Still reeling from the revelation that four Supreme Court Justices have withdrawn their support for the First Amendment to the United States Constitution, I am pulling myself together to bring you this week’s blog roundup.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.
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.
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.
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.
Peter 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”.
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.
My 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.
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.
Yesterday 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:
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:
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.
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.
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.
Yesterday 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?
Since 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?
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:
You 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.
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.
Since everyone else is doing end-of-year retrospectives, I thought I’d chime in with a list of the ten most-commented-upon posts here at The Big Questions blog in the year 2009. Now, this blog is only two months old, but we’ve already had roughly 75 posts, so a top 10 list at this point is perhaps not too presumptuous.
Of course, the number of comments may be a poor predictor of post quality. So after I give you the Top Ten, I’ll point you to a few others that I think equally worthy.
That having been said, the Top Ten are:
Finally, here are a few of my favorites that didn’t make the Top Ten for comments, though that might just mean they were uncontroversial. Or to put this another way—maybe these posts were so perfect that readers thought they had little to add!
I’m taking New Year’s Day off. I’ll see you Saturday.
If you’re my age, you’ll surely remember the great Pet Rock craze of the 1970’s. (If you’re not my age, maybe you’ve heard about it from your grandparents.) In any event, here’s proof—if it were still needed—that the world just keeps on getting better: While the old Pet Rock just sat there not doing anything, today you can get a pet rock with a USB connection! Here’s the product description:
Simply plug the USB cable into a free port and let the fun begin. The USB Pet Rock will instantly begin to work its magic. People will stop by and ask you what your USB Pet Rock does. Each time, you can make up a new story; for no matter what you say, it will be greater than the truth – because these USB Pet Rocks don’t do a dang thing. Except make you smile. And confuse your friends and coworkers, which will make you smile even more. So, get your USB Pet Rock today, and help make us rich tomorrow.
Now there’s something that could never have been produced under socialism!
(A grateful hat tip to my friend Johanna.)
In other news, the year is winding down, and everyone else is doing end-of-year retrospectives, so I shall do the same. Check this space tomorrow for a review of the Top Ten posts of 2009 here on The Big Questions blog. And Happy New Year.
In the theory of externalities—that is, costs imposed involuntarily on others—there have been exactly two great ideas. The first, forever associated with the name of Arthur Cecil Pigou (writing about 1920) is that things tend to go badly when people can escape the costs of their own behavior. Factories pollute too much because someone other than the factory owner has to breathe the polluted air. Nineteenth century trains threw off sparks that tended to ignite the crops on neighboring farms, and the railroads ran too many of those trains because the crops belonged to someone else. Farmers keep too many unfenced rabbits when they don’t care about the lettuce farmer next door.
Pigou’s solution—and it’s often a good one—is to make sure that people do feel the costs of their actions, via taxes, fines, or liability rules that allow the victims to sue for damages. Do a dollar’s worth of damage, and you’re charged a dollar.
Pigou endorsed this policy not because it seems fair, though it does seem fair to many, but because it yields, under what he believed to be very general conditions, the optimal amounts of damage. We don’t want too much pollution, but we don’t want too little, either, given that pollution is a necessary by-product of a lot of stuff we enjoy. Pigou offered a proof—now standard fare in all the textbooks—that his policies lead to the perfect compromises, in a sense that can be made precise.
The second great idea about externalities sprang full-blown from the mind of a law professor and subsequent Nobel prize winner named Ronald Coase, who stunned the profession in 1960 by pointing out that Pigou’s argument runs both ways. If you breathe the pollution from my factory, I’m imposing a cost on you—but at the same time, you’re imposing a cost on me. After all, if you lived somewhere else, you wouldn’t be complaining about the smoke and I wouldn’t be getting punished for it.
A couple of weeks ago, here at the University of Rochester, two fine student organizations—the History Council and the Finance/Economics Council—joined forces to sponsor a debate on the topic “Is Health Care a Right?”. The disputants were myself and history professor Ted Brown, who graciously agreed to speak first at my request.
