Author Archive for Steve Landsburg

Non-Simple Arithmetic

complexThe Intelligent Design folk tell you that complexity requires a designer.

The Richard Dawkins crowd tell you that complexity must evolve from simplicity.

I claim they’re both wrong, because the natural numbers, together with the operations of arithmetic, are fantastically complex, but were neither created nor evolved.

I’ve made this argument multiple times, in The Big Questions, on this blog, and elsewhere. Today, I aim to explain a little more deeply why I say that the natural numbers are fantastically complex.

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Health Care Postscript

Over at Econlog, Arnold Kling chides me for the way I concluded yesterday’s post on health care and Harvard Professor David Cutler:

My gut instincts point me in a different direction that Professor Cutler’s do, but I think we agree on what the big problems are and on what would count as solutions. I think almost all economists would agree on that much, and that’s a lot.

Here is Arnold:

My disagreement with Cutler is more than mere gut instinct. Cutler and I might agree that there is overuse of medical procedures with high costs and low benefits. We might agree that incentives affect this. However, Cutler is confident that central planning represents the solution, not the problem. He believes that remote bureaucrats can measure health care quality well enough and implement compensation schemes that are fine-grained enough to achieve significant improvement.

For the record, Arnold and I are saying the same thing, though I tried to say it a little more politely. David Cutler, Arnold Kling and I all agree that incentives matter and that it’s important to get them right. Arnold Kling and I agree that David Cutler probably doesn’t know how to do that.

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Making Health Care Work

Yesterday I had the privilege of meeting David Cutler—Harvard health economist, advisor to President Obama, and co-author of much of the health reform legislation currently moving through Congress. While I am very skeptical of some of Professor Cutler’s policy goals, I was reminded once again that, for all our bickering around the edges, nearly all economists of all political stripes have a shared and useful way of thinking about the world.

I took the opportunity to ask Professor Cutler about a question that arose on this blog last week. I had posted about my fear that a public health insurance option would be manipulated by politicians intervening to get better coverage for their contributors and constituents, while passing the costs off to less well-connected groups. Some of the commenters—notably Cos and Sierra Black—asked whether this has been a problem in other countries. I had to admit that I had no idea, so I put the question to Professor Cutler. Here is what he said:

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On the Amazon: Christmas Edition

Some gift ideas for the more unusual people on your Christmas list:

First, with a hat tip to my sister, three from Amazon.com.

  • For your ex’s divorce lawyer: A laptop desk to attach to your steering wheel! Proceed as follows (you’ll thank me, really): First cursor over the customer images on the left side of the page. Then read the customer reviews.
  • For the political activist on your list: Uranium ore!. Again, read the customer reviews. Again, you’ll thank me.
  • For your oddball cousin: Wolf urine!. Not a common taste, but for those who indulge, there simply is no substitute. And of course: Read the reviews.

And speaking of Amazon customer reviews, I was more than pleased to stumble on this quote in a review of The Big Questions:

Also, if you are a parent and are blessed with a math/science inclined child, please, please, please buy them a copy!

It’s not too late!

Finally, as a Christmas gift to my readers—or at least to that vocal subset of my readers who have been clamoring for answers to the honors questions I posted a couple of weeks ago: Your wish is my command.

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The Big Answers, Part I

A little while back, I posted the first half and then the second half of the honors exam in economics that I administered at Oberlin College. Since then, I’ve slowly doled out a few answers, but I’m getting more and more requests for the complete set. Here, then, are the questions and answers for the first half; I warn you that some of these are pretty technical. I’ll post the second half soon.

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Weekend Roundup

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What Else Went Wrong

The people at Big Think have posted their latest videos in the “What Went Wrong” series about the financial crisis; I am one of a consortium of bloggers who have been invited to submit questions the interviewees and to blog about their answers.

The most interesting of the current interviews is with hedge fund manager Peter Thiel. A few choice quotes:

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Postman’s Nightmare

map.sss

Courtesy of our frequent commenter Cos, I bring you a map of Silver Springs Shores, Florida, the place you most don’t want to be when you’re looking for an address. Go ahead. Click on the map to bring up the full sized version. Start reading the street names. I promise you, the longer you look the more hilarious it gets.

[Click here to comment.]

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Economists Calendar

aeaCalendarIf you were choosing 18 economists to highlight in a calendar, who would they be?

The American Economics Association has chosen, among others, Karl Marx, John Maynard Keynes, Milton Friedman, George Stigler, Friedrich von Hayek, Joseph Schumpeter, Adam Smith and Joan Robinson. (Can you identify the rest?) I haven’t yet held the Economists Calendar in my hands, but the reliable Mark Skousen has, and his verdict (via private email) is “Bravo!”

