Suppose that year after year, you spend more than you earn. You are worried that you’ve become fiscally irresponsible. Which of the following is not a path back to fiscal sanity for your household?

1. Spend less.
2. Earn more.
3. Stop at the ATM more often so you’ll have more cash in your pocket.

Do we all understand why the answer is C? Good. Now let’s try another one.

Suppose that year after year, your government spends more than it collects in taxes. You are worried that it’s become fiscally irresponsible. Which of the following is not a path back to fiscal sanity for the government?

1. Spend less.
2. Collect more taxes.

The answer is not A. Spending less—at least spending less on things you don’t need—can certainly be a path back to fiscal sanity for a government just as it is for a household.

What about B—raising taxes? There seems to be this idea floating around that raising taxes is sort of like earning more income, and can therefore also be a path back to fiscal sanity. But that’s wrong. Raising taxes is not at all like earning more income; instead it’s very like visiting the ATM.

Here’s why: The government’s chief asset—in fact, pretty much its only asset—is its ability to tax people, now and in the future. The taxpayers are the government’s ATM. Make a withdrawal today, and there’s less available tomorrow.

Now the ability to tax is a pretty huge asset and the government has not (yet!) come close to depleting it. In that sense, there’s a lot of money in the bank. But no matter how much you’ve got in the bank, a policy of ever-increasing withdrawals is nothing at all like a decision to earn more income. (Besides, a lot of us have other uses in mind for that money.) It’s important to get the analogy right. And it’s clear from the op-ed pages that not everybody gets this.

There is this notion abroad that an extra billion in federal spending can be converted from “irresponsible” to “responsible” as long as it’s accompanied by an extra billion in tax hikes. That’s like saying a $500 haircut can be converted from “irresponsible” to “responsible” as long as you withdraw the $500 from your bank account.

So when the president appoints a commission on fiscal responsibility, as he did a couple of weeks ago, I find myself hoping that its members understand this simple point—and worrying that they don’t. Fiscal responsbility means spending less. Taxes have almost nothing to do with it.

Of course the problem with spending cuts is that there’s always someone opposed to them. The solution is to package a whole lot of cuts together so almost everyone has something to gain. Here, then, is an idea to get the commission started: Currently the Department of Agriculture steals from workers and business owners to give to farmers, the Department of Labor steals from farmers and business owners to give to workers, and the Department of Commerce steals from workers and farmers to give to business owners—with a lot of wealth falling through the cracks along the way. Eliminate all three departments and every American will lose one friend and two enemies. It’s the responsible thing to do.

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What interests me in all this is the promiscuous use of the adjectives “anti-gay” and “hypocritical”. The senator seems to be charged with three counts of anti-gayness, with hypocrisy as an aggravating circumstance. First, he opposes anti-discrimination laws. Second, he opposes gay marriage. Third, he opposes an official day of recognition for gay rights activist Harvey Milk.

Now let’s take these one at a time.

• I share the senator’s opposition to anti-discrimination laws. If that makes me anti-gay, you can also label me anti-black, anti-Jewish, anti-Republican and anti-economist, because I support your right to discriminate against those groups as well. I support your rights not to date economists, not to drink with economists, and not to hire economists. I do not believe that makes me anti-economist and I do not believe it makes me a hypocrite.

  Now you might or might not think that the analogy between gays and economists, or the analogy between dating and hiring, is seriously flawed. We’ve had that discussion in comments elsewhere on this blog, I don’t propose to repeat it here. Here I’m asking you only to accept that some people (me, for example) find these analogies compelling and therefore share the outed senator’s position on discrimination law without bearing any animus toward gays.

  Moreover, as far as I am aware, there is no known correlation between sexual orientation and susceptibility to argument by analogy. Therefore, a gay man who shares my position ought not be suspected of hypocrisy.

• Next, we have the issue of gay marriage. I am for gay marriage. I am for polyamorous marriage. I am for marriage between three gay men, two eunuchs and a bull dyke. I am for recognition and enforcement of pretty much any lifestyle contract that consenting adults want to enter into. But I also have dear friends who oppose gay marriage, and I am quite sure that their opposition is not motivated by animus toward gays.