Over the course of the evening, I proposed a variety of mutually contradictory health care policies; my intent was not to endorse any one of them, but to demonstrate that all of them were preferable to Professor Brown’s pet proposals. I cribbed some important ideas from David Goldhill’s Atlantic Monthly article, and some important ideas and facts from the always insdispensable Bill Easterly. The format did not lend itself to citations or hyperlinks, but I’m glad to make amends here.
Like most blogs, we slowed down a little for the holidays and had a bit less content than usual—but we still managed to fit in a Christmas story, a cute puzzle, and the long-delayed solutions to my remaining honors problems.
Speaking of puzzles, I seem to have puzzled a substantial fraction of my readership with the subtlety of my sly Santa Claus reference. (I know this from my email.) Given the astute nature of this community, I am forced to infer that the fault is mine.
More holidays next week, and hence more days off, but I won’t disappear completely. Check back on Monday!
I’ve landed a consulting gig doing real-time optimal path computations for a gentleman who is planning to tour a graph with several hundred million nodes this evening, so I’m taking tomorrow morning off. To tide you over, I leave you with this literary composition, which can be read multiple times for added enjoyment.
—Three quarters of an infinite number of monkeys
Do have the best of all possible Christmases.
In the spirit of the season, I offer you one of the most popular of my old Slate columns. Merry Christmas.
Here’s what I like about Ebenezer Scrooge: His meager lodgings were dark because darkness is cheap, and barely heated because coal is not free. His dinner was gruel, which he prepared himself. Scrooge paid no man to wait on him.
Scrooge has been called ungenerous. I say that’s a bum rap. What could be more generous than keeping your lamps unlit and your plate unfilled, leaving more fuel for others to burn and more food for others to eat? Who is a more benevolent neighbor than the man who employs no servants, freeing them to wait on someone else?
I don’t normally blog on Sundays, but I’m starting to think of you guys as friends, so I want to share my delight at these valued words from Greg Mankiw, an economist I have long held in the highest esteem. From his blog:
Looking for a Christmas gift for that special econonerd in your life? Try Steven Landsburg’s new book, The Big Questions.
I recently finished it, and it is much fun. Reading it is like having dinner and sharing a bottle of claret with a smart, creative, iconoclastic friend. The conversation jumps from topic to topic in math, physics, philosophy, economics, public policy, etc., in a seemingly random fashion, and your friend does not always convince you of his point of view. But throughout you are entertained, and in the end you are even edified.
I’m of course delighted by the sales push, but even more so by hearing these words from someone I respect as much as Greg.
In a week when we took on the issues of health care and immigration, our most contentious issue turned out to be the complexity of arithmetic. We also touched on some odd Christmas gifts and the solutions to some old puzzles.
I’ll be back, of course, on Monday. But to tide you over the weekend, you might want to check out the interview with John Allison, the former CEO of BB&T, which is part of the “What Went Wrong” series over at BigThink. Needless to say, I can find parts to disagree with, but overall I think it’s one of the most insightful interviews yet in this series. A choice quote:
If you want to really think about what happened in the housing crises, it was a government policy, through Freddie Mac and Fannie Mae and affordable housing policies, what they call the community reinvestment act, etc., that created a massive misallocation of credit. If the government gets into allocating credit over time it will make sure we aren’t as productive as we should be. So the government regulations usually in the end look like credit allocations usually to those that are politically favored at the expense of making sure credit is allocated to the most productive segments in the economy. So I think government regulation in the long term is almost always destructive.
Over at National Review Online, John Derbyshire starts off with some kind words about The Big Questions, and then goes off on an ill-considered screed about immigration. First, by all means let’s quote the kind words:
Steven’s new book, The Big Questions, has a lot of good things in it, as one would expect from an author who proudly declares himself a math geek. His explanation of Heisenberg’s uncertainty principle (pages 135–141) is a model of clarity in the popularization of science. His geometrical illustration of a Talmudic rule on the division of an estate (pages 205–213) shows the mathematical imagination at its best.
Landsburg is an economist by profession — a professor of economics, in fact — and has the economist’s insight that many matters commonly discussed in terms of morality can be reduced to cold arithmetic: “When things are priced correctly, there’s no need to moralize about them.” He gives some illuminating examples.
But then things take a darker turn:
