On his blog A Blank Slate, Vishal Patel posts a cute little brain teaser (with a hat tip to the Cosmic Variance blog):
Jack is looking at Anne, but Anne is looking at George. Jack is married, but George is not. Is a married person looking at an unmarried person?
(a) Yes
(b) No
(c) Can not be determined
This reminded me of one of my favorite little “zinger” math proofs. (If you think about the brain teaser long enough, you’ll see the connection.)
I am a proud member of the Sierra Club. No, not that Sierra Club; what I mean to say is that I am a regular reader of the parenting blog ChildWild, and a fan of its wise and charming proprietor Sierra Black. I am therefore delighted that Sierra seems to have become a regular reader and frequent commenter here on The Big Questions, and glad to see she’s sticking around despite frequent disagreements—much as I do on ChildWild.
Over on another thread, amidst a discussion of the case for free trade, Sierra threw me for a brief loop with an issue I’d never seen raised before, though I’ve since learned that it’s commonplace in certain corners of the Internet. I thought, then, that it might be worth responding in a separate post.
(I’ll admit too that another motive for the separate post was my conviction that I’d be able to slip in a perfect pun around the phrase “Sierra, Madre”—Madre, of course. meaning mother, and what with her running a parenting blog and all and—well, it’s bad enough to have to explain your jokes, but here I am trying to explain a joke I couldn’t even figure out how to make. But by the time I’d realized the pun was stillborn, I was already committed to this post.)
Here’s the relevant part of Sierra’s comment:
Over on Econlog, Bryan Caplan uses an example from The Big Questions to illustrate his intuitionist approach to meta-ethics: Start with concrete, specific cases where your ethical intuition is clear, and reason by analogy from there. If you have multiple intuitions that lead you down conflicting paths, give some thought to which ones you’re most willing to jettison.
Bryan’s example is about discrimination, a subject that has come up before on this blog, but I want to emphasize that the argument Bryan quotes is quite separate from the arguments we got into in that earlier thread, and, for the sake of clarity, I hope we manage to keep them separate.
Bryan (paraphrasing me!) starts with the rather strong intuition that it’s okay for tenants and workers to discriminate. If you don’t want to live in an Albanian-owned building or an work for an Albanian employer, that’s your right (no matter how strongly we might strongly disapprove of your attitude). By analogy, then, it might seem that landlords and employers should have the same right to discriminate.
I’m going to dole out the answers to the first half of my honors exam slowly over the next several days. After that I’ll post the second half of the exam.
Let’s start with this one:
Question 3. Snidely Whiplash owns all the grocery stores and all the houses in the Yukon Territory. He charges a competitive price for groceries, and rents the houses at the highest price residents (who are all identical) are willing to pay. (If he charged any more, they’d all leave town). True or False: If Snidely raises the price of groceries, he’ll have to lower the price of housing, so he’ll be no better off than before.
Lots of economics this week. We celebrated the Dr. Jekyll side of Paul Krugman (after having lamented his Dr. Hyde a week ago), explored the economics of college admissions and of work and play, and ended the week with a pop quiz. I’ll discuss some of the quiz answers in the near future.
Midweek we took a break to celebrate the centenary of the great Johnny Mercer.
To round out the week’s economics theme, here’s some recommended reading from around the web:
Each year, the economics department at Oberlin College invites an outside examiner to determine who among its top graduating seniors should receive an honors degree. Last spring, I was that outside examiner. The seven candidates had several hours to complete a written exam (which I wrote), and then a few weeks later, I interviewed each of them face to face.
I thought my readers here might be interested in seeing the written exam. It’s by no means comprehensive; entire areas of economics are omitted. Instead, it’s supposed to test core material and ways of thinking that I believe should mostly be second nature to any top economics graduate.
Where necessary, I’ve translated some of these questions from the original economese to something approximating English. Occasionally, a little has been lost in the translation, but not, I think, too much.
There were ten questions on the exam. I’ll post five today and the remaining five next week.
