Notes on Neal Stephenson's Baroque novels
Earlier this year I was reading books by Robert Hooke, John Wilkins, Sir Thomas Browne, and other Baroque authors; people kept writing to me to advise me to read Neal Stephenson's "Baroque cycle", in which Hooke and Wilkins appear as characters.

I ignored this advice for a while, because those books are really fat, and because I hadn't really liked the other novels of Stephenson's that I'd read.

But I do like Stephenson's non-fiction. His long, long article about undersea telecommunications cables was one of my favorite reads of 1996, and I still remember it years later and reread it every once in a while. I find his interminable meandering pointless and annoying in his fiction, where I'm not sure why I should care about all the stuff he's describing. When the stuff is real, it's a lot easier to put up with it.

My problems with Stephenson's earlier novels, The Diamond Age and Snow Crash, will probably sound familiar: they're too long; they're disorganized; they don't have endings; too many cannons get rolled onstage and never fired.

Often "too long" is a pinheaded criticism, and when I see it I'm immediately wary. How long is "too long"? It calls to mind the asinine complaint from Joseph II that Mozart's music had "too many notes". A lot of people who complain that some book is "too long" just mean that they were too lazy to commit the required energy. When I say that Stephenson's earlier novels were "too long", I mean that he had more good ideas than he could use, and put a lot of them into the books even when they didn't serve the plot or the setting or the characters. A book is like a house. It requires a plan, and its logic dictates portions of the plan. You don't put in eleven bathtubs just because you happen to have them lying around, and you don't stick Ionic columns on the roof just because Home Depot had a sale on Ionic columns the week you were building it.

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The work totals about 2,700 pages. Considered as a trilogy, this is three very long books. Stephenson says in the introduction that it is actually eight novels, not three. He wants you to believe that he has actually written eight middle-sized books. But he hasn't; he is lying, perhaps in an attempt to shut up the pinheads who complain that his books are "too long". This is not eight middle-sized books. It is one extremely long book.

The narrative of the Baroque cycle is continuous, following the same characters from about 1650 up through about 1715. There is a framing story, introduced in the first chapters, which is followed by a flashback that lasts about 1,600 pages. Events don't catch up to the frame story until the third volume. If you consider Quicksilver to be a novel, the opening chapters are entirely irrelevant. If you consider it to be three novels, the opening chapters of the first novel are entirely irrelevant. It starts nowhere and ends nowhere, a vermiform appendix. But as a part of a single novel, it's not vestigial at all; it's a foreshadowing of later developments, which are delivered in volume III, or book 6, depending on how you count.

Another example: The middle volume, titled The Confusion, alternates chapters from two of the eight "novels" that make up the cycle. Events in these two intermingled ("con-fused") novels take place concurrently. Stephenson claims that they are independent, but they aren't.

So from now on I'm going to drop the pretense that this is a trilogy or a "cycle", and I'm just going to call this novel the "Baroque novel".

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This was quite a surprise to me. The world is full of incoherent ramblers, and most of them, if you really take the time to listen to them carefully, and at length, turn out to be completely full of shit. You get nothing but more incoherence.

Stephenson at 600 pages is a semi-coherent rambler; to really get what he is saying, you have to turn him up to 2,700 pages. Most people would have been 4.5 times as incoherent; Stephenson is at least 4.5 times as lucid. His ideas are great; he just didn't have enough space to explain them before! The Baroque novel has a single overarching theme, which is the invention of the modern world. One of the strands of this theme is the invention of science, and the modern conception of science; another is the invention of money, and the modern conception of money.

I've written before about what I find so interesting about the Baroque thinkers. Medieval, and even Renaissance thought seems very alien to me. In the baroque writers, I have the first sense of real understanding, of people grappling with the same sorts of problems that I do, in the same sorts of ways. For example, I've written before about John Wilkins' attempt to manufacture a universal language of thought. People are still working on this. Many of the particular features of Wilkins' attempt come off today as crackpottery, but to the extent that they do, it's only because we know now that these approaches won't work. And the reason we know that today is that Wilkins tried those approaches in 1668 and it didn't work.

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I find that almost all of Stephenson's annoying habits are much less annoying in the context of historical fiction. For example, many plot threads are left untied at the end. Daniel Waterhouse (fictional) becomes involved with Thomas Newcomen (real) and his Society for the Raising of Water by Fire. (That is, using steam engines to pump water out of mines.) This society figures in the plot of the last third of the novel, but what becomes of it? Stephenson drops it; we don't find out. In a novel, this would be annoying. But in a work of historical fiction, it's no problem, because we know what became of Newcomen and his steam engines: They worked well enough for pumping out coal mines, where a lot of coal was handy to fire them, and well enough to prove the concept, which really took off around 1775 when a Scot named James Watt made some major improvements. Sometime later, there were locomotives and nuclear generating plants. You can read all about it in the encyclopedia.

Another way in which Stephenson's style works better in historical fiction than in speculative fiction is in his long descriptions of technologies and processes. When they're fictitious technologies and imaginary processes, it's just wankery, a powerful exercise of imagination for no real purpose. Well, maybe the idea will work, and maybe it won't, and it is necessarily too vague to really give you a clear idea of what is going on. But when the technologies are real ones, the descriptions are illuminating and instructive. You know that the idea will work. The description isn't vague, because Stephnson had real source material to draw on, and even if you don't get a clear idea, you can go look up the details yourself, if you want. And Stephenson is a great explainer. As I said before, I love his nonfiction articles.

A lot of people complain that his novels don't have good endings. He's gotten better at wrapping things up, and to the extent that he hasn't, that's all right, because, again, the book is a historical novel, and history doesn't wrap up. The Baroque novel deals extensively with the Hanoverian succession to the English throne. Want to know what happened next? Well, you probably do know: a series of Georges, Queen Victoria, et cetera, and here we are. And again, if you want, the details are in the encyclopedia.

So I really enjoyed this novel, even though I hadn't liked Stephenson's earlier novels. As I was reading it, I kept thinking how glad I was that Stephenson had finally found a form that suits his talents and his interests.

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Reader's disease
Reader's disease is an occupational hazard of editors and literary critics. Critics are always looking for the hidden meaning, the clever symbol, and, since they are always looking for it, they always find it, whether it was there or not. (Discordians will recognize this as a special case of the law of fives.) Sometimes the critics are brilliant, and find hidden meanings that are undoubtedly there even though the author was unaware of them; more often, they are less fortunate, and sometimes they even make fools of themselves.

The idea of reader's disease was introduced to me by professor David Porush, who illustrated it with the following anecdote. Nathaniel Hawthorne's The Scarlet Letter is prefaced by an introduction called The Custom-House, in which the narrator claims to have found documentation of Hester Prynne's story in the custom house where he works. The story itself is Hawthorne's fantasy, but the custom house is not; Hawthorne did indeed work in a custom house for many years.

Porush's anecdote concerned Mary Rudge, the daughter of Ezra Pound. Rudge, reading the preface of The Scarlet Letter, had a brilliant insight: the custom house, like so many other buildings of the era, was a frame house and was built in the shape of the letter "A". It therefore stands as a physical example of the eponymous letter.

Rudge was visiting Porush in the United States, and told him about her discovery.

"That's a great theory," said Porush, "But it doesn't look anything like a letter 'A'."

Rudge argued the point.

"Mary," said Porush, "I've seen it. It's a box."

Rudge would not be persuaded, so together they got in Porush's car and drove to Salem, Massachusetts, where the custom house itself still stands.

But Rudge, so enamored of her theory that she could not abandon it, concluded that some alternative explanation must be true: the old custom house had burnt down and been rebuilt, or the one in the book was not based on the real one that Hawthorne had worked in, or Porush had led her to the wrong building.

But anyway, all that is just to introduce my real point, which is to relate one of the most astounding examples of reader's disease I have ever encountered personally. The Mary Rudge story is secondhand; for all I know Porush made it up, or exaggerated, or I got the details wrong. But this example I am about to show you is in print, and is widely available.

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Each extract is accompanied by some introductory remarks by Fadiman and sometimes by one of the contributing editors. One long section in the book concerns early articles about human flight; in the Second Edition (published 1778-1783) there was an article on "Flying" by then editor James Tytler. Contributing editor Bruce L. Felknor's remarks include the following puzzled query:

What did Tytler mean by his interjection of "Fa" after Friar Bacon's famous and fanciful claim that man had already succeeded in flying? It hardly seems a credulous endorsement, an attitude sometimes attributed to Tytler.

Fadiman adds his own comment on this:

As for Tytler's "Fa": Could it have been an earlier version of our "Faugh!"? In any case we suddenly hear an unashamed human voice.

Gosh, what could Tytler have meant by this curious interjection? A credulous endorsement? An exclamation of disgust? An unedited utterance of the unashamed human voice? Let's have a look:

The secret consisted in a couple of large thin hollow copper-globes exhausted of air; which being much lighter than air, would sustain a chair, whereon a person might sit. Fa. Francisco Lana, in his Prodromo, proposes the same thing...

Felknor and Fadiman have mistaken "Fa" for a complete sentence. But it is apparently an abbreviation of Father Francisco Lana's ecclesiastical title.

Oops.

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Serendipitous web searches
In yesterday's article about a paper of Robert French, I mentioned that I had run across it while looking for something entirely unrelated. The unrelated thing is pretty interesting itself.

Back in the 1950's and 1960's, James V. McConnell at the University of Michigan was doing some really interesting work on learning and memory in planaria flatworms, shown at right. They used to publish their papers in their own private journal of flatworm science, The Journal of Biological Psychology. They didn't have enough material for a full journal, so when you were done reading the Journal, you could flip it over and read the back half, which was a planaria-themed humor magazine called The Worm-Runner's Digest. I swear I'm not making this up.

(I think it's time to revive the planaria-themed humor magazine. Planaria are funny even when they aren't doing anything in particular. Look at those googly eyes!)

(For some reason I've always found planaria fascinating, and I've known about them from an early age. We would occasionally visit my cousin in Oradell, who had a stuffed toy which was probably intended to be a snake, but which I invariably identified as a flatworm. "We're going to visit your Uncle Ronnie," my parents would say, and I would reply. "Can I play with Susan's flatworm?")

Anyway, to get on with the point of this article, McConnell made the astonishing discovery that memory has an identifiable chemical basis. He trained flatworms to run mazes, and noted how long it took to do so. (The mazes were extremely simple T shapes. The planarian goes in the bottom foot of the T. Food goes in one of the top arms, always the same one. Untrained planaria swim up the T and then turn one way or the other at random; trained planaria know to head toward the arm where the food always is. Pretty impressive, for a worm.)

Then McConnell took the trained worms and ground them up and fed them to untrained worms. The untrained worms learned to run the maze a lot faster than the original worms had, apparently demonstrating that there was some sort of information in the trained worms that survived being ground up and ingested. The hypothesis was that the information was somehow encoded in RNA molecules, and could be physically transferred from one individual to another. Isn't that a wonderful dream?

You can still see echoes of this in the science fiction of the era. For example, a recurring theme in Larry Niven's early work is "memory RNA", people getting learning injections, and pills that impart knowledge when you swallow them. See World Out of Time and The Fourth Profession, for example. And I once had a dream that I taught a giant planarian to speak Chinese, then fried it in cornmeal and ate it, after which I was able to speak Chinese. So when I say it's a wonderful dream, I'm speaking both figuratively and literally.

Unfortunately, later scientists were not able to reproduce McConnell's findings, and the "memory RNA" theory has been discredited. How to explain the cannibal flatworms' improved learning times, then? It seems to have been sloppy experimental technique. The original flatworms left some sort of chemical trail in the mazes, that remained after they had been ground up. McConnell's team didn't wash the mazes in between tests, and the cannibal flatworms were able to follow the trails later; it had nothing to do with their diet. Bummer.

So a couple of years ago I was poking around, looking for more information about this, and in particular for a copy of McConnell's famous paper Memory transfer through cannibalism in planarium, which I didn't find. But I did find the totally unrelated Robert French paper. It mentions McConnell, as an example of another cool-sounding and widely-reported theory that took a long time to dislodge, because it's hard to produce clear evidence that cannibal flatworms aren't in fact learning from their lunch meat, and because the theory that they aren't learning is so much less interesting-sounding than the theory that they are. News outlets reported a lot about the memory RNA breakthrough, and much less about the later discrediting of the theory.

French's paper, you will recall, refutes the interesting-sounding hypothesis that infants resemble their fathers more strongly then they do their mothers, and has many of the same difficulties.

There are counterexamples. Everyone seems to have heard that the Fleischmann and Pons tabletop cold fusion experiment was an error. And the Hwang Woo-Suk stem cell fraud is all over the news these days.

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Do infants resemble their fathers more than their mothers?
Back in 1995, Christenfeld and Hill published a paper claimed to have found evidence that infants tended to resemble their fathers more than they resembled their mothers. The evolutionary explanation for this, it was claimed, is that children who resemble their fathers are less likely to be abandoned by them, because their paternity would be less likely to be doubted. The pop science press got hold of it—several years later, as they often do—and it was widely reported for a while. Perhaps you heard about it.

A couple years ago, while looking for something entirely unrelated, I ran across the paper of French et al. titled The Resemblance of One-year-old Infants to Their Fathers: Refuting Christenfeld & Hill. French and his colleagues had tried to reproduce Christenfeld and Hill's results, with little success; they suggested that the conclusion was false, and offered a number of arguments as to why the purported resemblance should not exist. Of course, the pop science press was totally uninterested.

At the time, I thought, "Wow, I wish I had a way to get a lot of people to read this paper." Then last month I realized that my widely-read blog is just the place to do this.

Before I go on, here is the paper. I recommend it; it's good reading, and only six pages long. Here's the abstract:

In 1995 Christenfeld and Hill published a paper that purported to show at one year of age, infants resemble their fathers more than their mothers. Evolution, they argued, would have produced this result since it would ensure male parental resources, since the paternity of the infant would no longer be in doubt. We believe this result is false. We present the results of two experiments (and mention a third) which are very far from replicating Christenfeld and Hill's data. In addition, we provide an evolutionary explanation as to why evolution would not have favored the result reported by Christenfeld and Hill.

In the first study done by French, participants were presented with a 1-, 3-, or 5-year-old child's face, and the faces of either the father and two unrelated men, or the mother and two unrelated women. The participants were invited to identify the child's parent. They did indeed succeed in identifying the children's parents somewhat more often than would have been obtained by chance alone. But the participants did not identify fathers more reliably than they identified mothers.

The second study was similar, but used only 1-year-old infants. (The Christenfeld and Hill claim is that one year is the age at which children most resemble their fathers.)

French points out that although the argument from evolutionary considerations is initially attractive, it starts to disintegrate when looked at more closely. The idea is that if a child resembles its father, the father is less likely to doubt his paternity, and so is less likely to withhold resources from the child. So there might be a selection pressure in favor of resembling one's father.

But now turn this around: if a father can be sure of paternity because the children look like him, then he can also be sure when the children aren't his because they don't resemble him. This will create a very strong selection pressure in favor of children resembling their fathers. And the tendency to resemble one's father will create a positive feedback loop: the more likely kids are to look like their fathers, the more likely that children who don't resemble their fathers will be abandoned, neglected, abused, or killed. So if there is a tendency for infants to resemble their fathers more than their mothers, one would expect it to be magnified over time, and to be fairly large by now. But none of the studies (including the original Christenfeld and Hill one) found a strong tendency for children to resemble their fathers.

But, as French notes, it's hard to get people to pay attention to a negative result, to a paper that says that something interesting isn't happening.

[ Addendum 20061206: Here's the original Christenfeld and Hill paper. ]

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Clockwise
A couple of weeks ago I was over at a friend's house, and was trying to explain to her two-year-old daughter which way to turn the knob on her Etch-a-Sketch. But I couldn't tell her to turn it clockwise, because she can't tell time yet, and has no idea which way is clockwise.

It occurs to me now that I may not be giving her enough credit; she may know very well which way the clock hands go, even though she can't tell time yet. Two-year-olds are a lot smarter than most people give them credit for.

Anyway, I then began wonder what "clockwise" and "counterclockwise" were called before there were clocks with hands that went around clockwise. But I knew the answer to that one: "widdershins" is counterclockwise; "deasil" is clockwise.

Or so I thought. This turns out not to be the answer. "Deasil" is only cited by the big dictionary back to 1771, which postdates clocks by several centuries. "Widdershins" is cited back to 1545. "Clockwise" and "counter-clockwise" are only cited back to 1888! And a full-text search for "clockwise" in the big dictionary turns up nothing else. So the question of what word people used in 1500 is still a mystery to me.

That got me thinking about how asymmetric the two words "deasil" and "widdershins" are; they have nothing to do with each other. You'd expect a matched set, like "clockwise" and "counterclockwise", or maybe something based on "left" and "right" or some other pair like that. But no. "Widdershins" means "the away direction". I thought "deasil" had something to do with the sun, or the day, but apparently not; the "dea" part is akin to dexter, the right hand, and the "sil" part is obscure. Whereas the "shins" part of "widdershins" does have something to do with the sun, at least by association. That is, it is not related historically to the sun, except that some of the people using the word "widdershins" were apparently thinking it was actually "widdersun". What a mess. And the words have nothing to do with each other anyway, as you can see from the histories above; "widdershins" is 250 years older than "deasil".

The OED also lists "sunways", but the earliest citation is the same as the one for deasil.

Anyway, I did not know any of this at the time, and imagined that "deasil" meant "in the direction of the sun's motion". Which it is; the sun goes clockwise through the sky, coming up on the left, rising to its twelve-o'-clock apex, and then descending on the right, the way the hands of a clock do. (Perhaps that's why the early clockmakers decided to make the hands of the clock go that way in the first place. Or perhaps it's because of the (closely related) reason that that's the direction that the shadow on a sundial moves.)

And then it hit me that in the southern hemisphere, the sun goes the other way: instead of coming up on the left, and going down on the right, the way clock hands do, it comes up on the right and goes down on the left. Wowzers! How bizarre.

I'm a bit sad that I figured this out before actually visiting the southern hemisphere and seeing it for myself, because I think I would have been totally freaked out on that first morning in New Zealand (or wherever). But now I'm forewarned that the sun goes the wrong way down there and it won't seem so bizarre when I do see it for the first time.

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Legal status of corpses in 1911 England
As you might expect from someone who browses at random in the library stacks, I own several encyclopedias, which I also browse in from time to time. You never know what you are going to find when you do this.

I got rid of one recently. It was a 1962 Grolier's. Obviously, it was out of date, but I was using it for general reference anyway, conscious of its shortcomings. But day I picked it up to read its article on Thurgood Marshall. It said that Marshall was an up-and-coming young lawyer, definitely someone to watch in the future. That was too much, and I gave it away.

But anyway, my main point is to talk about the legal status of corpses. One of the encyclopedias I have is a Twelfth Edition Encyclopaedia Britannica. This contains the complete text of the famous 1911 Eleventh Edition, plus three fat supplementary volumes that were released in 1920. The Britannica folks had originally planned the Twelfth Edition for around 1930, but so much big stuff happened between 1911 and 1920 that they had to do a new edition much earlier.

The Britannica is not as much fun as I hoped it would be. But there are still happy finds. Here is one such:

CORPSE (Lat. corpus, the body), a dead human body. By the common law of England a corpse is not the subject of property nor capable of holding property. It is not therefore larceny to steal a corpse, but any removal of the coffin or grave-cloths is otherwise, such remaining the property of the persons who buried the body. It is a misdemeanour to expose a naked corpse to public view. . .

(The complete article is available online.)

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Baseball team nicknames, again
Some addenda to my recent article about baseball team nicknames.

Several people wrote to complain that I mismatched the cities and the nicknames in this sentence:

The American League [has] the Boston Royals, the Kansas City Tigers, the Detroit Indians, the Oakland Orioles...

My apologies for the error. It should have been the Boston Tigers, the Kansas City Indians, the Detroit Orioles, and the Oakland Royals.

Phil Varner reminded me that the Chicago Bulls are in fact a "local color" name; they are named in honor of the Chicago stockyards.

This raises a larger point, brought up by Dave Vasilevsky: My classification of names into two categories conflates some issues. Some names are purely generic, like the Boston Red Sox, and can be transplanted anywhere. Other names are immovable, like the Philadelphia Phillies. In between, we have a category of names, like the Bulls, which, although easily transportable, are in fact local references.

The Milwaukee Brewers are a good baseball example. The Brewers were named in honor of the local German culture and after Milwaukee's renown as a world center of brewing. Nobody would deny that this is a "local color" type name. But the fact remains that many cities have breweries, and the name "Brewers" would work well in many places. The Philadelphia Brewers wouldn't be a silly name, for example. The only place in the U.S. that I can think of offhand that fails as a home for the Brewers is Utah; the Utah Brewers would be a bad joke. (This brings us full circle to the observation about the Utah Jazz that inspired the original article.)

The Baltimore Orioles are another example. I cited them as an example of a generic and easily transportable name. But the Baltimore Oriole is in fact a "local color" type name; the Baltimore Oriole is named after Lord Baltimore, and is the state bird of Maryland. (Thanks again to Dave Vasilevsky and to Phil Gregory for pointing this out.)

Or consider the Seattle Mariners. The name is supposed to suggest the great port of Seattle, and was apparently chosen for that reason. (I have confirmed that the earlier Seattle team, the Seattle Pilots, was so-called for the same reason.) But the name is transportable to many other places: it's easy to imagine alternate universes with the New York Mariners, the Brooklyn Mariners, the San Francisco Mariners, or the Boston Mariners. Or even all five.

And similarly, although in the previous article I classed the New York Yankees with the "local color" names, based on the absurdity of the Selma or the Charleston Yankees, the truth is that the Boston Yankees only sounds strange because it didn't actually happen that way.

I thought about getting into a tremendous cross-check of all 870 name-city combinations, but decided it was too much work. Then I thought about just classing the names into three groups, and decided that the issue is too complex to do that. For example, consider the Florida Marlins. Local color, certainly. But immovable? Well, almost. The Toronto Marlins or the Kansas City Marlins would be jokes, but the Tampa Bay Marlins certainly wouldn't be. And how far afield should I look? I want to class the Braves as completely generic, but consideration of the well-known class AA Bavarian League Munich Braves makes it clear that "Braves" is not completely generic.

So in ranking by genericity, I think I'd separate the names into the following tiers:

1. Pirates, Cubs, Reds, Cardinals, Giants, Red Sox, Blue Jays, White Sox, Tigers, Royals, Athletics
2. Braves, Mets, Dodgers, Orioles, Yankees, Indians, Angels, Mariners, Nationals, Brewers
3. Marlins, Astros, Diamondbacks, Rockies, Padres, Devil Rays, Twins
4. Phillies, Rangers

Readers shouldn't take this classification as an endorsement of the Phillies' nickname, which I think is silly. I would have preferred the Philadelphia Brewers. Or even the Philadelphia Cheese Steaks. Maybe they didn't need the extra fat, but wouldn't it have been great if the 1993 Phillies had been the 1993 Cheese Steaks instead? Doesn't John Kruk belong on a team called the Cheese Steaks?

Another oddity, although not from baseball: In a certain sense, the Montreal Canadiens have an extremely generic name. And yet it's clearly not generic at all!

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Etymological oddity
Sometimes you find words that seem like they must be related, and then it turns out to be a complete coincidence.

Consider pen and pencil.

Pen is from French penne, a long feather or quill pen, akin to Italian penne (the hollow, ribbed pasta), and ultimately to the word feather itself.

Pencil is from French pincel, a paintbrush, from Latin peniculus, also a brush, from penis, a tail, which is also the source of the English word penis.

A couple of weeks ago someone edited the Wikipedia article on "false cognates" to point out that day and diary are not cognate. "No way," I said, "it's some dumbass putting dumbassery into Wikipedia again." But when I checked the big dictionary, I found that it was true. They are totally unrelated. Diary is akin to Spanish dia, Latin dies, and other similar words, as one would expect. Day, however, is "In no way related to L. dies..." and is akin to Sanskrit dah = "to burn", Lithuania sagas = "hot season", and so forth.

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Damning with faint praise
If you have used evaporated milk, you may have noticed that the label says something like:

By adding one part water to one part of the contents of this can, a resulting milk product will be obtained which will not be below the legal standard for whole milk.

This sounds ghastly, doesn't it? "Will not be below the legal standard...". Shudder.

The purpose of this note is to let you know that:

1. I have done this,
2. more than once, and
3. it not only wasn't as ghastly as it sounds,
4. it wasn't ghastly at all.

From the warning on the label, you would expect maybe a 30% resemblance to milk; in truth, the resemblance is more like 85%. That's close enough to drink plain, if you're not too fussy, and it's certainly close enough to pour over your cereal without noticing the difference.

The wording of the label scares people off, but it works quite well, well enough that it is probably worth keeping a couple of cans in the closet for emergencies, like when you run out of milk for your cereal at 2 AM after the store is closed.

This has been a public service announcement of the Universe of Discourse. Happy Thanksgiving, everyone!

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Baseball team nicknames
Lorrie and I were in the car, and she noticed another car with a Detroit Pistons sticker. She remarked that "Pistons" was a good name for a basketball team, and particularly for one from Detroit. I agreed. But then she mentioned the Utah Jazz, a terrible mismatch, and asked me how that happened to be. Even if you don't know, you can probably guess: They used to be the New Orleans Jazz, and the team moved to Utah. They should have changed the name to the Teetotalers or the Salt Flats or something, but they didn't, so now we have the Utah Jazz. I hear that next month they're playing the Miami Fightin' Irish.

That got us thinking about how some sports team names travel, and others don't. Jazz didn't. The Miami Heat could trade cities or names with the Phoenix Suns and nobody would notice. But consider the Chicago Bulls. They could pick up and move anywhere, anywhere at all, and the name would still be fine, just fine. Kansas City Bulls? Fine. Honolulu Bulls? Fine. Marsaxlokk Bulls? Fine.

We can distinguish two categories of names: the "generic" names, like "Bulls", and the "local color" names, like "Pistons". But I know more about baseball, so I spent more time thinking about baseball team names.

In the National League, we have the generic Braves, Cardinals, Cubs, Giants, Pirates, and Reds, who could be based anywhere, and in some cases were. The Braves moved from Boston to Milwaukee to Atlanta, although to escape from Boston they first had to change their name from the Beaneaters. The New York Giants didn't need to change their name when they moved to San Francisco, and they won't need to change their name when they move to Jyväskylä next year. (I hear that the Jyväskylä city council offered them a domed stadium and they couldn't bear to say no.)

On the other hand, the Florida Marlins, Arizona Diamondbacks, and Colorado Rockies are clearly named after features of local importance. If the Marlins were to move to Wyoming, or the Rockies to Nebraska, they would have to change their names, or turn into bad jokes. Then again, the Jazz didn't change their name when they moved to Utah.

The New York Mets are actually the "Metropolitans", so that has at least an attempt at a local connection. The Washington Nationals ditto, although the old name of the Washington Senators was better. At least in that one way. Who could root for a team called the Washington Senators? (From what I gather, not many people could.)

The Nationals replaced the hapless Montreal Expos, whose name wasn't very good, but was locally related: they were named for the 1967 Montreal World's Fair. Advice: If you're naming a baseball team, don't choose an event that will close after a year, and especially don't choose one that has already closed.

The Houston Astros, and their Astrodome filled with Astroturf, are named to recall the NASA manned space center, which opened there in 1961. The Philadelphia club is called the Phillies, which is not very clever, but is completely immovable. Boston Phillies, anyone? Pittsburgh Phillies? New York Phillies? No? I didn't think so.

I don't know why the San Diego Padres are named that, but there is plenty of Spanish religious history in the San Diego area, so I am confident in putting them in the "local color" column. Milwaukee is indeed full of Brewers; there are a lot of Germans up there, brewing up lager. (Are they back in the National League again? They seem to switch leagues every thirty years.)

That leaves just the Los Angeles Dodgers, who are a bit of an odd case. The team, as you know, was originally the Brooklyn Dodgers. The "Dodgers" nickname, as you probably didn't know, is short for "Trolley Dodgers". The Los Angeles Trolley Dodgers is almost as bad a joke as the Nebraska Rockies. Fortunately, the "Trolley" part was lost a long time ago, and we can now imagine that the team is the Los Angeles Traffic Dodgers. So much for the National League; we have six generic names out of 16, counting the Traffic Dodgers in the "local color" group, and ignoring the defunct Expos.

The American League does not do so well. They have the Boston Royals, the Kansas City Tigers, the Detroit Indians, the Oakland Orioles, and three teams that are named after sox: the Red, the White, and the Athletics.

Then there are the Blue Jays. They were originally owned by Labatt, a Canadian brewer of beer, and were so-named to remind visitors to the park of their flagship brand, Labatt's Blue. I might have a harder time deciding which group to put them in, if it weren't for the (1944-1945) Philadelphia Blue Jays. If the name is generic enough to be transplanted from Toronto to Philadelphia, it is generic. I have no idea what name the Toronto club could choose if they wanted to avail themselves of the "local color" option rather than the "generic" option; it's tempting to make a cruel joke and suggest that the name most evocative of Toronto would be the Toronto Generics. But no, that's unfair. They could always call their baseball club the Toronto Hockey Fans.

