Monthly Archive for April, 2012

That Does Not Compute

stanleyStanley Tennenbaum was an itinerant mathematician with, for much of his adult life, no fixed address and no permanent source of income. Sometimes he slept on park benches. He didn’t have a lot of teeth.

But if you were involved with mathematics in the second half of the twentieth century, sooner or later you were going to cross paths with Stanley, probably near the coffee machine in a math department. He’d proudly show you the little book he carried in his breast pocket, with the list of people to whom he owed money. Then he’d teach you something, or he’d tell you a good story.

Stanley had little tolerance for convention. His one permanent job, at the University of Rochester, came to an abrupt end during a faculty meeting where he spit on the shoes of the University president and walked out. Surely the same personality trait had something to do with his departure from the University of Chicago without a Ph.D., though the paper he wrote there (at age 22) has acquired fame and influence far beyond many of the doctoral theses of his more conventionally successful classmates. I’d like to tell you a little about that paper and what I think it means for the foundations of mathematics.

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Best Negotiator Ever

With a hat tip to Kenneth Anderson at the Volokh Conspiracy:

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Golden Balls is a British game show where players decide, in secret, whether to adopt a strategy of “Split” or “Steal”. In this episode, they face the following payoffs (in British pounds):

This is almost, but not quite a classic Prisoner’s Dilemma situation. (To make it a true Prisoner’s Dilemma, where stealing always beats splitting, you could change the lower-right hand box to “1 each” instead of “0 each”.) As in the Prisoner’s Dilemma, you can never go wrong by stealing — though you can go horribly wrong when the other guy steals, so it makes sense to reach a no-stealing agreement — and then to violate it.

In other words you’d pretty much expect homo economicus to steal every time. But this game is far more interesting than the usual textbook version of the Prisoner’s Dilemma, because it’s played by real people for real money and they negotiate in public for half a minute before they choose their strategies. In principle, the negotiation shouldn’t change anything (unless the players come to care about each other, or about the way they’re perceived by the audience). But in this episode, the negotiation took an unexpected turn.

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Hi, Sierra

sierra-and-family-smallOur occasional commenter Sierra Black is the subject of a 20/20 documentary scheduled to air on ABC tomorrow night (Friday the 20th) at 10PM Eastern Standard Time. You should watch it.

I’ve had the great blessing of getting to know quite a lot of you (some better than others of course) in the few years I’ve been blogging, but Sierra is one of the few I’ve met face to face. She and her husband Martin have more than once been guests in my home; my daughter occasionally babysits for Sierra’s daughters Rio and Serena. (The picture at the top was taken in my living room.) My family and Sierra’s camp together (along with quite a few other friends) every summer, and while we’re not always in close touch, we do keep track of each other. They’re good people.

The 20/20 program will focus on Sierra and Martin’s unconventional relationship choices. We here at The Big Questions are strong enthusiasts for all things consensually unconventional.

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Agreed!

handshakeOften, all economists agree that we all agree. We just can’t agree about what it is that we all agree on. Now comes the remarkable IGM Economic Experts Panel to shed some light.

The experts in question are a small galaxy of economic stars, some plausible candidates for the Nobel Prize, and all highly regarded throughout the profession. Their political affiliations range from left to right to center to “I hate politics”. There are 41 of them altogether. And for several months now, they’ve been polled about important matters of theory and policy.

The very first survey, going back to last September, asked for responses to the following statement:

All else equal, the Fed’s new plan to increase the maturity of its Treasury holdings will boost expected real GDP growth for calendar year 2012 by at least one percentage point.

Exactly 0% of the experts checked “agree” or “strongly agree”. 33% were uncertain and 7% had no opinion. (One refreshing thing about these polls is that the respondent’s have apparently felt free to respond “no opinion” on matters where they are not well informed. Nobody, after all, can be an expert on everything.) When a statement is endorsed by exactly 0% of 41 distinguished experts from across the political spectrum, you can be pretty sure that statement is false.

This first question, though, strikes me relatively uninteresting, since it refers to a specific policy at a specific moment in time. Let’s move on to the next question, which has a bit more staying power:

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Cato University

This is a reminder that I’ll be teaching at this year’s Cato University, where I and a distinguished cast of faculty will lecture on the political, historic, philosophical and economic foundations of liberty. There will also be ample opportunity for informal conversations with the faculty and, even better, with the other students, who I have learned from past experience are always bright and lively and fun.

Come join us, July 29 through August 3, at Cato’s newly expanded headquarters in DC. The insights you’ll gain, and the friends you’ll meet, will last a lifetime.

