We had a summer day yesterday. It must have been 40°F.
We took James sledding. It's a lot of effort, somehow, to get everybody all suited up and out there. James was a little squirmy. He likes going downhill well enough, but all told that's a small fraction of the time you have to put in climbing, waiting for people to get out of the way, and so forth. It was a nice workout, though, and a lot of fun.
I'd like to go back today, but there's a lot of work ahead of me and not that much daylight.
In the excellent economic blog Marginal Revolution, Tyler Cowen recently wrote, “Raw ingredients in America—vegetables, butter, bread, meats, etc.—are below world standards. Even most underdeveloped countries have better raw ingredients than we do, at least if you have a U.S. income to spend there, and often even if one doesn't.”
Why is that? Today Cowen posted some guesses, all very interesting. Perhaps it's “an exogenous demand-side question. Americans have bad taste in food, just as the Chinese have bad taste in lounge music. Why, for that matter, do the Japanese like karaoke so much? Why do the Scots serve deep-fried Mars candy bars?” Why, indeed.
Or maybe it's just that canned and frozen foods are so cheap here, and we're so used to them, that the good stuff looks awfully expensive by comparison.
In Scrabble, the X tile is worth 8 points. But the expected value of drawing an X is more like 40 points, thanks to the five two-letter words AX, EX, XI, OX, and XU. (An ex is the guy you used to date. Xi is a Greek letter. The xu is a former Vietnamese monetary unit. But if you stop to read the definitions, you'll never be an elite Scrabbler.) If you know the trick, it's very easy to score up to six times the value of the tile.
So in casual Scrabble, the X is a bomb.
But in competitive Scrabble, each player in a typical two-player match will rack up around 350 points. This means the average play is already worth 30 points or so, and a good play, one where you play all your tiles, is worth 60 points at least. It's hard to play the X in a seven- or eight-letter word. So drawing the X is bad in championship Scrabble for the same reason it's so good in a casual game: it's good for 20-52 points, but beyond that it doesn't much reward skill.
We have perhaps sixty letter magnets on the refrigerator. James likes the X's. He knows exactly which ones they are. He knows the name of the letter x when he hears it, and if I ask for them, he can extract the X's from the other rabble in short order.
Last night I sat him in front of the computer, opened Notepad, set the font to thirty-six-point, and showed him where the X key was on the keyboard. He got it immediately and was pretty excited.
It's so exhiliarating to see realization dawn on your baby's face.
Change is coming to medicine. Ready or not.
More and more, doctor performance is being measured. The results are at once obvious and iconoclastic: not all doctors are equally good at saving lives.
Once we acknowledge that, no matter how much we improve our average, [this inequality] isn’t going away, we’re left with all sorts of questions. Will being in the bottom half be used against doctors in lawsuits? Will we be expected to tell our patients how we score? Will our patients leave us? Will those at the bottom be paid less than those at the top? The answer to all these questions is likely yes.
And about time, except for the bit about lawsuits. Read the full essay. Fascinating.
(Also gripping. I don't normally read the New Yorker; my amygdala is reeling.)
My coworker S.N. proposes the following scheme:
Suppose you have a child in second grade. Before the school year begins, the school sends you a list of all the second-grade teachers. You rank them: first choice, second choice, and so on. The school then does its best to assign your kid to the teacher of your choice. (Not everyone can have their first choice all the time, but there are plenty of fair, simple mechanisms for making sure the preferences are followed as closely as possible.)
That's it. That's the whole idea. What would this do?
The main intended consequence would be to force parents to get more involved in the quality of their children's classes. Parents would be much more likely to ask other parents what they thought of their children's teachers. Parents, in short, would be more aware of teacher quality. S.N. doesn't think parents do this now, and I think he is probably right.
But there are some problems with this:
Parents wouldn't have the power to do much with this information. If all parents are interested, they all obtain the best information possible, and they all choose the same rankings, then this has no effect. If only some parents are interested, their kids win at the expense of other kids whose parents expressed no preferences. In other words, it's a zero-sum game. The school as a whole doesn't improve.
Perhaps the propagation of new knowledge to parents in this way would improve schools indirectly. Perhaps parents armed with this knowledge would be more of a political force. Perhaps teachers would compete to improve their standings. Perhaps school principals can do something useful with this quantitative information. But it seems to me all these are secondary effects, if not wishful thinking. Unless parents' choices actually have the power to reward good teachers (schools) and penalize bad ones, it's hard to see how those choices can significantly improve the system as a whole.
To frame our disagreement another way, S.N. thinks the value of a free market is that people make better choices when those choices directly affect their own future well-being. Good overall decisions emerge from individual self-interested decisions. Parents don't care about teacher quality; ergo schools suck. I think the primary value of a free market is in destroying bad producers and powering the propagation of good ones. Parents can't fire bad teachers or withdraw their financial support from bad public schools; ergo schools suck.
This presumes that choosing good teachers over bad teachers is the way to improve education in the first place. Many important factors are not in the hands of teachers: class sizes, curriculum, interruptions, discipline, funding, and so forth. I think choosing good schools over bad schools is the right level for parents to express preferences.
I suspect the idea is doomed anyway, because teachers would hate it. People don't like being judged.
Interesting proposal, though. S.N. often comes up with original approaches to problems. I wonder how he does it.