Here, then, is Part I:
My post about Paul Krugman’s loopy proposals on employment policy generated some considerable discussion about why Europeans work so much less than Americans do. Actually, there are two separate questions here:
A few observations:
The greatest financial mistake of my life occurred on the day my father offered to bet his entire net worth against mine that the great Johnny Mercer had written the song Don’t Fence Me In. Now “Don’t Fence Me In” is a marvelous song, and Johnny Mercer could have been justifiably proud to write it—if only Cole Porter had not written it first. I happened to know this about Cole Porter; I knew it as surely as I know the authors of Romeo and Juliet and The Wealth of Nations. But for some reason I’ve never understood, I refused the bet, thereby condemning myself to a life of poverty. Still I console myself with the knowledge that you don’t have to be rich to be touched by the grace of Johnny Mercer, who was born one hundred years ago today.
The guy was a phenomenon. He wrote the lyrics for over 1500 songs, and the music for at least a few hundred. And he was a singer-songwriter decades before the likes of Bob Dylan, Phil Ochs and Joni Mitchell allegedly invented the genre. God, he was smooth. By and large, I’d rather hear Johnny Mercer sing his own songs than any of the myriad covers that have become American classics—and that’s saying something for a guy who was covered repeatedly by the likes of Frank Sinatra and Ella Fitzgerald.
Having recently bashed Paul Krugman, and in the full expectation that I’ll have occasion to bash him again, let me interject that Krugman is not just a first rate economist; he is also, when he wants to be, a superb economic communicator, with a long paper trail to prove it.
Take, for example his essay on the widespread failure of intellectuals to grasp Ricardo‘s theory of comparative advantage (the basis of the case for free trade). Instead of simply bemoaning the problem like the rest of us, Krugman makes a valiant and useful attempt to identify its root causes.
He starts with an analogy I’m also fond of (I’m not sure which of us has been using it longer): The theory of comparative advantage is like the theory of evolution by natural selection—to those who understand it, it is simple and compelling; yet non-experts can find it remarkably difficult to grasp.
In The Big Questions, I argue that this analogy ultimately breaks down: The theory of evolution is compelling largely because of the evidence that supports it, while Ricardo’s theory is compelling largely because of the logic that supports it. It’s not too surprising that a first-rate physicst or literary critic could be unfamiliar with a body of evidence, but it’s a little more unsettling when that same physicist or literary critic can’t follow a simple chain of logic.
The final chapter of The Big Questions is called “What to Study”. This post is about where to study it.
Stanford professor Carolyn Hoxby reports that in the college admissions market, the big change over the past 40 years is students’ increased willingness to travel far from home—not surprising since the costs of long distance travel and communication have fallen dramatically over that time. The main effects are these:
Lots of good discussion on the blog this week. We began with a lively debate about the moral basis for antidiscrimination laws, which inspired some thoughtful commentary from the anonymous Rust Belt Philosopher, leading to an extended dialogue over on his blog. That dialogue has pretty much wound down, but I think that much of it is well worth reading even if it’s a little late to jump in.
Our thread on free trade was equally provocative. I’m sure I’ll soon return to some of the issues that came up near the end of the thread.
I offered a brain teaser to illustrate a key point from The Big Questions, namely that honest truthseekers can’t agree to disagree. I threw in a comparison to a related brain teaser about blue-eyed islanders, and my own brain teaser was quickly forgotten as the blue-eyed islanders became the focus of discussion. That was never my intention, but I’m thrilled that people found something interesting to discuss. Those who insist on controlling their threads’ directions should take up sewing, not blogging.
We also met the Ass Meat Research Group, and I said a few words about Paul Krugman. In entirely separate threads, of course.
See you all on Monday!
It seems to be well known that supermarkets charge cereal companies for prime display space. It seems to be less well known that bookstores do the same thing. They do, though. For example, the publisher of The Big Questions is paying for prominent front-of-the-store display space at all Barnes and Noble and Borders stores—except for those located in Manhattan—through the month of November. (At least the B&N contract runs through the end of November; I’m unclear on whether the Borders contract runs as long.)
There have been several reports of individual stores failing to honor this commitment. My publisher will be having a chat about this with the Barnes and Noble folks in a couple of days, and prior to that discussion it would be useful to know just how widespread the problem is.