  I have one friend, for example, who has proved himself over many years to be one of the world’s great celebrators of diversity, but who opposes gay marriage because he fears that gays, moreso than straights, will game the system by marrying or unmarrying as needed to secure tax advantages. Straights might do the same, but they will do it less because they’re more likely to be locked into marriages through childbearing. I happen to think this argument is completely nuts. (For the record, I think my friend is absolutely right that gays will game the system somewhat more than straights will, and that that’s a bad thing. I just think he’s absolutely nuts to put quite so much weight on it.) But everyone I know believes at least ten things that I think are completely nuts. I do not jump to the conclusion that they believe those things because they are hostile or angry or anti-this-group-or-that. I think they believe these things because they are mistaken. (Or even possibly because they’re right and I’m mistaken.) And I don’t see any reason why gay people can’t be as easily mistaken as straight people. So I don’t see any reason why gay people can’t, like my friend, consistently, honestly, and non-hypocritically, oppose gay marriage, even while lamenting the hardships a marriage ban imposes on themselves, their partners and their friends.

  Or take Megan McArdle (a/k/a Jane Galt), who I do not know personally, but who has moved me with a clearly heartfelt account of her reasons for equivocating on the marriage issue. I don’t share her equivocation, but regarding her motivations, I think it would be insanely uncharitable to take her at anything other than her word.

• As for the third issue, the Harvey Milk Appreciation Day, this is just, of course, a bit of silliness. There are all sorts of reasons someone might think the calendar is already too cluttered with Appreciation Days. I would not even vote for an Isaac Newton appreciation day, and whatever you might think of Harvey Milk, he surely did less for the world than Isaac Newton. Someone else might disagree. And again, I don’t see any reason why your sexual orientation should influence your opinion on this matter.

So I think it would be good if everyone lightened up on the accusations and on the schadenfreude. The twin tragedies here are that a man’s life has been upended and that we live in the sort of world where this kind of thing can upend your life.

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I can’t figure out her point. I am all for identifying problems and brainstorming about radical solutions, but I have no idea what problem Lowrey thinks she’s addressing.

The primary problem with representative democracy is that our representatives are captured by special interests. My senators plot to steal from you and your senators plot to steal from me, with a lot of collateral damage along the way. (And yes, you and your neighbors do constitute a special interest, as do I and mine.) The problem is exacerbated by the fact that my neighbors and I have a lot of interests in common, making it easier to steal on all our behalves at the same time. The solution is to make each senator’s constituency more diverse, not, as Lowrey proposes, less.

In my book More Sex is Safer Sex, I offered a few ideas along these lines, culled from the past few years of lunch table chat:

• Divide senatorial constituencies according to the alphabet, so that instead of a senator from Alaska and a senator from Wisconsin, we’ll have a senator for everyone whose last name begins with AA through AE. The point being that it’s easy to think up earmarks and pork barrel projects that will benefit the citizens of Alaska at everyone else’s expense, but not so easy to think up pork barrel projects that will benefit everyone whose last name happens to begin with Q.
• Give each voter two votes to cast in every senatorial election. You get one vote to cast in your own state and one to cast in the state of your choice.

  Again, this forces senators to answer to broader and more diverse constituencies, diluting the power of localized special interests.

• This one’s not in the book but should have been: Give each senator a personal budget so that once he;s voted for $X billion worth of spending, he’s not allowed to vote for any more spending until he gets re-elected. This pits his various sub-constituencies against each other, so that the New York Senator who lobbies for subsidies to New York City is sure to get a negative earful from upstate.

Am I serious? Of course I’m serious. I’m serious about the importance of identifying deep problems, calling attention to them, and thinking outside the box. That’s why I was thrilled recently to run Jamie Whyte’s guest post, proposing a novel and thought-provoking solution to another problem with democracy, namely: Voters with little impact on the outcome have little incentive to become well informed.

What are your best proposals for political reform—and what problem do they address?

