantees you a better-than-even chance of winning, no matter what A and B are.

(To make this more precise: Your probability P of winning is a function of A, B and your strategy. Devise a strategy S such that P(A,B,S) is greater than 1/2 for all A and B.)

2) (Hat tip to Stan Wagon): Alice and Bob ran a marathon (assumed to be exactly 26.2 miles long) with Alice running at a perfectly uniform eight-minute-per-mile pace, and Bob running in fits and starts, but taking exactly 8 minutes and 1 second to complete each mile interval (so, for example, it takes him exactly 8 minutes and 1 second to get from the 3.78 mile mark to the 4.78 mile mark, exactly 8 minutes and 1 second to get from the 3.92 mile mark to the 4.92 mile mark, etc.). Is it possible that Bob finished ahead of Alice?

3) (Hat tip to my old friend Steve Maguire): The border between Delaware and its neighbors includes a section with a circular arc: on the circle ten miles from a church in Dover Delaware. Can you name another state border that is partially defined by a circular arc?

I’ll continue to check comments while I’m on the road, but perhaps just a tad less diligently than usual.

Quantum Game Theory

I’m sure this won’t be everyone’s cup of tea, but some readers might be interested. I’ve been invited to write the entry on Quantum Game Theory for the Wiley Encyclopedia of Operations Research and Management Sciences, and I thought I’d share the current draft. If this is your cup of tea, your feedback is welcome.

Real Numbers

numbersYesterday we started a conversation about whether mathematics is invented or discovered. Today I’ll give you my three best arguments for “discovered”. And to focus the discussion, I’ll talk not about mathematics generally but about the natural numbers (0,1,2, and so forth) in particular.

I believe the natural numbers exist, quite independently of whether anyone’s around to think of them. Here’s why: First, we perceive them directly. Second, we know non-trivial facts about them. Third, they can explain the Universe. In more detail:

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Jellyfish Math

livio
Is mathematics invented or discovered? In my experience, applied scientists often think of mathematics as a human invention, while actual mathematicians (with a few notable exceptions) feel sure that mathematics was always there to be discovered. (Of course, it’s sometimes hard to tell how much of this is genuine disagreement and how much is a language barrier.)

I’ve just finished reading an excellent book by Mario Livio which is entirely about the invention/discovery question, though he’s chosen the (somewhat unfortunate) title Is God a Mathematician? Much of the book is a lively romp through mathematical history, with a well chosen mix of biography and exposition. Although he parts company with them in the last chapter, Livio gives a more than fair hearing to the many great mathematicians who have insisted that they are discoverers, from Pythagoras through Galileo, G.H. Hardy, Kurt Godel, and the contemporary Fields Medalist Alain Connes (among others). Here, for example is Connes:

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Wind Production

Once upon a time in America, whenever an administration spokesman spouted economic nonsense, you could rely on Paul Krugman for a sneer, a blast of outrage, and frequently an imputation of the basest motives. That time ended on approximately January 20, 2009. Today Krugman sleeps at the wheel while administration press spokesman Robert Gibbs spews forth the following:

I think it’s safe to say that for quite some time, when it came to building the solar panels and the wind towers and the wind turbines and a lot of the manufactured equipment for clean energy, we had a number of foreign countries that were doing much better in addressing that demand than we were. And as the President has said often, the type of demand for these components in manufacturing is only going to increase as we seek solutions to our energy problems.

And we have to ask ourselves as a country, are we going to create those jobs and create those components, or are we going to import those components from overseas? The President believes that we have an opportunity to lead the world in this type of manufacturing.

Nobody in the Bush administration ever displayed more economic ignorance, but Krugman was all over those guys every time they came close. Now he lets it slide. So let me do his job for him:

When the domestic demand for a product increases, the law of comparative advantage tells you to import more of it, not less. If it is in fact true that “the type of demand for these components is only going to increase” then American manufacturers might want to start producing them, but American consumers will certainly want to import more of them, and any attempt to circumvent that is a good way to make Americans poorer.

(For those following along in their economics textbooks: The world supply and demand for, say, wind turbines, must be more elastic than the domestic supply and demand, so a demand shift has a smaller effect on the world price than the autarkic domestic price and so must increase the foreign comparative advantage—or decrease the domestic comparative advantage, if any.)

For goodness’s sake—if Barack Obama or Robert Gibbs discovers that he really likes bananas on his Cheerios, is his first thought that he’d better start growing bananas, or is his first thought that he’d better figure out where to buy them? That’s the kind of question Paul Krugman used to ask. I miss him.

