Author Archive for Steve Landsburg

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:

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.

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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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Block Grants and Bad Faith

Paul Krugman on last week’s Supreme Court arguments:

I was struck, in particular, by the argument over whether requiring that state governments participate in an expansion of Medicaid … constituted unacceptable “coercion.” One would have thought that this claim was self-evidently absurd. After all, states are free to opt out of Medicaid if they choose; Medicaid’s “coercive” power comes only from the fact that the federal government provides aid to states that are willing to follow the program’s guidelines. If you offer to give me a lot of money, but only if I perform certain tasks, is that servitude?

Wrong question. The right question is:

If you take a lot of money from me and then offer to give it back, but only if I perform certain tasks, is that servitude?

Because, you see, the federal government is not handing out its own money to state governments — it’s handing out money that it takes from the citizens of those very states for the purpose of (conditionally) handing it back. (Of course “handing it back” isn’t exactly right either, because the payments go not to taxpayers but to their state governments — but it’s a lot closer to right than Krugman’s formulation.)

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Meta-Limerick

There once was an X from place B,
Who satisfied predicate P,
The X did thing A,
In a specified way,
Resulting in circumstance C.

—Hat tip to our occasional commenter Alan Wexelblat, who hat-tips the author of the webcomic Partially Clips, who hat-tips Wikipedia, which offers no citation.

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And the Winner Is….

The Supreme Court has been a veritable festival of economic ignorance the past few days, but if I had to pick a prize specimen, I think it would be Paul Clement’s response to Justice Kennedy’s observation that the uninsured — given our unwillingness to turn them away from emergency rooms — impose a burden on the rest of us. Mr. Clement (the plaintiff’s attorney) tried to argue that the same is true in any market:

When I’m sitting in my house deciding whether to buy a car, I am causing the labor market in Detroit to go south…

thereby blurring the key distinction between a pecuniary and a non-pecuniary externality.

The point is that Mr. Clement’s decision not to buy a car (and therefore to drive down the price) is bad for Detroit auto workers only to the extent that it’s good for other car buyers. It is therefore in no sense a net burden on the rest of society. Contrast that with the clear burden imposed by the uninsured fellow who wants you to pick up his hospital tab.

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After the Nightmare

Our most recent nightmare scenario triggered some great discussion. (So did the earlier nightmare scenarios, which I’ll review in a day or two.) The conundrum was this:

 

In front of you are two childless married couples. For some reason, it’s imperative that you kill two of the four people. Your choices are:

A. Kill one randomly chosen member from each couple.
B. Kill both members of a randomly chosen couple.

All four people agree that if they die, they want to be well remembered. Therefore all four ask you, please, to choose A so that anyone who dies will be remembered by a loving spouse.

If you care about the four people in front of you, what should you do?

 

Commenters, interestingly, split pretty much 50-50 (though it’s hard to get an exact count because several equivocated). Many bought the argument that unanimous preferences should be respected (leading to A). About equally many bought the argument that the preferences of the dead don’t count, and it’s better to leave two happily married survivors than two grieving widows/widowers (leading to B).

A few highlights:

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Loose Ends

I’m eager to summarize the (largely excellent) discussion of last week’s nightmares and to talk about what it all means. I’ll surely get to that in the next few days. But meanwhile, we have another loose end to tie up.

I recently asked what comes next in the following series:

The answer, of course, is

Please raise your hand if you found this intuitively obvious.

In case your hand didn’t go up, consider the following sequence:

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Another Nightmare

nbcYesterday’s nightmare scenarios triggered some good discussion, so let me throw out another one, which I think will help to isolate some of the issues that came up yesterday. Sometime next week I’ll try to summarize the best of the comments and ponder what we’ve learned.

 
Today’s Dilemma

In front of you are two childless married couples. For some reason, it’s imperative that you kill two of the four people. Your choices are:

A. Kill one randomly chosen member from each couple.
B. Kill both members of a randomly chosen couple.

All four people agree that if they die, they want to be well remembered. Therefore all four ask you, please, to choose A so that anyone who dies will be remembered by a loving spouse.

If you care about the four people in front of you, what should you do?

 

Argument 1. For goodness’s sake, they’ve told you what to do. If you care about them, of course you should respect their wishes. Choose A.

Argument 2.Once the killings are over, Option A leaves two grieving spouses, whereas Option B leaves one relieved couple. Surely two dead plus two happy is better than two dead plus two sad. Choose B.