Anyway, moving on, we have the New York Yankees, which is not the least generic possible name, but clearly qualifies as "local color" once you pause to think about the Charleston Yankees, the Shreveport Yankees, and the Selma Yankees. The Tampa Bay Devil Rays are clearly "local color". The Minnesota Twins play in the Twin Cities of Minneapolis and St. Paul. The California, Anaheim, or Los Angeles Angels, whatever they're called this week, are evidently named for the city of Los Angeles. I would ridicule the Los Angeles Angels for having a redundant name, but as an adherent of the Philadelphia Phillies, I am living in a glass house.

The Texas Rangers are named for the famous Texas Rangers. I don't know exactly why the Seattle club is named Mariners; I wouldn't have considered Seattle to be an unusually maritime city, but their previous team was the Seattle Pilots, so the folks in Seattle must think of themselves so, and I'm willing to go along with it.

The tally for the American League is therefore eight generic, six local color. The total for Major League Baseball as a whole is 14 generic names out of 30.

This is a lot better than the Japanese Baseball League, which has a bunch of teams with names like the Lions, Tigers, Dragons, Giants, and Fighters. They make up for this somewhat in the names of the teams' corporate sponsors, so, for example, the Nippon Ham Fighters. They are sponsored by Nippon Ham, which does not make it any less funny. And the Yakult Swallows, which, if you interpret it as a noun phrase, sounds just a little bit like a gay porn flick set in Uzbekistan.

Incidentally, my favorite team name is the Wilmington Blue Rocks. The Blue Rocks' mascot is, alas, not a rock but a moose. Sometimes I dream of a team from Lansing, Michigan, called the Lansing Boils, but I know it will remain an unfulfilled fantasy.

[ Warning for non-Americans: Almost, but not quite everything in this article is the truth. Marsaxlokk does not actually have a Major League baseball club yet; however, they do have a class-A affiliate in the Mediterranean league, called the Marsaxlokk Moghzaskops. Also, the Giants are not scheduled to move to Jyväskylä until after the 2008 season. ]

[ Addendum 20061127: There is a followup article to this one. ]

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Etch-a-Sketch blue-skying, corrected
In my last article I discussed a scheme for improving the Etch-a-Sketch which contained a serious mechanical error. I was discussing attaching gears to the two knobs of the Etch-a-Sketch to force them to turn at the exact same rate. Supposing that the distance between the knobs is 1 unit, I said, then we can gear the two knobs together by attaching a gear of radius 1/2 to each knob; the two gears will mesh, and the knobs will then turn at the same rate, in opposite directions. This was fine.

Then I went astray, and suggested adding an axle peg midway between the two knobs, and putting gears of radius 1/3 on the peg and on the two knobs. This won't work.

The one person who wrote to me to ask about the problem is a very bright person, but been seriously confused about how I was planning to set up the gears, so I evidently I didn't explain it very well. It needed a picture. So this time I'm going to try to get it right, with pictures. Here is an Etch-a-Sketch:

Here are some gears, which happen to have radii 1/3, 1/4, and 1/6:

Here's a picture of an Etch-a-Sketch with a radius-1/2 gear mounted on each knob:

Here the knobs have been fitted with different-sized gears, one with radius 1/3 and the other with radius 2/3:

Then I suggested that you could drill a little hole in between the two knobs, and use it to mount a third axle and a third gear. If all three gears are the same size, the two knobs are forced to turn at the same rate, this time in the same direction, and you get a line with slope 1, from southeast to northwest:

This wrecks the rest of the details of my other article. Since we were already including gears of size 1/2 and 1/3, I reasoned, we can throw in a gear of size 1/6 and get some new behaviors from the 1/2 + 1/3 + 1/6 combination. The corresponding combination for 1/2 and 1/4 is 1/8:

So what next? The calculations are a bit less obvious than they were back in the happy days when I thought that installing two gears of size p and q left space for one of size 1-(p+q). It's tempting to consider a radius-1/3 gear next, since it's the simplest size I haven't yet installed. But to mount it on the knobs along with a size-1/2 gear, we need to include a size-1/12 gear to go in between:

Once we have the size-1/12 gear, we can mount it with the size-1/4 and size-1/3 that we already had:

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Etch-a-Sketch
I've always felt that the Etch-a-Sketch is a superb example of a toy that doesn't do as much as it could.

An Etch-a-Sketch is a drawing toy invented in 1959 by Arthur Granjean and marketed by the Ohio Art company since shortly afterward. It looks superficially like a flat-screen television with two knobs.

It is very easy to draw horizontal and vertical lines, but very difficult to draw diagonal lines. (Wikipedia says "Creating a straight diagonal line or smoothly curved line with an Etch A Sketch is notoriously difficult and a true test of coordination.") So although extremely complex drawings can be made with an Etch-a-Sketch:

(Etch-a-Sketch drawing of Albert Einstein by Nicole Falzone)

But it needn't be so. The most frustrating thing about the Etch-a-Sketch, I think, is that its potential has not yet begun to be unlocked.

Consider a forty-five degree line. To draw such a line, one must turn both the horizontal and the vertical knobs at the same time, at exactly the same rate. Suppose, for concreteness, that we're drawing a line from the upper left to the lower right. If you turn the horizontal knob a little too quickly, the diagonal line will bend rightward; if you turn it a little too slowly the diagonal line will bend downward. So in contrast to the mathematically exact vertical and horizontal lines that are easy to draw, it's next to impossible to draw a diagonal line that doesn't wiggle. And when you screw up, you can't fix the mistake without erasing the whole thing and starting over.

But the solution is obvious: If you can link the two knobs somehow, so that they can only turn simultaneously, you can easily draw a diagonal line. As a child, I experimented with rubber bands, trying to get one knob to drive the other. This wasn't successful. Clearly, a better solution is to use gears.

There are plenty of examples of toys that have good-quality cast-plastic gears. (Spirograph is one such.) The knobs on the Etch-a-Sketch could be geared together. If the gears are the same size, the knobs will rotate at the same rate, and the result will be a perfect 45° line.

If you gear the two knobs together directly, they will rotate in opposite directions, so that you can only draw lines with slope -1 (northwest to southeast), not with slope 1 (northeast to southwest). To fix this problem, we need to introduce more gears. There can be an axle peg sticking up from the case of the Etch-a-Sketch, in between the two knobs. Mounting three equal-sized gears on the two knobs and the axle peg gears will force the knobs to rotate in the same direction, at the same rate.

[ The remainder of this article contains a number of very dumb arithmetic errors. For example, you cannot fit three gears of size 1/3 on the knobs and pegs; you need to use three gears of size 1/4 instead. I will correct this on Monday, and provide an illustration to make it clearer what I mean. —MJD ]

[ Addendum 20061116: I have posted the correction, with illustrations. ]

Let's say that the distance between the centers of the two knobs is 1. We can get a line of slope -1 by mounting two gears, each with radius 1/2, on the two knobs; we can get a line of slope +1 by mounting three gears, each with radius 1/3, on the two knobs and on the axle peg. If we want to do both, we had better make the axle peg removable, or else it will interfere with the size-1/2 gears. This is no problem. It can mount into a socket on the front of the Etch-a-Sketch, and be pulled out when not needed.

But why have only one socket? We're including five gears already (two of size 1/2 and three of size 1/3) so we may as well put them to some more use. Throw in a size 1/6 gear, and add another socket for the axle peg, this time 1/3 of the way between the two knobs. Now you can mount a size 1/2 gear on the left knob, a size 1/6 gear on the axle peg, and a size 1/3 gear on the right knob. If the left knob turns at rate r, the middle gear turns at rate -3r and the right knob turns at rate 3r/2. This produces a line with slope 3/2, which is about a 56-degree angle.

Or put in another socket for the axle peg, 1/6 of the way between the knobs, and then mount size 1/2, size 1/3, and size 1/6 gears, in that order. The knobs are now producing a line with slope 3, a 72-degree angle. If you want a line with slope 1/3 (18°) instead, just reverse the order of the gears. (That is, exchange the large and the small ones.)

At this point adding a few more gears expands the repertoire significantly. Add a radius-2/3 gear and another radius-1/6 gear and you can mount [2/3, 1/3] to get lines with slope -1/2, [1/3, 2/3] to get slope -2, [2/3, 1/6, 1/6] to get slope 4, [1/6, 1/6, /23] to get slope 1/4.

Clearly, you can carry this onwards, limited only by the space for the axle holes and the expense of adding in more gears. Spirograph used to deliver fifteen or twenty plastic gears for a reasonable price, so it's clearly not implausible that Ohio Art could have done something like this.

Sometimes I even dare to think that they might have provided cams or elliptical gears. Properly designed cams could gear together the knobs to produce mathematically exact curved lines, squiggles, maybe even circles.

But no, as far as I can tell, it's never been done. Why not?

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Boring answers to Powell's questions
A while back I answered some questions for Powell's City of Books web site. I didn't know they had posted the answers until it was brought to my attention by John Gabriele. Thank you, John.

They sent fifteen questions and asked me to pick at least five. I had a lot of trouble finding five of their questions that I wanted to answer. Most of the questions were not productive of interesting answers; I had to work hard to keep my answers from being super-dull.

The non-super-dull answers are on Powell's site. Here are the questions I didn't answer, with their super-dull answers:

1. Have you ever taken the Geek Test? How did you rate?

   Hardly anyone seems to answer this question, and really, who cares? Except that Sir Roger Penrose said something like "There's a Geek Test?".

   I did take it once, but I forget how I scored. But if you read this blog, you can probably extrapolate: high on math, science, and programming. But really, who cares? Telling someone else about your geek test score is even more boring than telling them about your dreams.

2. What do you do for relaxation?

   I didn't answer this one because my answer seemed so uninteresting. I program. I read a lot; unlike most people who read a lot, I read a lot of different things. Sometimes I watch TV. I go for walks and drive the car.

   One thing I used to do when I was younger was the "coffee trick". I'd go to an all-night diner with pens and a pad of paper and sit there drinking coffee all night and writing down whatever came out of my caffeine-addled brain. I'm too old for that now; it would make me sick.

3. What's your favorite blog right now?

   I answered this one for Powell's, and cited my own blog and Maciej Ceglowski's. But if I were answering the question today I would probably mention What Jeff Killed. Whenever a new What Jeff Killed post shows up in the aggregator, I get really excited. "Oh, boy!" I say. "I can't wait to see What Jeff Killed today!".

   It occurs to me that just that one paragraph could probably give plenty of people a very clear idea of what I'm like, at least to the point that they would be able to decide they didn't want to know me.

4. Douglas Adams or Scott Adams?

   I think they're both boring. But I wasn't going to say so in my Powell's interview.

5. What was your favorite book as a kid?

   This should have been easy to answer, but none of the books I thought of seemed particularly revealing. When I was in sixth grade my favorite book was "The Hero from Otherwhere," by Jay Williams. (He also wrote the Danny Dunn books.) A few years back Andrew Plotkin posted on rec.arts.sf.written that he had recently read this, and that it occurred to him that it might have been his favorite book, had he read it in sixth grade, and had anyone had that experience. I wasn't the only one who had.

   I reread it a few years ago and it wasn't that good anymore.

   Robertson Davies writes about the awful juvenile-fiction magazines that he loved when he was a juvenile. Yes, they were terrible, but they fed something in him that needed to be fed. I think a lot of the books we love as children are like that.

6. What new technology do you think may actually have the potential for making people's lives better?

   I couldn't think of any way to answer this question that wouldn't be really boring. That probably says a lot more about me than about the question. I thought about gene therapy, land mine detection, water purification. But I don't personally have anything to do with those things, so it would just be a rehash of what I read in some magazine. And what's the point of reading an interview with an author who says, "Well, I read in Newsweek..."?

7. If you could be reincarnated for one day to live the life of any scientist or writer, who would you choose and why?

   This seems like it could have been interesting, but I couldn't figure out what to do with it. I might like to be Galileo, or to know what it's like to be Einstein, but that's not what the question says; it says that I'm me, living the life of Galileo or Einstein. But why would I want to do that? If I'm living the life of Einstein, that means I get to get up in the morning, go to an office in Zurich or Princeton, and sit behind a desk for eight hours, wishing I was smart enough to do Einstein's job.

   Some writers and scientists had exciting lives. I could be reincarnated as Evariste Galois, who was shot to death in a duel. That's not my idea of a good time.

   I once knew a guy who said he'd like to be David Lee Roth for one day, so that he could have sex with a groupie. Even if I wanted to have sex with a groupie, the question ("scientist or writer") pretty much rules out that form of entertainment. I suppose there's someone in the world who would want to be Pierre Curie, so that he know what it was like to fuck Marie Curie. That person isn't me.

8. What are some of the things you'd like your computer to do that it cannot now do?

   I came really close to answering this question. I had an answer all written. I wrote that I wanted the computer to be able to manufacture pornography on demand to the user's specification: if they asked for a kneecap fetish movie featuring Celine Dion and an overalls-wearing midget, it should be able to do that.

   Then I came to my senses and I realized I didn't want that answer to appear on my interview on the Powell's web site.

   But it'll happen, you wait and see.

   I also said I'd settle for having the computer discard spam messages before I saw them. I think the porn thing is a lot more likely.

9. By the end of your life, where do you think humankind will be in terms of new science and technological advancement?

   First I was stumped on this one because I don't know when the end of my life will be. I could be crushed in a revolving door next week, right?

   And assuming that I'll live another thirty years seems risky too. I'm hoping for a medical breakthrough that will prolong my life indefinitely. I expect it'll be along sooner or later. So my goal is to stay alive and healthy long enough to be able to take advantage of it when it arrives.

   Some people tell me they don't want to be immortal, that they think they would get bored. I believe them. People are bored because they're boring. Let them die; I won't miss them. I know exactly what I would do with immortality: I would read every book in the library.

   A few months ago I was visiting my mother, and she said that as a child I had always wanted to learn everything, and that it took me a long time to realize that you couldn't learn everything.

   I got really angry, and I shouted "I'm not done yet!"

   Well, even assuming that I live another thirty years, I don't think I can answer the question. When I was a kid my parents would go to the bank to cash a check. We got seven channels on the TV, and that was more than anyone else; we lived in New York. Nobody owned a computer; few people even owned typewriters. Big companies stored records on microfiche. The only way to find out what the law was was to go to the library and pore over some giant dusty book for hours until you found what you wanted.

   And sixty years ago presidential campains weren't yet advertising on television. Harry Truman campaigned by going from town to town on the back of a train (a train!) making speeches and shaking hands with people.

   Thirty years from now the world will be at least that different from the way things are now. How could I know what it'll be like?

10. Which country do you believe currently leads the world in science and technology? In ten years?

    In case you hadn't noticed, I hate trying to predict the future; I don't think I'm good at it and I don't think anyone else is. Most people who try don't seem to revisit their old predictions to see if they were correct, or to learn from their past errors, and the people who listen to them never do this.

    Technology prognosticators remind me of the psychics in the National Enquirer who make a hundred predictions for 2007: Jennifer Aniston will get pregnant with twins; space aliens will visit George Bush in the White House. Everyone can flap their mouth about what will happen next year, but it's not clear that anyone has any useful source of information about it, or is any better than anyone else at predicting.

    I read a book a few years back called The Year 2000: A Framework for Speculation on the Next Thirty Years, by Kahn and Weiner. It has a bunch of very carefully-done predictions about the year 2000, and was written in 1967. The predictions about computers are surprisingly accurate, if you ignore the fact that they completely failed to predict the PC. The geopolitical predictions are also surprisingly accurate, if you ignore the fact that they completely failed to predict the fall of the Soviet Union.

    But hardly anyone predicted the PC or the fall of the Soviet Union. And even now it's not clear whether the people who did predict those things did so because they were good at predicting or if it was just lucky guesses, like a stopped clock getting the time right twice a day.

    Sometimes I have to have dinner with predictors. It never goes well. Two years ago at OSCON I was invited to dinner with Google. I ended up sitting at a whole table of those people. Last year I was invited again. I said no thanks.

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Why two ears?
Aaron Swartz, remembering my earlier article about interesting science questions, sent me a reference to an interesting article about odd questions asked of students applying for admission to Cambridge and Oxford universities.

The example given in the article that I found most interesting was "Why don't we just have one ear in the middle of our face?". As I said earlier, I think the mark of a good question is that it's quick to ask and long to answer. I've been thinking about this one for several days now, and seems pretty long to answer.

Any reasonable answer to this question is going to be based on evolutionary and adaptive considerations, I think. When you answer from evolutionary considerations, there are only a few kinds of answers you can give:

1. It's that way because it confers a survival or reproductive advantage.
2. It's that way because that's the only way it can be made to work.
3. It's that way because it doesn't really matter, and that's just the way it happened to come out.

(Why only one heart? There's no benefit to having two; if you lose 50% of your cardiac capacity, you'll die anyway. Why one mouth? It needs to be big enough to eat with, and anyway, you can't lose it. Why one liver? No reason; that's just the way it's made; two livers would work just as well as one. Why two lungs? I'm not sure; I suppose it's a combination between "no reason, that's the way it's made" (#3 above) and "because that way you can still breathe even if one lung gets clogged up" (#1).)

The positioning of your ears is important. Having two ears far apart on the sides of your head allows you to locate sounds by triangulation. Triangulation requires at least two ears, and requires that they be as far apart as possible. This also explains why the ears are on the sides rather than the front.

Consider what would go wrong if the positions of the eyes and ears were switched. The ears would be pointed in the same direction, which would impede the triangulation-by-sound process. The eyes would be pointed in opposite directions, which would completely ruin the triangulation-by-sight process; you would completely lose your depth perception. So the differing position of the eyes and ears can be seen a response to the differing physical properties of light and sound: light travels in straight lines; sound does not.

The countervailing benefit to losing your depth perception would be that you would be able to see almost 180 degrees around you. Many animals do have their eyes on the side of their heads: antelopes, rabbits, and so forth. Prey, in other words. Predators have eyes on the fronts of their heads so that they can see the prey they are sneaking up on. Prey have eyes on the sides of their heads so that predators can't sneak up on their flanks. Congratulations: you're predator, not prey.

Animals do have exactly one nose in the middle of their face. Why not two? Here, triangulation is not an issue at all. Having one nose on each side of your head would not help you at all to locate the source of an odor. So the nose is stuck in the middle of the head, I suppose for mostly mechanical reasons: animals with noses evolved from animals with a long breathing tube down the middle of their bodies. The nose arises as sensors stuck in the end of the tube. This is another explanation for the one mouth.

Another consideration is symmetry. The body is symmetric, so if you want two ears, you have to put one on each side. Why is this? I used to argue that it was to save information space in the genome: there is only so much room in your chromosomes for instructions about how to build your body, so the information must be compressed. One excellent way to compress it is to make some parts like other parts and then express the differences as diffs. This, I used to say, is why the body is symmetric, why your feet look like your hands, and why men's and women's bodies are approximately the same.

I now think this is wrong. Well, wrong and right, essentially right, but mostly wrong. The fact is, there is plenty of space in the chromosomes for instructions about all sorts of stuff. Chromosomes are really big, and full of redundancy and junk. And if it's so important to save space in the chromosome, why is the inside of your body so very asymmetric?

I now think the reason for symmetries and homologies between body parts is less to do with data compression and storage space in the chromosome, and more to do with the shortness of the distance between points in information space. Suppose you are an animal with two limbs, each of which has a hand on the end. Then a freak mutation occurs so that your descendants now have four limbs. The four limbs will all have similar hands, because mutation cannot invent an entirely new kind of hand out of thin air. Your genome contains only one set of instructions for appendages that go on the ends of limbs, so these are the instructions that are available to your descendants. These instructions can be duplicated and modified, but again, there is no natural process by which a new set of instructions for a new kind of appendage can be invented from whole cloth. So your descendants' hands will look something like their feet for quite a long time.

Similarly, there is a certain probability, say p, of an earless species evolving something that functions as an ear. The number p is small, and ears arise only because of natural selection in favor of having ears. The chance that the species will simultaneously and independently evolve two completely different kinds of ear structures is no more than p², which is vanishingly small. And once the species has something earlike, the selection pressure in favor of the second sort of ear is absent. So a species gets one kind of ear. If having two ears is beneficial, it is extremely unlikely to arise through independent evolution, and much more likely to arise through a much smaller mutation that directs the same structure, the one for which complete instructions already exist in the genome, to appear on each side of the head.

So this is the reason for bodily symmetry. Think of (A) an earless organism, (B) an organism with two completely different ears, and (C) an organism with two identical ears. Think of these as three points in the space of all possible organisms. The path from point A to C is both much shorter than the path from A to B, and also much more likely to be supported by selection processes.

Now, why is the outside of the body symmetric while the inside is not? I haven't finished thinking this through yet. But I think it's because the outside interacts with the gross physical world to a much greater extent than the inside, and symmetry confers an advantage in large-scale physical interactions. Consider your legs, for example. They are approximately the same length. This is important for walking. If you had a choice between having both legs shortened six inches each, and having one leg shortened by six inches, you would certainly choose the former. (Unless you were a sidehill winder.) Similarly, having two different ears would mess up your hearing, particularly your ability to locate sounds. On the other hand, suppose one of your kidneys were much larger than the other. Big deal. Or suppose you had one giant liver on your right side and none on the left. So what? As long as your body is generally balanced, it is not going to matter, because the liver's interactions with the world are mostly on a chemical level.

So I think that's why you have an ear on each side, instead of one ear in the middle of your head: first, it wouldn't work as well to have one. Second, symmetry is favored by natural selection for information-conserving reasons.

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Bone names
Names of bones are usually Latin. They come in two types. One type is descriptive. The auditory ossicles (that's Latin for "little bones for hearing") are named in English the hammer, anvil, and stirrup, and their formal, Latin names are the malleus ("hammer"), incus ("anvil"), and stapes ("stirrup")

The fibula is the small bone in the lower leg; it's named for the Latin fibula, which is a kind of Roman safety pin. The other leg bone, the tibia, is much bigger; that's the frame of the pin, and the fibula makes the thin sharp part.

The kneecap is the patella, which is a "little pan". The big, flat parietal bone in the skull is from paries, which is a wall or partition. The clavicle, or collarbone, is a little key.

"Pelvis" is Latin for "basin". The pelvis is made of four bones: the sacrum, the coccyx, and the left and right os innominata. Sacrum is short for os sacrum, "the sacred bone", but I don't know why it was called that. Coccyx is a cuckoo bird, because it looks like a cuckoo's beak. Os innominatum means "nameless bone": they gave up on the name because it doesn't look like anything. (See illustration to right.)

On the other hand, some names are not descriptive: they're just the Latin words for the part of the body that they are. For example, the thighbone is called the femur, which is Latin for "thigh". The big lower arm bone is the ulna, Latin for "elbow". The upper arm bone is the humerus, which is Latin for "shoulder". (Actually, Latin is umerus, but classical words beginning in "u" often acquire an initial "h" when they come into English.) The leg bone corresponding to the ulna is the tibia, which is Latin for "tibia". It also means "flute", but I think the flute meaning is secondary—they made flutes out of hollowed-out tibias.

Some of the nondescriptive names are descriptive in Latin, but not in English. The vertebra in English are so called after Latin vertebra, which means the vertebra. But the Latin word is ultimately from the verb vertere, which means to turn. (Like in "avert" ("turn away") and "revert" ("turn back").) The jawbone, or "mandible", is so-called after mandibula, which means "mandible". But the Latin word is ultimately from mandere, which means to chew.

The cranium is Greek, not Latin; kranion (or κρανιον, I suppose) is Greek for "skull". Sternum, the breastbone, is Greek for "chest"; carpus, the wrist, is Greek for "wrist"; tarsus, the ankle, is Greek for "instep". The zygomatic bone of the face is yoke-shaped; ζυγος ("zugos") is Greek for "yoke".

The hyoid bone is the only bone that is not attached to any other bone. (It's located in the throat, and supports the base of the tongue.) It's called the "hyoid" bone because it's shaped like the letter "U". This used to puzzle me, but the way to understand this is to think of it as the "U-oid" bone, which makes sense, and then to remember two things. First, that classical words beginning in "u" often acquire an initial "h" when they come into English, as "humerus". And second, classical Greek "u" always turns into "y" in Latin. You can see this if you look at the shape of the Greek letter capital upsilon, which looks like this: Υ. Greek αβυσσος ("abussos" = "without a bottom") becomes English "abyss"; Greek ανωνυμος ("anonumos") becomes English "anonymous"; Greek υπος ("hupos"; there's supposed to be a diacritical mark on the υ indicating the "h-" sound, but I don't know how to type it) becomes "hypo-" in words like "hypothermia" and "hypodermic". So "U-oid" becomes "hy-oid".

(Other parts of the body named for letters of the alphabet are the sigmoid ("S-shaped") flexure of the colon and the deltoid ("Δ-shaped") muscle in the arm. The optic chiasm is the place in the head where the optic nerves cross; "chiasm" is Greek for a crossing-place, and is so-called after the Greek letter Χ.)

The German word for "auditory ossicles" is Gehörknöchelchen. Gehör is "for hearing". Knöchen is "bones"; Knöchelchen is "little bones". So the German word, like the Latin phrase "auditory ossicles", means "little bones for hearing".

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MadHatterDay 2006

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Job hunting stories
A guy named Jonathan Rentzsch bookmarked my article about creeping featurism and the ratchet effect, saying "I'd like to hire this guy just so I could fire him." Since I was looking for a new job last month, I sent him my résumé, inquiring about his company's severance package. He didn't reply.

I talked it over with my wife, and we decided that for $750,000 we would be willing for me to spend the year working in Milford, Iowa. $500,000, we decided, would not be sufficient, but $750,000 would. I forget by now how we arrived at this figure, but we took some care in coming up with it.

The headhunter called back. "Have you thought it over?" Yes, I had, I said. I had decided that $750,000 would be required to get me to Milford, Iowa.

He was really angry that I had wasted his time.

One day I was on a five-week business trip to Asia. (I hate commuting, but I like travelling.) I got email from a headhunter who was offering me a long-term contract in Elkton, Maryland. I had told this headhunter's company repeatedly that I was only interested in working in the Philadelphia area. (Elkton, Maryland is about as close to Philadelphia as you can get and still be in Maryland, which means that the only thing between Elkton and Philadelphia is the state of Delaware.)

I wrote back, from Tokyo, and said that his company should stop contacting me, because I had told them over and over that I would only work in Philadelphia, and they kept sending me offers of employment in places like Elkton. I said it was a shame that we should waste each others' time like this.

He suggested that the problem could be solved if I could just give him a "courtesy call". From Tokyo.

Instead, I solved the problem by putting his company in my spam filter file.

He didn't like my advice. I still think it was good advice. No nineteen-year-old needs a three-page résumé. I wonder if he eventually figured this out. You'd think so, but now that I have to read the résumés of people who are applying to me for jobs, it seems that hardly any of the applicants have figured out that you should leave out the job where you washed dishes for your fraternity.

I've talked to a couple of people lately who tell me that it's very rare to get a cover letter from an applicant that actually helps their chances of getting the job. At best, it's neutral. At worst, you get to see all their spelling and grammar errors.

I think most people don't know how to write a letter, or that they write one letter and send it with every application. Maybe they think it would be dishonest to send a different letter with every application.

I became a conference speaker and teacher of Perl classes in a similar way. I wanted to go to the second Perl conference, but I couldn't afford it. Someone mentioned to me that there was a $1,000 prize for the best user paper. I thought I could write a good paper, but I also thought that the best paper often doesn't win the prize. But I also found out that conference tutorial speakers were paid $1,500 and given free conference admission and airfare and hotel fees.

When you're submitting a proposal for a tutorial, it's perfectly honorable to go talk to the program committee behind the scenes and lobby them to accept your proposal instead of someone else's. If you do that with the contest judges, it's cheating. So I ignored the user paper contest and submitted a proposal for a tutorial, which was accepted.

I got back a peevish letter telling me that I wasn't qualified and to stop wasting the search committee's time. It was signed, in pen, "The Search Committee".

I accepted a job with the University of Pennsylvania instead.

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I get a new job
Where did my blog go for the past six weeks? Well, I was busy with another project. Usually, when I am busy with a project, it shows up here, because I am thinking about it, and I want to write about what I am thinking. As Hans Arp said, it grows out of me and I keep cutting it off, like toenails. But in this case I could not write about the project here, because it was a secret. I was looking for a new job, and I did not want my old job to find out before I was ready.

(Many people have been surprised to learn that I have a job; they remember that for many years I was intermittently a software consultant and itinerant programming trainer. But since January 2004 I have been regularly employed to do maintenance programming for the University of Pennsylvania's Networking and Telecommunications group.)

Anyway, the job hunt has come to a close. I accepted a new job, put in my resignation letters at the old one, and can stop thinking about it for a while. The new work will be head software engineer at the Penn Genomics Institute. I will try to develop software for genetic biologists to use in their research. I expect that the new job will suit me somewhat better than the old one. I like that it is connected to science, and that I will be working with scientists. The work itself is important; genomics is going to change everything in the world. Also, it pays rather more than the old one, although that was not the principal concern.

So with any luck blog posts will resume here, and eventually some genomics-related articles may start appearing.

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Oyster jokes
Last week I heard a pathetically bad joke about oysters. Here it is:

What did the girl oyster say to the boy oyster?

"You never open up to me."