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The Obama administration has its knickers all in a twist over rising health insurance premiums. As you wade through the rhetoric, here are a few things to keep in mind:

1. Greed does not cause rate hikes. I’m not sure why some premiums have shot up lately, but I’m quite sure that “greed” is not the answer. That’s because I’m quite sure that the insurance companies are no greedier today than they were a year ago. To explain a change in prices, you’ve got to point to something that’s changed. Greed is pretty much a constant.

   So what relevant factor has recently changed? The only plausible candidates are costs, including expected future costs due to health care “reform”. What costs, specifically? I wish I knew. Maybe some commenter does.

2. Greed, by itself, does not cause high prices either. In competitive markets, greed causes low prices as greedy companies struggle to steal each others’ customers.
3. Monopoly causes high prices. Monopoly power, like greed, can’t explain recent rate hikes because monopoly power in this market has not recently changed. But monopoly power, unlike greed, can explain permanently high prices. And there is considerable monopoly power in this market, partly because you’re not allowed to shop for insurance out of state and largely because your employer does your shopping for you. The Administration has shown almost no stomach for combatting this problem.

   Instead, their position is something very like this: “We can’t help ourselves from misusing our power to prop up this terrible monopoly, so give us the power to control it.” Kind of like the alcoholic who needs you to buy him a drink to steady his nerves before he drives home tonight. Don’t let him snow you.

4. Profits do not raise costs. The administration wants you to believe that we could lower the cost of insurance by limiting the profits of insurers. That’s bad economics, bad accounting and bad arithmetic.

   Imagine a hypothetical insurance company that forgoes profits in order to keep down premiums. That insurance company, just like any other, needs capital to operate—but it can’t attract investors, because it has nothing to attract them with. So where does the capital come from? It’s got to come from taxpayers—taxpayers who fork over money that could otherwise be earning income in retirement accounts. And that forgone income is a fullfledged cost.

   So yes, a publicly run insurance company could choose to earn $12 billion less in profit and return that saving to us in lower premiums—but only by taxing us enough and reducing our savings enough so we collectively earn $12 billion less in interest, dividends and capital gains.

   By analogy, that same public insurance company could hypothetically require 10,000 clerical workers to put in 40 hours a week at zero pay. Would that reduce the cost of insurance? Surely not. It would reduce the premiums, but not the cost. Instead, it shifts the cost to those 10,000 workers, who, I’m sure, would tell you quite forcefully that the cost to them is considerable.

   Capital and labor are costly. Those costs are quite literally unavoidable. They can be shifted around but they can’t be eliminated. Lowering wages does not lower costs; it just shifts them on to the backs of the conscripted workers. Lowering profits does not lower costs; it just shifts them on to the backs of the conscripted investors, for which read “taxpayers”.

   [These arguments apply to ordinary profits. If you think that profits in the insurance industry are excessive, then we're back to the issue of monopoly power, which is the only plausible source of consistently excessive profits. Keep in mind too that a single years' profits are the wrong way to measure excess; all industries have good years and bad years.]

5. Choices must be made. Adminstration spokesperson Robert Gibbs said the other day that you shouldn’t have to choose between having more health care and having more housing. Note well that when he says that’s a choice you shouldn’t have to make, what he means is that it’s a choice you shouldn’t get to make. He wants to make it for you.

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Edited to add: I don’t always read Krugman’s column, but since Don’s link sent me there today, I can’t resist noting one more outrage: Krugman thinks that extending estate tax relief to the top .25% of estates is a policy “on behalf of” that .25% of the population, as opposed to a policy on behalf of everyone who benefits from capital accumulation, higher wages and economic growth.

Or more precisesly, he doesn’t think that. But he says it.

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On Tuesday I made some snarky and cynical comments about the effects of health care reform on government spending. Fortunately, nobody at the Congressional Budget Office sued me for libel. Professor Joseph Weiler was not so lucky; when he posted a negative book review on a web site he edits, he was charged with criminal libel in France. Thursday’s post reviewed the astonishing story and Friday’s followed up with an account of the most devastating book review I know of (though commenters offered some good alternatives).

We paused midweek to acknowledge the birthday of Georg Cantor, and to summarize how he taught the world to think about infinity.

