## Monthly Archive for September, 2010

### The Mathematical Universe

Some quick words about the mathematical universe, which is the theme of the first chapter of The Big Questions:

1. A “mathematical object” consists of abstract entities (that is, “things” with no intrinsic properties) together with some relations among them. For example, the euclidean plane that you studied in high school geometry consists of points, together with certain relations among them (such as “points A, B and C are collinear”). Mathematical objects can be very complicated. Mathematical objects can have “substructures”, which is a fancy name for “parts”. A line in the plane, for example, is a substructure of the plane.

2. Every modern theory of physics says that our universe is a mathematical object, and that we are substructures of that object. Theories differ only with regard to which mathematical object we happen to be a part of. Particles, forces and energy are not just described by equations; they are the equations (together with abstract, purely mathematical relations among those equations).

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### Ungodly Ignorance

According to a study by the Pew Forum on Religion and Public Life, forty-five percent of Americans Catholics are unaware that, according their own professed religion, the physical body of Jesus Christ tastes rather like a cracker. Protestants and Jews are equally ignorant of key facts about their own religions, though (at least according to the examples quoted in the New York Times) the gaps in their knowledge were less about theology and more about the roles of historical figures.

I can understand being simultaneously devout and a little hazy on religious history, but I don’t understand how you can be both devout and so hazy about the doctrines of your own church. In the words of Bryan Caplan, who blogged this first:

### The Grand Design

To understand the universe at the deepest level, we need to know not only how the universe behaves, but why.

• Why is there something rather than nothing?
• Why do we exist?
• Why this particular set of laws and not some other?

So say Stephen Hawking and Leonard Mlodinow in their book The Grand Design, and so say I.

The Big Big Question is the first one: Why is there something rather than nothing? Hawking’s answer: The laws of physics — and especially the form of the law of gravity — allow for the spontaneous creation of universes out of nothing at all. We live in one of those spontaneously created universes. But this, of course, only serves to raise a new Big Big Question, namely: Why are the laws of physics as they are? Hawking’s answer: The laws of physics must be consistent and must predict finite results for the quantities we can measure. It turns out that those criteria pretty much dictate the form of the laws of physics.

So unless I’ve misunderstood him, here is Hawking’s position: In order for us to be able to measure the things that we measure, the laws of physics must have a certain form, and in order for them to have that form, universes must be able to arise from nothing. Therefore our universe was able to arise from nothing. But this does not seem to answer the question of why things couldn’t have been very different. Why couldn’t there have been no us, no measurements, no laws of physics and no anything?

### Off the Grid

I am traveling, my hotel has no wireless, and my ethernet adapter isn’t working.
So I have extremely limited net access and won’t be posting anything substantive today or tomorrow. I’ll be back Monday for sure.

PS—This means I’ll also be slower than usual re responding to comments, and that some comments might spend longer than usual in the moderation queue. I’ll do what I can toward checking in every now and then.

### The Least Painful Tax

Some taxes are more painful than others. It’s not as simple as “the more you pay, the more it hurts”. Consider these two taxes, for example:

• Tax A: Shoes are taxed at \$0 per pair.
• Tax B: Shoes are taxed at \$100,000 per pair.

Under Tax A, everybody pays zero. Under Tax B, nobody buys shoes and everybody still pays zero. But Tax B is more painful, because it leaves us barefoot.

That’s of course an exceptionally simple example, but the same point arises in much subtler contexts. The pain caused by a tax is measured not just by what you pay, but also by what you do to avoid paying more.

So let’s try something more interesting:

• Tax A: A tax of 50% on all wages.
• Tax B: A tax of 40% on all wages and interest

### Escaping the Forest

You’re lost in a forest. What’s the best way to get out?

The great macroeconomist Bob Lucas once asked me this question, and I had no answer for him. I still don’t.

The assumption is that you know the size and shape of the forest, but you don’t know where you are or which way you’re facing. And the forest is so dense that you can never see any significant distance in front of you. What path should you follow?

### How to Get Rich

A few years ago, billionaire David Koch donated \$25 million to his alma mater, Deerfield Academy. From his presentation speech:

You might ask: How does David Koch happen to have the wealth to be so generous? Well, let me tell you a story. It all started when I was a little boy. One day, my father gave me an apple. I soon sold it for five dollars and bought two apples and sold them for ten. Then I bought four apples and sold them for twenty. Well, this went on day after day, week after week, month after month, year after year, until my father died and left me three hundred million dollars.

Now on the one hand I love this story. But wouldn’t it have been more plausible if he’d sold the first apple for, say, a nickel?

Well, maybe not much more plausible. Doubling your money every day, it takes just a little over a month to grow a nickel into three hundred million dollars.

I still like the story though.

### Weekend Roundup

The topics of the week were daughters and divorce, capital taxation, capital taxation again, and intelligent childhood questions. I’ll be back with more, of course, on Monday.