But it seems to me that there is a lot of unexploited material to be gotten from oysters.

For example, oysters, considered as food, are famous for their aphrodisiac properties. It ought to be possible to do something with that. What do the boy and the girl oyster use as aphrodisiacs? Does it involve oyster cannibalism? So much the better. Can the aphrodisiac cannibalism be tied to oral sex somehow? Better still. How could a joke about oyster cunnilingus fail to be hilarious?

Moreover, oysters are hermaphrodites. Surely there is some farcical oyster humor available from the fact that the boy and the girl oysters might in fact be the same individual. Now we have oyster autofellatial autocannibalism. It's both dirty and disgusting!

I was not able to come up with any oyster jokes, however, and a quick web search turned up nothing of value. Really nothing. Don't waste your time. I found one joke that was introduced with "Jennifer sent in this great oyster joke..." and then the joke wasn't even about oysters; it was about the ingestion of testicles. And I had heard it before.

I think there's a small gap in the world just the size and shape of a good oyster-themed joke. Don't you? Here is your big chance to make up a joke that nobody has ever heard before. Please send me your oyster jokes.

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Phrasal verbs
My mom teaches English to visiting foreign students, and last time I met her she was talling me about phrasal verbs. A phrasal verb is a verb that incorporates a preposition. Examples include "speed up", "try out", "come across", "go off", "turn down". The prepositional part is uninflected, so "turns down", "turned down", "turning down", not *"turn downs", *"turn downed", *"turn downing". My mom says she uses a book that has a list of all of them; there are several hundred. She was complaining specifically about "go off", which has an unusually peculiar meaning: when the alarm clock goes off in the morning, it actually goes on.

This reminded me that "slow up" and "slow down" are synonymous. And there is "speed up", but no "speed down". And you cannot understand "stand down" by analogy with "stand up", "sit up", and "sit down". And you also cannot understand "nose job" by analogy with "hand job". But I digress.

One of the things about the phrasal verbs that gives the foreign students so much trouble is that the verbs don't all obey the same rules. For example, some are separable and some not. Consider "turned down". I can turn down the thermostat, but I can also turn the thermostat down. And I can try out my new game, and I can also try my new game out. And I can stand up my blind date, and I can stand my blind date up. But while I can come across a fountain in the park, I can't *come a fountain across in the park. And while I can go off to Chicago, I can't *go to Chicago off. There's no way to know which of these work and which not, except just by memorizing which are allowed and which not.

And sometimes the separable ones can't be unseparated. I can give back the map, and I can give the map back, and I can give it back, but I can't *give back it. I can hold up the line, and I can hold the line up, and I can hold us up, but I can't *hold up us. I don't know what the rule is exactly, and I don't want to go to the library again to get the Cambridge Grammar, because last time I did that I dropped it on my toe.

I hadn't realized any of this until I read this article about them, but when I did, I had a sudden flash of insight. I had not realized before what was going on when someone set up us the bomb. "Set up" is separable: I can set up the bomb, or set the bomb up, or someone can set us up. But "us", as noted above, is not deseperable, so you cannot have *set up us. But I think I understand the mistake better now than I did before; it seems less like a complete freak and more like a member of a common type of error.

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Contravariant types
I just had a slightly frustrating discussion with some colleagues, involving a small matter of object-oriented design. I don't want to get into the details of the problem here, except to say that it involved a class A and its derived class B; I was asking for advice about the design of a "demote" method that would take a B object and turn it into an A object.

The frustrating part was that about half of the people in the conversation were confused by my use of the word "demotion" and about whether A was inheriting from B or vice versa. I had intended for B to inherit from A. The demotion, as I said, takes a B object and gives you back an equivalent but stripped-down A object.

To me, this makes perfect sense, logically and terminologically. Demotion implies movement downward. Downward is toward the base class; that's why it's the "base" class. A is the base class here, so the demotion operation takes a B and gives you back an A.

Or, to make the issue clearer with an example, suppose that the two classes are Soldier and General. Which inherits from the other? Obviously, General inherits from Soldier, and not vice-versa. Soldiers support methods for marching, sleeping, and eating. Generals inherit all these methods, and support additional methods for ordering attacks and for convening courts martial. What does a demotion method do? It turns a General into a Soldier. It turns an object of the derived class into an object of the base class.

So how could people get this mixed up? I'm not sure, but I think one possibility is that they were thinking of subclasses and superclasses. The demotion method takes an object in the subclass and returns an object in the superclass. The terminology here is backwards. There are lots and lots of people, me included, who never use the terms "subclass" and "superclass", for precisely this reason. Even if my colleagues weren't thinking of these terms, they were probably thinking of the conventional class inheritance diagram, in which the base class, contrary to its name, is at the top of the diagram, with the derived classes hanging under it. The demotion operation, in this picture, pushes an object upwards, toward the base class.

The problem with "subclass" and "superclass" runs deeper. Mathematical terminology for sets is well-established and intuitive: A is a "subset" of B if set A is entirely contained in set B, if every element of A is an element of B. For example, the set of generals is a subset of the set of soldiers. The converse relation is that B is a superset of A: the set of soldiers is a superset of the set of generals. We expect from the names that a subset will be a smaller set than its superset, and so it is. There are fewer generals than soldiers.

Now let's consider programming language types. A type can be considered to be just a set of values. For example, the int type is the set of all integer values. The real type is the set of all real number values. Since every integer is also a real number, we might say that the int type is a subset of the real type. In fact, the word we usually use is that int is a subtype of real. But "subtype" means no more and no less than "subset".

Now let's consider the types General and Soldier of all objects of classes General and Soldier respectively. Clearly, General is a subtype of Soldier, since every General is a Soldier. This matches the OOP terminology also: General is a subclass of Soldier.

The confusing thing for data types, I think, is that there are two ways in which a type can be a "subtype" of another. A could be a smaller set than B, in which case we use the words "subtype" and "subclass", in accordance with mathematical convention. But A could also support a smaller set of operations than B; in OOP-world we would say that A is a base class and B a derived class. But then B is a subclass of A, which runs counter to the terminological implication that A is at the "base".

(It's tempting to add a long digression here about how computer scientists always draw their trees with the root at the top and the leaves at the bottom, and then talk about how many nodes are under the root of the tree. I will try to restrain myself.)

Anyway, this contravariance is what I really wanted to get at. If we adopt the rule of thumb that most values support few operations, and a few values support some additional operations, then the containment relation for functionality is contravariant to the containment relation for sets. Large sets, like Soldier, support few operations, such as eat and march; smaller sets support more operations, such as convene_court_martial.

The thing that struck me about this is that functions themselves are contravariant. Suppose A and B are types. Now consider the type A×B of pairs of values where the first component is an A and the second is a B. This pairing operation is covariant in A and B. By this I mean that if A' is a subtype of A, then A'×B is a subtype of A×B. Similarly, if B' is a subtype of B, then A×B' is a subtype of A×B.

Similarly, +, the type sum operation, is also covariant in both of its arguments.

But function types are different. Suppose A → B is the type of functions whose arguments have type A and whose return values are type B. Then A → B' is a subtype of A → B. Here's a simple example: Let A and B be real, and let A' and B' be int. Then every int → int---that is, every function from integers to integers---is also an example of a int → real; it can be considered as a function that takes an int and returns a real. That's because it is actually returning an int, and an int is a kind of real.

But A' → B is not a subtype of A → B. Just the opposite: A → B is a subtype of A' → B.

I remember standing on a train platform around 1992 and realizing this for the first time, that containment of function types was covariant in the second component but contravariant in the first component. I was quite surprised.

I suspect that the use of "covariant" and "contravariant" here suggests some connection with category theory, and with the notions of covariant and contravariant functors, but I don't know what the connection is.

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Addenda to recent articles 200604
Here are some notes on posts from the last month that I couldn't find better places for.

• Stan Yen points out that I missed an important aspect of the convenience of instant mac & cheese: it has a long shelf life, so it is possible to keep a couple of boxes on hand for when you want them, and then when you do want macaroni and cheese you don't have to go shopping for cheese and pasta. M. Yen has a good point. I completely overlooked this, because my eating habits are such that I nearly always have the ingredients for macaroni and cheese on hand.

  M. Yen also points out that some of the attraction of Kraft Macaroni and Cheese Dinner is its specific taste and texture. We all have occasional longings for the comfort foods of childhood, and for many people, me included, Kraft dinner is one of these. When you are trying to recreate the memory of a beloved food from years past, the quality of the ingredients is not the issue. I can sympathize with this: I would continue to eat Kraft dinner if it tasted the way I remember it having tasted twenty years ago. I still occasionally buy horrible processed American cheese slices not because it's a good deal, or because I like the cheese, but because I want to put it into grilled cheese sandwiches to eat with Campbell's condensed tomato soup on rainy days.

• Regarding the invention of the = sign, R. Koch sent me two papers by Florian Cajori, a famous historian of mathematics. One paper, Note on our sign of Equality, presented evidence that a certain Pompeo Bolognetti independently invented the sign, perhaps even before Robert Recorde did. The = sign appears in some notes that Bolognetti made, possibly before 1557, when Recorde's book The Whetstone of Witte was published, and certainly before 1568, when Bolognetti died. Cajori suggests that Bolognetti used the sign because the dash ----- was being used for both equality and subtraction, so perhaps Bolognetti chose to double the dash when he used it to denote equality. Cajori says "We have here the extraordinary spectacle of the same arbitrary sign having been chosen by independent workers guided in their selection by different considerations."

  Order A History of Mathematical Notations with kickback no kickback

  The other paper M. Koch sent is Mathematical Signs of Equality, and traces the many many symbols that have been used for equality, and the gradual universal adoption of Recorde's sign. Introduced in England in 1557, the Recorde sign was first widely adopted in England. Cajori: "In the seventeenth century Recorde's ===== gained complete ascendancy in England." But at that time, mathematicians in continental Europe were using a different sign , introduced by René Descartes. Cajori believes that the universal adoption of Recorde's = sign in Europe was due to its later use by Leibniz. Much of this material reappears in Volume I of Cajori's book A History of Mathematical Notations. Thank you, M. Koch.

  Ian Jones at the University of Warwick has a good summary of Cajori's discussion of this matter.
  

• Regarding Rayleigh scattering in the atmosphere, I asserted:

  The sun itself looks slightly redder ... this effect is quite pronounced ... when there are particles of soot in the air ... .

  Neil Kandalgaonkar wrote to inform me that there is a web page at the site of the National Oceanic and Atmospheric Administration that appears at first to dispute this. I said that I could not believe that the NOAA was actually disputing this. I was in San Diego in October 2003, and when I went outside at lunchtime, the sun was red. At the time, the whole county was on fire, and anyone who wants to persuade me that these two events were entirely unrelated will have an uphill battle.

  Order Light and Color in the Outdoors with kickback no kickback

  Fortunately, M. Kandalgaonkar and I determined that the NOAA web page not asserting any such silly thing as that smoke does not make the sun look red. Rather, it is actually asserting that smoke does not contribute to good sunsets. And M. Kandalgaonkar then referred me to an amazing book, M. G. Minnaert's Light and Color in the Outdoors.

  This book explains every usual and unusual phenomenon of light and color in the outdoors that you have ever observed, and dozens that you may have observed but didn't notice until they were pointed out. (Random example: "This explains why the smoke of a cigar or cigarette is blue when blown immediately into the air, but becomes white if it is been kept in the mouth first. The particles of smoke in the latter case are covered by a coat of water and become much larger.") I may report on this book in more detail in the future. In the meantime, Minnaert says that the redness of the sun when seen through smoke is due primarily to absorption of light, not to Rayleigh scattering:

  The absorption of carbon increases rapidly from the red to the violet of the spectrum; this characteristic is exemplified in the blood-red color of the sun when seen through the smoke of a house on fire.

• A couple of people have written to suggest that perhaps the one science question any high school graduate ought to be able to answer is "What is the scientific method?" Yes, I quite agree.

  Nathan G. Senthil has also pointed out Richard P. Feynman's suggestion on this topic. In one of the first few of his freshman physics lectures, Feynman said that if nearly all scientific knowledge were to be destroyed, and he were able to transmit only one piece of scientific information to future generations, it would be that matter is composed of atoms, because a tremendous amount of knowledge can be inferred from this one fact. So we might turn this around and suggest that every high school graduate should be able to give an account of the atomic theory of matter.

• I said that Pick's theorem Implies that every lattice polygon has an area that is an integer multiple of 1/2, "which I would not have thought was obvious." Dan Schmidt pointed out that it is in fact obvious. As I pointed out in the Pick's theorem article, every such polygon can be built up from right triangles whose short sides are vertical and horizontal; each such triangle is half of a rectangle, and rectangles have integer areas. Oops.

• Seth David Schoen brought to my attention the fascinating phenomenon of tetrachromacy. It is believed that some (or all) humans may have a color sensation apparatus that supports a four-dimensional color space, rather than the three-dimensional space that it is believed most humans have.

  As is usual with color perception, the complete story is very complicated and not entirely understood. In my brief research, I discovered references to at least three different sorts of tetrachromacy.

  1. In addition to three types of cone cells, humans also have rod cells in their retinas. The rod cells have a peak response to photons of about 500 nm wavelength, which is quite different from the peak responses of any of the cones. In the figure below, the dotted black line is the response of the rods; the colored lines are the responses of the three types of cones.

     

     So it's at least conceivable that the brain could make use of rod cell response to distinguish more colors than would be possible without it. Impediments to this are that rods are poorly represented on the fovea (the central part of the retina where the receptors are densest) and they have a slow response. Also, because of the way the higher neural layers are wired up, rod vision has poorer resolution than cone vision.

     I did not find any scientific papers that discussed rod tetrachromacy, but I didn't look very hard.

  2. The most common form of color blindness is deuteranomaly, in which the pigment in the "green" cones is "redder" than it should be. The result is that the subject has difficulty distinguishing green and red. (Also common is protanomaly, which is just the reverse: the "red" pigment is "greener" than it should be, with the same result. What follows holds for protanomaly as well as deuteranomaly.)

     Genes for the red and green cone pigments are all carried on the X chromosomes, never on the Y chromosomes. Men have only one X chromosome, and so have only one gene each for the red and green pigments. About 6-8% of all men carry an anomalous green pigment gene on their X chromosome instead of a normal one and suffer from deuteranomaly.

     Each of these men inherited his X chromosome from his mother, who must also therefore carry the anomalous gene on one of her two X chromosomes. The other X chromosome of such a woman typically carries the normal version of the gene. Since such a woman has genes for both the normal and the "redder" version of the green pigment, she might have both normal and anomalous cone cells. That is, she might have the normal "green" cones and also the "redder" version of the "green" cones. If so, she will have four different kinds of cones with four different color responses: the usual "red", "green" and "blue" cones, and the anomalous "green" cone, which we might call "yellow".

     The big paper on this seems to be A study of women heterozygous for colour deficiencies, by G. Jordan and J. D. Mollon, appeared in Vision Research, Volume 33, Issue 11, July 1993, Pages 1495-1508. I haven't finished reading it yet. Here's my summary of the abstract: They took 31 of women who were known to be carriers of the anomalous gene and had them perform color-matching tasks. Over a certain range of wavelengths, a tetrachromat who is trying to mix light of wavelengths a and b to get as close as possible to perceived color c should do it the same way every time, whereas a trichromat would see many different mixtures as equivalent. And Jordan and Mollon did in fact find a person who made the same color match every time.

     Another relevant paper with similar content is Richer color experience in observers with multiple photopigment opsin genes, by Kimberly A. Jameson, Susan M. Highnote, and Linda M. Wasserman, appeared in Psychonomic Bulletin & Review 2001, 8 (2), 244-261. Happily, this is available online for free.

     My own description is highly condensed. Ryan's Sutherland's article Aliens among us: Preliminary evidence of superhuman tetrachromats is clear and readable, much more so than my explanation above. Please do not be put off by the silly title; it is an excellent article.

  3. The website Processes in Biological Vision claims that the human eye normally contains a color receptor that responds to very short-wavelength violet and even ultraviolet light, but that previous studies have missed this because the lens tends to filter out such light and because indoor light sources tend not to produce it. The site discusses the color perception of persons who had their lenses removed. I have not yet evaluated these claims, and the web site has a strong stink of crackpotism, so beware.

• In discussing Hero's formula, I derived the formula (2a²b² + 2a²c² + 2b²c² - a⁴ - b⁴- c⁴)/16 for the square of the area of a triangle with sides of lengths a, b, and c, and then wondered how to get from that mess to Hero's formula itself, which is nice and simple: p(p-a)(p-b)(p-c), where p is half the perimeter.

  François Glineur wrote in to show me how easy it is. First, my earlier calculations had given me the simpler expression 16A² = 4a²b² - (a²+b²-c²)², which, as he says, is unfortunately not symmetric in a, b and c. We know that it must be expressible in a symmetric form somehow, because the triangle's area does not know or care which side we have decided to designate as side a.

  But the formula above is a difference of squares, so we can factor it to obtain (2ab + a² + b² - c²)(2ab + c² - a² - b²), and then simplify the a² ±2ab + b² parts to get ((a+b)² - c²)(c² - (a-b)²). But now each factor is itself a difference of squares and can be factored, obtaining (a+b+c)(a+b-c)(c+a-b)(c-a+b). From here to Hero's formula is just a little step. As M. Glineur says, there are no lucky guesses or complicated steps needed. Thank you, M. Glineur.

  M. Glineur ended his note by saying:

  In my opinion, an even "better" proof would not break the symmetry between a, b and c at all, but I don't have convincing one at hand.

  Gareth McCaughan wrote to me with just such a proof; I hope to present it sometime in the next few weeks. It is nicely symmetric, and its only defect is that it depends on trigonometry.

• Carl Witty pointed out that my equation of the risk of Russian roulette with the risk of driving an automobile was an oversimplification. For example, he said, someone playing Russian roulette, even at extremely favorable odds, appears to be courting suicide in a way that someone driving a car does not; a person with strong ethical or religious beliefs against suicide might then reject Russian roulette even if it is less risky than driving a car. I hadn't appreciated this before; thank you, M. Witty.

  I am reminded of the story of the philosopher Ramon Llull (1235–1315). Llull was beatified, but not canonized, and my recollection was that this was because of the circumstances of his death: he had a habit of going to visit the infidels to preach loudly and insistently about Christianity. Several narrow escapes did not break him of this habit, and he was eventually he was torn apart by an angry mob. Although it wasn't exactly suicide, it wasn't exactly not suicide either, and the Church was too uncomfortable with it to let him be canonized.

  Then again, Wikipedia says he died "at home in Palma", so perhaps it's all nonsense.

• Three people have written in to contest my assertion that I did not know anyone who had used a gas chromatograph. By which I mean that three people I know have asserted that they have used gas chromatographs.

  It also occurred to me that my cousin Alex Scheeline is a professor of chemistry at UIUC, and my wife's mother's younger brother's daughter's husband's older brother's wife's twin sister is Laurie J. Butler, a professor of physical chemistry at the University of Chicago. Both of these have surely used gas chromatographs, so they bring the total to five.

  So it was a pretty dumb thing to say.

• In yesterday's Google query roundup, I brought up the following search query, which terminated at my blog:

               a collection of 2 billion points is completely enclosed
               by a circle.  does there exist a straight line having
               exactly 1 billion of these points on each side
  

  This has the appearance of someone's homework problem that they plugged into Google verbatim. What struck me about it on rereading is that the thing about the circle is a tautology. The rest of the problem does not refer to the circle, and every collection of 2 billion points is completely enclosed by a circle, so the clause about the circle is entirely unnecessary. So what is it doing there?

  All of my speculations about this are uncharitable (and, of course, speculative), so I will suppress them. I did the query myself, and was not enlightened.

  If this query came from a high school student, as I imagine it did, then following question probably has at least as much educational value:

          Show that for any collection of 2 billion points, there is a
          circle that completely encloses them.
  

  It seems to me that to answer that question, you must get to the heart of what it means for something to be a mathematical proof. At a higher educational level, this theorem might well be dismissed as "obvious", or passed over momentarily on the way to something more interesting with the phrase "since X is a finite set, it is bounded." But for a high school student, it is worth careful consideration. I worry that the teacher who asked the question does not know that finite sets are bounded. Oops, one of my uncharitable speculations leaked out.

[Other articles in category /addenda] permanent link

Google query roundup
Once again I am going to write up the interesting Google queries that my blog has attracted this month.

Probably the one I found most interesting was:

           1 if n + 1 are put inside n boxes, then at least one box
             will contain more than one ball. prove this principle by
             induction.

Another mathematical question that came up was:

           1 a collection of 2 billion points is completely enclosed
             by a circle.  does there exist a straight line having
             exactly 1 billion of these points on each side

What might happen in the middle is that you might have one billion minus n points on the left, and then suddenly the line intersects more than n points at once, so that the number of points on the left jumps up by a whole bunch, skipping right past one billion, instead of ticking up by one at a time. So what we really need is to ensure that this never happens. But that's no trouble. Taking the points two at a time, we can find the slope of the line that will pass through the two points. There are at most 499,999,999,500,000,000 such slopes. If we pick a line that has a slope different from one of these, then no matter where we put it, it cannot possibly intersect more than one of the points. Then as we slide the line from one side to the other, as above, the count of the number of points on the left never goes up by more than 1 at a time, and we win.

Another math query that did not come from Google is:

        Why can't there be a Heron's formula for an arbitrary quadrilateral

All three quadrilaterals have exactly the same edge lengths, but their areas are different, so there couldn't possibly be a formula to tell you the area from just the edge lengths.

The following query is a little puzzling:

           1 undecidable problems not in np

It might be that the querent was looking for decidable problems that are not in NP. Here the answer is more interesting. There are many possibilities, but surprisingly few known examples. The problem of determining whether there is any string that is matched by a given regex is known to require exponential time, if regular expressions are extended with a {2} notation so that a{2} is synonymous with aa. Normally, if someone asks you if there is any string that matches a regex, you can answer just by presenting such a string, and then the querent can check the answer by running the regex engine and checking (in polynomial time) that the string you have provided does indeed match.

But for regexes with the {2} notation, the string you would provide might have to be gigantic, so gigantic that it could not be checked efficiently. This is because one can build a relatively short regex that matches only enormous strings: a{2}{2}{2}{2}{2}{2}{2}{2}{2}{2}{2}{2}{2}{2}{2}{2}{2}{2}{2}{2} is only 61 characters long, and it does indeed match one string, but the string it matches is 1,048,576 characters long.

Many problems involving finding the good moves in certain games are known to be decidable and believed to not be in NP, but it isn't known for sure.

Many problems that involve counting things are known to be decidable but are believed to not be in NP. For example, consider the NP-complete problem discussed here, called X3C. X3C is in NP. If Sesame Workshop presents you with a list of episodes and a list of approved topics for dividing the episodes into groups of 3, and you come up with a purported solution, Sesame Workshop can quickly check whether you did it right, whether each segment of Elmo's World is on exactly one video, and whether all the videos are on the approved list.

But consider the related problem in which Sesame Workshop comes to you with the same episodes and the same list of approved combinations, and asks, not for a distribution of episodes onto videotapes, but a count of the number of possible distributions. You might come back with an answer, say 23,487, but Sesame Workshop has no way to check that this is in fact the right number. Nobody has been able to think of a way that they might do this, anyhow.

Such a problem is clearly decidable: enumerate all possible distributions of episodes onto videos, check each one to see if it satisfies Sesame Workshop's criteria, and increment a counter if so. It is clearly at least as hard as the NP-complete problem of determining whether there is any legal distribution, because if you can count the number of legal distributions, there is a legal distribution if and only if the count of legal distributions is not 0. But it may well be outside of NP, because seems quite plausible that there is no quick way to verify a purported count of solutions, short of generating, checking, and recounting all possible distributions.

This is on my mind anyway, because this month I got email from two separate people both asking me for examples of problems that were outside of NP but still decidable, one on March 18:

I was hoping to get some information on a problem that is considered np-hard but not in NP (other than halting problem).

I was visiting your website in search of problems that are NP-Hard but not NP-Complete which are decision problems, but not the halting problem.

Here's one that was surprising:

           1 wife site:plover.com

           1 mathematical solution for eliminating debt

        [18/Jan/2006:09:10:46 -0500] eliminate debt using linear math
        [08/Feb/2006:13:48:13 -0500] linear math system eliminate debt
        [08/Feb/2006:13:53:28 -0500] linear math system eliminate debt
        [25/Feb/2006:15:12:01 -0500] how to get out of debt using linear math
        [23/Apr/2006:10:32:18 -0400] Mathematical solution for eliminating debt
        [23/Apr/2006:10:33:43 -0400] Mathematical solution for eliminating debt

           1 which 2 fraction did archimedes add together to write 3/4

There are several algorithms for writing any fraction as a sum of fractions of the form 1/n. The greedy algorithm suffices. Say you want to write 2/5. This is bigger than 1/3 and smaller than 1/2, so write 2/5 = 1/3 + x. x is now 1/15 and we are done. Had x had a numerator larger than 1, we would have repeated the process.

The greedy algorithm produces an Egyptian fraction representation of any number, but does not always do so conveniently. For example, consider 19/20. The greedy algorithm finds 19/20 = 1/2 + 1/3 + 1/9 + 1/180. But 19/20 = 1/2 + 1/4 + 1/5, which is much more convenient. So the problem of finding good representations for various numbers was of some interest, and the Ahmes papyrus, one of the very oldest mathematical manuscripts known, devotes a large amount of space to the representations of various numbers of the form 2/n.

           1 why does pi appear in both circle area and circumference?

           1 the only two things in our universe starting with m & e

Order The Cyberiad with kickback no kickback

"Never heard of it," said the machine.

"What? But it's only sodium. You know, the metal, the element..."

"Sodium starts with an s, and I work only in n."

"But in Latin it's natrium."

"Look, old boy," said the machine, "if I could do everything starting with n in every possible language, I'd be a Machine That Could Do Everything in the Whole Alphabet, since any item you care to mention undoubtedly starts with n in one foreign language or another. It's not that easy. I can't go beyond what you programmed. So no Sodium."

I think The Cyberiad is uproarious. It is easily the funniest book I have ever read. I laugh out out every time I read it.

The most amazing thing about it is that it was originally written in Polish. The translator, Michael Kandel, is a genius. I would not have dared to translate a Polish story about a machine that can make anything that begins with n. It is an obvious death trap. Eventually, the story is going to call for the machine to manufacture something like napad rabunkowy ("stickup") that begins with n in Polish but not in English. Perhaps the translator will get lucky and find a synonym that begins with n in English, but sooner or later his luck will run out.

I once met M. Kandel, and I asked him if it had been n in the original, or if it had been some other letter that was easy in Polish but impossible in English, like z, or even ł. No, he said it had indeed been n. He said that the only real difficulty he had was that Trurl asks the machine to make nauka ("science") and he had to settle for "nature".

(Incidentally, I put the word napad rabunkowy into the dictionary lookup at poltran.com and it told me angrily "PLEASE TYPE POLISH WORDS USING CAPITAL LETTERS ONLY!" Yeah, that's a good advertisement for your software.)

Order Consciousness Explained with kickback no kickback

By the way, narghiles are like hookahs, and nankeens are trousers made of a certain kind of cotton cloth, also called nankeen.

The most intriguing query I got was:

           1 consciousness torus photon core

My favorite result from this query is unfortunately offline, available only from the Google cache:

The photon is actually composed of two tetrahedrons that are joined together, as we see in figure 4.6, and they then pass together through a cube that is only big enough to measure one of them at a time.

Also, I got 26 queries from people looking for the Indiana Pacers' cheerleaders, and 31 queries from people looking for examples of NP-complete problems.

This is article #100 on my blog.

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Google query roundup
A highly incomplete version of this month's Google query roundup appeared on the blog on Saturday by mistake. It's fixed now, but if you are reading this through an aggregator, the aggregator may not give you the chance to see the complete version.

The complete article is available here.

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Abbreviations in medieval manuscripts
In an earlier article I discussed my surprise at finding "examples" and "alteration" abbreviated to "exãples" and "alteratiõ" in Robert Recorde's 1557 book The Whetstone of Witte. Then later I quoted Jonathan Hoefler, an expert in typographical matters:

Diacritical marks have been used to abbreviate printed words ever since Gutenberg, and early English printers adopted the same conventions that Gutenberg used for Latin (a trick he picked up from medieval scribes.)

1. I can't make head or tail of most of it, but
2. the fourth line begins mella locustis.

Eventually I did what I should have done in the first place and plugged mella locustis into Google. The result was quite conclusive. The words here are from a very famous hymn about John the Baptist, attributed to Paulus Diaconus (c. 720 -799). The hymn is in three parts, and this is the beginning of the second part. The words here are:

Antra deserti teneris sub annis
civium turmas fugiens, petisti,
n levi saltim maculare vitam
famine posses.

Praebuit hirtum tegimen camelus,
artubus sacris strofium bidentis,
cui latex haustum, sociata pastum
mella locustis.

Caeteri tantum cecinere vatum
corde praesago iubar adfuturum;
...

The amount of abbreviation here is just amazing. In the first line, deserti is abbreviated deseti, and the s and the e are all squashed together, sub is abbreviated sb, annus is abbreviated ãnis, civium is abbreviated civiû and is illegible anyway, because the letters all look alike, as in Russian cursive. (I have a similar problem with cui on the third line.)