Next week: Commentary on health insurance premium hikes and much much more. Come back on Monday!

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The review I’ll be emailing is a classic of the genre. It was written by Andre Weil, one of the most influential mathematicians of the twentieth century, and possibly the most erudite person who ever lived. Here’s how I described Weil shortly after his death:

His profound grasp of mathematical history made him seem all the more a part of that history; he was the natural heir to the tradition he cherished. In paper after paper, Weil exhibited his own ideas as natural extensions of the foundations long since laid by great masters like Fermat, Euler, and Gauss in the 17th, 18th and 19th centuries.

Steeped in the history of mathematics and the history of civilization, he was thoroughly a scholar. He spoke and read multiple languages (besides his native French, Weil was comfortable in Sanskrit, Latin, Greek, English, German, Portuguese and probably more), wrote poetry and literary criticism, mastered the Bhaghavad Gita and the Upanishads, and was renowned for the clarity and directness of his prose. He spoke incisively and knowledgeably about philosophy, painting, music and architecture.

Weil’s presence was enhanced, as is the case with many great geniuses, by his personal eccentricities and the legends they inspired—the strangely guttural French accent, the acerbic wit, the exacting standards, the complete inability to tolerate any form of stupidity (quite a burden for a man compared to whom almost everyone else in the world was basically a dunce), and the mischievous vanity. These traits live on in his writings and in the oral history that is lovingly preserved by mathematicians worldwide.

In 1973, an associate professor at Princeton University had the temerity to write a biography of Weil’s revered Fermat, and the bad luck to draw Weil as a reviewer. Weil begins by reminding us that “in order to write even a tolerably good book about Fermat, a modicum of abilities is required”. He then lists these abilities:

• ordinary accuracy
• the ability to express simple ideas in plain English
• some knowledge of French
• some knowledge of Latin
• some historical sense
• some familiarity with the work of Fermat’s contemporaries and of his successors
• knowledge and sensitivity to mathematics

Weil then proceeds to consider these requisites one by one, and to argue—via annotated quotations from the book under review—that the author apparently possesses none of them. The full text is here.

For its incisiveness, its acerbicism, and the towering authority of its author, I nominate this as the most devastating book review in the history of academic journalism. Can you suggest another contender?

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The book in question is The Trial Proceedings of the International Criminal Court by the Israeli law professor Dr. Karin N. Calvo-Goller. According to the reviewer the main part of the book “simply restates the…relevant parts of the ICC Statute.” This rehashing, he adds, is particularly unproductive since a large part of the volume consists of a reprint of the Statute itself.

The author, Dr. Calvo-Goller, disagrees, and has instigated a case of criminal libel against the editor, Professor Weiler. According to Dr. Calvo-Goller:

[The] review…contains false factual statements which the author of the review, a professor of criminal law, could not reasonably believe to be true. Professor Weigend’s review is libellous. It may cause harm to my professional reputation and academic promotion.

Dr. Calvo-Goller also contends that the review is an insult to those who took the time to read and comment on earlier drafts of her book. And she notes that the very same book received a positive review from Judge Kai Ambos, who, she pointedly observes, she has never met.

Dr. Calvo-Goller (who is, after all a law professor) concedes in a letter to Professor Weiler that she is aware of the extent of freedom of expression under the First Amendment to the Constitution of the United States. (Professor Weiler teaches at NYU, well within the boundaries of that country.) However, she notes, “the extent of that freedom ends where its exercise damages the reputation of an individual.”

Professor Weiler responded at great length to Dr. Calvo-Goller’s letter, and to a follow-up letter, defending the good faith and integrity of the reviewer, rejecting the notion that a critical book review constitutes an insult to advance readers, observing that it is not uncommon for a single book to receive both negative and positive reviews, and suggesting that the question of what constitutes a “rehash” might be a matter at least partly of opinion and not of clearcut fact. He invited Dr. Calvo-Goller to respond on the website and passed on her objections to the original reviewer with an invitation to read them and modify his review, an invitation which was not accepted. A year later, Professor Weiler was summoned to appear before a French Examining Judge, and his criminal trial was set for June 25.