The calendar includes, according to Skousen, “an amazingly complete listing of top economists through the ages”, along with the featured 18. There’s still time to order before Christmas.

[Click here to comment.]

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Centennial

Red CloudOne hundred years ago today, Red Cloud, the last of the great Sioux warrior chiefs, died in peace on the Pine Ridge reservation at the age of 89. He was preceded in death by the way of life he fought so valiantly to preserve.

If there is such a thing as a just war, Red Cloud’s War of 1866 was more just than most. Black Kettle‘s village of peaceful Cheyenne had been recently and wantonly slaughtered by the Colorado militia under Colonel John Chivington at Sand Creek. (The survivors of this unhappy band would meet their deaths a few years later at Washita Creek, at the equally murderous hands of General George Armstrong Custer.) Against this background, the chiefs had been betrayed at Fort Laramie, where the government had summoned them to negotiate for the right to build roads through Indian territory. With the conference still in session and no agreement in sight, Colonel Henry Carrington and a force of 700 men arrived to build the Bozeman Trail.

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Reviews

Some recent reviews of
The Big Questions:

Here and here.

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Playing Politics

If you want to understand why a public health insurance option is such a bad idea, just imagine a world where we’ve passed the Coburn Amendment, requiring all members of Congress to subscribe to that public option. In that world, a powerful Senator who develops a hankering for a nose job can make a few phone calls and nudge the public insurance commissioner toward a new appreciation for the moral imperative of covering cosmetic surgery.

And if the Senator is successful, where do the funds come from? Either higher premiums, paid for mostly by subscribers who never wanted this kind of coverage, or by dipping into general revenues. After all, the funds have to come from somewhere.

With or without the Coburn Amendment, and however unlikely you might find this particular scenario, the public option is nakedly vulnerable to exactly this type of corruption. A Senator who would never dream of intervening quite so blatantly on his own behalf might think nothing of intervening on behalf of a big campaign contributor, and will certainly think nothing of intervening on behalf of politically potent interest groups—that, after all, is what politicians do for a living.

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Playing Games

Here are solutions to the two game theory problems from my honors exam:

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The Big Answers

To the many people who have recently requested answers to my Honors Exam, Part I and Part II:

I’ve already posted answers to the Snidely Whiplash and “Rank the Taxes” problems. I’ll post solutions to the “Jack and Jill” and “Dukes of Earl” problems in the next day or two, and the remainder soon thereafter. Thanks for your patience.

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It’s Not Rocket Science

James Hansen heads the NASA Goddard Institute for Space Studies. If you have a question about radiative transfer in planetary atmospheres, he’s your go-to guy. But if you have a question about economics—say, about the merits of cap-and-trade programs—you might want to consult a different sort of specialist. Hansen’s recent New York Times piece provides ample confirmation of that.

The column oozes nonsense throughout, but it will be instructive to hone in on one exceptionally silly paragraph. Here is Hansen trying to explain why cap-and-trade is inferior to a carbon tax:

Consider the perverse effect cap and trade has on altruistic actions. Say you decide to buy a small, high-efficiency car. That reduces your emissions, but not your country’s. Instead, it allows somebody else to buy a bigger S.U.V.—because the total emissions are set by the cap.

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Ethics by Pronouncement

14ethicist_190In this week’s insult to his readers’ intelligence, Randy Cohen, the designated “Ethicist” at the New York Times, responds to two reader inquiries: May I refuse to hire someone because I don’t like his politics? (Answer: “No you may not”.) And: May I, as a doctor, refuse to treat someone because I don’t like his occupation? (Answer, in essence: “Yes you may”.)

More striking even than Cohen’s characteristic “ethics by pronouncement”, refusing to acknowledge, let alone address, the underlying issues, is that he doesn’t even seem to notice that these questions have something in common. He treats them as two separate reader inquiries, from two separate and non-overlapping universes. Thus it’s okay for the doctor to turn away a patient because “You cannot be forced to practice medicine” and because the patient can always find another doctor. One might wonder, then, in the case of the employer, why it’s not true/relevant/dispositive that “You cannot be forced to provide employment” and/or that the candidate can always find another job.

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Between the Folds

0501_1Between The Folds is a striking documentary about the art and science of origami. I’ve watched an advance copy, provided by the producers, and it’s really quite mesmerizing. Roughly half the program is devoted to artists like Satoshi Kamiya, who folded this extraordinary dragon, according to the rules of origami, from a single piece of paper with no cuts. In the second half, we meet mathematicians and scientists like Robert Lang,
eyeglasspictured here in front of the folding lens he designed for the Hubbell Space Telescope—folded, it fits inside a small rocket ship for delivery to its destination in space, where it unfolds automatically—and Erik Demaine, the paperfolding enthusiast and Macarthur “genius” award winner who is applying origami to the design of synthetic proteins that fold reliably into the proper configurations.