On the second line, artubus is written artub3; Hoefler had already pointed out to me that the 3 was a common notation in 16th-century printing. On the third line, pastum is written pa'tû, where the wiggly mark between the a and the t denotes an elided s. Or perhaps the scribe left it out by mistake and then went back to squeeze it in later.

Probably the most amazing abbreviations in the whole thing are in the fourth line. (I wonder if perhaps the scribe realized he was running out of room and wanted to squeeze in as much as possible.) The word caeteri is abbreviated to ceti, tantum to tm, and praesago to p'sago. (Also note uatû, which is an abbreviation for vatum; I had been wondering for some time what Uatu had to do with it.)

There are a number of other typographical features of interest. The third word in the second line is apparently hirtum. The hi in the manuscript is written as a sort of a V-shape. The r in corde on the fourth line (and elsewhere) is a form that was once common, but is now obsolete.

This hymn, by the way, is the one that gives us the names do, re, mi, fa, so, la, si for the notes of the major scale. The first part of the hymn begins:

Ut queant laxis resonare fibris
mira gestorum famuli tuorum,
solve polluti labii reatum,
sancte Iohannes!

The thing about the locusts and wild honey reminds me of something else. I was once on a business trip to Ottawa and found that there was a French Bible in my hotel room. And I discovered that, although I cannot read French, I could read the Bible in French, because I already knew what it was going to say. So I lay in bed and read the French Bible and enjoyed the rather strange sensation of being able to pretend to myself to be able to read French.

Two points struck me at the time. One was that when I read "Dieu dit: Que la lumière soit!" ("God said, 'Let there be light'") my instant reaction was to laugh at how absurd it was to suggest that God had spoken French when He created the universe. It's like that Reader's Digest joke about the guy who thinks the Spanish-speaking folks are silly for talking to the squirrels in the park in Spanish, because squirrels don't speak Spanish. I didn't know I had that in me, but there I was, laughing at the silly idea of God saying "Que la lumière soit!" You know, I still find it silly.

The other memorable occurrence was a little less embarrassing. The part in Matthew (excuse me; "Matthieu") about John the Baptist eating locusts and wild honey was "Il se nourrissait de sauterelles et de miel sauvage." I was impressed at how tasty it sounded, in French. It is not hard to imagine going into an expensive restaurant and ordering sauterelles et de miel sauvage off the menu. I concluded that food always sounds better in French, at least to an anglophone like me.

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Yellow
Most of the academic part of high school is mercifully gone from my memory, dissolved together into a uniform blur of dullness. I wrote recently about one question I remember fondly from one final exam. I only remember a few specific exam questions, and probably that is the only one I remember because it was such a good question.

The one exam question that sticks most clearly in my mind was from my eighth-grade science class: What color do you see if you look at a yellow light through a monochromatic red filter?

I said it would look red, and was marked wrong. I argued my answer with the teacher, Mr. Goodman, but he would not give me credit. I puzzled over this for a long time, and eventually understood what had happened.

The word "yellow" is not a designation of physics alone; it refers to a certain experience, and is a perceptual phenomenon, not a purely physical one. It's possible to phrase the question to avoid this, but the question was not phrased in that way; it was expressly phrased in perceptual terms. A person who was achromatopsic might see a yellow light through a monochomatic red filter in a very unusual way.

To bring up the possibility of achromatopsia in the context of an exam is just nitpicking; I mention it only to point out that the question, as posed, must involve a consideration of human perception. And the objection I raised at the time is certainly not just nitpicking, because there are two entirely different physical phenomena that both go by the name of "yellow". The confusion of these two things occurs in the human retina.

The perception of color is a very complicated business, and I can't explain it in complete detail today. Partly this is because it isn't understood in complete detail, partly because I don't know everything that is understood, and partly it is because this article is about something else, and I want to try to come to the point eventually. So all my assertions about color perception in this article should be taken as metaphors for what is really happening. Although they give a correct general idea of a perceptual process that is something like what actually occurs, they are not accurate and are not intended to be accurate.

With that warning in place, I will now explain human color perception. Color is sensed by special "cone cells" in the retina. Different cone cells are sensitive to different frequencies of photons. Cone cells come in three types, which we will call "red", "green", and "blue", although all three of these are misnomers to one degree or another. The "red" cone cells are sensitive to red and yellow photons; the "green" cone cells to yellow and green photons. We will ignore the blue cones.

Photons with a wavelength of around 570 nanometers stimulate both the red and the green cone cells, and this stimulation is eventually perceived as the color yellow. But you can stimulate the cone cells the same way without using any light with a frequency around 570 nm. If you bombard the retina with photons of 650 nm, you stimulate only the red cones, and the light looks red; if you bombard the retina with photons of 520 nm, you stimulate only the green cones, and the light looks green. If you bombard the retina with both kinds of photons at once, both the red and green cones are stimulated, just as they were by the 570 nm photons. They have no way to know that they are being stimulated by two different groups of photons instead of by the same group, so the perception is the same.

This is why your computer monitor and your television can display the color yellow, despite having no source of yellow light. The monitor has little red phosphors and little green phosphors. When it activates both of them at once, the red and green photons stream out and get into your eye, where they stimulate the red and green cones, and you perceive the color yellow.

But from a purely physical point of view, this "yellow" phenomenon is not at all like the one that occurs when you look at a lemon or at a sodium vapor street light. The photons coming off the lemon are all of about the same frequency, around 570 nm. The photons coming off the computer monitor picture of the lemon are two different frequencies, some around 520 nm, and some around 650 nm. Your eye is not equipped to tell the difference.

Now, suppose you are looking at "yellow light" through a monochromatic red filter that passes only 650 nm photons. What do you see?

Well, if it was monochomatic yellow light, say from a lemon, then you see nothing, because the filter stops the 570 nm photons. This was Mr. Goodman's exam answer.

But if it was the yellow light that comes from a television picture of a lemon, then it contains some 520 nm photons, which are stopped by the filter, and some 650 nm photons, which are not stopped. You would see a red lemon. This was my exam answer.

The perception of mixed red and green light as yellow was part of the curriculum that year---we had had a classroom demonstration of it---and so it was fair game for the exam. Mr. Goodman's exam question, as posed, was genuinely ambiguous. There are two physical phenomena that are both described as "yellow", and he could have meant either one.

This confusion of two distinct physical phenomena by the retina is something we take for granted, but it is by no means inevitable. I often imagine our meeting with the aliens, and their surprise when they learn that all of us, every human on earth, are color-blind. They will find this out quickly, as soon as they see a television or a computer monitor. "Your monitor is broken," Zxaxgr will say.

"It looks all right to me," replies Flash Gordon.

"Is there something wrong with your eyes? The color adjustment for yellow is completely off. It is coming out as redgreen instead of as yellow."

"I see nothing wrong with the color adjustment for yellow," replies Flash.

"There must be something wrong with your eyes."

And yes, Zxaxgr is right. There is something wrong with our eyes. There is an intrinsic design flaw in our computer monitors, none of which can display yellow, and we don't care, because none of us can tell the difference between redgreen and yellow.

To empathize with Zxaxgr's puzzlement, imagine how strange it would be to learn that the alien televisions cannot display green; they display purple instead: purple trees, purple broccoli, purple frogs, purple flags of Saudi Arabia. And the aliens have never noticed the problem. You want to ask them about it, but your English-to-Alien dictionary doesn't have an entry for "purple". When you ask them about it, they say you're nuts, everything looks green, as it should. You learn that they have no word for purple; they just call it green, and eventually you find out that it's because they can't tell the difference between purple and green.

Whatever you're thinking now, that's what Zxaxgr is going to think.

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The One Theory to Explain Everything
One of Matt Groening's Life in Hell comics had a list of the nine teachers to beware of. The one I remember is the teacher who has "one theory to explain everything". The cartoon depicted this teacher with wild, staring eyes, and a speech balloon that said "The nation that controls magnesium controls the world!"

(This theory, of course, is idiotic. They key element, as I mentioned on Saturday, is radioactive potassium. What good is a crazy theory that doesn't involve nuclear energy?)

The big problem with this teacher is that he will expect you to discourse on the One Theory on the final exam. You'll get a final exam question like "explain the significance of magnesium in the 1993 Oslo accords" or "how would the couse of World War II been changed if Chile had had access to sufficient supplies of high-grade magnesium ore" or just "Explain how magnesium the most important factor in determining the course of history." Or it's phrased the other way round: "what is the most important factor in determining the course of history?" and then if you happened to miss the class in which the professor had his insane rant about magnesium, you're doomed.

But the joke is not as poignant for me as it is for some people, because I've seen its good side. When I was in ninth grade, I took a music history class. When the final exam arrived, the first question was:

What is the single most influential development in the history of music?

I had a vague recollection that Mr. Rosenberg had said something about his theory of the single most important development in the history of music, but it had been way back at the beginning of the semester, and I no longer remembered what he had said. But my exam-taking style has never been to try to remember what the teacher said, so I tried to figure it out.

Trying to figure it out is usually a pretty bad strategy for answering questions on high-school exams, because the exams are designed for regurgitation and parroting of what the teacher said, not for figuring things out. And the question looked up front like one of those magnesium questions, where the answer is totally unguessable if you don't subscribe to the insane theory, where even if you come up with a plausible answer, you lose, unless it happens to be the one answer the teacher was thinking of.

To be fair, the question must admit only one reasonable answer. And that is true of very few questions of this type. But I think it is true of this one. It isn't an insane theory, and I did figure it out, which I think reflects a lot of credit on Mr. Rosenberg.

The single most influential development in the history of music is the invention of recording, or perhaps radio. Before these things, music was a participant sport, and afterwards, it was a product, something that could be passively consumed. When I thought of recording, I said "aha", and wrote it down in big letters, adding radio as an afterthought. I imagine that Mr. Rosenberg would have accepted either one alone.

Isn't it nice when things turn out to be better than they first appear? Thanks, Mr. Rosenberg.

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Diacritics and horseheads
In my recent article about Robert Recorde's invention of the = sign, I pointed out that Recorde's 1557 book The Whetstone of Witte contained a remarkable typographic feature: words like "examples" and "alteration" are rendered as "exãples" and "aleratiõ".

I wrote to Jonathan Hoefler to ask about this. Jonathan Hoefler is one of the principals of the typography firm Hoefler & Frere-Jones, and his mind is a vast storehouse of typographical history and arcana. I was sure M. Hoefler would know about the tildes, and would have something interesting to say about them, and I was not disappointed:

Diacritical marks have been used to abbreviate printed words ever since Gutenberg, and early English printers adopted the same conventions that Gutenberg used for Latin (a trick he picked up from medieval scribes.) As you say, tildes and macrons (and circles and odder things still) were used to mark the elision of letters or entire word parts: the "Rx" ligature that we know from prescriptions (Lat. 'recipe') was also used as shorthand for the "-rum" Latin ending, among other things. The French circumflex is a holdover from the same tradition, as it once the absence of a succeeding 's' ("hôpital" for "hospital", etc.) All of these were compositors' tricks to help in the justification of an entire paragraph, something that was considerably easier in the days before standard spelling and orthography!

I should mention, in case it isn't clear, that justification of paragraphs is not merely a cosmetic feature. If you are a printer in 1577, you are laying out metal types into a square frame, and if the frame isn't completely filled, the types will fall out when you turn it over. In particular, you must make each line of each paragraph fully extend from left to right, or it will be unprintable. The Renaissance printers must have to justify the text somehow. One way to do this is by inserting blank spaces of suitable lengths between the words of each line; I asked M. Hoefler why the Renaissance printers didn't just use blank space, and he replied:

They did that as well, but I think the general principle (which endures) is that wordspacing really isn't as flexible as you'd hope -- "rivers" are the effect of adjacent lines being overjustified, and they really interrupt reading. Even with today's very sophisticated H&J [Hyphenation and Justification] algorithms -- some of which can even scale the actual dimensions of letterforms in order to improve copyfit -- the chief ingredient in good H&J controlling the number of letters per line. Contemporary newspapers do this through aggressive hyphenation; their forbears did it through colorful spelling. (Although any headline with the word "Prez" suggests that this tradition lives on.)

Order Higher-Order Perl with kickback no kickback

I think Marshall McLuhan said something about the new media cannibalizing the old, and although I'm not sure what he meant (if he did say that) I don't think it matters much, because the phrase so perfectly encapsulates the way new information technologies tend to adopt the obsolete forms of the technologies they replace. I've been collecting examples of this for a few years. In the early days of the web, there was a web dictionary which would lay out the pages just like a real dictionary, with an unreadably tiny font, page breaks in inconvenient places, and "next page" and "previous page" buttons at the bottom. The tiny font was bad enough, but the "next page" buttons just killed me. I wanted to redesign the application with another button that you could press if you wanted to simulate what happens when you read the dictionary in the bathtub and drop it in the water by mistake.

I call these phenomena "horseheads", after the false horse heads that were mounted on the hoods of old automobiles, which still survive as in vestigial form as hood ornaments. My favorite horsehead is a Citibank ATM design from around 1987 or so. The old ATMs, which the new design was replacing, had green phosphor display, about 20×40 characters, four menu buttons down the side, and a telephone-style keypad with ten digits and # and * signs. The new ATM had no buttons. Instead, it had a color touch-sensitive screen that was used to display a touch-sensitive picture of four menu buttons down the side, and, when appropriate, a telephone-style keypad with ten digits and # and * signs.

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TeX and the long S
It just occurs to me, reading today's article, that the final sentence is one of the strangest I've written in quite a while. It says:

stock TeX does not have any way to make a long medial s.

Strange or not, the substance of my remark is correct, since standard TeX's fonts do not provide a long s in a size suitable for use in running text in place of a regular s.

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On baroque long S
Jokes about the long medial 's' are easy to make. Stan Freberg's album Stan Freberg Presents: The United States of America, Volume I: The Early Years has a scene in which John Adams or Benjamin Franklin or one of those guys is reading Thomas Jefferson's draft of the Declaration of Independence: "'Life, liberty, and the purfuit of happinefs'? Tom, all your s's look like f's!"

A story by Frances Warfield, appropriately titled "Fpafm", gets probably as much juice out of the joke as there is to be got. I believe the copyright has expired, so here it is, in its entirety:

FPAFM

by Frances Warfield

I ordered ham and eggs, as I always do on the diner, and then, as I always do, looked around for pamphlets. There was one handy, "Echoes of Colonial Days," it was called, "being a little fouvenir iffued from time to time, for the benefit of the guefts of The Baltimore & Ohio Railroad Company as a reminder of the pleafant moments fpent..." Involuntarily, my lips began to move. I reached for a pencil. But the man across from me already had his pencil out. He had written:

"Oh, fay can you fee?"

I said, "Fing Fomething Fimple."

"Filly, ifn't it?" he said, and kept on writing.

I wrote: "Fing a Fong of Fixpence."

"Oh, ftop the fongs," he said, "Too eafy." He wrote: "The Courtfhip of Miles Fandifh," "I fee a fquirrel," "I undereftimate ftatefmanfhip," "My fifter feems fuperfenfitive," and, seeing that I did not appreciate the last one, which he evidently thought very fine, he wrote: "Forry to fee you fo ftupid."

I ate my lunch grouchily. How could I help it if he was in practice and I was not? He had probably taken this train before.

"Pafs the falt," I said.

"Pleafe pafs the falt," he triumphed.

I paid no attention. "Waiter!" I said. The waiter did not budge.

"You muft fpeak the language," said the man opposite me. "Fay, Fteward!"

The waiter jumped to attention. "Fir?" he said.

"Pleafe fill the faltcellar."

"The faltcellar fhall be replenifhed inftantly," replied the waiter, with a superior gleam in his eyes.

I smiled and my companion unbent a little. "Let's try for hard ones," he invited.

"Farcafm," he said.

"Fubftance."

"Fubfiftence," he scored.

"Fcythe."

"S's inside now," he ruled.

Perfuafive," I said instantly.

"Lanfguifh."

"Bafilifk."

"Quiefcent."

"Nonfenfe," I finished. "Fon of a fpeckled fea monfter."

"Ftep-fon of a poifonous fnake!" he cried.

"You don't fay fo!" I retorted.

"I do fay fo," he replied, getting up and leaving the diner.

"Fool!" I called after him, fniffiling.

Reading Baroque scientific papers, you see a lot of long-medial-s. Opening to a random page of the Philosophical Experiments and Observations of Robert Hooke, for example, we have:

The ſecond Experiment, was made, to ſhew a Way, how to find the true and comparative Expanſion of any metal, when melted, and ſo to compare it both with the Expanſion of the ſame metal, when ſolid, and likewiſe with the Expanſion of any other, either fluid or ſolid Body.

What hasn't happened, however: it hasn't become completely transparent. The long s really does look a lot like an f, so much so that I can find it confusing when the context doesn't help me out. The fact that these books are always facsimiles and that the originals were printed on coarse paper and the ink has smudged, does not make it any easier to tell when one is looking at an s and when at an f. So far, the most difficult instance I have encountered involved a reference to "the Learned Dr. Voſſius". Or was it Voffius? Or Vofſius? Or was it Voſfius? Well, I found out later it was indeed Vossius; this is Dr. Gerhard Johann Voss (1577-1649), Latinized to "Vossius". But I was only able to be sure because I encountered the name somewhere else with the short s's.

This typographic detail raises a question of scholarly ethics that I don't know how to answer. In an earlier article, I needed to show how 17th-century writers referred to dates early in the year, which in common nomenclature occurred during one year, but which legally were part of the preceding year. Simply quoting one of these writers wasn't enough, because the date was disambiguated typographically, with the digit for the legal year directly above the digit for the conventional year. So I programmed TeX to demonstrate the typography:

1. Most permissible is to replace the original 17th-century font with a modern one.

2. Slightly less permissible would be to reduce the heavy 17th-century usage of italic face, in Royal Society for example, replacing it with roman typefaces.

3. Slightly less permissible still would be to replace the 17th-century capitalization conventions with 20th-century conventions. For example, in C20 we would not capitalize "Remark".

4. Then can I replace obsolete 17th-century contractions such as "consider'd" with 20th-century equivalents such as "considered"? If that is acceptable, then what about "'tis"? Can I replace "3dly" with "thirdly"?

5. Can I replace obsolete Baroque spellings such as "plaister", "fatt", and "it self" with "plaster", "fat", and "itself"?

6. Can I replace obsolete Baroquisms such as "strow'd" in "strow'd on Ice" with "strewn", or "stopple" with "stopper"?

7. At the bottom of the list, I could just rewrite the whole thing in a modern style and pass it off as what Derham actually wrote.

[ Addendum 20060405 ]

[Other articles in category /lang] permanent link

Google query roundup
Once again I am going to write up the interesting Google queries that my blog has attracted this month. The blog is now about eleven weeks old and has had a meteoric rise. The theme of this month's Google query roundup will be the idea of authority on the web, and the attribution of authority by links.

Of the 32 million blogs that Technorati.com knows about, they consider The Universe of Discourse to be the 13th most-authoritative blog on the subject of mathematics. Okay, I can almost buy that, because I do know a fair amount about mathematics, a lot of people know that about me, and I can probably write more clearly and convincingly than most mathematics experts. But their same ranking process says that The Universe of Discourse is tied for 16th place as one of the most-authoritative blogs on the subject of physics. Considering that I know next to nothing about physics, this is rather sad. If I wrote an article explaining how spacetime was curved like an artichoke, and a thousand people linked to it because they enjoyed the spectacle of someone making a fool of himself in public, my blog would move up the list to fourth place.

Google rankings are similarly weird. My whole web site is considered authoritative in general, because of various articles I've written and projects I've hosted over the years. The way Google works is that each page has an absolute pagerank, and then you get the pages with greatest pagerank that contain your search terms. So if my relatively high-ranking pages happen to contain your search terms, that's what you get, even if that doesn't really make sense.

For example, a Google search for "baroque writing" turns up my blog post about it as hit #5, because my site has high pagerank, and the sites that are really about baroque writing have low pagerank. But the high pagerank of my pages is primarily because I also host a long-established and popular website about Perl, and lots of people have linked to it over the years. So Google recommends my thoughts about Baroque writing because I'm an authority on the Perl programming language. This is not obviously a good reason to recommend a page about Baroque writing.

Of course one can argue that it's unreasonable to expect Google to judge whether I know what I'm talking about or not. But there is a way that they could do it, at least in principle, that would make more sense. Instead of computing pageranks globally, and saying "well, Dominus's pages are generally well thought-of, so we'll recommend those pages whenever they might be relevant to the query", one could compute pageranks per subject. So suppose you first considered only those pages that mention Baroque writing, and discard all the others. Then you do the pagerank calculation to see which of these pages link to which others. You would find a much better pagerank for searches about Baroque writing. My page would have low rank, because it is linked to by few pages about Baroque writing, rather than the high rank it does have because it is linked to by many pages about Perl.

Strange authority

           1 ashley indiana pacemate
           4 "lindsay" indiana pacemate
           1 pacemate lindsay

Not-so-strange authority

Sometimes there are weird side effects. My authority on the puzzle about the banana and the rope and the monkey's mother also pulls in people looking for stuff that sounds similar, but probably isn't:

           1 "monkey rope" joke
           1 monkey & banana game source code
           1 monkeys holding up the moon
           1 steps on how to draw a monkey holding a banana
           1 how to draw a banana
           1 picture of a monkey holding a banana

Other matters

           2 smallest positive value with no leading zeros such that
             rotating it is the same as multiplying it by p/q + puzzle 

Oh, you wanted the smallest value with at least two digits? That's obviously 10.

Oh, you wanted the resulting number to have no leading zeroes either? Then it's obviously 11.

Oh, you wanted the resulting number to be different from the original one? Then it's obviously 12, because when you rotate it, you get 21, which the same as multiplying it by 21/12.

In fact, for any number, rotating it has the same effect as multiplying it by p/q for some p and q. Maybe the author wanted p and q specified in advance.

Islamic history and Arabic etymology

	   1 qamara
	  11 qamara
	   1 qamara arabic
	   2 qamara camera
	   3 qamara camera obscura
	   2 camera obscura qamara
	   1 ibn haitham qamara

There might have been some other queries of a similar nature. For example, this one probably is:

	   1 arabic saqq

	   1 saqq

	   3 etymology cheque
	   1 cheque + etymology

Vallely may have gotten his misinformation from the execrable 1001 Inventions web site, which is a mountain of misinformation on this topic. I expect to write at more length about this in the future. In the meantime, here is my summary of the web site:

Did you know that the belt was invented by Muslim tailor al-Qurashi in the year 1274, and was not widely adopted in Europe until the 14th century? Before that, Europeans had to walk around holding up their trousers with their hands, and had nothing from which to hang their wallets! The word 'belt' is from the Arabic 'balq', which means 'look down!'

[Other articles in category /google-roundup] permanent link

Addenda to recent articles 200603
Here are some notes on posts from the last month that I couldn't find better places for.

• In my close attention to the most embarrassing moments of the Indiana Pacemates, I completely missed the fact that Pacemate Nikki, the only one who admitted to farting in public, also reports that she was born with twelve fingers.

• Regarding the manufacture of spherical objects, I omitted several kinds of spherical objects that are not manufactured in any of the ways I discussed.
  • One is the gumball. It's turned out to be surprisingly difficult to get definitive information about how gumballs are manufactured. My present understanding is that the gum is first extruded in a sort of hollow pipe shape, and then clipped off into balls with a pinching device something like the Civil-War-era bullet mold pictured at right. The gumballs are then sprayed with a hard, shiny coating, which tends to even out any irregularities.

    [ Addendum 20070307: the bullet mold at right is probably not used in the way I said. See this addendum for more details. ]

  • Glass marbles are made with several processes. One of the most interesting involves a device invented by Martin Frederick Christensen. (US Patent #802,495, "Machine For Making Spherical Bodies Or Balls".) The device has two wheels, each with a deep groove around the rim. The grooves have a semicircular cross-section. The wheels rotate in opposite directions on parallel axes, and are aligned so that the space between the two grooves is exactly circular.

    The marble is initially a slug of hot glass cut from the end of a long rod. The slug sits in the two grooves and is rolled into a spherical shape by the rotating wheels. For more details, see the Akron Marbles web site.

    Fiberglas is spun from a big vat of melted glass; to promote melting, the glass starts out in the form of marbles. ("Marbles" appears to be the correct jargon term.) I have not been able to find out how they make the marbles to begin with. I found patents for the manufacture of Fiberglas from the marbles, but nothing about how the marbles themselves are made. Presumably they are not made with an apparatus as sophisticated as Christensen's, since it is not important that the marbles be exactly spherical. Wikipedia hints at "rollers".

  • The thingies pictured to the right are another kind of nearly-spherical object I forgot about when I wrote the original article. They are pellets of taconite ore. Back in the 1950s, the supply of high-quality iron ore started to run out. Taconite contains about 30% iron, but the metal is in the form of tiny particles dispersed throughout very hard inert rock. To extract the iron, you first crush the taconite to powder, and then magnetically separate the iron dust from the rock dust.

    But now you have a problem. Iron dust is tremendously inconvenient to handle. The slightest breeze spreads it all over the place. It sticks to things, it blows away. It can't be dumped into the smelting furnace, because it will blow right back out. And iron-refining processes were not equipped for pure iron anyway; they were developed for high-grade ore, which contains about 65% iron.

    The solution is to take the iron powder and mix it with some water, then roll it in a drum with wet clay. The iron powder and clay accumulate into pellets about a half-inch in diameter, and the pellets are dried. Pellets are easy to transport and to store. You can dump them into an open rail car, and most of them will still be in the rail car when it arrives at the refinery. (Some of them fall out. If you visit freight rail tracks, you'll find the pellets. I first learned about taconite because I found the pellets on the ground underneath the Conrail freight tracks at 32nd and Chestnut Streets in Philadelphia. Then I wondered for years what they were until one day I happened to run across a picture of them in a book I was reading.)

    When the pellets arrive at the smelter, you can dump them in. The pellets have around 65% iron content, which is just what the smelter was designed for.

• Regarding my assertion that there is no way to include a menu of recent posts in the "head" part of the Blosxom output, I said:

  With stock Blosxom, however, this is impossible. The first problem you encounter is that there is no stories_done callback.

  Todd Larason pointed out that this is mistaken, because (as I mentioned in the article) the foot template is called once, just after all the stories are processed, and that is just what I was asking for.

  My first reaction was "Duh."

  My second reaction was to protest that it had never occurred to me to use foot, because that is not what it is for. It is for assembling the footer!

  There are two things wrong with this protest. First, it isn't a true statement of history. It never occurred to me to use foot, true, but not for the reason I wanted to claim. The real reason is that I thought of a different solution first, implemented it, and stopped thinking about it. If anything, this is a credit to Blosxom, because it shows that some problems in Blosxom can be solved in multiple ways. This speaks well to the simplicity and openness of Blosxom's architecture.

  The other thing wrong with this protest is that it assumes that that is not what foot is for. For all I know, when Blosxom's author was writing Blosxom, he considered adding a stories_done callback, and, after a moment of reflection, concluded that if someone ever wanted that, they could just use foot instead. This would be entirely consistent with the rest of Blosxom's design.

  M. Larason also pointed out that even though the head template (where I wanted the menu to go) is filled out and appended to the output before the article titles are gathered, it is not too late to change it. Any plugin can get last licks on the output by modifying the global $blosxom::output variable at the last minute. So (for example) I could have put PUT THE MENU HERE into the head template, and then had my plugin do:

          $blosxom::output =~ s/PUT THE MENU HERE/$completed_menu/g;
  

  to get the menu into the output, without hacking on the base code.

  Thank you, M. Larason.

• My article on the 20 most important tools attracted a lot of attention.
  • I briefly considered and rejected the spinning wheel, on the theory that people have spun plenty of thread with nothing but their bare fingers and a stick to wind it around.

    Brad Murray and I had a long conversation about this, in which he described his experience using and watching others use several kinds of spinning tools, including the spinning wheel, charkha (an Indian spining wheel), drop spindle, and bare fingers, and said "I can't imagine making a whole garment with my output sans tools." It eventually dawned on me that I did not know what a drop spindle was.

    A drop spindle is a device for making yarn or thread. The basic process of making yarn or thread is this: you take some kind of natural fiber, such as wool, cotton, or flax fiber, which you have combed out so that the individual fibers are more or less going the same direction. Then you twist some of the fibers into a thread. So you have this big tangled mass of fiber with a twisted thread sticking out of it. You tug on the thread, pulling it out gently, while still twisting, and more fibers start to come away from the mass and get twisted into the thread. You keep tugging and twisting and eventually all the fiber is twisted into a thread. "Spinning" is this tugging-twisting process that turns the mass of combed fibers into yarn.

    You can do this entirely by hand, but it's slow. The drop spindle makes it a lot faster. A drop spindle is a stick with a hook stuck into one end and a flywheel (the "whorl") near the other end. You hang the spindle by the hook from the unspun fiber and spin it.

    As the spindle revolves, the hook twists the wool into a thread. The spindle is hanging unsupported from the fiber mass, so gravity tends to tug more fibers out of the mass, and you help this along with your fingers. The spindle continues to revolve at a more-or-less constant rate because of the flywheel, producing a thread of more-or-less constant twist. If you feed the growing thread uniformly, you get a thread of uniform thickness.