Click here to comment or read others’ comments.

Lifeboats on the Titanic

titanicShould RMS Titanic have carried more lifeboats? Yes, probably. But it took me a few minutes to convince myself.

Roughly 1500 died on the Titanic; according to Wikipedia, it would have cost about $16,000 to equip her with additional lifeboats sufficient to save them all. Call it $10 per life saved. The price level today is roughly 22 times what it was in 1912, so in today’s terms that’s $220 per life.

Now, if I were boarding a ship for a luxury cruise, and was offered the chance to pay an additional $220 for a guaranteed seat on a lifeboat in the event of a sinking, I’m quite sure I’d take a pass — and I’m quite sure so would virtually all of my fellow passengers. So if the Titanic had been designed to cross the ocean once and then spend the rest of its days in a museum, it would have been insane to equip her with extra lifeboats. But of course if the Titanic had been designed to cross the ocean once and then spend the rest of its days in a museum, it would have been insane to build her in the first place. So that’s not the right calculation.

The right calculation accounts for the fact that a single lifeboat provides security to passengers on multiple voyages. How many voyages? Well, the Titanic was intended to make the round trip between Europe and America every three weeks; that’s two voyages per three-week period. I’m not sure how long the sailing season was, but we know it was underway by mid-April (and perhaps earlier; it’s often mentioned that if the Titanic had been ready earlier she would have sailed earlier) so (assuming sailing conditions are roughly symmetric around the solstice) it must have lasted till at least mid-August. That’s time for five round trips at a minimum, and I’m guessing this is a quite conservative assumption.

If a lifeboat lasts a year, then, it does its job at least ten times. If it lasts five years (which is, I suspect, another quite conservative assumption), it does its job fifty times. Now we’re in the vicinity of $4 per passenger (and of course much less if my assumptions are indeed quite conservative).

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The Armchair Economist: Revised, Updated, and Available May 1 — or for pre-order now!

FROM THE PREFACE:

One day in 1991, I walked into a medium sized bookstore and counted over 80 titles on quantum physics and the history of the Universe. A few shelves over I found Richard Dawkins’s bestseller The Selfish Gene along with dozens of others explaining Darwinan evolution and the genetic code.

In the best of these books, I discovered natural wonders, confronted mysteries, learned new ways of thinking, and felt I had shared in a great intellectual adventure, founded on ideas that are dazzling in their scope and their simplicity.

Economics, too, is a great intellectual adventure, but I could find, in 1991, not a single book that proposed to share that adventure with the general public. There was nothing that revealed the economist’s unique way of thinking, using a few simple ideas to illuminate the whole range of human behavior, shake up our preconceptions, and jolt us into new ways of seeing the world.

I resolved to write that book. The Armchair Economist was published in 1993, and attracted much critical praise along with a large and devoted following. But what I take most pride in is that The Armchair Economist is still widely recognized among economists as the book to give your mother when she wants to understand what you do all day.

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The Path to Prosperity

If you want to know why some countries are rich and others are poor, a good starting place is this graph, which I took from the first edition of David Weil‘s quite marvelous textbook on Economic Growth:

Because I took this from Weil’s first edition, these data are several years old, and some countries might have moved up or down the ladder since then. But the overall picture is clear: More capital per worker means more output per worker, and more output per worker means more income per worker. This relationship — in fact, the nearly linear relationship that you see on the graph — is just what standard economic theory predicts. It’s nice to see that prediction so powerfully confirmed.

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Some Days I’m A Super Genius

wileI want to build a large addition to my house. The town limits my above-ground square footage to the point where all I can build is a relatively small addition.

But underground square footage doesn’t count! So I toyed with the idea of building a 3/4-acre basement under my 3/4-acre yard.

This turns out to be rather expensive.

Therefore, I used my brain.

My new plan is to completely bury my existing house under an enormous mound of dirt, declare the whole thing a basement, and build a new house on top of it, with an internal staircase going down into the old house. The new construction can then be quite large, since I’m starting from zero above-ground square feet. A system of periscopes will preserve the views from the new “basement” windows.

This has got to be far cheaper than fresh underground construction. Dirt is notoriously cheap. That’s where the expression “dirt cheap” comes from.

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Humpty Dumpty’s Math Puzzle

humptyGreg Mankiw, with a hat tip to his son Nicholas, asks for a plot of the function xx, where x is a real variable. The answer he points to (provided by Pedagoguery Software) gives this picture/expanation:

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