Professor Weiler has invited letters of indignation and support to be sent to EJIL.academicfreedom@gmail.com, preferably via attachments on letterhead indicating your affiliation. He has also requested scanned or digital copies of book reviews which are at least as critical as the one in question so as to illustrate that this kind of thing happens all the time.

Tomorrow, I’ll tell you about the book review I’m about to scan.

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What does it mean for some infinities to be larger than others? Well, for starters, some infinite sets can be listed, while others are too big to list. The natural numbers, for example, are already packaged as a list:

The integers, by contrast (that is, the natural numbers plus their negatives) aren’t automatically listed because a list, by definition, has a starting point, whereas the integers stretch infinitely far in both directions. But we can fix that by rearranging them:

So the integers can also be listed.

The positive rational numbers (that is, numbers expressible as fractions) appear even harder to list than the integers, because they have no immediate successors. What is the next rational number after 1/2, for example? Answer: there is no next number. Between any two rationals lie infinitely many more.

We can still list them, though—after a suitable rearrangement of course. There are many ways to do this; here’s probably the simplest: First list all the fractions whose numerator and denominator add to 2, then all the fractions whose numerator and denominator add to 3, then all the fractions whose numerator and denominator add to 4, then 5, and so on, like so:

and finally string them all together:

There’s some repetition here (for example, 2/2 is the same number as 1/1), but just cross out the repeats and you’ve got your list.

What if you wanted to list all the rational numbers, both positive and negative? Easy! Just combine the two tricks we’ve already used. Start with the list just above, and stick in the negatives:

Now the only missing rational is zero, which you can throw in anyplace you like—say at the very beginning.

At this point you should begin to suspect that any infinite set can be listed, given enough cleverness. Not so, though. Let’s try to list all the real numbers—that is, all numbers expressible as (possibly infinite) decimals—between 0 and 1.

Now offhand, I can’t think of any way to do this, but that doesn’t prove anything about the real numbers; it might just prove I’m not as clever as I ought to be. But Cantor, with one incredibly simple argument, demonstrated that no attempt to list those real numbers can be successful.

Here’s the argument. Suppose you believe you have managed to list all those real numbers. Maybe your list looks something like this:

(For convenience, I’ve displayed this list vertically instead of horizontally, so the first item on the list is .8410729…., the second is .1415926…, and so on.) Now I’m going to prove you wrong—that is, I’m going to prove your list is incomplete—by writing down a number that’s definitely missing. First I write down a decimal point. Then I write down any first digit other than 8 (say 6). This insures that the number I’m writing down is not the same as .8410729….. Then I write down any second digit other than 4 (say 5). This insures that the number I’m writing down is not the same as .1415926….. Then I’ll write down any third digit other than 3 (say 7). This insures that the the number I’m writing down is not the same as .3333333….. Continuing in this way, I get a number

that is definitely nowhere on your list.

(If it bothers you to imagine that I could make infinitely many choices, just imagine that I make all the choices at once by applying some fixed rule. For example: Whenever I need a digit other than 1, I’ll pick 7; whenever I need a digit other than 2, I’ll pick 5…)

If you say “oops, I forgot that number; I’ll stick it in my list somewhere”, I’ll just pull the same trick again and find another number that’s not on your list. So no matter how clever you are, you can never list all the real numbers—or even just the real numbers between 0 and 1.

But we saw that there is a way to list all the rational numbers. So in what turns out to be a profound and fundamental sense, the infinity of real numbers is bigger than the infinity of rational numbers.

With that discovery, Cantor taught the world how think about infinity, rocked the foundations of mathematics, and, with a lag of a hundred and some years, changed my life.

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Of course, my friend wasn’t entirely serious; he was just gearing up for a possible future at the Congressional Budget Office, which says we can reduce government spending by enacting the president’s health reform proposal. They’ve got it figured that if we pass this proposal now, it will motivate future cuts in Medicare (even though nobody’s ever had the stomach for those cuts before). If I understand the numbers right, they’re counting that as a “saving” of several hundred billion dollars. Well, pass me that cake.

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