    When you have enough thread (or when the spindle gets too close to the floor) you unhook the thread temporarily, wind the spun thread onto the shaft of the spindle, rehook it, and continue spinning.

    A spinning wheel is an elaboration of this basic device. The flywheel is separate from the spindle itself, and drives it via a belt arrangement. (The big wheel you probably picture in your mind when you think of a spinning wheel is the flywheel.) The flywheel keeps the spindle revolving at a uniform rate. The spinning wheel also has a widget to keep the tension constant in the yarn. With the wheel, you can spin a more uniform thread than with a drop spindle and you can spin it faster.

    I tried hard to write a coherent explanation of spinning, and although spinning is very simple it's awfully hard to describe for some reason. I read several descriptions on the web that all left me scratching my head; what finally cleared it up for me was the videos of drop spinning at the superb The Joy of Handspinning web site. If my description left you scratching your head, check out the videos; the "spinning" video will make it perfectly clear.

    The drop spindle now seems to me like a good contender for one of the twenty most-important tools. My omission of it wasn't an oversight, but just plain old ignorance. I thought that the spinning wheel was an incremental improvement on simpler tools, but I misunderstood what the simpler tools were.

    The charkha, by the way, is an Indian configuration of the spinning wheel; "charkha" is just Hindi for "wheel". There are several varieties of the charkha, one of which is the box charkha, a horizontal spinning wheel in a box. The picture to the right depicts Gandhi with a box charkha.

    
    

  • Doug Orleans asked whether I had considered the key. I hadn't, but I think it's exempt from consideration for the same kinds of reasons as those I cited for the remote control: any particular key serves not a general door-opening function but a specific one. Not that keys aren't important, but rather, they seem to be outside the scope of this particular discussion.

  • Mike Krell asked why I would list the radio on my third-tier list and omit the computer. Obviously, the question is not one of usefulness or of importance, but of whether the "computer" is a "tool" in the original sense of the list, or whether it is disqualified by reason of being too general, too abstract, too complex, or something like that. I made several arguments, most of which I think he refuted.

    My initial answer was that computers are disqualified for the same reason that remote controls are: people do carry calculators, cell phones, personal organizers, handheld GPS devices, and (if they work for FedEx) package tracking gizmos. All of these are tools that incorporate computers, but they don't really seem to be merely different forms of the same thing. Each one is a tool, but "computer" is not, similar to the way that the microscope and the telescope are different tools, and not merely variations of "the lens".

    Perhaps so, but then I had a fit of insanity and asserted that people do not walk around toting general-purpose computers in case they happen upon some data that needs processing. M. Krell very gently pointed out that yes, they do exactly that: "I see them every time I fly on an airplane, breaking them out to process some data for work (or play) as soon as the flight attendant says it's OK." Whoops. Quite so.

    M. Krell suggested that by restricting the definition of "tool" to devices that perform a single specific function or a few such functions, I have circumscribed the definition of "tool" in an arbitrary way that "does not accurately reflect the realities of our current Information Age". Okay.

  • Jon Evans said "Everyone always forgets the hoe." I did indeed forget the hoe. Not quite a knife, not quite a shovel...

• Regarding the start of the year prior to 1751, when it was moved from 25 March to 1 January. You may recall that I had a series of articles (1 2 3 4) in which I was concerned that Benjamin Franklin might be only 299 years old, not 300, because of confusion about just what year was meant in discussions of the date "6 January 1706". (The legal year 1705 ran from 25 March 1705 through 24 March 1706.) This ambiguity was confusing at the time as well. It makes little difference to my life whether Franklin is 300 years old or only 299, but if you were a person living in 1706, you might like to be sure, when someone said they would pay you fifty shillings on 6 January 1706, when the payment would be.

  It seems that baroque authors had a convention to disambiguate such dates. Here's a quote from William Derham's 1726 introduction to Robert Hooke's notes on the invention of the barometer:

  
  

  And similarly, from Richard Waller's summary of The Life of Dr. Robert Hooke:

  

• * In an earlier post, I referred to "Ramanujan's approximation to π":

  

  But this isn't the formula I was thinking of; I showed the wrong formula! It's obviously not an approximation to π. The approximation formula I was thinking of is no less astonishing:

  

• Finally, in my article on the 20 most important tools, I said that I didn't think I knew anyone who had used a gas chromatograph; Geoffrey Young pointed out that he had used one.

[Other articles in category /addenda] permanent link

Archimedes and the square root of 3
In my recent discussion of why π might be about 3, I mentioned in passing that Archimedes, calculating the approximate value of π used 265/153 as a rational approximation to √3. The sudden appearance of the fraction 265/153 is likely to make almost anyone say "huh"? Certainly it made me say that. And even Dr. Chuck Lindsey, who wrote up the detailed explanation of Archimedes' work from which I learned about the 265/153 in the first place, says:

Throughout this proof, Archimedes uses several rational approximations to various square roots. Nowhere does he say how he got those approximations—they are simply stated without any explanation—so how he came up with some of these is anybody's guess.

Suppose you are a mathematician and you do not have a pocket calculator. You are sure to need some rational approximations to √3 somewhere along the line. So you should invest some time and effort into calculating some that you can store in the cupboard for when you need them. How can you do that?

You want to find pairs of integers a and b with a/b ≈ √3. Or, equivalently, you want a and b with a² ≈ 3b². But such pairs are easy to find: Simply make a list of perfect squares 1 4 9 16 25 36 49..., and their triples 3 12 27 48 75 108 147..., and look for numbers in one list that are close to numbers in the other list. 2² is close to 3·1², so √3 ≈ 2/1. 7² is close to 3·4², so √3 ≈ 7/4. 19² is close to 3·11², so √3 ≈ 19/11. 97² is close to 3·56², so √3 ≈ 97/56.

Even without the benefits of Hindu-Arabic numerals, this is not a very difficult or time-consuming calculation. You can carry out the tabulation to a couple of hundred entries in a few hours, and if you do you will find that 265² = 70225, and 3·153² is 70227, so that √3 ≈ 265/153.

Once you understand this, it's clear why Archimedes did not explain himself. By saying that √3 was approximately 265/153, had had exhausted the topic. By saying so, you are asserting no more and no less than that 3·153² ≈ 265²; if the reader is puzzled, all they have to do is spend a minute carrying out the multiplication to see that you are right. The only interesting point that remains is how you found those two integers in the first place, but that's not part of Archimedes' topic, and it's pretty obvious anyway.

[ Addendum 20090122: Dr. Lindsey was far from the only person to have been puzzled by this. More here. ]

In my article about the peculiarity of π, I briefly mentioned continued fractions, saying that if you truncate the continued fraction representation of a number, you get a rational number that is, in a certain sense, one of the best possible rational approximations to the original number. I'll eventually explain this in detail; in the meantime, I just want to point out that 265/153 is one of these best-possible approximations; the mathematics jargon is that 265/153 is one of the "convergents" of √3.

The approximation of √n by rationals leads one naturally to the so-called "Pell's equation", which asks for integer solutions to ax² - by² = ±1; these turn out to be closely related to the convergents of √(a/b). So even if you know nothing about continued fractions or convergents, you can find good approximations to surds.

Here's a method that I learned long ago from Patrick X. Gallagher of Columbia University. For concreteness, let's suppose we want an approximation to √3. We start by finding a solution of Pell's equation. As noted above, we can do this just by tabulating the squares. Deeper theory (involving the continued fractions again) guarantees that there is a solution. Pick one; let's say we have settled on 7 and 4, for which 7² ≈ 3·4².

Then write √3 = &radic(48/16) = √(49/16·48/49) = 7/4·&radic(48/49). 48/49 is close to 1, and basic algebra tells us that &radic(1-&epsilon) &asymp 1 - &epsilon/2 when &epsilon is small. So √3 &asymp 7/4 · (1 - 1/98). 7/4 is 1.75, but since we are multiplying by (1 - 1/98), the true approximation is about 1% less than this, or 1.7325. Which is very close—off by only about one part in 4000. Considering the very small amount of work we put in, this is pretty darn good. For a better approximation, choose a larger solution to Pell's equation.

More generally, Gallagher's method for approximating √n is: Find integers a and b for which a² ±1 = nb²; such integers are guaranteed to exist unless n is a perfect square. Then write √n = √(nb² / b²) = √((a² ± 1) / b²) = √(a²/b² · (a² ± 1)/a²) = a / b · √((a² ± 1) / a²) = a/b · √(1 ± 1/a²) ≈ a/b · (1 ± 1 / 2a²).

Who was Pell? Pell was nobody in particular, and "Pell's equation" is a complete misnomer. The problem was (in Europe) first studied and solved by Lord William Brouncker, who, among other things, was the founder and the first president of the Royal Society. The name "Pell's equation" was attached to the problem by Leonhard Euler, who got Pell and Brouncker confused—Pell wrote up and published an account of the work of Brouncker and John Wallis on the problem.

Order A Mathematician's Apology with kickback no kickback

[Other articles in category /math] permanent link

Mysteries of color perception
Color perception is incredibly complicated, and almost the only generalization of it that can be made is "everything you think you know is probably wrong." The color wheel, for example, is totally going to flummox the aliens, when they arrive. "What the heck do you mean, 'violet is a mixture of red and blue'? Violet is nothing like red. Violet is less like red than any other color except ultraviolet! Red is even less like violet than it is like blue, for heaven's sake. What is wrong with you people?"

Well, what is wrong with us is that, because of an engineering oddity in our color sensation system, we think red and violet look somewhat similar, and more alike than red and green.

But anyway, my real point was to note that the colors in look a lot different against a gray background than they do against the blue background in the bar on the left. People who read this blog through an aggregator are just going to have to click through the link for once.

[Other articles in category /aliens] permanent link

More on Emotions
In yesterday's long article about emotions, I described the difficulty like this:

There's another kind of embarrassment that occurs when you see something you shouldn't. For example, you walk into a room and see your mother-in-law putting on her bra. You are likely to feel embarrassed. What's the connection with the embarrassment you feel when you fall off a ledge? I don't know; I'm not even sure they are the same. Perhaps we need a new word.

I also thought of another emotion that was not on my list of basic emotions, but seems different from the others. This emotion does not, so far as I know, have a word in English. It is the emotion felt (by most people) when regarding a happy baby, the one that evokes the "Awwww!" response.

This is a very powerful response in most people, for evolutionarily obvious reasons. It is so powerful that it is even activated by baby animals, dolls, koala bears, toy ducks, and, in general, anything small and round. Even, to a slight extent, ball bearings. (Don't you find ball bearings at least a little bit cute? I certainly do.)

The aliens might or might not have this emotion. If they are aliens who habitually protect and raise their young, I think it is inevitable. The aliens might be the type to eat their young, in which case they probably will not feel this way, although they might still have that response to their eggs, in which case expect them to feel warmly about ball bearings.

I also gave some more thought to Ashley, the Pacemate who claimed that her most embarrassing moment was crashing into the back of a trash truck and totaling her car. I tried to understand why I found this such a strange response. The conclusion I finally came to was that I had found it inappropriate because I would have expected fear, anger, or guilt to predominate. If Ashley is in a vehicle colision severe enough to ruin her car, I felt, she should experience fear for her own safety or that of others, anger at having wrecked her car, guilt at having carelessly damaged someone else's property or health. But embarrassment suggested to me that her primary concern was for her reputation: now the whole world thinks that Ashley is a bad driver.

If you don't see what I'm getting at here, the following situational change might make it clearer:

Most Embarrassing moment

Ashley (alternate universe version): Crashing into the back of a school bus full of kids and totaling my car!

Having made the analysis explicit for myself, and pinned down what seemed strange to me about Ashley's embarrassment, it no longer seems so strange to me. Here's why: It wasn't a school bus, but a garbage truck. Garbage trucks are big and heavy. The occupants were much less likely to have been injured than was Ashley herself, partly because they were in a truck and also because Ashley struck the back of the truck and not the front. The truck was almost certainly less severely damaged than Ashley's car was, perhaps nearly unscathed. And of course it was impossible that the truck's cargo was damaged. So a large part of the motivation for fear and guilt is erased, simply because the other vehicle in the collision was a garbage truck. I would have been angry that my car was wrecked, but if Ashley isn't, who am I to judge? Probably she's just a better person than I am.

But I still find the reaction odd. I wonder if some of what Ashley takes to be embarrassment isn't actually disgust. But at least I no longer find it completely bizarre.

Finally, thinking about this led me to identify another emotion that I think might belong on the master list: relief.

[Other articles in category /aliens] permanent link

Emotions
I was planning to write another article about π, and its appearance in Coulomb's law, or perhaps an article about how to calculate the volume of a higher-dimensional analogue of a sphere.

But John Speno says he always skips the math stuff on my blog, and the last couple of days have been unrelievedly mathematical. So instead, John, I have written an article about the comparison of emotions, whether the 18-toed Sirian ghost worms will understand why you are holding your nose, Homer Simpson, the evolutionary justification for disgust, the Indiana Pacers cheerleading squad, Paris Hilton, and maggots. Skip this, I dare you.

But one day she pushed the idea too far and asserted that those were the only emotions there are.

That's clearly wrong. Even discounting emotions that might be considered variations on the big four, such as: (anger) rage, annoyance, resentment, frustration, (sadness) grief, disappointment, remorse, loneliness, (happiness) delight, joy, pride, (fear) nervousness, dread, terror, panic, and so on, we still have:

• Boredom
• Disgust
• Envy
• Guilt
• Jealousy
• Lust
• Shame
• Surprise

Some of these may require explanation. People sometimes use the word "disgust" metaphorically to refer to a feeling that is really nine parts anger to one part boredom, as when they say they are disgusted with the state of American politics. But that's not what I mean by it here. The disgust I'm referring to is the feeling you have when you have been on vacation and come back to discover that the power went out while you were away and the meat in the refrigerator has spoiled and slid out onto the kitchen floor where it is now festering with thousands of squirming, white, eyeless maggots, and the instant you see it, your reaction is to (a) turn away, (b) hold your nose, and (c) vomit. I suppose it's possible that some people would have that very reaction to American politics; it's certainly understandable. But I don't think that's what people usually mean when they say that politics disgusts them. Or if they do mean it, they mean it only in a hyperbolic sense.

People often confuse guilt and shame, but they are really orthogonal. You feel guilt when you have done something you believe is ethically or morally wrong. You feel shame when other people observe you doing something that they shouldn't see, whether or not that thing is ethically or morally wrong. The problem is with the observing, not with the thing that is being observed. I think the following example will help clear up the confusion: One might or might not feel guilty about picking one's nose, although I think most people don't feel guilty when they do it. But even someone who picks their nose entirely without guilt, probably feels ashamed if someone else catches them in the act.

The other two that are often confused are envy and jealousy. Here I think the confusion is caused simply because people don't know what the words mean. Envy is what you feel when you want what someone else has; you can envy someone else's car or their lunch or their special relationship with their lover. Jealousy is much more specific. You are jealous when you have a special relationship with a person, and you are afraid that you are going to lose them to a third person. You can envy someone else's possession of a ham sandwich, but jealousy of a ham sandwich is impossible.

I might be willing to believe the proposition these eight, plus the original four (anger, sadness, happiness, and fear) constitute a complete set of "primary colors" for human emotion, and that you can consider the others as being mixtures of various amounts of these twelve. For example, you go up on stage to accept an award, and your trousers fall off, and you feel embarrassed. What is embarrassment? It's maybe five parts shame, two parts fear, and one part surprise. Take away any of these three things, and you no longer have embarrassment, but something else. Add in anger and you have humiliation.

If someone wants to argue that jealousy is compounded from fear, anger, and envy, and should be removed from the list in favor of affection or confusion, I won't complain. The list is necessarily dependent on culture, and even more so on the individual making it. Not every culture will have anything like jealousy; perhaps most won't. Romantic love seems to be a uniquely European invention, dating from around the 13th century.

Another problem with the list is that even within one culture, there may not be agreement on which kinds of feelings qualify as emotions. Does hunger qualify? Or fatigue? It seems to me that some emotions are more rooted in the physical processes of the body, and others less so. Guilt is at the "high" end of that scale: it refers to a feeling you have in your mind when you have done something that you feel you shouldn't have. It is hardly associated with the body at all. A brain in a vat could feel guilt, and probably does. At the "low" end of the scale is disgust, the experience of which is much less about an the social constructions in your mind than it is about your stomach trying to turn itself inside out. I think hunger and fatigue are even farther down the scale of body-vs-mind than disgust; below even those is pain, and at the very bottom are feelings like the one you have in your arm when you open a door, which is purely physical and has no emotional content whatsoever. The counterparts at the top end of the scale are plans, analyses, and the like, which are purely mental and have no emotional content. Emotion is somewhere in between, and I can imagine that someone else could want to exclude disgust or guilt from a list of emotions because they were too far down from the middle of the scale.

An exercise I love to do is to try to consider what we will have in common with the space aliens. For example, do the space aliens consider the P=NP problem interesting? Do the space aliens consider the set of real numbers as a fundamental object, or as an obscure construction only of interest to set theorists? I will probably address these topics in future articles. Meanwhile, this article, believe it or not, started out as a discussion of whether the space aliens, when they arrive, will already know how to play chess. (Well, obviously not. But it is less obvious that they will not already know how to play go. I will write that article sooner or later.)

But now we might ask what kinds of emotions the aliens will have. The question seems at first glance to be completely impossible. But I believe that partial answers are possible.

As emotions get higher up on the body-to-mind scale, it becomes less likely that they will be shared by the aliens; such emotions are not even cross-cultural among humans. Our experience of guilt is very much dependent on our culture, and in particular on our relationship to law and authority, much of which is the result of two thousand years of Christian philosophizing. The converse is that emotions that are low on the body-to-mind scale are much more universal among people. Perhaps not everyone feels guilt. But everyone feels disgust.

Disgust is particularly easy to analyze from the point of view of natural selection. It is to a large extent an aversion to dangerous biohazards: rotten food and carcasses; decay, including mold, and things that look like mold; excrement, vomit, and other body substances that should be inside but that have come out; disembowelment and bodily mutilation; deformity and disease. Rotting meat is extremely poisonous, so an automatic aversion reaction makes evolutionary sense: the people who turned away in disgust lived longer than the people who saw an opportunity for a free lunch. Excrement, and particularly human excrement, harbors bacteria dangerous to humans, so an automatic aversion reaction makes evolutionary sense. Deformity is similar. Perhaps whatever caused it is not contagious—but perhaps it is, and evolution wants to stay on the safe side.

I think it is inevitable that the aliens will have these same kinds of reactions, for the same reasons. Aliens will have a strong aversion reaction if you put them in front of a chunk of rotting alien flesh, or show them an alien with its internal organs on the outside. Why? Because those things are dangerous to aliens, and so all the aliens who didn't have that reaction have died long ago of horrible diseases. I don't think it's a big step to identify this reaction with disgust.

Similarly, aliens might not have eyes, if they come from a place with no ambient short-wavelength electromagnetic radiation; say, the surface of Jupiter. But the aliens will have chemical senses, analogous to smell and taste, because there are chemicals everywhere. Every life form on earth has chemical senses, even down to bacteria. This is because you cannot use the Homer Simpson strategy of ingesting everything you encounter; you would quickly die. (Homer is fictitious, or he would be dead long ago.) You need some way of distinguishing which items are food, so that you can eat the things that are food and ignore the other things. So you need to have a sense of smell and taste.

What happens when you smell or taste something that is really harmful? You had better have some kind of aversion reaction, and you do, because all the 18-toed Sirian ghost worms without those reactions ate stuff that disagreed with them, and died young; you are the product of a long line of ghost worms that do have a sense of smell and feel disgust when they wander into a biohazard zone.

We can push this even further. I conjecture that we can even predict some of the aliens' body language. When presented with something that smells bad—say rotten food—an alien's response will be to hold its nose, if it has an olfactory sense that can be disabled by closing the organ off from the outside world. If the alien asks me what I think of Paris Hilton, and I hold my nose, the alien will understand that Paris Hilton is being insulted, and will understand something of the way in which Paris Hilton is being insulted. Chemical senses, I think, must be so universal that even noseless aliens will understand the gesture, once the structure and function of the human nose is explained to them. "Oh, I see," says the alien. "You have closed off your chemical sense organ so that Ms. Hilton's noxious effluvia cannot penetrate. Yes, I quite understand! Unfortunately, for us it is not possible since our olfactory bulbs are distributed throughout our skins. But I am sure we have all wanted to do something like that at one time or another."

Disgust, being one of the lowest emotions on the mind-body scale, is one of the easiest to attribute to the aliens. Even going a little higher is risky. Will the aliens feel lust? Quite possibly. Even a giant amoeba that reproduces by fission might feel something akin to lust when the time comes, a powerful urge to divide in two. Will the aliens feel anger? Perhaps, but here we're on shaky ground.

Long ago, I had a conversation with Matthew Stone, in which he told me how different cultures have different notions of even apparently simple emotions such as rage. Rage, he said, is characterized by the following situation: you want something, but there is some insurmountable obstacle to your getting it, and so you are frustrated. When you become enraged, your response is to attack the obstacle and try to destroy it.

But, said M. Stone, in Polish, when you want something, and there is an insurmountable obstacle, and you are frustrated, you do not have a fit of rage in which you go nuts and attack the obstacle. Instead, you have a fit of złost, in which you go nuts and attack everything around you at random.

Or, in some other culture that I forget, if you want something to which there is an insurmountable obstacle, and you are frustrated, then you have a fit of some emotion I don't remember the name of, in which you go nuts and kill yourself.

These seem to me to be distinctly different from rage, if not fundamentally so. Variations on jealousy are even easier to invent.

I don't know how much of all this is true, how much was wrong before M. Stone heard it, how much he said that was right but I misunderstood, and how much I understood correctly but got wrong between then and now. It might all be nonsense. But one can still get some mileage out of attributing złost, rather than rage, to the aliens.

Embarrassment is another one of the more universal emotions. I've seen my cat act embarrassed, typically when he falls off of a ledge, or tries to jump from A to B but only makes it partway, and goes splat.

There's another kind of embarrassment that occurs when you see something you shouldn't. For example, you walk into a room and see your mother-in-law putting on her bra. You are likely to feel embarrassed. What's the connection with the embarrassment you feel when you fall off a ledge? I don't know; I'm not even sure they are the same. Perhaps we need a new word.

The Indiana Pacers basketball team has a web site on which they list the "most embarrassing moments" of each of their cheerleaders, the Pacemates. (I keep wanting to call them the "Pacemakers", but even I know that is wrong.)

When I first planned to discuss this, it was because my random sample of responses picked up mostly strange ones, and I was ready to conclude that the Pacemates and I were not of the same species. I planned to complain that none of the Pacemates had apparently ever farted in public. But a more thorough survey revealed that the Pacemates were much less surprising in their embarrassment than I had originally thought. As embarrassing moments go, you would be hard-pressed to find a more typical example than that of falling down in the middle of a carefully-choreographed public dance exhibition, and that is mostly what they said. Both I and my cat can understand the embarrassment of these mishaps:

Lindsay: I usually don't get embarrassed, but one time, I did fall off stage at a national dance competition.

Darcy: Last year during Pacers player introductions when the lights were out, Boomer ran into me and knocked me down to the floor!

Amanda: When I was cheering at an IU game, I went back for a back handspring and in the middle of Assembly Hall court, I landed flat on my head.

Kim: When I was in sixth grade, I slipped and fell on the ice trying to get on the school bus. I had on a skirt and dress shoes and was carrying my trumpet!

I find it rather comforting that the Pacemates are embarrassed by the same things that embarrass me or my cat or both. I had been worried that all the embarrassing moments would be strange and puzzling, like this one:

Ashley: Crashing into the back of a trash truck and totaling my car!

Nikki: During speech class of my freshman year of college, I was giving a speech on the health care industry and I...well, let's just say for the rest of the semester, my classmates nicknamed me "Toot-Toot!"

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Naomi Wolf and Big Ethel
Aaron Swartz has done a text search of The Beauty Myth and concluded that Wolf never intended Big Ethel to serve as an example of intelligence, contrary to what I asserted in my previous article. M. Swartz says:

Judging from a search on Amazon, the only time Ethel is mentioned is in the context of noting that an attractive woman is often paired with an unattractive one: "... Veronica and Ethel in Riverdale; ... and so forth. Male culture seems happiest to imagine two women together when they are defined as being one winner and one loser in the beauty myth." (59f)

The most serious error here is mine: I should have considered and discussed the possibility that my friend was misquoting Wolf. That I didn't do this was unfair to Wolf and entirely my fault. Since I haven't read the book myself, I should have realized what shaky ground I was on, and taken pains to point this out. And yet other possibilities are:

• That my friend didn't misquote Wolf at all, and I misunderstood her at the time, or
• that my friend correctly quoted Wolf and I understood her at the time, but my memory of the episode (which occurred around 1993) is faulty.

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On saying too much, or, bad things come in threes
Long ago, I had a conversation with a woman who had recently read Naomi Wolf's book The Beauty Myth. She was extolling the book, which I had not read, and mentioned that Wolf had an extensive discussion of the popular dichotomy between beauty and intelligence. She told me that Wolf had cited Archie comics as containing an example of this dichotomy, in the characters of Veronica and Big Ethel.

I had been nodding and agreeing up to that point. But at the mention of Big Ethel I was quite startled, and said that that spoiled the argument for me, and made me doubt the conclusion. I now had doubts about what had seemed so plausible a moment before.

Veronica is indeed one half of a contrasting pair in Archie comics. But Veronica and Big Ethel? No. Veronica is not complementary to Big Ethel. The counterpart of Veronica is Betty. The contrast is not between beauty and brains but between rich and poor, and between their derived properties, spoiled and sweet. A good point could be made about Veronica and Betty, but it was not the point that Wolf wanted to make; her citation of Veronica and Big Ethel as exemplifying the opposition of beauty and intelligence was just bizarre. Big Ethel, to my knowledge, has never been portrayed as unusually intelligent. She is characterized by homeliness and by her embarrassing and unrequited attraction to Jughead, not by intelligence.

Why would this make me doubt the conclusion of Wolf's argument? Because I had been fully ready to believe the conclusion, that our culture manufactures a division between attractiveness and intelligence for women, and makes them choose one or the other. I had imagined that it would be easy to produce examples demonstrating the point. But the example Wolf chose was completely inept. And, as I said at the time, "Naomi Wolf is very smart, and has studied this closely and thought about it for a long time. If that is the best example that she can come up with, then perhaps I'm wrong, and there really aren't as many examples as I thought there would be." Without the example, I would have agreed with the conclusion. With the example, intended to support the conclusion, I wasn't so sure.

Now, I come to the real point of this note. Paul Vallely has written an article for The Independent on "How Islamic inventors changed the world". He lists twenty of the most influential contributions of the Muslim world, including the discovery of coffee, inoculation, and the fountain pen. I am not so clear on the history of the technology here. Some of it I know is correct; some is plausible; some is extremely dubious. (The crank, not invented before 1206? Please.) But the whole article is spoiled for me, except as a topic of derision, because of three errors.

Item #1 concerns the discovery of the coffee bean. One might expect this to have been discovered in prehistoric times by local Ethiopians, long before the founding of Islam. But I'm in no position to argue with it, and I was ready to give Vallely the benefit of the doubt.

Item #2 on Vallely's list was more worrying. It says "Ibn al-Haitham....set up the first Camera Obscura (from the Arab word qamara for a dark or private room)." It may or may not be true that "qamara" is an "Arab word" (by which I suppose Vallely means an "Arabic word") for "chamber", but it is certainly true that this word, if it exists, is not the source of the English word "camera". I don't know from "qamara", but "camera obscura" is Latin for "dark chamber". "Camera" means "chamber" in Latin and has for thousands of years. The two words, in fact, are etymologically the same, which is why they have almost the same spelling. It is for this reason that the part of a legal hearing held in the judge's private chambers is said to be "in camera".

There might be an Arabic word "qamara", for all I know. If there is, it might be derived from the Latin. (The Latin word is not derived from Arabic, either; it is from Greek καμαρα, which refers to anything with an arched cover.) Two things are sure: The English word "camera" is not derived from Arabic, and Vallely did not bother to pick up a dictionary before he said that it was.

Anyone can make a mistake. But I started to get excited when I read item 3, which is about the game of chess. Vallely says "The word rook comes from the Persian rukh, which means chariot." This is true, sort of, but it is off in a subtle way. The rooks or castles of modern chess did start out as chariots. (Moving castles around never did make much sense.) And "rook" is indeed from Persian rukh. But rukh doesn't exactly mean a chariot. It means a chariot in the game of chess. The Persian word for a chariot outside of chess was different. (I don't remember what it was.) Saying that rukh is the Persian word for chariot is like saying that "rook" is the English word for castle.

I was only on item 3 and had already encountered one serious error of etymology and one other item which although it wasn't exactly an error, was peculiar. I considered that I wouldn't really have enough material for a blog post, unless Vallely made at least one more serious mistake. But there were still 17 of 20 items left. So I read on. Would Vallely escape?

No, or I would not have written this article. Item 17 says "The modern cheque comes from the Arabic saqq, a written vow to pay for goods when they were delivered...". But no. The correct etymology is fascinating and bizarre. "Cheque" is derived from Norman French "exchequer", which was roughly the equivalent of the treasury and internal revenue department in England starting around 1300. Why was the internal revenue department called the exchequer? Because it was named after the chessboard, which was also called "exchequer".