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Nightmare Scenarios

scream

Here’s a question to ponder:

Question 1: If forced to choose, which of these nightmare scenarios would you prefer?

Scenario A: An evil alien flips a coin. If it comes up heads, he destroys all human life; otherwise he goes home.

Scenario B: The same evil alien flips 7 billion coins, one for each person on earth. He destroys anyone whose coin comes up heads.

I’ll tell you in a minute why I ask, but first let’s consider arguments in each direction:

Argument 1. In scenario A, I have a 50-50 chance of death, and a 50-50 chance of continuing my current life. In scenario B, I have a 50-50 chance of death, and a 50-50 chance of a life in which half my loved ones are gone. Surely I should take A.

Argument 2. In scenario A, there’s a 50-50 chance that all future generations will be destroyed-in-advance. In scenario B, even if the coin comes up heads, people will continue to be born, and in the very long run, the evil alien will be a forgotten memory. Surely I should take B.

Your answer to this question, I think, is likely to reveal a lot about how much you think we owe to future generations. If you think we owe them nothing, then Argument 1 is definitive. If you think we owe them the same respect we owe our contemporaries, then Argument 2 is definitive. If you think we owe them something in between, you might waver.

Now that sort of question might strike you as nothing more than Sunday-afternoon dorm room fare, but I don’t believe it can be dismissed so easily. It is pretty much impossible to take a coherent stand on issues ranging from Social Security reform to environmental conservation without first deciding how much we are obligated to care about future generations. A lot of people seem to think those issues are worth debating, which pretty much forces us to face up to the fundamental issues.

On the other hand, come to think of it, I suppose a person might prefer Scenario B to Scenario A for reasons that have nothing to do with future generations — namely the desire to be remembered. Is that something we care about? To focus on that issue, here’s another question:

Question 2: Suppose you’re happily married. If forced to choose, which of these nightmare scenarios would you prefer?

Scenario A: An evil alien flips a coin. If it comes up heads, he kills you and your spouse; otherwise he goes home.

Scenario B: The same evil alien flips a coin. If it comes up heads, he kills just you; if it comes up tails, he kills just your spouse.

Here again we have:

Argument 1. In scenario A, I have a 50-50 chance of death, and a 50-50 chance of continuing my current life. In scenario B, I have a 50-50 chance of death, and a 50-50 chance of a life in which my beloved spouse is gone. Surely I should take A.

Argument 2. In scenario A, there’s a 50-50 chance that my spouse and I will both be dead and unremembered (or at least unremembered by anyone who knows us as intimately as we know each other). In scenario B, however, we each get to live on, at least in the memory of a loved one. Surely I should take B.

Your answer to Question 2 will tell me something about how much being remembered matters to you, which will help me interpret your answer to Question 1.

The original version of this post included several more followup questions. But I suspect these two are grist enough for a day or two of discussions. I’ll post the followups after those responses start to peter out.

Related post here.

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Touched by Greatness

Roger Godement, 1970I continue to be bowled over daily by the high quality of the discussion at MathOverflow, and the prominence of many of the frequent participants. But this one was special:

A newbie poster asked for a pointer to a proof of the “de Rham-Weil” theorem. There’s a bit of ambiguity about what theorem this might refer to, but I had a pretty good of what the poster meant, so I responded that the earliest reference I know of is in Grothendieck‘s 1957 Tohoku paper — which led another poster to ask if this meant de Rham and Weil had had nothing to do with it.

This triggered an appearance from the legendary Roger Godement (had he been lurking all this time?), now aged 91 and one of the last survivors of the extraordinary circle of French mathematicians who rewrote the foundations of topology and geometry in the mid-20th century and changed the look, feel and content of mathematics forever. I tend to think of them as gods and demigods. Godement’s indispensable Theorie des Faisceaux was my constant companion in late graduate school. And now he has emerged from retirement for the express purpose of chastising me:

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Some Questions for Uwe Reinhardt

First Greg Mankiw wrote a good piece in the New York Times about how there’s sometimes a hazy line between ordinary income and legitimate capital gains. Then Uwe Reinhardt wrote a puzzling (at least to me) followup in which he concluded that we might as well just give up and tax both at the same rate. I have some questions for Professor Reinhardt.