### Outage

The Big Questions is hosted by bluehost.com, and I’ve been thrilled with their service. Last night, through no fault of their own, the folks at bluehost were down for several hours (apparently a transformer blew out at an electrical plant down the street from them). As a result, the site was down for several hours and I never managed to get a post up for this morning. We’re back now, though.

### Speed Math

Over the course of my childhood, I remember asking exactly one intelligent question. Unfortunately, I couldn’t make my parents understand what I was asking. Perhaps it was that frustration that deterred me from ever formulating an intelligent question again.

I was, I think, six years old at the time, and my question was this: If you’re traveling at 50 miles an hour at 1:00, and you’re traveling at 70 miles an hour at 2:00, must there be a time in between when you’re traveling exactly 60 miles an hour?

What made this question intelligent—and probably what made it incomprehensible to my parents—was that I was very keen to distinguish it from the question of whether your speedometer would have to pass through the 60-mile-an-hour mark. It seemed clear to me that the answer to that one was yes—that even if your true velocity could somehow skip directly from 50 to 70, the speedometer needle, in the course of whipping around from one reading to the other, would have to pass through the midpoint.

### Capital Gains Followup

A short followup to yesterday’s post on capital gains. This came up in the comments, and I think it’s worth highlighting:

Suppose we rewrite the tax code as follows: Every March 15, women pay 20% of their incomes and men pay nothing. Every April 15th, women pay 10% and men pay 20%.

Now someone writes a letter to the New Yorker complaining that the April tax is unfair to men, who pay twice as much as women do. I think it would be fair to dismiss this complaint as silly. Yes, it’s true that if you look at the April tax in isolation, men pay more than women. But there is no sensible reason to look at the April tax in isolation. If you look at the combined effect of the March and April taxes, women pay 30% and men pay 20%. By any sensible reckoning, women are taxed at a higher rate than men.

### Getting It Right

The New Yorker arrived today, leading off with this letter to the editor about income tax rates:

…The very rich pay at significantly lower rates, because most of their income consists not of compensation for services but of capital gains and dividends, which are capped at a fifteen per cent rate.

This is wrong, wrong, wrong, wrong, wrong, wrong, wrong, and you can’t begin to think clearly about tax policy if you don’t understand why. Even if capital gains taxes were capped at one percent, income subject to those taxes would be taxed at a higher rate than straight compensation. That’s because capital gains taxes (like all other taxes on capital income) are surtaxes, assessed over and above the tax on compensation.

It always pays to think through stylized examples. Alice and Bob each work a day and earn a dollar. Alice spends her dollar right away. Bob invests his dollar, waits for it to double, and then spends the resulting two dollars. Let’s see how the tax code affects them.

### Psychology Yesterday: Daughters and Divorce

Back in 2003, I reported (here, here and in more detail here) that in disparate cultures around the world, from the U.S. to Kenya and from Mexico to Vietnam, parents of daughters are more likely to get divorced. This phenomenon, discovered by the economists Gordon Dahl and Enrico Moretti, is based on a sample size over 3 million and is therefore surely no coincidence.

After seven years, psychologist Anita Kelly, writing in Psychology Today (which might want to consider changing its name to Psychology Yesterday) has penned a response. She accurately summarizes the original argument:

Dahl and Moretti have summarized attempts to explain their facts as follows: Sons may either improve the quality of married life or worsen the pain of divorce (perhaps by becoming more distraught when the father leaves). Landsburg chooses the former explanation based on the fact that parents, on average, prefer having boys over having girls.

If you don’t blog, you might be surprised by how many spam comments show up every day. (These are automatically generated comments with no content beyond “Loved this post”, together with an attempt to get you to click through to the commenter’s web site.) I use the phenomenally great (and free!!!) software Akismet to snag these comments before they ever get through, and it’s amazingly accurate, though every once in a while there’s a false positive. That is, sometimes a legitimate comment gets tagged as spam (often because it contains a lot of links but sometimes for no apparent reason). So every now and then, I look through the spam folder and rescue those comments, if any.

But a moment ago, I hit a wrong button and permanently deleted 200 spam comments (all generated within the past few hours!) before I’d looked at them. Statistically, there was probably nothing legit in there anyway. But if by chance I threw your baby out with my bathwater, I do apologize — and please try again.

### Weekend Roundup

This week we completed our three-part series on efficiency. The three posts covered a lot of ground, but here were the major themes:

First, why we should care about efficiency.

Second, why the efficiency criterion is sometimes incoherent, why those episodes of incoherence are fortunately rare, and why efficiency therefore remains, in most cases, a good guide to policy.

Third, why our instinctive recoil from cold-blooded efficiency is often misplaced.

We also revisited last week’s probability puzzle and reposted some past videos in a new improved format.

I am off in the woods and largely away from the Internet for the rest of the weekend, so I might be a little slow to see your comments, but rest assured that I’ll all get read—and that I’ll be back on Monday.