What do chessboards have to do with internal revenue? Ah, I am glad you wondered. Hindu-Arabic numerals had not yet become popular in Europe; numbers were still recorded using Roman numerals. It is extremely difficult to calculate efficiently with Roman numerals. How, then did the internal revenue department calculate taxes owed and amounts payable?

They used an abacus. But it wasn't an abacus like modern Chinese or Japanese abacuses, with beads strung on wires. A medieval European abacus was a table with a raised edge and a grid of squares ruled on it. The columns of squares represented ones, tens, hundreds, and so on. You would put metal counters, called jettons, on the squares to represent numbers. Three jettons on a "hundred" square represented three hundred; four jettons on the square to its right represented forty. Each row of squares recorded a separate numeral. To add two numerals together, just take the jettons from one row, move them to the other row, and then resolve the carrying appropriately: Ten jettons on a square can be removed and replaced with a single jetton on the square to the left.

The internal revenue department, the "exchequer", got its name from these counting-boards covered with ruled squares like chessboards.

(The word "exchequer" meaning a chessboard was derived directly from the name of the game: Old French eschecs, Medieval Latin scacci, and so on, all from shah, which means "king" in Persian. The word "checkered" is also closely related.)

So, in summary: the game is "chess", or eschek in French; the board is therefore exchequer, and since the counting-tables of the treasury department look like chessboards, the treasury department itself becomes known as the exchequer. The treasury department, like all treasury departments, issues notes promising to pay certain sums at certain times, and these notes are called "exchequer notes" or just "exchequers", later shortened (by the English) to "cheques" or (by Americans) to "checks". Arabic saqq, if there is such a word, does not come into it. Once again, it is clear that Vallely's research was shoddy.

While I was writing up this article, yet another serious error came to light. Item 11 says "The windmill was invented in 634 for a Persian caliph...". Now, I am not very knowledgeable about history, and my historical education is very poor. But that was so peculiar that it startled even me. 634 seemed to me much too early for any clever inventions to be attributed to Muslims. Then I looked it up, and so it was. Muhammad himself had only died in 632.

As for the Persian caliph Vallely mentions, he did not exist. The caliphs are the successors of Muhammad, so of course there was one in 634---the first one, in fact. Abu Bakr reigned from the death of the Prophet in 632 until his own death in 634; he was succeeded by `Umar. Neither was Persian. They were both Arabs, as you would expect of Muslim leaders in 634. There were no Persian caliphs in 634.

My own ignorance of Islam and its history is vast and deep, but at least I had a vague idea that 634 was extremely early. Vallely could have looked up the date of the founding of the caliphate as easily as I did. Why didn't he? Well, perhaps it was just a typo, and should have said 834 or 934. In that case it's just poor editing and inattention. But perhaps it was a genuine factual error, in which case Vallely was not only not paying attention, but is apparently even less familiar with Islamic history than I am, difficult as that is to achieve. In which case we have this article about the twenty greatest contributions of Islam written by a guy who literally does not know the first thing about Islam.

And so this article, which I hoped to enjoy, was spoiled by a series of errors. I am very sympathetic to the idea that the brilliant history of Islamic science and engineering has been neglected by European scholarship. One of my very first blog posts was about the Islamic use of algebra to solve complex probate problems. Just last week I was reading about al-Biruni's invention, around 1000 years ago, of an improved method for measuring the size of the earth, a topic that Vallely treats as item 18. But after reading Vallely's article, I worried a bit that the case might have been overstated. Perhaps the contributions of Muslims are not as large as I had thought?

Fortunately, there was an alternative: the conclusion is correct, and the inept support from the author speaks only to the author's ineptness, not to the validity of the conclusion. I did not have that alternative with Naomi Wolf, who is not inept. (Also, see this addendum.)

With only cursory attention, I found three major errors of fact in this one short article. How many more did I miss, I wonder? Did Abbas ibn Firnas really invent a working parachute, as Vallely says? Maybe it was someone else. Maybe there was no parachute. Maybe there was, but it didn't work. Maybe the whole thing is a propaganda invention by someone who wants to promote Islam, and has suckered Vallely into repeating fiction. Maybe all of these. Someone knows the truth, but it isn't me, and I can't trust Vallely.

Were the Turks vaccinating people eighty years before the Europeans, or did Vallely swallow a tall tale? I don't know, and I can't trust Vallely.

People sometimes joke "I am stupider for having read this," but I really believe this was the case here. The article is worse than useless, because it has polluted my brain with a lot of unreliable non-information. I will have to be careful not to think that quilted fabrics were first brought to Europe by the crusaders, who got them from the Muslims. My real fear is that the "fact" will remain in my brain for years, long after I have forgotten how unreliable Vallely is, and that I will bring it out again as real information, which it is not. True or not, it is too unreliable to be information.

The best I can hope for now is that I will forget everything Vallely says, and meet the true parts again somewhere else in the future. In the meantime, I am worse off for having read it.

[Other articles in category /lang/etym] permanent link

The Wrong Alcott
I went to the library yesterday, and as usual I was wandering in the stacks hoping for a lucky find. This time I got "The Young Husband" (subtitle: "Duties of Man in the Marriage Relation") by "Alcott".

This book was written in 1846 by William Andrus Alcott, as a sequel to his 1844 (presumably successful) book "The Young Wife". It is a book of domestic advice for recently-married men. Like many advice books, it is a curious mix of good advice, bad advice, and totally bizarre advice that apparently came from the planet Zorkulon. For example, Alcott advises the young husband to forbid his family all fictional literature. He thinks it's all trash, and time spent reading it is time wasted that could have been spent reading something moral and improving, such as (presumably) Alcott's own series of moral and improving advice books. He says that arguments in favor of any particular novel are akin to arguments in favor of champagne: this particular liquor may seem tasty and harmless, but it's still the demon alcohol in a pretty disguise, sure to lead the imbiber to ruin and despair.

I took the book off the shelf not because I have a specific interest in moral advice for Victorian-age Americans, but because I knew a bit about Louisa May Alcott's family life. Louisa May Alcott, as I am sure you recall, was the author several extremely popular books for children, including, most notably, Little Women, which has been continuously in print since its publication in 1868. I settled down to read her father's advice book intending to savor the delicious irony, because Alcott's father was an amazingly bad husband, and this is visible throughout all of her fiction.

Little Women, for example, concerns the life of the four March sisters and their mother. Where is Mr. March? He's off fighting in the Civil War, not because he was drafted, and not because his family doesn't need him, but as a matter of principle. He barely appears, while the female Marches struggle along without him.

I'm more familiar with Eight Cousins, which is even weirder. The story concerns Rose and her extended family, twenty-one people in all, and among those twenty-one people there is no example of a wholly and happily married couple. Rose, the protagonist, has been orphaned shortly before the story opens. She is sent away into the care of her aunts. The aunts include Aunt Plenty, who is a widow; Aunts Clara and Jessie, whose husbands are away on a trading voyages for the entire book; Aunt Myra, also a widow, and Aunt Peace, whose fiancé died the day of their wedding.

Aunt Jane does have a husband, who is a busy, industrious merchant—except when Jane is around; then he is always asleep. Rose's guardian is Uncle Alex, who is a bachelor.

This theme of the absent or ineffective husband and father runs all through Louisa May Alcott's fiction, and it's easy to guess why: her own father was often absent, and when he was around he was still useless. He made little money, and spent what money he did make on utopian schemes. Lorrie told me a story about how he got the idea that they should eat nothing but apples, and so they did. The only thing that stood between the Alcotts and starvation was the income from Louisa May's writing.

So I was really interested to see what advice Alcott's dad would have to offer on the subject of being a good husband and father, and chuckled whenever he talked insistently about the duties that the husband owes to his family. I quite enjoyed it.

Unfortunately, it was all in vain, because the author, William Andrus Alcott, was not the father of Louisa May Alcott. He was a cousin. Louisa May's father was Amos Bronson Alcott. Whoops.

All of which is presented as a partial explanation of why I have not posted any blog items this week. Sometimes the stuff I'm reading and thinking about is suitable for the blog, sometimes not. I was all excited at the prospect of writing about William Andrus Alcott's advice book, but the humor and irony vanished in a case of mistaken identity.

I could post about what I had for breakfast, but I foreswore such stuff when I decided to start the blog in the first place. If you want that kind of blog, you can't do better than to visit the always engaging blog of Eric Brill.

[Other articles in category /book] permanent link

My favorite NP-complete problem
At last year's open source conference, I gave a talk about fundamental problems of computer science. I talked about undecidable problems and NP-complete problems, and some other stuff. It was only a 45-minute talk, but I worked hard to make it as accessible as I could.

For the NP-completeness section, I discussed the knapsack problem. In this problem, you have a bunch of items you can take on a trip, each of which has a value and a size. Your luggage is of limited size, so the total size of the items you take on the trip must not exceed this limit. Subject to this constraint, you want to take the items whose total value is as large as possible. (Actually, in the talk, I used the decision problem version of this, rather than the optimization problem version, to avoid sticky questions from the know-it-alls in the audience.)

Knapsack is a pretty good example problem. It's simple, easy to understand, and reasonably easy to see why it might be interesting. But after I gave the talk, I thought of a much better example. I deeply regret that I didn't come up with it in time to put it in the talk. Fortunately, I now have a blog. Read on; here's the coolest NP-complete problem ever.

Each episode of Sesame Street now ends with a fifteen-minute segment called Elmo's World, featuring Elmo, a small red monster. Elmo is extremely popular, and the segments have been released on videotape and DVD. Each of these segments has a topic of interest to toddlers, such as:

Babies	Dancing	Food
Bananas	Dogs	Games
Baths	Drawing	Hair
Bicycles	Ears	Hands
Birds	Exercise	Mail
Birthdays	Families	Music
Books	Farms	Plants
Bugs	Feet	Singing
Cats	Firefighters	Water

(These are all real examples.)

When the segments are released on video, they are bundled in groups of three. Usually, the three segments will have a common theme. For example, the video Wake Up With Elmo! (left) gathers together the three segments about "sleep", "getting dressed", and "tooth brushing". Another video (right) collects the segments about "food", "water", and "exercise".

Your job is to plan the video releases. Sesame Workshop gives you a list of which sets of three segments are considered to be thematically related. Your job is to select items from this list that exhaust the available segments, without using any segment more than once.

Each segment might be part of several different thematically-related groups. For example, the "dancing" segment could be released on a physical-activity-themed video, along with the "bicycle" and "exercise" segments, or it could be released on a party-themed video, along with the "birthday" and "games" segments. If you choose to release the physical activity collection, you foreclose the possibility of releasing the party collection, and you will have to find something else to do with the "birthday" and "games" segments.

This problem is NP-complete. The official computer science jargon name for it is exact cover by 3-sets, or just X3C.

The Sesame Workshop people were not able to solve the problem. One of the videos in the series is about flowers, bananas, and hair.

[Other articles in category /CS] permanent link

Google query roundup
My blog continues to attract interesting Google queries. I had fun looking over the queries and writing about them last month, so I thought I'd try it again.

Sometimes the queries are for very specific information that I can't provide:

	   1  the four type of flowers by aristotle
	   1 c-source code for earth revolving sun
	   1 colleges christian goldbach went to 
	   1 moon sky rhode island position feb 01-feb 14
	   1 what is robert hooke' s middle name?
	   1 scientific definition on why fingers get pruney
	   1 source code of unrestricted simplex protocol in c

Order An Essay Towards a Real Character and a Philosophical Language with kickback no kickback

In the "you're asking the wrong question, so all you'll get is the wrong answer" department:

	   1 books typical copies sold

	   1 "typical royalties" 
	   1 total o'reilly books sold
	   1 typical royalties

In the "damn, I wish I had the foggiest idea" department:

	   1 what happens inside the chrysalis

Sometimes, the page to which the user is referred is just perfect for their query:

	   1 every natural number is either a fibonacci number or it
  	     can be written as a sum of nonconsecutive fibonacci numbers 

	   6 how many people can use an armonica properly

Contrary to this, however, is this recurring query:

	   1 linear math system eliminate debt

Some of the queries are even more depressing. For example:

	   1 which expression represents the number 96 written as a
             product of primes? 

Here's another one like that:

	   1 greatest common factor of 36 and 63

But sometimes searching for the exact question you want answered does work:

 	   1 a rope lying over the top of a fence is the same length
  	     on each side.  it weighs one third of a pound per foot.
  	     on one end hangs a monkey holding a banana, and on the
  	     other end a weight equal to the weight of the monkey. the
  	     banana weighs two ounces per inch.  the rope is as long
  	     (in feet) as the age of the monkey (in years), and the
  	     weight of the monkey (in ounces) is the same as the age
  	     of the monkey's mother.  the combined age of the monkey
  	     and its mother is thirty years.  one half of the weight
  	     of the monkey, plus the weight of the banana, is one
  	     forth as much as the weight of the weight and the weight
  	     of the rope.  the monkey's mother is half as old as the
  	     monkey will be when it is three times as old as its
  	     mother was when she she was half as old as the monkey
  	     will be when when it is as old as its mother will be when
  	     she is four times as old as the monkey was when it was
  	     twice as its mother was when she was one third as old as
  	     the monkey was when it was old as is mother was when she
  	     was three times as old as the monkey was when it was one
  	     fourth as old as it is now.  how long is the banana?

Speaking of problems that are simpler than they first appear, Jeff Abrahamson told me a good one a few months ago: One-tenth of a sphere is painted red, the rest blue. Show that there must exist eight blue points that lie at the vertices of a cube.

	   1 how did they invent the chinese symbols

Order Writing Systems with kickback no kickback

Others are phonetically motivated. For example, the word for "ridgepole" is a compound of "wood" and "east" . The tree makes sense, because ridgepoles are made of wood, but why "east"? It's because the word for "ridgepole" is pronounced dòng, exactly the same as the word for "east". Lots of words are dòng, but this is the wooden dòng. The "east" component tells you how to pronounce it, and the "wood" component hints at the meaning.

Writing Systems, by Geoffrey Sampson, has a chapter about this; I recommend both the chapter and the rest of the book.

	   1 fundamental theorem of phyllotaxis 

Other fundamental theorems include: the fundamental theorem of arithmetic, which says that every positive integer has a unique factorization into primes; the fundamental theorem of algebra, which says that every nth degree polynomial has n roots over the complex numbers; and the fundamental theorem of calculus, which relates the integral and differential calculus by saying that if f' is the derivative function of f, then:

	   1 doctor dolittle racism
	   1 dr dolittle prince bumpo racism
	   1 dr doolittle racism

I think a lot could be said about the presence or absence of racism in the Dolittle books, although I wouldn't expect much agreement on such a hot-button topic. But I imagine there would be more agreement that the changes that were made to the book in the name of greater racial sensitivity are rather weird.

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Addenda to recent articles 200602
Here are some notes on posts from the last month that I couldn't find better places for.

• Regarding my bad solution to the problem of preventing multiple simultaneous SMTP connections from the same place, Chris Siebenmann suggests that a better strategy is to centralize all SMTP access through a single server that can manage the connections in any convenient way, without IPC, and fork child processes to perform the actual SMTP transactions. I had ended my post with "duh", but this suggestion requires an even bigger "duh", because I am already running such a server and modifying it appropriately would have been even easier than the modification I did make to the SMTP program. Thank you, M. Siebenmann. Duh!

• Regarding the 3n+1 domain, I should mention first that my use of the word "domain" is incorrect here. A domain, properly speaking, is required to have both addition and multiplication; the 3n+1 system supports only multiplication. Addition doesn't work because (for example) 1+1 is undefined in this system, 2 having been omitted.

  I may discuss this in more detail in a future post.

• Regarding Perl's accidental s/.../.../ee feature, John Macdonald remarks that he thinks it was first discovered by Randal Schwartz, not Tom Christiansen, as I said. M. Macdonald suggests that M. Schwartz first used it in the form s/.../.../eieio in a "Just Another Perl Hacker" signature, and that M. Christiansen then invented the s/(\$\w+)/$1/ee form as a way to make real use of it.

• Regarding Robert Hooke's mismeasurement of the frequency of G above middle C, I referred to Benjamin Wardhaugh's suggestion that the error was in the length of the pendulum he used to mention the time. Carl Witty points out that this is unlikely, for two reasons. First, Hooke would have been quite familiar with how to make a pendulum of the correct length to time a one-second interval; indeed, he probably would have had such pendulums sitting around, ready to be used. And second, the period of a pendulum is proportional to the square root of its length, so to get the error of a factor of √2 in the measurement of the frequency of the brass wire, Hooke's pendulum would have had to be twice as long as it should have been.

  In reply, I suggested several possible causes of error:

  1. Perhaps the initial wire was not vibrating at precisely 1 Hz. Synchronization with the 1 Hz pendulum might have been done by eye. Any error in the original frequency would have been multiplied by 136 in the final result.

  2. The halving of the wire might not have been exact.

  3. If the tension in the wire changed during the halving process, the shortened wire would have a frequency different from twice that of the unshortened wire.
  4. The note produced by the one-foot wire might not have been exactly G. it could have varied somewhat from true G without being detected by the musical observers.

  5. G in 1664 wasn't 384 Hz anyway. In fact, I haven't finished finding out just what Hooke meant by it, since pitches weren't fully standardized; I don't know what Hooke intended for the reader to understand from his assertion that it was 272 Hz. See Wikipedia's discussion, for example.

  6. I don't yet know that the second was accurately measured. You need a pendulum that strokes exactly 86,400 times per day. They would have had to calibrate it against sandglasses and such things. How accurate was that calibration?

  7. Even if the second was accurately measured, was it the same second that we use today? I'm not sure. I should be able to find this out by reading Hooke's lectures on gravitation (which I have handy) and seeing what he gives as the acceleration due to the earth's gravity.

  There may be some other possible causes of error that I haven't thought of. Which of these actually contributed, and how much, I do not know.

  M. Witty also wondered if the fact that apparent error in the measurement was almost exactly √2 was a coincidence. I imagine so, but I could easily be wrong.

• Regarding non-oral reading, I said:

  Someone once told me that some famous scholar, I think perhaps Thomas Aquinas, was the only one of his contemporaries to read non-orally, that they were astonished at how the information would just fly from the book into his mind without his having to read it.

  Ricardo J. B. Signes has confirmed this, except that it wasn't Aquinas. He says that Augustine wrote of Ambrose that "When he read, his eyes travelled over the page and his heart sought the sense, but voice and tongue were silent." Thanks, Ricardo.

• Regarding John Wilkins' artificial language, I said:

  . . . a certain bishop John Wilkins had invented a language in which the meaning of each word would be immediately apparent from its spelling.

  (I don't have an example handy, so I will make one up. All words that begin with "p" are animals. Words beginning with "pa" are birds, those with "pe" are fish, and so forth. Words beginning with "pel" are fish with fins and scales. Words for fin-fish that live in rivers and streams all begin with "pela". "pelam" is a salmon.)

  I have now obtained a copy of this book, and it uses "salmon" as an example. Wilkins' word for "salmon" is "zana". The first two letters always identify one of forty primary classifications for things; animal words begin with "z", and fish with "za". Each major group is divided into nine subgroups; the third letter identifies which of the nine subgroups the thing is in, with "n" denoting the ninth. The ninth subgroup of fish are "squamous river fish". Each subgroup is then divided into (usually) nine species, and the fourth letter identifies which of the nine species the thing is in with "a" denoting the second. The "squamous river fish" are divided as follows:

          Bigger fish
            Voracious fish
              With loose scales
                With one fin, near the tail; wide mouths, and sharp teeth (1)
                With two fins
                  Common to both fresh and salt water (2)
                  Common to fresh water only
                    Spotted (3)
                    Not spotted
                      More round (4)
                      More broad or compressed (5)
              With close, compact scales    (6)
            Not voracious
              Bigger
                Those that live in standing waters (7)
                Those that live in running waters
                  Those that are thick and round (8)
                  Those that are broad and deep (9)
              Lesser (10)
          Smallest river fish
            In the lower parts of the water
              With one fin on the back (11)
              With two fins and a broad head (12)
            In the upper parts of the water (13)
  

• Regarding British assertions that Americans speak of nothing but dollars, John Bodoni writes in with the following quotation from Ayn Rand's book Atlas Shrugged:

  "If you ask me to name the proudest distinction of Americans, I would choose--because it contains all the others--the fact that they were the people who created the phrase 'to make money.' No other language or nation had ever used these words before; men had always thought of wealth as a static quantity--to be seized, begged, inherited, shared, looted or obtained as a favor. Americans were the first to understand that wealth has to be created."

  I looked this up, and I found that it is not true. The OED has citations back to 1472:
  • 1472 R. CALLE in Paston Lett. (1976) II. 356, I truste be Ester to make of money..at the leeste l marke.
  • 1546 O. JOHNSON in H. Ellis Orig. Lett. Eng. Hist. 2nd Ser. II. 175 Besides the monney that I shal make of the said wares.
  • 1583 T. STOCKER tr. Tragicall Hist. Ciuile Warres Lowe Countries II. 64 [They] furnished him with all the money they were able to make.
  • 1588 R. PARKE tr. J. G. de Mendoza Hist. China 45 Then may the husband afterwardes sell his wife for a slave, and make money of her for the dowrie he gaue her.

  I suppose it's possible that the phrase only became common in the United States, but Rand's assertion that "No other nation had ever used these words before" is mistaken.

[Other articles in category /addenda] permanent link

Oral and non-oral reading

Order Mercury, or, The Swift and Secret Messenger with kickback no kickback

The following passage appears on page 3:

How strange a thing this art of writing did seem at its first invention, we may guess by the late discovered Americans, who were amazed to see men converse with books, and could scarce make themselves believe that a paper could speak; especially, when after all their attention and listening to any writing . . . they could never perceive any words or sound to proceed from it.

To Babu-aha-iddina, governor of Eridu, say thus:

You have not sent me the blueberry pie recipe you promised; why haven't you sent it? . . .

So says Tukulti-Ninurta, high king.

The idea that it is the letter itself that speaks seems to be a natural one. Wilkins tells a story of an Indian who is sent to deliver a letter and a basket of figs to a man in the next village. The messenger ate half the figs on the way, and was surprised to be found out upon his arrival when the quantity of figs he delivered did not match the quantity described in the letter. He responded by cursing the letter as a false and lying witness. On the next trip, he was careful to bury the letter under a rock while he ate the figs, so that it would not be able to accuse him when it was delivered.

Order Writing Systems with kickback no kickback

Children first learn to read by pronouncing the words aloud and hearing them; when they hear, they understand. Hearing is much easier than reading, and I think this is one reason why people like to attend lecture classes instead of just reading the book. People who "move their lips when they read" are widely ridiculed. But reading aloud is a good strategy for anyone faced with difficult material. When I can't make sense of a difficult paragraph, especially a long and confused one, I always back up and try reading it aloud, and this often resolves the difficulty. Even when I have forgotten the words at the beginning by the time I get to the end, I find that I still retain the sense of them. Reading aloud is also a good exercise for writers. If you read aloud what you wrote, you are much more likely to notice when it doesn't make sense. If you are too self-conscious to read aloud, or if the sign says QUIET PLEASE, try subvocalizing; it is still a big help.

Some kinds of literature should always be read aloud. Poetry, of course. If it is good poetry, it loses a lot of its value when read silently. I find that humor also loses its savor for me when I read it non-orally. When I first read Fear and Loathing in Las Vegas myself, I thought it was just stupid. When I heard James Woodyatt read it aloud, it was riotously funny. Lorrie and I found that Louise Erdrich's stories and novels, which can seem unrelievedly depressing when you read them alone, when read aloud became rich, complex, funny, sometimes bitter, sometimes joyful, and often sad---but never depressing.

Someone once told me that some famous scholar, I think perhaps Thomas Aquinas, was the only one of his contemporaries to read non-orally, that they were astonished at how the information would just fly from the book into his mind without his having to read it. Their failure to understand non-oral reading may be surprising today, when everyone is expected to do it. But I can remember making the same mistake myself. I was sitting on the floor, reading (aloud) the Sunday comics pages one evening, and I remarked that grown-ups did not actually read; they only looked at the pictures. My mother told me that they did read, but they did so silently. This was the first time I had encountered this idea, which I immediately adopted. I can't remember a time before I could read, but I do remember that occasion of my first silent reading.

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On the prolixity of Baroque authors
As readers of my blog know, I have lately been reading scientific and philosophical works of Robert Hooke, the diary of Samuel Pepys, and various essays by John Wilkins, all written during the 17th century. I've also been reading various works of Sir Thomas Browne, also from around the same time; I'm not sure how I've avoided mentioning him so far. (Had I been writing the blog back in December, Browne would have been all over it. I'm sure he will appear here sooner or later.)

Order Gulliver's Travels with kickback no kickback

The reason why that motion which is caused by the earth does appear as if it were in the heavens, is, because the sensus communit in judging of it, does conceive the eye to be itself immoveable (as was said before) there being no sense that does discern the effects of any motion in the body; and therefore it does conclude every thing to move, which it does perceive to change its distance from it: so that the clouds do not seem to move sometimes, when as notwithstanding they are everywhere carried about with our earth, by such a swift revolution; yet this can be no hindrance at all, why we may not judge aright of their other particular motions, for which there is not the same reason.

Baroque writing suits me just fine. The sentences are long, but always clear, if read with care and attention, and I like being required to read with care and attention. I'm good at it, and most modern writing does not offer the reader much repayment for that talent.

The long discussions full of allusion and quotation make me feel as though I'm part of a community of learned scholars, engaged in a careful and centuries-long analysis of the universe and Man's place in it. That's something I've always wanted, something I think we don't have much of today. In these authors I've at last begun to find it. When Wilkins mentions something that Vossius said on some topic, it doesn't bother me that I've never heard of Vossius. I feel that Wilkins is paying me a compliment by assuming that I will know who he's talking about, and that I might even recognize the quotation, or that even if I don't I will want to find out.

These authors do not patronize the reader or try to amuse him with cheap tricks. They assume that the reader wants to think, and that to be instructed is to be entertained.

But as usual I have wandered from the main point, which is to present a couple of contrasts to the usual 17th-century verbosity.

One is from Robert Hooke, in a review he wrote about John Dee's Book of Spirits. Dee was a mathematician, scholar, and occultist of the previous century. Hooke starts by saying:

Having lately met a book, which . . . I never had the Curiosity to examine further into, than upon opening here and there to read some few Lines, which seeming for the most very extravagant, I neglected any further Inquiry into it. . .

Nor was I frighted from this my Purpose, either by the six pretended Conjurers prefixt to the Title. . .; nor by the Title, viz. A true and full Relation of what passed for many Years between Dr. John Dee (a Mathematician of great Fame in Queen Elizabeth and King James, their Reigns) and some spirits, tending (had it succeeded) to a General Alteration of most States and Kingdoms in the World, &c. . . . No, nor thirdly the long and frighting Preface of the Publisher. . .

Another contrast is provided by Wilkins again. He is discussing the same point as the sentence I quoted above: what would be the observable effects of the rotation of the earth. In particular, the current point is whether a spinning earth would cause tall buildings to fall down, I suppose because their bottoms would be swept away by the earth while the tops stayed in place. (Yes, Wilkins provides a reference to someone who thinks this.) Wilkins answers at some length:

The motion of the earth is always equal and like itself; not by starts and fits. If a glass of beer may stand firmly enough in a ship, when it moves swiftly upon a smooth stream, much less then will the motion of the earth, which is more natural, an so consequently more equal, cause any danger unto those buildings that are erected upon it.

But supposing (saith Rosse) that this motion were natural to the earth, yet it is not natural to towns and buildings, for these are artificial.

To which I answer: ha, ha, he.

Order Graphical Evolution with kickback no kickback

Graphical evolution: An introduction to the theory of random graphs, wherein the most relevant probability models for graphs are described together with certain threshold functions which facilitate the careful study of the structure of a graph as it grows and specifically reveal the mysterious circumstances surrounding the abrupt appearance of the unique giant component which systematically absorbs its neighbors, devouring the larger first and ruthlessly continuing until the last isolated vertices have been swallowed up, whereupon the giant is suddenly brought under control by a spanning cycle. The text is laced with challenging exercises especially designed to instruct, and its accompanied by an appendix stuffed with useful formulas that everyone should know.

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Saguaros
In a recent post, I discussed an uninteresting travel book I had read recently, and compared it with Kon-Tiki, which is an interesting travel book. I'm sure I'll write more about travel books later; I have at least one post coming up about Kon-Tiki, and at least one about William Bligh's book about the mutiny on the H.M.S. Bounty. This latter one may not sound much like a travel book, but it is, and it's a corker.

Order Blue Highways with kickback no kickback

Everywhere he went, Heat Moon stopped and talked to people: men refurbishing an 18th-century log cabin in Kentucky; a monk in Georgia; hang-gliders in Washington; farmers in New York and fishermen in Maine; old folks and young folks. All of them have interesting things to say, and Heat Moon has interesting things to say about all of them. You can open up the book anywhere and strike gold.

