This seminar probes how economic thinkers from the right and left view human behavior and the proper role of government in society. Each week, seminar participants read and discuss a brief, nontechnical, policy-oriented book by a prominent economist. Regular writing assignments are also required. Students should have some background in economics, such as an AP economics course in high school or simultaneous enrollment in Social Analysis 10.

The ten books on tap for this semester are:

• The Worldly Philosophers, by Robert Heilbroner
• Reinventing the Bazaar: A Natural History of Markets, by John McMillan
• Thinking Strategically, by Avinash Dixit and Barry Nalebuff
• Capitalism and Freedom, by Milton Friedman
• Equality and Efficiency: The Big Tradeoff, by Arthur Okun
• Nudge, by Richard Thaler and Cass Sunstein
• How the Economy Works, by Roger E.A. Farmer
• The Return of Depression Economics, by Paul Krugman
• The Road to Serfdom, Friedrich Hayek
• The Myth of the Rational Voter, by Bryan Caplan
• The Big Questions, by Steven Landsburg

What would your list have been?

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• Househould Robot. Does my Roomba count?
• Magnetic Train. Check.
• Flat-Screen TV. Check.
• Flat-Screen 3-D TV. Check.
• Two-Way Wrist Radio. We are so far past this.
• Two-Way Wrist TV. Ditto.
• Intelligent Computer. My computer’s a lot smarter than it looks, honest. It just acts dumb when it has to run Microsoft products.
• Instant Access to All Human Knowledge. Check!
• Human Clones. Getting there.
• First Woman President. Does Secretary of State count?
• First Black President. Check!!
• Universal Language. That would be English.
• X-Ray Specs. My infrared camera sees through clothes.
• World War III. By some accounts, we’re about 9 years into it.
• Access to Other Dimensions. Talk to the string theorists.
• Immortality. Check?
• Spelling Reform. OMG! I cn chk ths 1 off 2.

Some of the other entries, like “Home Holographs”, “Personal Rocket”, and “My Trip to Other Galaxy” might be a bit farther off. But things sure change in a hurry.

What else about your current life do you think would most surprise a time traveler from 25 years ago?

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I led Nine Section for a time; leading or not, I was part of it. They were my mates, and to them I was bound by ties of duty, loyalty and honor… Could I say, yes, Grandarse or Nick or Forster were expendable, and should have died rather than the victims of Hiroshima? No, never. And the same goes for every Indian, American, Australian, African, Chinese and other soldier whose life was on the line in August, 1945. So [I'd have said]: drop the bomb.

…

And then I have another thought.

You see, I have a feeling that if—and I know it’s an impossible if—but if, on that sunny August morning, Nine Section had known all that we know now of Hiroshima and Nagasaki, and could have been shown the effect of that bombing, and if some voice from on high had said: “There — that can end the war for you, if you want. But it doesn’t have to happen, the alternative is that the war, as you’ve known it, goes on to a normal victorious conclusion, which may take some time, and if the past is anything to go by, some of you won’t reach the end of the road. Anyway, Malaya’s down that way … it’s up to you”, I think I know what would have happened. They would have cried “Aw, fook that!”, with one voice, and then they would have sat about, snarling, and lapsed into silence, and then someone would have said heavily, “Aye, weel” and got to his feet, and been asked “W’eer th’ ‘ell you gan, then?”, and given no reply, and at last, the rest would have got up, too, gathering their gear with moaning and foul language and ill-tempered harking back to the long dirty bloody miles from the Imphal boxes to the Sittang Bend and the iniquity of having to do it again, slinging their rifles and bickering about who was to go on point, and “Ah’s aboot ‘ed it, me!” and “You, ye bugger, ye’re knackered afower ye start, you!”, and “We’ll a’ git killed!”, and then they would have been moving south. Because that is the kind of men they were.

I’ll add no comments, though yours, of course, are welcome.

[A hat tip to my Mom and Dad, who told me to read this book. So should you.]

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Be that as it may, I finished the novel with a few hours left to spare, so of course I was inspired to work on Fermat’s Last Theorem, or at least on the simplest cases. The problem, if you’ll recall, is to show that there are no integer solutions to any of the equations x³+y³=z³ , x⁴+y⁴=z⁴ and so on, except for the so-called trivial solutions in which one or more variables take the value zero.

This is relatively easy to prove in the n=4 case (that is, for the equation x⁴+y⁴=z⁴), and in fact I was able to reconstruct two separate proofs, one using elementary algebra and the other using a little geometry. (”Reconstruct” means that there was a time in my life when I knew these proofs well—and even taught them at a graduate level—but that was long long ago.) And I was able to reconstruct Lamé’s flawed proof, which, when supplemented with some more work, can be converted to a correct proof for a large class of exponents (beginning with n=5). The attempt to understand when Lame´’s argument can (or can’t) be patched up inspired a century of progress in algebraic number theory. Alas, that work reveals that there are plenty of exponents for which the proof is irreparable, beginning with n=37. The only known proof, associated in the popular imagination with the great Andrew Wiles, but more properly attributed to Frey, Serre and Ribet, is nothing like Lamé’s (and about one octillion times more difficult).