“Between the Folds” has its national television debut tomorrow night (Tuesday, December 8 on PBS; check your local listings for the time). Or check here for additional showings.

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Weekend Roundup

This was a week of economics, religion and miscellanea.

Two weeks ago, I’d posted the first half of my honors exam in economics. This week I posted the second half, and continued my practice of slowly doling out the answers with a post on the best and worst ways to be taxed.

A complimentary note from my old friend Deirdre McCloskey triggered a thread about religion and inspired my mini-review of John Polkingohorne’s, theology.

An offhand remark from a mobster inspired a thread about remarkable coincidences, and the most recent shallow pontification from the self-proclaimed “Ethicist” inspired me to complain.

I’ll be back on Monday with more deep thoughts and light diversions, along with some holiday gift ideas.

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What Went Wrong?

I am part of a consortium of bloggers who have been recruited by the proprietors of Big Think to explore the roots of the financial crisis. Big Think is conducting a series of video interviews with a variety of experts; we bloggers are invited to submit questions to be asked in these interviews, and we have agreed to blog more or less simultaneously about those interviews as they are posted.

The first interview, with David Wessel of the Wall Street Journal, is now posted. Some of what he says strikes me as right, some strikes me as wrong, and some strikes me as confusing.

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The Honors Class, Part II

Two weeks ago, I posted the first half of the honors exam that I administered last spring at Oberlin college. I am following up today with the second half. Once again, I’ve translated some of the questions from economese to English, but am fairly confident that nothing significant has been lost in the translation. This starts with Question 6:

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Braaaaains!

Henry Molaison, it is said, was a man who lived in the past—an amnesia victim unable to form new long term memories, so that each new experience was quickly forgotten. From age 27 (when he underwent brain surgery for epilepsy) to age 82 (when he died last year), Henry Molaison could remember only the first 27 years of his life.

Today—and I literally mean today—Henry Molaison’s brain is being sliced and diced at the U.C. San Diego Brain Observatory in furtherance of neurological research. And starting soon, you can watch the slicing live via webcam. The process started yesterday, and they’re currently (as of 12:20PM eastern time on Thursday, December 3) on break, but a note on the site says that “cutting will resume shortly”.

The World Wide Web is a strange and wonderful place.

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Amazing But True

John Gottti Junior, fresh from his fourth mistrial on racketeering and murder conspiracy charges, reports a miracle: Over the past few days, two songs that remind him of his father (the late and legendary mobster John Gotti Senior) have come up on the radio at exactly 10:27 PM—and 10/27 is his father’s birthday.

From the New York Times:

Did the son feel that the father was was watching over him?

“How else do you explain it?”, he said.

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Life, the Universes and Everything

As I mentioned the other day, I’ve recently (at the direction of my old friend Deirdre McCloskey) been reading some of the work of John Polkinghorne, the physicist-turned-theologian who seems to write about a book a week attempting to reconcile his twin faiths in orthodox science and orthodox Christianity.

Although Belief in God in an Age of Science is a very short book, it is too long to review in a single blog post. Fortunately, though, much of the non-lunatic content is concentrated in roughly the first ten pages, so I’ll comment here only on those.

Polkinghorne begins in awe. He is awestruck by the extent to which our Universe seems to have been fine-tuned to support life; this is the subject matter of the much-discussed anthropic cosmological principle. To take just one example (which Polkinghorne does not mention): The very existence of elements other than hydrogen and helium depends on the fact that it’s possible, in the interior of a star, to smoosh three helum atoms together and make a carbon atom; everything else is built from there. But it’s not enough to make that carbon atom; you’ve also got to make it stick together long enough for a series of other complicated reactions to occur. Ordinarily, that doesn’t happen, but now and then it does. And the reason it happens even occasionally is that the carbon atom happens to have an energy level of exactly 7.82 million electron volts. In fact, this energy level was predicted (by Fred Hoyle and Edwin Salpeter) before it was observed, precisely on the basis that without this energy level, there could be no stable carbon, no higher elements, and no you or me.

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The Best of Taxes and the Worst of Taxes

Today I’ll give the solution to another of the problems from my honors exam:

Question 5. Rank these taxes in order of how much you’d dislike paying them:

  • A tax on consumption
  • A tax on wages
  • A tax on income (including wages, interest and dividends)

Assume that the tax rates are adjusted so that your total tax bill is the same in each case.