For example, on page 11, Heat Moon stops in Shelbyville, Kentucky, for dinner:

Just outside of town and surrounded by cattle and pastures was Claudia Sanders Dinner House, a low building attached to an old brick farmhouse with red roof. I didn't make the connection in names until I was inside and saw a mantel full of coffee mugs of a smiling Harlan Sanders. Claudia was his wife, and the Colonel once worked out of the farmhouse before the great buckets-in-the-sky poured down their golden bounty of extra crispy. The Dinner House specialized in Kentucky ham and country-style vegetables.

She came back with grape jelly. In a land of quince jelly, apple butter, apricot jam, blueberry preserves, pear conserves, and lemon marmalade, you always get grape jelly.

Order Point, Long Island, was a few houses and a collapsed four-story inn built in 1810, so I went to Greenport for gas. At an old-style station, the owner himself came out and pumped the no-lead and actually wiped the windshield. I happened to refer to him as a New Yorker.

"Don't call me a New Yorker. This is Long Island."

"I meant the state, not the city."

"Manhattan's a hundred miles from here. We're closer to Boston than the city. Long Island hangs under Connecticut. Look at the houses here, the old ones. They're New England-style because the people that built them came from Connecticut. Towns out here look like Connecticut. I don't give a damn if the city's turned half the island into a suburb—we should rightfully be Connecticut Yankees. Or we should be the seventh New England state. This island's bigger than Rhode Island any way you measure it. The whole business gets my dander up. We used to berth part of the New England whaling fleet here, and that was a pure Yankee business. They called this part of the island 'the flikes' because Long Island even looks like a whale. But you go down to the wharf now and you'll see city boats and a big windjammer that sells rides to people from Mamaroneck and Scarsdale."

He got himself so exercised he overfilled the tank, but he didn't pipe down. "If the East River had've been ten miles wide, we'da been all right." He jerked the nozzle out and clanked it into the pump. "We needed a bay and we got a bastard river no wider than a stream of piss."

But as usual, what I planned to write about was a completely different passage:

The saguaro is ninety percent water, and a big, two-hundred-year-old cactus may hold a ton of it—a two-year supply. With this weight, a plant that begins to lean is soon on the ground; one theory now says that the arms, which begin sprouting only after forty or fifty years when the cactus has some height, are counterweights to keep the plant erect.

I wonder how you'd test something like that? You can't just tip a saguaro over a bit and see where the arms grow out, because those arms can take years and years to grow. (Also, it's not good for the plant, which is an endangered species. There's a reason that biologists like to study fruit flies.) Well, there's another thing on my list of things to look up after I'm granted immortality.

The Monday I drove northeast out of Phoenix, saguaros were in bloom—comparatively small, greenish-white blossoms perched on top of the trunks like undersized Easter bonnets; at night, long-nosed bats came to pollinate them. But by day, cactus wrens, birds of daring aerial skill, put on the show as they made kamikaze dives between toothpick-sized thorns into nest cavities, where they were safe from everything except the incredible ascents over the spines by black racers in search of eggs the snakes would swallow whole.

But the cosmic balance was preserved, because the cameraman was having the best day of his life.

I can just imagine how Mirza Abu Taleb Khan would have related this same journey:

We saw some large and remarkable plants as we left Phoenix. Mr. Charles Hightower informed me that they are called "cactus". These plants grew in many surprising and diverse shapes.

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Generating strings of balanced parentheses
About a year and a half ago, the Perl Quiz of the Week question was to write a program which, given an argument n, printed out all the strings containing n balanced pairs of parentheses. For example, if the argument was 3, the output was to contain the lines:

        ()()()
        (())()
        (()())
        ()(())
        ((()))

Enumerating parentheses is important because the parentheses obviously correspond to all the forms that an infix expression can take, so any attempt to enumerate all possible expressions of some form can be built atop a parenthesis-enumerator. But also, there's a straightforward correspondence between parentheses and tree structures, so by enumerating parentheses you are also enumerating all possible tree structures.

There were quite a few correct solutions posted to the list, and also some wrong ones. The commonest mistake to make was to assume that any string of n+1 pairs of balanced parentheses must have the form S(), ()S, or (S), where S is a string of n pairs of balanced parentheses. But this isn't so; (())(()) doesn't have this form. The commonest strategy that worked correctly was to generate all the strings of the right length of the form (S)S, where S is a shorter balanced string. This can be done recursively as follows:

        sub parens {
          my ($N) = @_;
          return ("") if $N == 0;
          my @result;
          for my $i (0 .. $N-1) {
            for $a (parens($i)) {
              for $b (parens($N-$i-1)) {
                push @result, "($a)$b";
              }
            }
          }
          return @result;
        }

        print join "\n", parens(shift()), "";

        sub parens {
          my $N = shift;
          $pattern = @_ ? shift : "S";
          if ($N == 0) {
            $pattern =~ tr/S//d;
            return $pattern;
          }
          return unless $pattern =~ /S/;
          my $new_pattern_a = my $new_pattern_b = $pattern;
          $new_pattern_a =~ s/S/S(S)/;
          $new_pattern_b =~ s/S//;
          return parens($N-1, $new_pattern_a), parens($N, $new_pattern_b);
        }

        print join "\n", parens(shift()), "";

        sub parens {
            my ($N, $unclosed, $s) = @_;
            $unclosed ||= 0;
            $s ||= "";
            return $s if $N == 0;
            my @result;
            push @result, parens($N,   $unclosed+1, "$s(")  if $unclosed < $N;
            push @result, parens($N-1, $unclosed-1, "$s)")  if $unclosed > 0 ;
            return @result;
        }

        print join "\n", parens(shift()), "";

        #!/usr/bin/perl -l

        print $_ = "()" x shift();
        print while s{^  ( \(+ )  ( \)+ ) \(  }
                     {"()" x (length($2) - 1)
                      . "("  x (length($1) - length($2) + 2) 
                      . ")" 
                     }xe;

I can explain how I thought it up, although I'm not sure whether the explanation will be helpful or whether it will sound like "I just counted the legs and divided by four."

One of the other list members suggested an alternative representation for the strings that seemed promising, so I tried out some examples. Close examination of those examples reminded me of a technique I had used to solve some other problems, so I tried to apply it in this case with the necesary variations. It worked well enough to continue the investigation, but the alternative representation was getting in the way. So I took what I had learned from applying the technique to the alternative representation and tried to write an algorithm to do the same thing directly to the strings of parentheses. Then I optimized the result for speed and code compactness.

I had originally planned to write a recursive solution, but before I started I thought it would be smart to investigate alternative representations. (Someday I'm going to write a long essay about this. I mentioned to Kurt Starsinic last week that the one sure sign of a program written by a novice programmer is that it will represent the data internally in the same format in which it needs to be output, typically as strings.)

One of the representations I looked at was one that had earlier been mentioned by Roger Burton West on the list. In this representation, a string of one "(" followed by n ")"'s becomes the number n, thus:

        ()()()()        1111
        ()()(())        1102
        ()(())()        1021
        ()(()())        1012
        ()((()))        1003
        (())()()        0211
        (())(())        0202
        (()())()        0121
        (()()())        0112
        (()(()))        0103
        ((()))()        0031
        ((())())        0022
        ((()()))        0013
        (((())))        0004

The essence of a counting process is that you find the rightmost column that has a certain property, and then you do a little transformation on it so that it gets a little less of that property and the columns to the right get reset to have more of it.

I realize that if you've never thought of it that way that is going to sound totally bizarre, so here's an example. Let's count base-10 numerals. The magic property in this case is the property of being less than 9. 0 has the largest possible amount of this property, since it is as much less than 9 as any digit can be. 8 has very little of this property, since it is just a little less than 9. 9 itself does not have any of this property, since it is not less than 9.

When you count, you find the rightmost column that is less than 9 and then you do a little transformation on it so that it has a little less of that property, so that it a little closer to 9:

        387
        388
        389

        390

        391
        392
        ...
        399

        400

Probably the next simplest example is when the property of interest is that the n'th column contains a number less than or equal to n:

        0000
        0010
        0100
        0110
        0200
        0210
        1000
        1010
        1100
        1110
        1200
        1210
        2000
        2010
        ...
        3210

Order Higher-Order Perl with kickback no kickback

Another example I was already familiar with is like the base-2 counting example, but with the added restriction that you are not allowed to have two adjacent 1's:

        0000000
        0000001
        0000010
        0000100
        0000101
        0001000
        0001001
        0001010
        0010000
        0010001
        0010010
        0010100
        0010101
        0100000
        ...

        s/00((10)*1?)$/"01" . "0" x length $1/e;

So anyway, I was already familiar with this idea, and when I saw the parenthesis numbers, it reminded me strongly of one of these counting processes. Here they are again:

        1111
        1102        
        1021
        1012
        1003
        0211
        0202
        0121
        0112
        0103
        0031
        0022
        0013
        0004

Since a number n here represents the string ()))...), with n close parentheses, we have the constraints that the leftmost column may not exceed 1; the sum of the two leftmost columns may not exceed 2, and so on. Under these constraints, 1111 is clearly an extreme case, and no string has the 1's any farther to the left. To go from 1111 to 1102, the rightmost moveable 1, which is in the third column, moves to the right, into the fourth column, which I now imagine contains a heap of two 1's.

Now the rightmost 1 is in the second column. So I reset the columns to the right of that (getting back 1111) and then move the 1 from the second to the third column, yielding 1021. Again, I imagine that the 2 here represents a heap of two 1's. These 1's can move to the right, yielding 1012 and then 1003.

Now I'll need to move the 1 from the first to the second column, so I reset the columns to the right of that (getting back 1111 again) and move the 1 from the first to the second column, yielding 0211. Then the 1 in the third column moves, yielding 0202, and then I reset the third and fourth columns back to 0211 so that I can move a 1 from the second to the third column, yielding 0121.

My first cut at implementing this actually manipulated these digit strings directly, like this:

        output while s/([1-9])(0*)([1-9])$/($1-1).($3-length($2)+1).1x length($2)/e;

Translated back into parentheses, the algorithm might even be simpler to understand. The property we are trying to reduce is appearances of )(, in which ( appears to the right of ). In ()()()...(), the open parentheses are as far to the right as they can be, so this represents the maximal configuration. At each step, we're going to find the rightmost moveable open parenthesis, and we're going to move it one step to the left. That is, we're going to find the rightmost )( and change it to (). If there are other parentheses to the right of the ones that moved, we'll reset them into their minimal configuration. In what follows, the )( that just changed to () is in red, and the parentheses to its right that were reset are in blue. The )( that is about to change to () in the next step is in boldface.

In the initial configuration, the rightmost )( is in positions 6-7:

        ()()()()                        1111

        ()()(())                        1102

        ()(()))()                       1021

        ()(()())                        1012

        ()((()))                        1003

        (())()()                        0211

        (())(())                        0202
        (()())()                        0121
        (()()())                        0112
        (()(()))                        0103
        ((()))()                        0031
        ((())())                        0022
        ((()()))                        0013
        (((())))                        0004

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The Almighty Dollar

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(On the bright side, we are getting to see more of Mark Tapley. Mark is kind, astute, thrifty, and above all, cheerful. Born with a naturally jolly disposition, he has chosen it as his life goal to remain jolly under even the most trying circumstances. In pursuit of this goal, he seeks out the most trying circumstances possible, the better to do himself credit by his unfailing jollity. When we first meet him, he is working at the Blue Dragon pub, but is planning to quit:

`What's the use of my stopping at the Dragon? It an't at all the sort of place for me. When I left London (I'm a Kentish man by birth, though), and took that situation here, I quite made up my mind that it was the dullest little out-of-the-way corner in England, and that there would be some credit in being jolly under such circumstances. But, Lord, there's no dullness at the Dragon! Skittles, cricket, quoits, nine-pins, comic songs, choruses, company round the chimney corner every winter's evening. Any man could be jolly at the Dragon. There's no credit in that.'

`But if common report be true for once, Mark, as I think it is, being able to confirm it by what I know myself,' said Mr. Pinch, `you are the cause of half this merriment, and set it going.'

`There may be something in that, too, sir,' answered Mark. `But that's no consolation.'

Martin thought this an uncomfortable custom, but he kept his opinion to himself for the present, being anxious to hear, and inform himself by, the conversation of the busy gentlemen . . . .

It was rather barren of interest, to say the truth; and the greater part of it may be summed up in one word. Dollars. All their cares, hopes, joys, affections, virtues, and associations, seemed to be melted down into dollars. Whatever the chance contributions that fell into the slow cauldron of their talk, they made the gruel thick and slab with dollars. Men were weighed by their dollars, measures gauged by their dollars; life was auctioneered, appraised, put up, and knocked down for its dollars. The next respectable thing to dollars was any venture having their attainment for its end. The more of that worthless ballast, honour and fair-dealing, which any man cast overboard from the ship of his Good Name and Good Intent, the more ample stowage-room he had for dollars. Make commerce one huge lie and mighty theft. Deface the banner of the nation for an idle rag; pollute it star by star; and cut out stripe by stripe as from the arm of a degraded soldier. Do anything for dollars! What is a flag to them!

I heard an Englishman, who had been long resident in America, declare that in following, in meeting, or in overtaking, in the street, on the road, or in the field, at the theatre, the coffee-house, or at home, he had never overheard Americans conversing without the word DOLLAR being pronounced between them. Such unity of purpose, such sympathy of feeling, can, I believe, be found nowhere else, except, perhaps, in an ants' nest. The result is exactly what might be anticipated. This sordid object, for ever before their eyes, must inevitably produce a sordid tone of mind, and, worse still, it produces a seared and blunted conscience on all questions of probity.

Martin Chuzzlewit was written in 1843-1844. Dickens had travelled in America for the first time in 1842. I wonder how much of what he saw and thought was colored by Trollope's account, which I imagine he had read.

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The Kansas state quarter
In the 1986 Baseball Abstract, sportswriter Bill James, a Kansas native, included an article titled A History of Being a Kansas City Baseball Fan. The article begins:

I am, and have been for as long as it is possible to remember, a fan of the Kansas City baseball teams. In my youth this required that I support the Kansas City Athletics, the only team in modern history which has never had a .500 or better season.

At every insurgence of the national media, Kansas City press packets were handed out repeating a number of overworked boasts about the place. "Kansas City has more fountains than Rome." . . . "Kansas City has more miles of boulevards than Paris." This one always conjures up images of the International Board of Boulevard Certification, walking along saying "No, I'm afraid this one is just an 'Avenue' unless you widen the curb space by four more inches and plant six more trees per half mile." . . . The city's image would improve a lot of they would just accept themselves for what they are, and stop handing out malarkey about how many miles of boulevard they have.

And, unlike most of the other state quarters, it has no extraneous text. No patronizing caption. No vapid mottoes. No "Land of Lincoln" or "Pioneers of Aviation". No cutesy state nickname. No malarkey about how many miles of boulevard. Just "Kansas 1861". The designers let the picture speak for itself. That takes confidence, and I think it paid off.

Good job, Kansans.

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Petard corrections
Eric Cholet has written in to mention that he is familiar with the fried choux pastry that I mentioned yesterday, but under the name pets de nonne, not pets de soeurs, as I said. (Nonne, of course, is "nun". The word soeur is literally "sister", but in this context means "nun". ) I had cited On Food and Cooking as mentioning pets de soeurs, but it agrees with Eric, not with me.

It appears, though, that many people do use the name pets de soeurs to refer to these fritters, and some people also use it to refer to a kind of soda-raised cinnamon roll. Citations to various cookbooks are available through the usual searches.

Eric also points out that petard is the current word for a firecracker, and also now refers to a doobie. I was already aware of this because pictures of those things appeared when I did Google image seach for petard. Thank you, Eric.

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Petard
A petard is a Renaissance-era bomb, basically a big firecracker: a box or small barrel of gunpowder with a fuse attached. Those hissing black exploding spheres that you see in Daffy Duck cartoons are petards. Outside of cartoons, you are most likely to encounter the petard in the phrase "hoist with his own petard", which is from Hamlet. Rosencrantz and Guildenstern are being sent to England with the warrant for Hamlet's death; Hamlet alters the warrant to contain R&G's names instead of his own. "Hoist", of course, means "raised", and Hamlet is saying that it is amusing to see someone screw up his own petard and blow himself sky-high with it.

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Another fart-related word is "partridge", so named because its call sounds like a fart.

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Google query roundup
Now that I have a reasonably-sized body of blog posts, my blog is starting to attract Google queries. It's really exciting when someone visits one of my pages looking for something incredibly specific and obscure and I can tell from their query in the referrer log that I have unknowingly written exactly the document they were hoping to find. That's one of the wonders of the Internet thingy.

For example:

	   1 monkey rope banana weight
	   1 "how long is the banana"
	   3 monkey's mother problem
	   1 "basil brown" carrot juice
	   1 story about diophantus,how old was diophantus when he got married

And this visitor got rather more than they wanted:

	   1 what pennsylvanian can we thank for daylight savings time

Although you'd think that by now the middle schooler would have figured out that questions that start with "What Pennsylvanian can we thank for..." are about Benjamin Franklin with extremely high probability.

I think this person was probably fairly happy:

	   3 franklin "restoration of life by sun rays"

Similarly, I imagine that this person was pleased:

	   1 monarch-like butterfly

Some of the queries are intriguing. I wonder what this person was looking for?

	   1 spanish armada & monkey

	   1 there is a cabinet with 12 drawers. each drawer is opened
	     only once. in each drawer are about 30 compartments, with
	     only 7 names.

Sometimes I know that the searches did not find what they were looking for.

	   1 eliminate debt using linear math

	   1 armonica how many people can properly use it

I had the good fortune to attend an armonica recital by Dean Shostak as part of the Philadelphia Fringe Festival a few years ago. Mr. Shostak is one of very few living armonica players. (He says that there are seven others.) The armonica is not popular because it is bulky, hard to manufacture, and difficult to play. The bowls must be constructed precisely, by a skilled glassblower, to almost the right pitch, and then carefully filed down until they are exactly right. If you overfile one, it is junk. If a bowl goes out of tune, it must be replaced; this requires that all the other bowls be unmounted from the spindle. The bowls are fragile and break easily.

The operator's hands must be perfectly clean, because the slightest amount of lubrication prevents the operator from setting the glass vibrating. The operator must keep his fingertips damp at all times, continually wetting them from a convenient bowl of water. By the end of a concert, his fingers are all pruney and have been continually rubbed against the rotating bowls; this limits the amount of time the instrument can be played.

Shostak's web site has some samples that you can listen to. Unfortunately, it does not also have any videos of him playing the instrument.

	   1 want did an wang invent 

An Wang invented the magnetic core memory that was the principal high-speed memory for computers through the 1950s and 1960s. In this memory technology, each bit was stored in a little ferrite doughnut, called a "core". If the magnetic field went one way through the doughnut, it represented a 0; the other way was a 1. Thousands of these cores would be strung on wire grids. Each core was on one vertical and one horizontal wire. The computer could modify the value of the bit by sending current on the core's horizontal wire and vertical wire simultaneously. The two currents individually were too small to modify the other bits in the same row and column. If the bit was actually changed, the resulting effect on the current could be detected; this is how bits were read: You'd try to write a 1, and see if that caused a change in the bit value. Then if it turned out to have been a 0, you'd put it back the way it was.

The cores themselves were cheap and easy to manufacture. You mix powdered iron with ceramic, stamp it into the desired shape in a mold, and bake it in a kiln. Stringing cores into grids was more expensive. and was done by hand.

As the technology improved, the cores themselves got smaller and the grids held more and more of them. Cores from the 1950s were about a quarter-inch in diameter; cores from the late 1960s were about one-quarter that size. They were finally obsoleted in the 1970s by integrated circuits.

When I was in high school in New York in the 1980s, it was still possible to obtain ferrite cores by the pound from the surplus-electronics stores on Canal Street. By the 1990s, the cores were gone. You can still buy them online.

An Wang got very rich from the invention and was able to found Wang computers. Around 1980 my mother's employer had a Wang word-processing system. It was a marvel that took up a large space and cost $15,000. ($35,000 in 2006 dollars.) She sometimes brought me in on weekends so that I could play with it. Such systems, the first word processors, were tremendously popular between 1976 and 1981. They invented the form, which, as I recall, was not significantly different from the word processors we have today. Of course, these systems were doomed, replaced by cheap general-purpose machines within a few years.

The undergraduate dormitories at Harvard University are named mostly for Harvard's presidents: Mather House, Dunster House, Eliot House, and so on. One exception was North House. A legend says Harvard refused an immense donation from Wang, whose successful company was based in Cambridge, because it came with the condition that North house be renamed after him. (Similarly, one sometimes hears it said that the Houses are named for all the first presidents of Harvard, except for president number 3, Leonard Hoar, who was skipped. It's not true; numbers 2, 4, and 5 were skipped also.)

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Travels of Mirza Abu Taleb Khan
In a couple of recent posts, I talked about the lucky finds you can have then you browse at random in strange libraries. Sometimes the finds don't turn out so well.

I'm an employee of the University of Pennsylvania, and one of the best fringe benefits of the job is that I get unrestricted access to the library and generous borrowing privileges. A few weeks ago I was up there, and found my way somehow into the section with the travel books. I grabbed a bunch, one of which was the source for my discussion of the dot product in 1580. Another was Travels of Mirza Abu Taleb Khan, written around 1806, and translated into English and published in English in 1814.

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Wow, what a find, I thought, when I discovered it in the library. How could such a book fail to be fascinating? But if you take that as a real question, not as a rhetorical one, an answer comes to mind immediately: Mirza Abu Taleb does not have very much to say!

A large portion of the book drops the names of the many people that Mirza Abu Taleb met with, had dinner with, went riding with, went drinking with, or attended a party at the house of. Opening the book at random, for example, I find:

The Duke of Leinster, the first of the nobles of this kingdom honoured me with an invitation; his house is the most superb of any in Dublin, and contains a very numerous and valuable collection of statues and paintings. His grace is distinguished for the dignity of his manners, and the urbanity of his disposition. He is blessed with several angelic daughters.

Here's another:

[In Paris] I also had the pleasure of again meeting my friend Colonel Wombell, from whom I experienced so much civility in Dublin. He was rejoiced to see me, and accompanied me to all the public places. From Mr. and Miss Ogilvy I received the most marked attention.

Even when Abu Taleb has something to say, he usually doesn't say it:

I was much entertained by an exhibition of Horsemanship, by Mr. Astley and his company. They have an established house in London, but come over to Dublin for four or five months in every year, to gratify the Irish, by displaying their skill in this science, which far surpasses any thing I ever saw in India.

I don't know. That's all there is about Mr. Astley and his company.

Almost the whole book is like this. Abu Taleb is simply not a good observer. Good writers in any language can make you feel that you were there at the same place and the same time, seeing what they saw and hearing what they heard. Abu Taleb doesn't understand that one good specific story is worth a pound of vague, obscure generalities. This defect spoils nearly every part of the book in one degree or another:

[The Irish] are not so intolerant as the English, neither have they austerity and bigotry of the Scotch. In bravery and determination, hospitality, and prodigality, freedom of speech and open-heartedness, they surpass the English and the Scotch, but are deficient in prudence and sound judgement: they are nevertheless witty, and quick of comprehension.

Thus my land lady and her children soon comprehended my broken English; and what I could not explain by language, they understood by signs. . . . When I was about to leave them, and proceed on my journey, many of my friends appeared much affected, and said: "With your little knowledge of the language, you will suffer much distress in England; for the people there will not give themselves any trouble to comprehend your meaning, or to make themselves useful to you." In fact, after I had resided for a whole year in England, and could speak the language a hundred times better than on my first arrival, I found much more difficulty in obtaining what I wanted, than I did in Ireland.

Here's another passage I liked:

In this country and all through Europe, but especially in France and in Italy, statues of stone and marble are held in high estimation, approaching to idolatry. Once in my presence, in London, a figure which had lost its head, arms, and legs, and of which, in short, nothing but the trunk remained, was sold for 40,000 rupees (£5000). It is really astonishing that people possessing so much knowledge and good sense, and who reproach the nobility of Hindoostan with wearing gold and silver ornaments like women, whould be thus tempted by Satan to throw away their money upon useless blocks. There is a great variety of these figures, and they seem to have appropriate statues for every situation. . .

. . . thus, at the doors or gates, they have huge janitors; in the interior they have figures of women dancing with tambourines and other musical instruments; over the chimney-pieces they place some of the heathen deities of Greece; in the burying grounds they have the statues of the deceased; and in the gardens they put up devils, tigers, or wolves in pursuit of a fox, in hopes that animals, on beholding these figures will be frightened, and not come into the garden.

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Another similarly good travel book is Sir Richard Francis Burton's 1853 account of his pilgimage to Mecca. Infidels were not allowed in the holy city of Mecca. Burton disguised himself as an Afghan and snuck in. I expect I'll have something to say about this book in a future article.

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The octopus and the creation of the cosmos
In an earlier post, I mentioned the lucky finds you sometimes make when you're wandering at random in a library. Here's another such. In 2001 I was in Boston with my wife, who was attending the United States Figure Skating Championships. Instead of attending the Junior Dance Compulsories, I went to the Boston Public Library, where I serendipitously unearthed the following treasure:

Although we have the source of all things from chaos, it is a chaos which is simply the wreck and ruin of an earlier world....The drama of creation, according to The Hawaiian account, is divided into a series of stages, and in the very first of these life springs from the shadowy abyss and dark night...At first the lowly zoophytes and corals come into being, and these are followed by worms and shellfish, each type being declared to conquer and destroy its predecessor, a struggle for existence in which the strongest survive....As type follows type, the accumulating slime of their decay raises land above the waters, in which, as spectator of all, swims the octopus, the lone survivor of an earlier world.

Everyone, it seems, recognizes the octopus as a weird alien, unique in our universe.

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"Farther" vs. "further"
People mostly use "farther" and "further" interchangeably. What's the difference?

I looked it up in the dictionary, and it turns out it's simple. "Farther" means "more far". "Further" means "more forward".

"Further" does often connote "farther", because something that is further out is usually farther away, and so in many cases the two are interchangeable. For example, "Hitherto shalt thou come, but no further" (Job 38:11.)

But now when I see people write things like China Steps Further Back From Democracy (The New York Times, 26 November 1995) or, even worse, Big Pension Plans Fall Further Behind (Washington Post, 7 June 2005) it freaks me out.

Google finds 3.2 million citations for "further back", and 9.5 million for "further behind", so common usage is strongly in favor of this. But a quick check of the OED does not reveal much historical confusion between these two. Of the citations there, I can only find one that rings my alarm bell. ("1821 J. BAILLIE Metr. Leg., Wallace lvi, In the further rear.")

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Morphogenetic puzzles
In a recent post, I briefly discussed puzzling issues of morphogenesis: when a caterpillar pupates, how do its cells know how to reorganize into a butterfly? When the blastocyst grows inside a mammal, how do its cells know what shape to take? I said it was all a big mystery.

A reader, who goes by the name of Omar, wrote to remind me of the "Hox" (short for "homeobox") genes discussed by Richard Dawkins in The Ancestor's Tale. (No "buy this" link; I only do that for books I've actually read and recommend.) These genes are certainly part of the story, just not the part I was wondering about.

The Hox genes seem to be the master controls for notifying developing cells of their body locations. The proteins they manufacture bind with DNA and enable or disable other genes, which in turn manufacture proteins that enable still other genes, and so on. A mutation to the Hox genes, therefore, results in a major change to the animal's body plan. Inserting an additional copy of a Hox gene into an invertebrate can cause its offspring to have duplicated body segements; transposing the order of the genes can mix up the segments. One such mutation, occurring in fruit flies, is called antennapedia, and causes the flies' antennae to be replaced by fully-formed legs!

So it's clear that these genes play an important part in the overall body layout.

But the question I'm most interested in right now is how the small details are implemented. That's why I specifically brought up the example of a ring finger.

Or consider that part of the ring finger turns into a fingernail bed and the rest doesn't. The nail bed is distally located, but the most distal part of the finger nevertheless decides not to be a nail bed. And the ventral part of the finger at the same distance also decides not to be a nail bed.

Meanwhile, the ear is growing into a very complicated but specific shape with a helix and an antihelix and a tragus and an antitragus. How does that happen? How do the growing parts communicate between each other so as to produce that exact shape? (Sometimes, of course, they get confused; look up accessory tragus for example.)

In computer science there are a series of related problems called "firing squad problems". In the basic problem, you have a line of soldiers. You can communicate with the guy at one end, and other than that each soldier can only communicate with the two standing next to him. The idea is to give the soldiers a protocol that allows them to synchronize so that they all fire their guns simultaneously.

It seems to me that the embryonic cells have a much more difficult problem of the same type. Now you need the soldiers to get into an extremely elaborate formation, even though each soldier can only see and talk to the soldiers next to him.

Omar suggested that the Hox genes contain the answer to how the fetal cells "know" whether to be a finger and not a kneecap. But I think that's the wrong way to look at the problem, and one that glosses over the part I find so interesting. No cell "becomes a finger". There is no such thing as a "finger cell". Some cells turn into hair follicles and some turn into bone and some turn into nail bed and some turn into nerves and some turn into oil glands and some turn into fat, and yet you somehow end up with all the cells in the right places turning into the right things so that you have a finger! And the finger has hair on the first knuckle but not the second. How do the cells know which knuckle they are part of? At the end of the finger, the oil glands are in the grooves and not on the ridges. How do the cells know whether they will be at the ridges or the grooves? And the fat pad is on the underside of the distal knuckle and not all spread around. How do the cells know that they are in the middle of the ventral surface of the distal knuckle, but not too close to the surface?