Weekend Roundup

We led off the week with two posts about unwarranted beliefs—my own unwarranted belief in the power of bathtub hardware and Moody’s economist Mark Zandi’s unwarranted belief in the power of fiscal stimulus.

The rest of the week was devoted to my gallery of heroes, with followup discussions here and here.

Along the way, there were many provocative suggestions for additions to the gallery, of which some struck me as fully worthy, some struck me as implausible, and some I’d never heard of. Below, without commentary, is the full list of suggested additions, with the suggesters names in parentheses; apologies if I overlooked a few. The name most frequently mentioned was Richard Feynman; my mom cast an extra vote for Feynman by email.

I’ll be back, of course, on Monday.

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Who’s Who

In a triumph of collective action, commenters have now managed to identify all of the personal heroes in my portrait gallery, either in comments to the original post or to the followup. For those who would like to check their answers, here is the gallery again, with full captions. After all the pictures, I’ve attached some brief commentary explaining who’s who and why some of these people are here. I’ll write in more detail about some of them over the coming weeks.

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Unidentified Persons

attemptYesterday I posted a portrait gallery honoring 60 of my personal heroes; readers were quick to identify 47, with remarkably few mistakes, all of which were quickly corrected. As of this writing, thirteen remain. Among these thirteen are the greatest mathematician of the 17th century (assuming we classify Newton as a physicist) and the three greatest mathematicians of the 20th; one of these is quite probably the greatest mathematician of all time. (All in my educated-but-not-fully-educated opinion, of course.) Musical, literary and cinematic greatness are also well represented here.

Over the next couple of weeks, I will try to tell you a little bit more about some of these 60 people. Meanwhile, here are the thirteen mystery men/women. I’ve retained the numbering from yesterday’s post. Who can you identify?

Continue reading ‘Unidentified Persons’

The World Wide Wall

wallselectionSince childhood, I have dreamed of someday having a house with a portrait gallery, where I would hang portraits of people I greatly admire. Every time I’ve either moved or redecorated, I’ve thought about dedicating a wall to this, but I never really had that much wallspace to spare.

A short time ago, it dawned on me that I actually have an infinite amount of wall space! My wall space is called the World Wide Web. And the World Wide Web is better than a physical wall, because the images are readily available (as opposed to hiding away in antique shops), and it’s easy to put things up and take things down, and you can share it with people you might not want to invite to your house.

So now I am prepared to unveil my World Wide Wall, or at least a first draft. I am well aware that many of these heroes are deeply flawed. I did not disqualify anyone for slaveholding, Louisiana purchases, Nazi sympathies or the imposition of protective tariffs. Not all of them are at the very top of their professions. The only criterion for inclusion was to make my heart go pit-a-pat.

My wall. Let me show you it. How many of these do you recognize? (No fair answering if you’re a personal friend who’s already seen an early draft of this.) And who would be on your wall?

Continue reading ‘The World Wide Wall’

What Went Wrong

At Big Think, a consortium of bloggers (including me) have been invited to submit questions for use in video interviews with major players in the financial crisis. I posed a question to Mark Zandi, the chief economist at Moody’s, who had recently said this:

“It’s no coincidence that the great recession ended just as the stimulus package began providing its maximum economic benefit.”

My question was:

How do you know?

Here, from the video, is Mr. Zandi’s answer:

Continue reading ‘What Went Wrong’

Unbelievable

bathtubYou know that metal plate in your bathtub? The one with the little lever on it that opens and closes the drain? What happens when the water level rises above that plate?

When my sister asked me this question over Thanksgiving dinner, I answered, with the utmost confidence, that it causes (quite instantaneously) an enormous flood. (Note the exact wording. This will be important later.) My sister nodded sagely and said “That’s what I thought, too.” My sister and I had the same mother, you see.

And then she asked, quite innocently, “So. How exactly does that work?”. And I was stunned—absolutely stunned—to realize not only that I had no answer to this question, but that there could not plausibly be an answer. Which somehow had never occurred to me in the half century or so that I’d been harboring this ridiculous notion.

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Weekend Roundup

It was another abbreviated week due to holidays, but we still had time for our first video post, a celebration of Ronald Coase’s 99th birthday (and a summary of the ideas behind his well-deserved Nobel prize), and a bit of silliness before capping off the week (and the year) with a survey of 2009′s Top Ten posts here at the Big Questions blog.

Today I am off to the annual meeting of the American Economic Association in Atlanta, Georgia. As usual, I’m taking Sunday off, but I’ll be back here Monday, blogging from Atlanta.