So—if you happen to be going past a Barnes and Noble (or a Borders) in the next couple of days, I’ll be most grateful to know whether you found The Big Questions out on the front table where it ought to be. You can comment here or email me at “questions at landsburg dot com”. Please include the address of the store, or the street it’s on, or the town it’s in —whatever you’ve got. Thanks for your help!
It’s always impressive to see one person excel in two widely disparate activities: a first-rate mathematician who’s also a world class mountaineer, or a titan of industry who conducts symphony orchestras on the side. But sometimes I think Paul Krugman is out to top them all, by excelling in two activities that are not just disparate but diametrically opposed: economics (for which he was awarded a well-deserved Nobel Prize) and obliviousness to the lessons of economics (for which he’s been awarded a column at the New York Times).
The mathematician John Baez has been dazzling science lovers on the web for over 15 years with his weekly Finds in Mathematical Physics. (He was a blogger long before there were blogs). Baez recently gave a lovely series of talks on his favorite numbers (they are 5, 8 and 24) in which he mentions Euler’s observation that if you sum up all the positive integers (1 + 2 + 3 + 4 + …) you get -1/12. (I promise, this is not a joke.)
Baez’s “proof” uses a little calculus, but I’ve reworked it into a form you can share with your middle schoolers—and better yet, have them share with their teachers.
I suppose I should be gratified to learn that this blog is so influential, but I can feel nothing but sadness at Amazon’s response to my post about Ass Meat Research Group and his co-authors Frozen Horse and Chilled and Frozen Hors the Fresh (formerly Chilled the Fresh). These authors’ names have been removed from all Amazon listings. I am so very glad that I saved the screenshot.
Here’s a brain teaser I wish I’d invented in time to include it in The Big Questions:
John and Mary live in an isolated village where they have no access to reference materials, no contact with the outside world, and nobody to talk to except each other. One day an anthropologist arrives in this village, sits down for coffee with John and Mary, and quizzes them about their knowledge of the world. John says he’s sure that men have walked on the moon; Mary says she’s sure they haven’t. Never having discussed this issue before, each of them is astonished and flabbergasted by the others’ apparent ignorance. Rather than risk losing all respect for each other, John and Mary agree never to speak of the subject again. But the anthropologist mentions that she’ll be stopping by once a day from now on, and will be glad to know if either of them ever has a change of mind on this topic. If so, the anthropologist will inform the other. Otherwise, the anthropologist will never bring it up either.
The next day (a Monday) nobody’s mind has changed, and therefore the subject is not discussed. The same thing happens on Tuesday, Wednesday and Thursday. Can this go on forever?
A reader has just emailed me a link to a Washington Post story about North Carolina workers losing their jobs to foreign competition. Presumably he believes there’s a larger moral here, because his subject line is “Wrong again, Steve”. Here is a slightly edited version of my emailed response:
It would be dishonest for me or anyone else to defend free trade by pointing to its advantages while ignoring its disadvantages.
It is equally dishonest to oppose free trade by pointing to its disadvantages while ignoring its advantages.
What you need is a framework that accounts for all the advantages and disadvantages, together with enough of a logical structure to instill confidence that nothing imporant has been overlooked. Thats what economic theory supplies. You can find that theory in the economics textbooks. You can also find (I think) a pretty good summary of it in The Big Questions.
My correspondent wrote back with a pointer to a website with fifty years of what he calls “extrapolatable stats” that he thinks supply the necessary framework. This misses the point entirely. There is no way a hodgepodge of numbers can settle the question of whether something’s been left out. For that you need a theory.
Suppose you’d written a book. And suppose, for some odd reason, that your middle name happened to be “And”. Suppose, for example, that mother had named you “Cary And Grant”.
Then the software at Amazon.com, not unreasonably, would assume that you were two people, and would list the book’s authors as (1) Cary and (2) Grant.
Now suppose, even more oddly, that your name contained a comma. Not the word “comma”, but the actual punctuation mark. Suppose, for example, that your mother had named you “Cary, Grant”. Then Amazon’s software, again not unreasonably, would assume that your name was being presented in the format “Last, First” and would reverse the order, listing the author as Grant Cary.