But what really surprised me was that I didn’t have a clue how to solve the case n=3. And even now, I have no memory of ever having known how to solve the case n=3. I was aware that it took Euler to solve it in the first place, and that I am not as smart as Euler (by a factor of about one octillion), but I was also aware that I know a lot of fancy techniques that Euler didn’t have. So, like the character in the novel, I thought I’d give it a go.

My first idea was to use Fermat’s favorite technique: Pretend you’ve got a solution, and show that from that solution, you can construct a smaller solution. Keep repeating and your solutions get smaller forever, which is quite impossible with integers. (If your first solution involved x=100 and x gets smaller each time, you’re going to get stuck after 100 iterations—x can’t go below zero). This means you never had a solution in the first place. (Fermat called this the “Method of Infinite Descent”.)

So I pretended I had a solution—that is, a set of numbers x, y, z that satisfy x³+y³=z³—and used a little geometry to construct a new solution. I did this using what is, for a geometer, the obvious idea. Namely:

• Set X=x/z and Y=y/z, and observe that X³+Y³=1
• Observe that (0,1) and (X,Y) are both points on the curve defined by the equation x³+y³=1
• Draw the line connecting these two points. Because the curve is defined by a third degree equation, that line will hit the curve three times. We already know it hits at (0,1) and (X,Y). Compute the third point. Because everything else in sight is a rational number, that third point will have rational coordinates.
• Write the coordinates of that point as (a/c,b/c), where a, b and c are integers. (You can always make the two denominators equal by choosing a common denominator). Then because this point sits on the curve, it satisfies the equation (a/c)³+(b/c)³=1. This in turn implies that a³+b³=c³.

So starting with one solution (x,y,z), we get a new solution (a,b,c). If (a,b,c) is in any reasonable sense smaller than (x,y,z), we can keep repeating till we get a contradiction.

When I did this, I got a = x(1+y³), b = -y(1+x³) and c = x³-y³. (You can check by hand that if x,y,z solve the Fermat equation then so do a,b,c.) Sadly, this doesn’t help because the new solution is not smaller than the old solution in any reasonable sense that I can think of. (I’d expected as much, because if something this simple had any chance of working, it wouldn’t have taken Euler to solve the problem.)

So I futzed around with a few other ideas that didn’t work (e.g. instead of drawing the line that connects two points, you could draw the tangent line at the point (X,Y)) and finally looked up Euler’s proof, which I must say, rang absolutely no bells with me, meaning either that I must have been curiously uncurious about this when I was younger or that my memory is failing even more precipitously than I realized. On a side note, I also learned (for the first time, as far as I can recall) that Euler’s first published attempt was incorrect.

Well, at least I got a blog post out of this, and more importantly it was fun. Sometimes it pays to have a short memory. Every now and then (especially when I’m stuck in a boring meeting) I compute the sum of the infinite series 1 + 1/2ⁿ + 1/3ⁿ + 1/4ⁿ + … for various values of n, which is another problem that Euler got to before I did. The main idea stays with me, but the details are new every time.

Edited to add: For those who are playing along at home—I copied incorrectly from my notes. The a, b and c announced above come not from the line that connects (0,1) to (X,Y), but from the tangent line at (X,Y). If you use the line connecting (0,1) to (X,Y), you get a=-x, b= z, c=y, which is even less useful.

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What does David get out of this? Well first, of course, he wants you to read his book. But second, he’s about to start preparing a third edition and welcomes reader feedback. If you post your comments here, I’ll make sure he sees them.

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I’ll be back on Tuesday with, I expect, something new to say.

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I’m not sure if this counts as serious engagement, but I am reminded of the apparently little-known fact that the singer/actor/TV phenomenon Dean Martin did exactly this. In fact, he overdid exactly this. By the time he was 27 years old, Martin had sold 10% of himself to MCA Records, 20% to his manager DIck Richards, 35% to his other manager Lou Perry, and 25% to the mobster Frank Costello. That left him with 5% of himself—”$50 for every grand he made” in the words of writer Nick Tosches. A year later, he hired yet another manager and sold him another 10%. Having now sold 105% of himself, it became imprudent to earn money. Therefore, in need of something to live on, Martin sold yet another 10% of himself to nighclub owner Angel Lopez.

It took two years of bankruptcy proceedings to untangle the mess and give Martin a fresh start. (The story is engagingly told in Tosches’s book Dino: Living High in the Dirty Business of Dreams.)

Is there something about this kind of contract that particularly invites fraud?

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When we meet Pans, he is hovering over a glass contraption—a perpetual motion machine, really—consisting of a circular tube containing several colored beads, which travel around the tube, some clockwise, some counterclockwise, all at the same speed, bouncing off each other in perfectly elastic collisions whenever they collide. Pans is currently tugging at his earrings so hard as to cause some concern for the integrity of his earlobes, as he ponders the following question:

But wull tha’ aver gut bark to weer tha’s started, at a’, at a’?