Question 1:

  1. Sometimes there is a hazy line between quotation and plagiarism. Does it follow that we should treat every quotation as an instance of plagiarism?
  2. Sometimes there is a hazy line between a pat on the back and an assault with intent to harm. Does it follow that we should treat every pat on the back as an intent to harm?
  3. Sometimes there is a hazy line between adolescence and maturity. Does it follow that we should treat everyone as an adolescent?
  4. If the answer to any of the above is no, what’s different about capital gains?

Professor Reinhardt goes on to instance the case of a person who buys a vacation home for $500,000 and sells it two years later for $1.5 million, suggesting that it would be unfair to let this person hang on to all of this gain, so it should therefore be taxed at the same rate as ordinary income. This brings me to the next questions:

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IQ Test

What comes next in the following series?

(Hint: This is a calculus problem.)

Click here for the answer. Explanation forthcoming in a few days.

Click here to comment or read others’ comments.

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The Analogists

    

Viagra analogies have been in the news a lot lately, both in connection with contraceptive coverage and in connection with state laws restricting abortion. I love good analogies and I hate bad ones, so I’d like to take a little time to sort out the bad from the good.

Because there are several scattered points to be made here, I’m putting them in sections and labeling them with Roman numerals, to make it easier for commenters to tell us just which section(s) they’re responding to.

I.

My insurance policy covers Viagra. I would prefer that it didn’t. Given the costs and the probabilities, erectile dysfunction seems to me like a crazy thing to be insured against. There are a whole lot of other things I feel the same way about. I’d prefer not to be insured against losing my eyeglasses. On the other hand, I’m very glad to be insured against needing chemotherapy or kidney dialysis.

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Uh Oh

How secure is Internet security? A team of researchers recently set out to crack the security of about 6.6 million sites around the Internet that use a supposedly “unbreakable” cryptosystem. The good news is that they succeeded only .2% of the time. The bad — and rather shocking — news — is that .2% of 6.6 million is almost 13,000. That’s 13,000 sites with effectively no security. The interesting part is what went wrong. It’s a gaping security hole that I’d never stopped to consider, but is obvious once it’s pointed out.

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More Sex and More Sex

In England last month, I had the privilege of speaking to two fabulous audiences.

The Warwick Economics Conference is an entirely student-run affair that draws several hundred students from the University of Warwick and all over Europe to hear over a dozen talks about economics and related subjects, and to hobnnob with the speakers and each other. I had the chance to talk to a lot of these students one-on-one and I was absolutely blown away by their cleverness, their thoughtfulness, and their eagerness to tackle hard problems. On Saturday night, I sat up until far into the early morning chatting with a dozen or so of these kids, and I’d have happily gone on longer if they hadn’t eventually thrown us out of the building.

Then a few days later, I gave pretty much the same talk all over again to another bright and enthusiastic audience at the Adam Smith Institute. Once again, I had a blast talking to these people before and afterwards.

Below the fold you’ll find video of both talks. They’re almost identical, except that the Warwick talk includes pictures of my family. I’m disappointed that in both cases, the lively Q&A sessions have been deleted from the videos. (I do sometimes talk on other topics as well! See here for example.)

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Letter to a Reporter

I suspect we’re all getting bored of talking about Sandra Fluke, contraception policy, alternative solutions, and the reaction thereto, but I’ve just had an email from a reporter who’s confused on a point so basic, I thought it might be worth clearing it up for a larger audience.

The reporter writes:

As you might suspect, I disagree with your assertion that “All she said, in effect, was that she and others want contraception and they don’t want to pay for it.” I was wondering if you happened to catch the part of her speech where she talked about wanting women whose doctors have prescribed birth control pills to treat medical disorders like endometriosis to be able to get such drugs without having to pass tests demanded by religious institutions? Is this an unimportant part of the debate?

Here is a slightly edited version of my reply:

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Aftermath

Joel Seligman, the president of the University of Rochester, has, in his words, exercised his right to express his views with a dissent from my recent posts about contraceptive subsidies.

Several news organizations have asked me for a statement. Here is what I sent them. (Below the fold is a copy of my email response to President Seligman.)

President Seligman says that the mission of the university is to promote the free exchange of ideas and lively debate, and I agree. That mission is undermined whenever a member of the academic community elevates raw self-interest over the exchange of ideas.

That’s what Sandra Fluke did. She observed that contraceptives are expensive, and therefore demanded that somebody other than herself and her fellow students pick up the tab. She didn’t even pretend to be interested in debating any of the serious issues raised by the question of when some of us should pick up the tab for others’ expenses.