The book on Olivia's bedside table begins, “The place was called Gorgantum.” If you don't know why this struck me as funny, either you've never read a fantasy novel or you've read too many. The Prologue continues in a similarly hilarious vein after that, but the first sentence can't be topped.
Or not by much. Curious, I flipped through the book to a page at random and read this: “Tanaros gazed over a sea of Fjel, with thick hides of smooth grey, of a pebbled greenish-brown, or black with bristles. His troops, his men.” Tolkien meets Dr. Seuss.
Eugene Volokh is a law professor and blogger. Today he posted a link to a short story he wrote, “The Love Charm”, and—bonus feature!—its original ending which I think I prefer to the published one.
Although “The Love Charm” is interesting in its own right, I'm posting this because the story reminds me of poormattie. It is a story about love, cruelty, and ethical dilemmas. But its tone is abstract and casual, as though the narrator made a secret decision not to venture too close to the story in the retelling, for fear of reliving the pain.
It might be interesting to rewrite this story as a collection of highly emotional scenes and see how much punch could be got out of it.
Passage by Connie Willis, 2001.
If, as I recommend, you choose to pick up this book, don't read the blurb on the back. It may reveal too much.
Two scientists study near-death experiences. The book does a lot right. The attitudes toward death ring true. The characters ring true, mostly. The plot is interesting, the writing thrilling, the portrait of humanity immensely gratifying, the emotional range fantastic.
A certain extended metaphor, which I won't reveal much about, figures centrally in Passage. But only the symbolic side of the metaphor is revealed at first, and its real-world analogue is hidden. The meaning of the metaphor is the central mystery of the book, and it's a clever one. So far, so good. But there are a few problems with the book.
One is that the metaphor Ms Willis chose is, through no fault of hers, rather overexposed as metaphors go.
But the main problem is that Connie Willis is too much a character in this book. Death is a marvelous mirror; in it we each see our own beliefs about the fundamental nature of the universe. Ms Willis's own views come through quite clearly in Passage, and her portrayal of other views unfortunately doesn't bear the same verisimilitude as the rest of the book. It would have been possible for the protagonist, a scientist, to despise her unscientific counterpart without Ms Willis piling on. Similarly, too much of the suspense in reading the book is due to the question of where the author is going. One wonders whether the book will maintain its hard-nosed scientific attitude to the bitter end; whether the author will ultimately try to give some kind of answer to the question of the experience of death, which hangs over the entire story; and so on.
Still, a hell of an effort by the reigning champ of science fiction novelry.
A-.
You know who has a surprisingly bad front page on their web site? The NFL.
By my count the front page has three hundred trillion links on it. Some of the links aren't even accessible to me because I don't have a paid subscription; these are conveniently marked with the green-F, white-P icon (this stands for "fmembers-only pcontent".) There are 8 separate boxes for: the top story, "Headlines", "NFL Network", "Today in the NFL", "My Team News and Sites", "Analysis and Opinion", "Video", and "NFL on Sportsline.com".
Suppose you want to see the league standings. Viewing standings is easy from nfl.com. All you have to do is click on "Standings". If you can find it.
How do people actually use this site? When I go to nfl.com on a weekday (when there isn't a game), I'm interested in one of three possible things:
Not only should this stuff be easy to find, it really ought to be just about the only thing on the page. All the NFL news-style content should be clumped in the center, blog-style. Each story should have a headline, photo, teaser, and "read more" link. The newest news should be listed first. That way, it's easy to find new content.
The frustrating thing about all this is that the content on nfl.com is quite good. It has rich statistics on every team and every player in the league, and is updated regularly with fresh news and commentary. But too many people will never know, because the front page is so alienating.
Scientists, mathematicians, and writers were asked, “What do you believe is true even though you cannot prove it?”
Their answers. Moderately interesting.
I was blown away by this document: How Culture Shapes Math Instruction in Japan, Germany, and the United States. (1997.)
Researchers videotaped a few hundred real 8th-grade math lessons in three countries. The results are fascinating:
And on and on. But I'll stop here, because this last topic is of particular interest. A proof is simply a step-by-step, defensible logical explanation of why a particular mathematical statement is true. All of higher mathematics is entirely about proofs. Isn't it a little weird that we never teach this to schoolkids?
As I mentioned in a previous post, the first proof I can remember encountering showed that the area of a circle is πr2. I found it in my third-grade textbook. (Here is a rough version of this proof online.) I was fascinated. The teacher never tried to use it in class.
Why do you think American and Japanese classes end up being so different? The document answers that question, too. There are two apparent reasons. First: Japanese teachers care about and labor incessantly to increase lesson quality. They intentionally teach large classes (40 students or more) so that they'll have time to critique and improve their lessons, which they do constantly. In the U.S., individual teachers make their own lesson plans or get them out of textbooks. Classes are small. Teachers spend most of their day teaching classes and, typically, none of it looking back. Second: the goal of a Japanese lesson is to teach the kids math concepts and how to think about math. In the U.S., the goal is to teach the kids how to solve problems. I think this translates to “how to solve the homework problems”, all of which are similar for any given lesson and can be solved without much thought. (If you read the paper, you'll get a much clearer idea of how profound all these differences are.)
The paper argues that the underlying cause of these differences is cultural, which might be true. Or it might be economic or political.
(Found on Isabel's math blog.)