Well, okay, maybe I’m not Pans. Maybe I’m the character Sherloch Humes, a “trim but rather wrinkled gentleman in worsteds”, who calculates for Pans’s benefit that “the configuration of beads is guaranteed to have exactly replicated itself by the year two thousand and nineteen”. I believe that I am the inspiration for one of these characters and that the mathematician Leonid Vaserstein (who is neither Scottish nor wrinkled) is the inspiration for the other, and here is why:

Many years ago, for reasons I can no longer remember, Vaserstein and I posed ourselves the following question: Suppose several point particles, all of different colors, are located on a circle, with some traveling clockwise and others counterclockwise, all at the same speed. Whenever two particles collide, they instantly bounce off each other and proceed in the opposite of their original directions, still at the same speed. Take a snapshot of this system at, say, 12PM. Must there be some time in the future when another snapshot of the system will look identical? In other words, does the history of the system repeat itself?

As I said, I can no longer remember how we came up with this question, but I do remember that it triggered a vigorous discussion. We were riding in a car at the time, myself in the passenger seat and Vaserstein in the rear. Victor Snaith, who some years later was to write The Yukiad, was driving.

The solution—which I’m pretty sure Vaserstein contributed more to than I did—is beautiful and elegant and crystal clear once you see it. Do you see it?

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I’m late to the party, but here’s my list:

1. Clown Town, by Dixie Willson The book I fell in love with before I could read.
2. Space and Time in Special Relativity, by N. David Mermin. As I said in the introduction to The Big Questions, this is the book that taught me, at age 16, that it is possible to think.
3. Topics in Algebra, by I.N. Herstein. The book that taught me algebra.
4. The Waste Land and Other Poems, by T.S. Eliot.
5. Exchange and Production by Armen Alchian and William Allen. The book that taught me to think like an economist.
6. The Red Book of Varieties and Schemes, by David Mumford. The book that taught me geometry, before it was a book. I still have my tattered copy of Mumford’s manuscript, which circulated unpublished for many years.
7. Collected Poems, by Dylan Thomas
8. Under Milk Wood, by Dylan Thomas
9. A Child’s Christmas in Wales, by Dylan Thomas
10. Poems, by Gerard Manley Hopkins
11. Quantum Reality, by Nick Herbert. This survey, aimed at the “physics for poets” crowd, inspired me to start working through textbooks, culminating in entry number 16 below.
12. Collected Poems, by W.B. Yeats
13. Recoltes et Semailles, by Alexandre Grothendieck. I am inspired above all by Grothendieck’s vision of geometry, but I got my first taste of that vision from Mumford’s red book, not from the primary sources, which I have therefore not listed here. This gripping and intensely personal and memoir is inspiring and saddening in a thousand different ways.
14. Joe Gould’s Secret, by Joseph Mitchell
15. Consciousness Explained, by Daniel Dennett
16. Quantum Mechanics and the Particles of Nature, by Anthony Sudbery

Notably absent from this list is Derek Parfit’s Reasons and Persons, which I have somehow never read front-to-back though it’s been fifteen years since Tyler told me it’s a must-read. I haven’t done a careful count, but I believe that Parfit is the most frequently mentioned book on the lists cited above. I really must get to it.

Do share your own lists.

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One of the various unsatisfactory answers I keep getting is something like: “Umm. You wouldn’t care.” But I know that’s wrong, because I’ve read Clown Town.

Clown Town was my most favorite book since before I could read. Fortunately for the various adults who were called upon to read it to me morning, noon and night, I managed to memorize it before I could even read it myself. The key dilemma faced by the residents of Clown Town is what to name the baby. The day is saved by the baby’s father, who invents the name “pood”, which, of course, is perfect, because it reads the same in both directions.

In my memory, I was an exceptionally dull and unquestioning child (I remember asking exactly one intelligent question in my first ten years on this earth; unfortunately my parents couldn’t figure out what I was asking, so I figured there was no point in ever asking another) but even I could see that there was a gap in the reasoning here. I remember being bothered by it then, and I’ve been bothered by it ever since.

Fast forward to the modern age, when my increasingly internet-savvy parents managed to find me a copy of my beloved book. (Of course, it might have been better to just not throw it out in the first place, but I’ll take what I can get.) And I just reread the story (as can you if you follow the link). And here’s what I found out:

ALTHOUGH I READ THIS BOOK 94,578 TIMES AS A CHILD, I MANAGED TO MISS THE ENTIRE POINT EVERY SINGLE GODDAM TIME.

Because, you see, here’s what actually happens in this story: The town meets to discuss a name. The schoolmaster shows up to record the proceedings. But he insists on writing all the names upside down on his blackboard, making them entirely indecipherable to the masses. He does this, basically, just to be a dick. (It’s been suggested that this part of the story might have had a formative influence on my personality.) But the child’s father saves the day by inventing the name “pood” which utterly defeats the schoolmaster’s diabolical joke.

It took awhile, but I get it now. My next project is to reread Jack and the Beanstalk.

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