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The Lament of Deirdre

Deirdre McCloskey has changed my life several times, and always for the better. I had my first economics lessons from friends who were so inspired by Deirdre’s lectures that they felt compelled to repeat them to me over dinner; she was one of my most influential teachers long before I’d ever laid eyes on her. Later on, I had the privilege of knowing her personally, counting her as a treasured friend, and being repeatedly re-inspired by her twin passions to understand the world and to make it work better.

When I decided to write a textbook that competed directly with Deirdre’s own, she was my strongest booster. When I decided to follow up with a book for the general public—the book that became The Armchair Economist—Deirdre told me exactly how to sell it to the publishers. Fifteen years later, the Armchair Economist remains one of the bestselling popular economics books in at least six languages, and at multiple levels—intellectual, practical and personal—I owe it all to Deirdre.

So it was with considerable delight that I received Deirdre’s recent email with subject line “Your Splendid Book”. But as I fully expected (having had this conversation with her more than once), her praise was tempered with disapproval of my “adolescent” atheism:

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The Oracle of Eighth Avenue

Randy Cohen, the house ethicist at the New York Times, frequently strikes me as disappointingly shallow. Take, for example, his latest column, posing this ethical quandary:

You’re redesigning a website and you want to include a photo of a generic customer. The client does not want the generic customer to be African-American, partly because he has never had an African-American customer and thinks it unlikely that he ever will. Is this okay?

My objection is not to Cohen’s answer (which is “no”) but to the way it’s dispensed, as if from an oracle, with no attempt at a derivation from clearly stated principles.

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Weekend Roundup

We started the week with the solution to one problem from Part I of my honors exam; I still owe you answers to the remaining four questions, and I still owe you the questions from Part II. Stay tuned.

We revisited the recurring issues of anti-discrimination policy and free trade. Reader comments, particularly from the ever-thoughtful Sierra Black, made me realize something new (to me) and important: When I write about free trade, I tend to focus on “why trade is good for us” (where “us” means the United States) rather than “why trade is good for the other guys” (where “the other guys” often means developing nations). I do this because most of the anti-trade screeds I run across are written by people who think trade is bad for us. But by presenting the arguments in a one-sided context I’ve misled readers like Sierra into wondering whether they also apply to developing nations. The answer is “Yes, only more so”—while trade benefits everyone, it benefits the smallest and poorest countries the most. Sometime soon when we revisit this topic, I’ll have to make a point of elaborating on the theory and evidence behind that.

We had a little math this week, and then some more serious math, including my attempt to squeeze the entire gist of Godel’s argument into one blog post. If you want to understand how we can know that not all true statements in arithmetic can be proven, that’s the post you should read.

We closed the week with posts on the spirit of Thanksgiving and the spirit of the day after Thanksgiving. I’ll be back on Monday.

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In the Spirit of the Day

If you’re at work on this post-Thanksgiving morning, it’s probably a slow day around the office (unless you’re in retail, in which case you’re probably not reading this). So to help you while away the hours, here are a few of my favorite logic puzzles from around the net:

Warning: These are majorly addictive. Enjoy, but resolve not to let them take over your life. You have a blog to get back to.

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Giving Thanks

After the philosopher Daniel Dennett was rushed to the hospital for lifesaving surgery to replace a damaged aorta, he had an epiphany:

I saw with greater clarity than ever before in my life that when I say “Thank goodness!” this is not merely a euphemism for “Thank God!” (We atheists don’t believe that there is any God to thank.) I really do mean thank goodness! There is a lot of goodness in this world, and more goodness every day, and this fantastic human-made fabric of excellence is genuinely responsible for the fact that I am alive today. It is a worthy recipient of the gratitude I feel today, and I want to celebrate that fact here and now.

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Godel in a nutshell

Godel’s theorem (or at least one of Godel’s theorems) says that no matter what axioms you adopt, there will always be true statements in arithmetic that can’t be proven. In Chapter 10 of The Big Questions I give an explicit example of such a statement, involving Hercules’s ability to win a certain game against a very persistent hydra.

There are many popularizations of Godel’s original argument, of which at least one (by Nagel and Newman) is superb. They do a marvelous job of boiling the argument itself and the surrounding issues down to a little over a hundred sparse pages. But I can boil it down further, into a single blog post. I can do this via the magic of one of my favorite expository techniques, a technique I call “lying”. I will lie to you throughout this post, by sweeping important technical details under the rug and (slightly) corrupting some important ideas to make them easier to grasp—but without, I think, sacrificing the flavor and the gist of the argument. At the end, once we’re clear on the big picture, I’ll ‘fess up to some of those lies.

Here, then, is (more or less) how Godel proved that arithmetic contains true but unprovable statements:

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