Now take this one step further and suppose your name contained both the word “And” and a comma. Perhaps more than once. Suppose, for example, that your name happened to be The Fresh, Chilled and Frozen Horse and Ass Meat Research Group. Then, in accordance with its not unreasonable rules, Amazon’s software would conclude that there are three separate authors, namely:
Partially blind gamer Alexander Stern wants Sony to make its games more accessible to him and others like him—and he’s gone to court to force the issue. This raises the question: Exactly what does Sony owe to Alexander Stern (and others like him)?
A similar issue comes up in Chapter 20 of The Big Questions, where Mary the landlord won’t rent to, say, Albanians. Ought we force her to?
It’s been a great week on the blog with thoughtful and thought-provoking comments cropping up everywhere. Several threads have touched on the question phrased most succinctly by Al. V. on the Unreasonable Effectiveness of Physics thread:
Are the laws of mathematics inherent in our universe, and therefore really a product of physics (and not the other way around), or are they supra-universal?
This question, of course, plays a starring role in The Big Questions , where I’ve explained why I believe that the supra-universality of mathematics (thanks for that word, Al!) gives the most coherent explanation of why anything exists at all.
It is well known (to the sort of people to whom such things are well known) that the Scottish engineer Fleeming Jenkin was the first to formalize a toy model of Darwin’s evolutionary theory—with results that were most unfavorable to Darwin: The model predicts that random improvements, even when they confer survival advantages, still tend to disappear over the course of a few generations. This was in 1867.
It seems to be far less well known that Jenkin’s model also predicts that all life on earth dies out after a few generations, which would seem to cast doubt on its assumptions. Jenkin was apparently unaware of this, and so, presumably, was Darwin, who gave considerable credence to the Jenkin model in the final edition of The Origin of Species. This was in 1872.
It seems to be even less well known that the inadequacy of Jenkin’s model was identified in a little-noticed letter to the editor of Nature by the mathematician Arthur Sladen Davis. In that letter, Davis corrected Jenkin’s error and supplied an alternative model that he believed was favorable to Darwin. This was in 1871, but apparently Darwin never heard about it.
And it seems to be known only to me (and now, to the readers of this blog!) that Davis’s model is also flawed, in the opposite direction from Jenkin’s, in that it predicts that any species population must grow without bound following the appearance of a beneficial mutation. And as a result of this, the Davis model undercuts Darwin more than it supports him.
I’ve adjusted Davis’s model much as Davis adjusted Jenkin’s, and gotten a result that could be considered favorable to Darwin. In fact, it’s more or less the result that Davis thought he’d gotten, but hadn’t.
Here comes the more technical part. If this is not your cup of tea, stop reading now. Do come back tomorrow though. I’m not always like this.
The “Look Inside” text for The Big Questions should be up on Amazon’s website in a few days. Meanwhile, Snorri Godhi suggested in comments that I should post the index for your perusal. Good idea, Snorri. Just click on “Index” at the top of this page.
A while back, the BBC sent me a questionnaire that I had some fun with, and I was disappointed when they published only excerpts. But now that I have a blog, I get to post anything I want in its entirety! So here’s the whole thing. Do use the comments to suggest better answers.
Continue reading ‘Some Big (and small) Questions’
I have recently finished reading Hunters and Gatherers, a (quite good) novel written and set in 1991, which includes the following plot elements:
1) A door-to-door saleswoman pitches (hardcopy) encyclopedias to customers who eagerly seek easy access to vast quantities of information.
2) A man is eager to read an obscure novel he’s heard about, so he scours used book stores, hoping to find a copy. In the meantime, he’s not sure what the novel is about, and has no way to find out.
3) A comedian stores his collection of jokes on notecards, filling two rooms worth of file cabinets.
4) A collector of sound effects stores her collection on cassette tapes, and has no cost-effective way to create backups.
5) A man is unable to stay in close contact with his (adult) children, because long distance calling rates are prohibitively high.