### Ruthless Efficiency

People are dying so that you can read this blog. Your internet access fees could more than double the income of a \$400-a-year Ghanaian laborer. People are starving to death, and there you sit, with resources enough to save them (and with reputable charities standing by to effect the transfers), padding your own already luxuriant lifestyle. That’s a choice you made. It’s a choice almost everyone in the First World makes. It might or might not be a horrific choice, but it’s one for which we easily forgive each other.

(Do you already give money to Ghanaian laborers? I applaud you and I wish others would do the same. But it doesn’t change the fact that other Ghanaian laborers are dying so you can have your Internet.)

Someday you might find yourself strolling through a desert with a bottle of water and stumble on a man dying of thirst. I bet you’ll offer him some water, and I bet you’d think much less of anyone who didn’t. But there is, as far as I can see, no important moral difference between surfing the web while Africans starve and strolling through the desert while men die in front of you.

Last week I posed this problem:

Several commenters did a wonderful job of explaining the answer. Let me just add a few words on the issue of “How can Tuesday be relevant?”

If the Tuesday part weren’t there, the problem would be easy. With two children, there are three equally likely ways to have (at least) one boy: The children in birth order might be Boy/Boy, Boy/Girl, or Girl/Boy. That gives a 1/3 chance of Boy/Boy.

So what does “Tuesday” have to do with it? Answer: Having (at least) one Tuesday boy is a lot more likely when you’ve got two boys than when you’ve got only one. So among those moms with a Tuesday boy, the Boy/Boy moms outnumber either of the other types. The three possibilities aren’t equally likely anymore.

### Efficiency: The Hard Cases

Bill Gates is walking through the desert carrying a bottle of water. He passes a man who is half dead of thirst. Should he offer the man a drink? Should the law require him to?

We’ve been talking about economic efficiency and why it’s a good thing to care about. Today I want to look at this hardest of cases through the efficiency lens.

Let’s suppose Bill’s water is worth, say, \$10,000 to him. He’d be willing to pay that much for it, and he wouldn’t cheerfully sell it for less. Why such a high number? It’s not because Bill enjoys his water any more than you or I do — it’s just because Bill happens to be filthy rich.

And the dying fellow? He’s willing to pay up to \$100 for that water. He’d pay more if he had it, but \$100 happens to be all he has in the world.

Should the law require Bill to give up his water? And regardless of the law, what’s his moral obligation?

A few observations:

### Weekend Roundup

We had substantive posts this week on two of our recurring topics — economic efficiency and the foundations or arithmetic.

The former brought us the honor of an extended visit from Uwe Reinhardt, who, as far as I can tell, objects not to the concept of efficiency or to its usefulness, but to its name. But any crusade to change a well-established technical term is, I think, doomed to failure.

Efficiency, of course, is only one of the normative criteria in the economist’s arsenal. I pointed, for example, to an earlier post where I’d outlined a toy framework for evaluating some of the normative claims made by one of Professor Reinhardt’s Princeton colleagues. That toy framework employs a utilitarian criterion that goes beyond efficiency. It evaluates policies on the basis of “what an amnesiac would prefer”, which is very different than a pure efficiency criterion. This kind of analysis is perfectly standard in economics, so any allegation that we fixate exclusively on efficiency is a bum rap.

On the other hand, some fixation on efficiency can be an extremely valuable exercise, for reasons that I hope this week’s post made clear.

Re the foundations of arithmetic, I posted to dismiss the view that the natural numbers are fictitious. As one commenter pointed out, this was largely an attack on a straw man, because almost nobody believes otherwise. Indeed it was. This was intended as an educational post, not a contentious one, and attacking straw men can be a very effective form of education. When I teach students about continuous functions, I ask them to imagine a hostile party who insists that the function f(x) = x is not continuous, and we talk about how you could most effectively convince him otherwise. The hostile party is imaginary, but there’s a lot to be learned from thinking about how you’d refute him.

We also speculated on the defining idea of the next decade and the ideal reading list for a course on how economists view the world.

And then there was the probability problem: A woman has two children, one of whom is a boy born on a Tuesday. What is the probability they’re both boys? Several commenters explained the answer very clearly. In case you haven’t read the comments and don’t want me to give away the answer, I’ll just say that it’s greater than 45% but less than 49%. See the comments on the original post for the reason why.

We’re coming up on a long weekend, and I’m taking Labor Day off. I’ll see you Tuesday.

### The Harvard Classics

If you happen to be attending Harvard this semester, one of your course options is Greg Mankiw’s Freshman Seminar 43j, “The Economist’s View of the World”:

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:

### Puzzle Corner

With a hat tip to the mathematician John Baez, who in turn tips his hat to the science fiction author Greg Egan, who in turn credits the journalist Alex Bellos, who got this from the puzzle designer/collector Gary Foshee (who seems to have no website):

(For those who want more precision: We gather all those women in the world who have exactly two children, tell each of them to “go home unless you have a boy born on a Tuesday”, and select a woman randomly from those who remain. Assume that births are equally likely to occur on any day of the week, and that on any given day, boys and girls are equally likely.)