Sometimes we should, sometimes we shouldn’t, and there’s a lot to be said, discussed, and debated about the particulars. An emotional appeal for one’s preferred outcome, ignoring all the substantive issues, is the
exact antithesis of the free exchange of ideas that President Seligman claims to endorse.

I’ve had three blog posts on this subject, here, here, and here. The commenters have offered many bright and lively arguments and observations, some of which have led me to modify some of my views.
This is a wonderful thing. It’s also the very opposite of Sandra Fluke’s approach, which amounts to a contemptuous dismissal of the very possibility of engaging these issues through intellectual discourse. I’d have expected a distinguished academic to feel the same way.

And now, my letter to President Seligman:

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Let’s Just Tax Men

pillsA few final thoughts (following up on this post and this post) re mandated insurance coverage for contraceptive pills:

  1. Mandated insurance coverage means that the government requires everyone who doesn’t use contraceptive pills to contribute to the costs of everyone who does. This is exactly equivalent to a tax on not using contraceptive pills.
  2. The burden of that tax falls on three groups: Men, infertile women, and fertile women who choose not to use contraceptive pills. We can consider separately the wisdom of each of these taxes.
  3. The tax on men is easily the most defensible. First, it’s non-distorting: There is (correct me if I’m wrong) currently no technology by which a man can convert himself into a fertile woman. So we don’t have to worry about the tax changing anyone’s behavior. Second, men, on average, earn more than women do, so if you believe in redistributive taxes at all, this is a great one. (We can have, someday, a separate discussion about the merits of redistributive taxes. But given that there’s a substantial constituency for those taxes, and given that we’re therefore going to have them, it seems far wiser to tax people for being male or white than for earning high incomes, since the redistribution goes for the most part in the right direction with essentially no disincentive effects.)
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Consumer Tip

sudafedHaving trouble getting Sudafed? Does your local pharmacy close at night? No problem: all you need is a set of simple step-by-step instructions for synthesizing Sudafed from crystal meth, which is readily available 24 hours a day in most American cities:

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Contraceptive Sponges

todayOver the last week, we’ve heard a lot from the people who (with a hat tip to one Joker), I now call “contraceptive sponges” — people who want others to pay for their contraception because — well, just because they don’t want to pay for it themselves.

I don’t think we need to take those people seriously. But others have taken the trouble to make actual arguments, both on this blog and elsewhere. Some but not all of those attempts deserve serious attention.

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Rush to Judgment

rushRush Limbaugh is under fire for responding in trademark fashion to the congressional testimony of Georgetown law student Sandra Fluke, who wants you to pay for her contraception. If the rest of us are to share in the costs of Ms. Fluke’s sex life, says Rush, we should also share in the benefits, via the magic of online video. For this, Rush is accused of denying Ms. Fluke her due respect.

But while Ms. Fluke herself deserves the same basic respect we owe to any human being, her position — which is what’s at issue here — deserves none whatseover. It deserves only to be ridiculed, mocked and jeered. To treat it with respect would be a travesty. I expect there are respectable arguments for subsidizing contraception (though I am skeptical that there are arguments sufficiently respectable to win me over), but Ms. Fluke made no such argument. All she said, in effect, was that she and others want contraception and they don’t want to pay for it.

To his credit, Rush stepped in to provide the requisite mockery. To his far greater credit, he did so with a spot-on analogy: If I can reasonably be required to pay for someone else’s sex life (absent any argument about externalities or other market failures), then I can reasonably demand to share in the benefits. His dense and humorless critics notwithstanding, I am 99% sure that Rush doesn’t actually advocate mandatory on-line sex videos. What he advocates is logical consistency and an appreciation for ethical symmetry. So do I. Color me jealous for not having thought of this analogy myself.

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Frank Redux

Thirteen years ago, in 1999, when I wanted to illustrate the astonishing march of progress, my Exhibit A was a new $250 stereo system that held 60 CD’s and could play tracks in random order.

My new Exhibit A is the fact that it’s been only thirteen years since this was a great example.

That was in an essay focused mostly on Robert Frank’s hypothesis that people care largely about relative position as opposed to absolute wealth. I was reminded of that essay following yesterday’s post, and I managed to dig out a copy, which I’ve posted here. Despite the dated examples, I still think it’s pretty good.

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