Among the things you’re sure of, which are you surest of? For Richard Dawkins, writing in the Wall Street Journal, it’s the theory of evolution:
We know, as certainly as we know anything in science, that [evolution] is the process that has generated life on our own planet.
Now, I would be thunderstruck if the theory of evolution turned out to be fundamentally wrong, but not nearly so thunderstruck as if arithmetic turned out to be inconsistent. In fact, I can think of quite a few things I’m more sure about than evolution. For example:
1. The consistency of arithmetic. (This amounts to saying that a single arithmetic problem can’t have two different correct answers.)
2. The existence of conscious beings other than myself.
3. The fact that the North won the American Civil War. (That is, historians are not universally mistaken about this. I am not interested in quibbling about what constitutes a “win”; I mean to assert that the North won in the everyday sense of the word, as reported in all the history texts.)
Continue reading ‘What Are You Surest Of?’
I once owned a book where page 317, in its entirety, read as follows:
ERRATA On page 317, change ERRATA to ERRATUM.
It’s a good thing I didn’t steal that joke. Because as it happens, The Big Questions contains an actual erratum. True, it’s only two missing letters. But of all the letters in the book, these are probably the two I’d least like to have seen go missing.
Fortunately, I discovered this erratum within minutes of receiving my first hardcover books a couple of weeks ago, and the Free Press division of Simon and Schuster sprang into action. Everyone, from the publisher to the editorial assistants to the warehouse managers, understood immediately that we needed to fix this. Better yet, they kept me involved and informed throughout the process, which contrasts dramatically with experiences I’ve had with other publishers.
Doubly fortunately, I happened to pour out my woes to the brilliant psychometrician Ellen Julian, who suggested that we make up cards much like the one illustrated here and somehow get them into the tens of thousands of books that were scheduled to leave the warehouse the following Monday morning. (This was a Thursday.) The Free Press made it happen in a day, and all would have been well had I not awakened on Saturday to the sickening realization that the cards contained the wrong URL. Now it was the weekend and too late to have new cards made in-house.
Continue reading ‘Today’s the Day’
Steve Levitt and Steve Dubner, the SuperFreakonomics guys (formerly the Freakonomics guys) have raised a lot of temperatures with their chapter on global warming. The backlash began with Paul Krugman, who in turn was neatly skewered by several authors, but most effectively by the journalist Ari Armstrong.
The critics have raised two objections that come perilously close to contradicting each other: First, Levitt and Dubner are accused of minimizing the problem. Second, they are accused of overeagerness to solve the problem, as opposed to, say, demonizing the responsible parties. Of these, only the first deserves to be taken seriously.
In The Big Questions (pages 18-19) I talk (channeling the physicist Eugene Wigner) about the apparently unreasonable effectiveness of mathematics in revealing truths about the physical world. In Wigner’s words, “It is difficult to avoid the impression that a miracle confronts us here.”
But the physicist Peter Landsberg (no relation!) observes that sometimes the miracle runs in the opposite direction, and offers a curious use of physical reasoning to reveal a purely mathematical truth!
Continue reading ‘The Unreasonable Effectiveness of Physics’
Wow. The response to this blog—in comments, in email, and in mentions around the web—has been huge and overwhelmingly positive. I am particularly struck by the many thoughtful (and thought-provoking) comments from attentive readers. We’re only two days into this and I’ve learned a lot already. Thank you.
I’m taking the weekend off, but I’ll be back on Monday to amuse, enlighten, provoke and continue to learn. In the meantime, for your amusement, I present this letter to the editor from the estimable organizer of Freedomfest, correcting a possible Freudian slip at the New York Times:
Here’s a lovely suit of clothes that can be had for, oh, about $10,000. It’s the result of a project conceived by Drexel University instructor Kelly Cobb to make a man’s suit entirely from materials produced within 100 miles of her home. According to an article by Paul Adams in Wired magazine, the suit was produced by a team of 20 artisans, requiring a total of 500 man-hours.
Let’s see, that’s 500 hours of skilled or semi-skilled labor by artisans whose time is probably worth something on the order of $20 an hour. For about $10,000 I can have one made for you.
Continue reading ‘The $10,000 suit’