Somehow the fat pad arises in just the right place, and decides to stop growing when it gets big enough. The hair cells arise only on the dorsal side and the oil glands only on the ventral side.

How do they know all these things? How does the cell decide that it's in the right place to differentiate into an oil gland cell? How does the skin decide to grow in that funny pattern of ridges and grooves? And having decided that, how do the skin cells know whether they're positioned at the appropriate place for a ridge or a groove? Is there a master control that tells all the cells everything at once? I bet not; I imagine that the cells conduct chemical arguments with their neighbors about who will do which job.

One example of this kind of communication is phyllotaxis, the way plants decide how to distribute their leaves around the stem. Under certain simple assumptions, there is an optimal way to do this: you want to go around the stem, putting each leaf about 360°/φ farther than the previous one, where φ is ½(1+√5). (More about this in some future post.) And in fact many plants do grow in just this pattern. How does the plant do such an elaborate calculation? It turns out to be simple: Suppose leafing is controlled by the buildup of some chemical, and a leaf comes out when the chemical concentration is high. But when a leaf comes out, it also depletes the concentration of the chemical in its vicinity, so that the next leaf is more likely to come out somewhere else. Then the plant does in fact get leaves with very close to optimal placement. Each leaf, when it comes out, warns the nearby cells not to turn into a leaf themselves---not until the rest of the stem is full, anyway. I imagine that the shape of the ear is constructed through a more complicated control system of the same sort.

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Vitamin A poisoning

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B and C vitamins are not toxic in large doses; they are water-soluble so that excess quantities are easily excreted. Vitamins A and D are not water-soluble, so excess quantities are harder to get rid of. Apparently, though, the liver is capable of storing very large quantities of vitamin D, so that vitamin D poisoning is extremely rare.

The only cases of vitamin A poisoning I've heard of concerned either people who ate the livers of polar bears, walruses, sled dogs, or other arctic animals, or else health food nuts who consumed enormous quantities of pure vitamin A in a misguided effort to prove how healthy it is. In On Food and Cooking, Harold McGee writes:

In the space of 10 days in February of 1974, an English health food enthusiast named Basil Brown took about 10,000 times the recommended requirement of vitamin A, and drank about 10 gallons of carrot juice, whose pigment is a precursor of vitamin A. At the end of those ten days, he was dead of severe liver damage. His skin was bright yellow.

There was a period in my life in which I was eating very large quantities of carrots. (Not for any policy reason; just because I like carrots.) I started to worry that I might hurt myself, so I did a little research. The carrots themselves don't contain vitamin A; they contain beta-carotene, which the body converts internally to vitamin A. The beta-carotene itself is harmless, and excess is easily eliminated. So eat all the carrots you want! You might turn orange, but it probably won't kill you.

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Butterflies
Yesterday I visited the American Museum of Natural History in New York City, for the first time in many years. They have a special exhibit of butterflies. They get pupae shipped in from farms, and pin the pupae to wooden racks; when the adults emerge, they get to flutter around in a heated room that is furnished with plants, ponds of nectar, and cut fruit.

The really interesting thing I learned was that chrysalises are not featureless lumps. You can see something of the shape of the animal in them. (See, for example, this Wikipedia illustration.) The caterpillar has an exoskeleton, which it molts several times as it grows. When time comes to pupate, the chrysalis is in fact the final exoskeleton, part of the animal itself. This is in contrast to a cocoon, which is different. A cocoon is a case made of silk or leaves that is not part of the animal; the animal builds it and lives inside. When you think of a featureless round lump, you're thinking of a cocoon.

Until recently, I had the idea that the larva's legs get longer, wings sprout, and so forth, but it's not like that at all. Instead, inside the chrysalis, almost the entire animal breaks down into a liquid! The metamorphosis then reorganizes this soup into an adult. I asked the explainer at the Museum if the individual cells retained their identities, or if they were broken down into component chemicals. She didn't know, unfortunately. I hope to find this out in coming weeks.

How does the animal reorganize itself during metamorphosis? How does its body know what new shape to grow into? It's all a big mystery. It's nice that we still have big mysteries. Not all mysteries have survived the scientific revolution. What makes the rain fall and the lightning strike? Solved problems. What happens to the food we eat, and why do we breathe? Well-understood. How does the butterfly reorganize itself from caterpillar soup? It's a big puzzle.

A related puzzle is how a single cell turns into a human baby during gestation. For a while, the thing doubles, then doubles again, and again, becoming roughly spherical, as you'd expect. But then stuff starts to happen: it dimples, and folds over; three layers form, a miracle occurs, and eventually you get a small but perfectly-formed human being. How do the cells in the fingers decide to turn into fingers? How does the cells in the fourth finger know they're one finger from one side of the hand and three fingers from the other side? Maybe the formation of the adult insect inside the chrysalis uses a similar mechanism. Or maybe it's completely different. Both possibilities are mind-boggling.

This is nowhere near being the biggest pending mystery; I think we at least have some idea of where to start looking for the answer. Contrast this with the question of how it is we are conscious, where nobody even has a good idea of what the question is.

Other caterpillar news: chrysalides are so named because they often have a bright golden sheen, or golden features. (Greek "khrusos" is "gold".) The Wikipedia picture of this is excellent too. The "gold" is a yellow pigmented area covered with a shiny coating. The explainer said that some people speculate that it helps break up the outlines of the pupa and camouflage it.

I asked if the chrysalis of the viceroy butterfly, which, as an adult, resembles the poisonous monarch butterfly, also resembled the monarch's chrysalis. The answer: no, they look completely different. Isn't that interesting? You'd think that the pupa would get at least as much benefit from mimicry as the adult. One possible explanation why not: most pupae don't make it to adulthood anyway, so the marginal benefit to the species from mimicry in the pupal stage is small compared with the benefit in the adult stage. Another: the pupa's main defense, which is not available to the adult, is to be difficult to see; beyond that it doesn't matter much what happens if it is seen. Which is correct? I don't know.

For a long time folks thought that the monarch was poisonous and the viceroy was not, and that the viceroy's monarch-like coloring tricked predators into avoiding it unnecessarily. It's now believed that both speciies are poisonous and bad-tasting, and that their similar coloring therefore protects both species. A predator who eats one will avoid both in the future. The former kind of mimicry is called Batesian; the latter, Müllerian.

The monarch butterfly does not manufacture its toxic and bad-tasting chemicals itself. It is poisonous because it ingests poisonous chemicals in its food, which I think is milkweed plants. Plant chemistry is very weird. Think of all the poisonous foods you've ever heard of. Very few of them are animals. (The only poisonous meat I can think of offhand is the liver of arctic animals, which has a toxically high concentration of vitamin D.) If you're stuck on a desert island, you're a lot safer eating strange animals than you are eating strange berries.

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Franklin and Daylight Saving Time
You often hear it asserted that Benjamin Franklin was the inventor of daylight saving time. But it's really not true.

The essential feature of DST is that there is an official change to the civil calendar to move back all the real times by one hour. Events that were scheduled to occur at noon now occur at 11 AM, because all the clocks say noon when it's really 11 AM.

The proposal by Franklin that's cited as evidence that he invented DST doesn't propose any such thing. It's a letter to the editors of The Journal of Paris, originally sent in 1784. There are two things you should know about this letter: First, it's obviously a joke. And second, what it actually proposes is just that people should get up earlier!

I went home, and to bed, three or four hours after midnight. . . . An accidental sudden noise waked me about six in the morning, when I was surprised to find my room filled with light. . . I got up and looked out to see what might be the occasion of it, when I saw the sun just rising above the horizon, from whence he poured his rays plentifully into my chamber. . .

. . . still thinking it something extraordinary that the sun should rise so early, I looked into the almanac, where I found it to be the hour given for his rising on that day. . . . Your readers, who with me have never seen any signs of sunshine before noon, and seldom regard the astronomical part of the almanac, will be as much astonished as I was, when they hear of his rising so early; and especially when I assure them, that he gives light as soon as he rises. I am convinced of this. I am certain of my fact. One cannot be more certain of any fact. I saw it with my own eyes. And, having repeated this observation the three following mornings, I found always precisely the same result.

I considered that, if I had not been awakened so early in the morning, I should have slept six hours longer by the light of the sun, and in exchange have lived six hours the following night by candle-light; and, the latter being a much more expensive light than the former, my love of economy induced me to muster up what little arithmetic I was master of, and to make some calculations. . .

Franklin finishes by offering his brilliant insight to the world free of charge or reward:

I expect only to have the honour of it. And yet I know there are little, envious minds, who will, as usual, deny me this and say, that my invention was known to the ancients, and perhaps they may bring passages out of the old books in proof of it. I will not dispute with these people, that the ancients knew not the sun would rise at certain hours; they possibly had, as we have, almanacs that predicted it; but it does not follow thence, that they knew he gave light as soon as he rose. This is what I claim as my discovery.

OK, I'm not done yet. I think the story of how I happened to find this out might be instructive.

I used to live at 9th and Pine streets, across from Pennsylvania Hospital. (It's the oldest hospital in the U.S.) Sometimes I would get tired of working at home and would go across the street to the hospital to read or think. Hospitals in general are good for that: they are well-equipped with lounges, waiting rooms, comfortable chairs, sofas, coffee carts, cafeterias, and bathrooms. They are open around the clock. The staff do not check at the door to make sure that you actually have business there. Most of the people who work in the hospital are too busy to notice if you have been hanging around for hours on end, and if they do notice they will not think it is unusual; people do that all the time. A hospital is a great place to work unmolested.

Pennsylvania Hospital is an unusually pleasant hospital. The original building is still standing, and you can go see the cornerstone that was laid in 1755 by Franklin himself. It has a beautful flower garden, with azaleas and wisteria, and a medicinal herb garden. Inside, the building is decorated with exhibits of art and urban archaeology, including a fire engine that the hospital acquired in 1780, and a massive painting of Christ healing the sick, originally painted by Benjamin West so that the hospital could raise funds by charging people a fee to come look at it. You can visit the 19th-century surgical amphitheatre, with its observation gallery. Even the food in the cafeteria is way above average. (I realize that that is not saying much, since it is, after all, a hospital cafeteria. But it was sufficiently palatable to induce me to eat lunch there from time to time.)

Having found so many reasons to like Pennsylvania Hospital, I went to visit their web site to see what else I could find out. I discovered that the hospital's clinical library, adjacent to the surgical amphitheatre, was open to the public. So I went to visit a few times and browsed the stacks.

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Preface
The Ingenious Dr. Franklin
Daylight Saving
Treatment for Gout
Cold Air Bath
Electrical Treatment for Paralysis
Lead Poisoning
Rules of Health and Long Life
The Art of Procuring Pleasant Dreams
Learning to Swim
On Swimming
Choosing Eye-Glasses
Bifocals
Lightning Rods
Advantage of Pointed Conductors
Pennsylvanian Fireplaces
Slaughtering by Electricity
Canal Transportation
Indian Corn
The Armonica
First Hydrogen Balloon
A Hot-Air Balloon
First Aerial Voyage by Man
Second Aerial Voyage by Man
A Prophecy on Aerial Navigation
Magic Squares
Early Electrical Experiments
Electrical Experiments
The Kite
The Course and Effect of Lightning
Character of Clouds
Musical Sounds
Locating the Gulf Stream
Charting the Gulf Stream
Depth of Water and Speed of Boats
Distillation of Salt Water
Behavior of Oil on Water
Earliest Account of Marsh Gas
Smallpox and Cancer
Restoration of Life by Sun Rays
Cause of Colds
Definition of a Cold
Heat and Cold
Cold by Evaporation
On Springs
Tides and Rivers
Direction of Rivers
Salt and Salt Water
Origin of Northeast Storms
Effect of Oil on Water
Spouts and Whirlwinds
Sun Spots
Conductors and Non-Conductors
Queries on Electricity
Magnetism and the Theory of the Earth
Nature of Lightning
Sound
Prehistoric Animals of the Ohio
Toads Found in Stone
Checklist of Letters and Papers
List of Correspondents
List of a Few Additional Letters

Anyway, the moral of the story, as I see it, is: If you make your way into strange libraries and browse through the stacks, sometimes you find some good stuff, so go do that once in a while.

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The Bowdlerization of Dr. Dolittle

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When it was decided to reissue the Doctor Dolittle books, we were faced with a challenging opportunity and decision. In some of the books there were certain incidents depicted that, in light of today's sensitivities, were considered by some to be disrespectful to ethnic minorities and, therefore, perhaps inappropriate for today's young reader. In these centenary editions, this issue is addressed.

. . . After much soul-searching the consensus was that changes should be made. The deciding factor was the strong belief that the author himself would have immediately approved of making the alterations. Hugh Lofting would have been appalled at the suggestion that any part of his work could give offense and would have been the first to have made the changes himself. In any case, the alterations are minor enough not to interfere with the style and spirit of the original.

Many of the changes concern Prince Bumpo, a character who first appeared in The Story of Doctor Dolittle. Bumpo is a black African prince, who, at the beginning of Voyages, is in England, attending school at Oxford. Bumpo is a highly sympathetic character, but also a comic one. In Voyages his speech is sprinkled with inappropriate "Oxford" words: he refers to "the college quadrilateral", and later says "I feel I am about to weep from sediment", for example. Studying algebra makes his head hurt, but he says "I think Cicero's fine—so simultaneous. By the way, they tell me his son is rowing for our college next year—charming fellow." None of this humor at Bumpo's expense has been removed from the Centenary Edition.

Bumpo's first appearance in the book, however, has been substantially cut:

The Doctor had no sooner gone below to stow away his note-books than another visitor appeared upon the gang-plank. This was a most extraordinary-looking black man. The only other negroes I had seen had been in circuses, where they wore feathers and bone necklaces and things like that. But this one was dressed in a fashionable frock coat with an enormous bright red cravat. On his head was a straw hat with a gay band; and over this he held a large green umbrella. He was very smart in every respect except his feet. He wore no shoes or socks.

The Doctor had no sooner gone below to stow away his note-books than another visitor appeared upon the gang-plank. This was a black man, very fashionably dressed. (p. 128)

I very soon grew to be quite fond of our funny black friend Bumpo, with his grand way of speaking and his enormous feet which some one was always stepping on or falling over.

This is typical. Most of the changes are excisions of rather ordinary references to the skin color of the characters. For example, the original:

It is quite possible we shall be the first white men to land there. But I daresay we shall have some difficulty in finding it first."

Another typical cut:

"Great Red-Skin," he said in the fierce screams and short grunts that the big birds use, "never have I been so glad in all my life as I am to-day to find you still alive."

In a flash Long Arrow's stony face lit up with a smile of understanding; and back came the answer in eagle-tongue.

"Mighty White Man, I owe my life to you. For the remainder of my days I am your servant to command."

Another, larger change of this type, where apparently value-neutral references to skin color have been excised, is in the poem "The Song of the Terrible Three" at the end of part V, chapter 5. The complete poem is:

THE SONG OF THE TERRIBLE THREE

Oh hear ye the Song of the Terrible Three
And the fight that they fought by the edge of the sea.
Down from the mountains, the rocks and the crags,
Swarming like wasps, came the Bag-jagderags.

Surrounding our village, our walls they broke down.
Oh, sad was the plight of our men and our town!
But Heaven determined our land to set free
And sent us the help of the Terrible Three.

One was a Black—he was dark as the night;
One was a Red-skin, a mountain of height;
But the chief was a White Man, round like a bee;
And all in a row stood the Terrible Three.

Shoulder to shoulder, they hammered and hit.
Like demons of fury they kicked and they bit.
Like a wall of destruction they stood in a row,
Flattening enemies, six at a blow.

Oh, strong was the Red-skin fierce was the Black.
Bag-jagderags trembled and tried to turn back.
But 'twas of the White Man they shouted, "Beware!
He throws men in handfuls, straight up in the air!"

Long shall they frighten bad children at night
With tales of the Red and the Black and the White.
And long shall we sing of the Terrible Three
And the fight that they fought by the edge of the sea.

Here's an interesting change:

Long Arrow said they were apologizing and trying to tell the Doctor how sorry they were that they had seemed unfriendly to him at the beach. They had never seen a white man before and had really been afraid of him—especially when they saw him conversing with the porpoises. They had thought he was the Devil, they said.

In some cases the changes seem completely bizarre. When I first heard that the books had been purged of racism I immediately thought of this passage, in which the protagonists discover that a sailor has stowed away on their boat and eaten all their salt beef (p. 142):

"I don't know what the mischief we're going to do now," I heard her whisper to Bumpo. "We've no money to buy any more; and that salt beef was the most important part of the stores."

"Would it not be good political economy," Bumpo whispered back, "if we salted the able seaman and ate him instead? I should judge that he would weigh more than a hundred and twenty pounds."

"How often must I tell you that we are not in Jolliginki," snapped Polynesia. "Those things are not done on white men's ships—Still," she murmured after a moment's thought, "it's an awfully bright idea. I don't suppose anybody saw him come on to the ship—Oh, but Heavens! we haven't got enough salt. Besides, he'd be sure to taste of tobacco."

"I don't know what the mischief we're going to do now," I heard her whisper to Bumpo. "We've no money to buy any more; and that salt beef was the most important part of the stores."

"Would it not be good political economy," Bumpo whispered back, "if we salted the able seaman and ate him instead? I should judge that he would weigh more than a hundred and twenty pounds."

"Don't be silly," snapped Polynesia. "Those things are not done anymore.—Still," she murmured after a moment's thought, "it's an awfully bright idea. I don't suppose anybody saw him come on to the ship—Oh, but Heavens! we haven't got enough salt. Besides, he'd be sure to taste of tobacco."

"There were great doings in Jolliginki when he left. He was scared to death to come. He was the first man from that country to go abroad. He thought he was going to be eaten by white cannibals or something.

"You know what those niggers are—that ignorant! Well!—But his father made him come. He said that all the black kings were sending their sons to Oxford now. It was the fashion, and he would have to go. Bumpo wanted to bring his six wives with him. But the king wouldn't let him do that either. Poor Bumpo went off in tears—and everybody in the palace was crying too. You never heard such a hullabaloo."

"But his father made him come. He said that all the African kings were sending their sons to Oxford now. It was the fashion, and he would have to go. Poor Bumpo went off in tears—and everybody in the palace was crying too. You never heard such a hullabaloo."

There are some apparently trivial changes:

"Listen," said Polynesia, "I've been breaking my head trying to think up some way we can get money to buy those stores with; and at last I've got it."

"The money?" said Bumpo.

"No, stupid. The idea—to make the money with."

"Poor perishing heathens!" muttered Bumpo. "No wonder the old chief died of cold!"

"No wonder the old chief died of cold!" muttered Bumpo.

When I found out this had been excised, I thought it was unfortunate. It seems to me that it was easy to view the original plot as a commentary on the cultural appropriation and racism that accompanies colonialism. (Bumpo wants to be a white prince because he has become obsessed with European fairy tales, Sleeping Beauty in particular.) Perhaps had the book been left intact it might have sparked discussion of these issues. I'm told that this subplot was replaced with one in which Bumpo wants the Doctor to turn him into a lion.

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Franklin is indeed 300 years old
I can now happily report that my determination that Benjamin Franklin is only 299 years old this year was mistaken. To my relief, Franklin is really 300 years old after all.

After hearing an alternative analysis from Corprew Reed, I double-checked with Daniel K. Richter, a Professor of History at the University of Pennsylvania, and director of the new McNeil Center for Early American Studies.

Richter confirms Reed's analysis: By the 18th century, nearly everyone was reckoning years to start on 1 January except certain official legal documents. The official change of New Year's day was only to bring the legal documents into conformance with what everyone was already doing. So when Franklin's birthdate is reported as 6 January 1706, it means 1706 according to modern reckoning (that is, January 300 years ago) and not 1706 in the "official" reckoning (which would have been only 299 years ago).

Deke Kassabian also wrote in with a helpful reference, referring me to an article that appeared Wednesday in Slate. The relevant part says:

. . . according to documents from Boston's city registrar, he actually came into the world on the old-style Jan. 6, 1705. So, this year's tricentennial is right on time.

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Franklin is probably 300 years old after all
In a recent post, I surmised that Benjamin Franklin is only 299 years old this year, not 300, because of rejiggering of the start of the calendar year in England and its colonies in 1751/1752.

However, Corprew Reed writes to suggest that I am mistaken. Reed points out that although the legal start of the year prior to 1752 was 25 March, the common usage was to cite 1 January as the start of the year. The the British Calendar Act of 1751 even says as much:

WHEREAS the legal Supputation of the Year . . . according to which the Year beginneth on the 25th Day of March, hath been found by Experience to be attended with divers Inconveniencies, . . . as it differs . . . from the common Usage throughout the whole Kingdom. . .

If so, this would be a great relief to me. It was really bothering me that everyone might be clebrating Franklin's 300th birthday a year early without realizing it.

I'm going to try to see who here at Penn I can bother about it to find out for sure one way or the other. Thanks for the suggestion, Corprew!

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Why 3--13 September?
In an earlier post about the British adjustment from the Julian to the Gregorian calendar, I pointed out that the calendar dates were synchronized with those in use in the rest of Europe by the deletion of 3 September through 13 September, so that Wednesday, 2 September 1752 was followed immediately by Thursday, 14 September 1752. I asked:

Why September 3-13? I don't know, although I would love to find out.

The reason for deleting the 3rd - 13th of September is that in that span there are no significant Holy Days on the Anglican calendar (at least that I can tell). September 8th's "Birth of the Blessed Virgin Mary" is actually an alternate to August 14th. It's also one of the few places on the 1752 calendar where this empty span occurs beginning at midweek.

This would also allow the autumnal equinox (one of the significant events mentioned in the Act) to fall properly on the 21st of September wheras doing the adjustment in October (the other late 1752 span of no Holy Days) wouldn't permit that.

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Daniel Dennett on sleep

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But to my lasting surprise, this essay really had something to say. Dennett marshaled an impressive amount of factual evidence for his point of view, and found arguments that I wouldn't have thought of. At the end, I felt as though I really knew something about this topic, whereas before I read the essay, I wouldn't have imagined that there was anything to know about it. Since then, I've tried hard to read everything I can find that Dennett has written.

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A teleological explanation is one the explains the existence or occurrence of something by citing a goal or purpose that is served by the thing. Artifacts are the most obvious cases; the goal or purpose of an artifact is the function it was designed to serve by its creator. There is no controversy about the telos of a hammer: it is for hammering in and pulling out nails. The telos of more complicated artifacts, such as camcorders or tow trucks or CT scanners, is if anything more obvious. But even in simple cases, a problem can be seen to loom in the background:

"Why are you sawing that board?"
"To make a door."
"And what is the door for?"
"To secure my house."
"And why do you want a secure house?"
"So I can sleep nights."
"And why do you want to sleep nights?"
"Go run along and stop asking such silly questions."

This exchange reveals one of the troubles with teleology: where does it all stop? What final cause can be cited to bring this hierarchy of reasons to a close? Aristotle had an answer: God, the Prime Mover, the for-which to end all for-whiches. The idea, which is taken up by the Christian, Jewish, and Islamic traditions, is that all our purposes are ultimately God's purposes. . . . But what are God's purposes? That is something of a mystery.

. . . One of Darwin's fundamental contributions is showing us a new way to make sense of "why" questions. Like it or not, Darwin's idea offers one way—a clear, cogent, surprisingly versatile way—of dissolving these old conundrums. It takes some getting used to, and is often misapplied, even by its staunchest friends. Gradually exposing and clarifying this way of thinking is a central project of the present book. Darwinian thinking must be carefully distinguished from some oversimplified and all-too-popular impostors, and this will take us into some technicalities, but it is worth it. The prize is, for the first time, a stable system of explanation that does not go round and round in circles or spiral off in an infinite regress of mysteries. Some people would very much prefer the infinite regress of mysteries, apparently, but in this day and age the cost is prohibitive: you have to get yourself deceived. You can either deceive yourself or let others do the dirty work, but there is no intellectually defensible way of rebuilding the mighty barriers to comprehension that Darwin smashed.

Anyway, there's one place in this otherwise excellent book where Dennett really blew it. First he quotes from a 1988 Boston Globe article by Chet Raymo, "Mysterious Sleep":

University of Chicago sleep researcher Allan Rechtshaffen asks "how could natural selection with its irrevocable logic have 'permitted' the animal kingdom to pay the price of sleep for no good reason? Sleep is so apparently maladaptive that it is hard to understand why some other condition did not evolve to satisfy whatever need it is that sleep satisfies.

But why does sleep need a "clear biological function" at all? It is being awake that needs an explanation, and presumably its explanation is obvious. Animals—unlike plants—need to be awake at least part of the time in order to search for food and procreate, as Raymo notes. But once you've headed down this path of leading an active existence, the cost-benefit analysis of the options that arise is far from obvious. Being awake is relatively costly, compared with lying dormant. So presumably Mother Nature economizes where she can. . . . But surely we animals are at greater risk from predators while we sleep? Not necessarily. Leaving the den is risky, too, and if we're going to minimize that risky phase, we might as well keep the metabolism idling while we bide our time, conserving energy for the main business of replicating.

This is a terrible argument, because Dennett has apparently missed the really interesting question here. The question isn't why we sleep; it's why we need to sleep. Let's consider another important function, eating. There's no question about why we eat. We eat because we need to eat, and there's no question about why we need to eat either. Sure, eating might be maladaptive: you have to leave the den and expose yourself to danger. It would be very convenient not to have to eat. But just as clearly, not eating won't work, because you need to eat. You have to get energy from somewhere; you simply cannot run your physiology without eating something once in a while. Fine.

But suppose you are in your den, and you are hungry, and need to go out to find food. But there is a predator sniffing around the door, waiting for you. You have a choice: you can stay in and go hungry, using up the reserves that were stored either in your body or in your den. When you run out of food, you can still go without, even though the consequences to your health of this choice may be terrible. In the final extremity, you have the option of starving to death, and that might, under certain circumstances, be a better strategy than going out to be immediately mauled by the predator.

With sleep, you have no such options. If you're treed by a panther, and you need to stay awake to balance on your branch, you have no options. You cannot use up your stored reserves of sleep. You do not have the option to go without sleep in the hope that the panther will get bored and depart. You cannot postpone sleep and suffer the physical consequences. You cannot choose to die from lack of sleep rather than give up and fall out of the tree. Sooner or later you will sleep, whether you choose to or not, and when you sleep you will fall out of the tree and die.

People can and do go on hunger strikes, refuse to eat, and starve to death. Nobody goes on sleep strikes. They can't. Why not? Because they can't. But why can't they? I don't think anyone knows.

The question isn't about the maladaptivity of sleeping itself; it's about the maladaptivity of being unable to prevent or even to delay sleep. Sleep is not merely a strategy to keep us conveniently out of trouble. If that were all it was, we would need to sleep only when it was safe, and we would be able to forgo it when we were in trouble. Sleep, even more than food, must serve some vital physiological role. The role must be so essential that it is impossible to run a mammalian physiology without it, even for as long as three days. Otherwise, there would be adaptive value in being able to postpone sleep for three days, rather than to fall asleep involuntarily and be at the mercy of one's enemies.

Given that, it is indeed a puzzle that we have not been able to identify the vital physiological role of sleep, and Rechtshaffen's puzzlement above makes sense.

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An adjustment to Franklin's birthday
Thanks to the wonders of the Internet, the text of the British Calendar Act of 1751 is available. (Should you read the Act, it may be helpful to know that the obscure word "supputation" just means "calculation".) This is the act that adjusted the calendar from Julian to Gregorian and fixed the 11-day discrepancy that had accumulated since the Nicean Council in 325 CE, by deleting September 3-13, so that the month of September 1752 had only 19 days:

September 1752
Sun	Mon	Tue	Wed	Thu	Fri	Sat
		1	2	14	15	16
17	18	19	20	21	22	23
24	25	26	27	28	29	30

And why September? Had I been writing the Act, I think I would have preferred to delete a chunk of February; nobody likes February anyway.

Anyway, the effect of this was to make the year 1752 only 355 days long, instead of the usual 366.

I hadn't remembered, however, that this act was also the one that moved the beginning of the year from 25 March to 1 January. Since 1752 was the first civil year to begin on 1 January, that meant that 1751 was only 282 days long, running from 25 March through 31 December. I used to think that the authors of the Unix cal program were very clever for getting September 1752 correct:

        % cal 1752

                                       1752                                

               January               February                 March        
        Su Mo Tu We Th Fr Sa   Su Mo Tu We Th Fr Sa   Su Mo Tu We Th Fr Sa 
                  1  2  3  4                      1    1  2  3  4  5  6  7
         5  6  7  8  9 10 11    2  3  4  5  6  7  8    8  9 10 11 12 13 14
        12 13 14 15 16 17 18    9 10 11 12 13 14 15   15 16 17 18 19 20 21
        19 20 21 22 23 24 25   16 17 18 19 20 21 22   22 23 24 25 26 27 28
        26 27 28 29 30 31      23 24 25 26 27 28 29   29 30 31

                April                   May                   June         
        Su Mo Tu We Th Fr Sa   Su Mo Tu We Th Fr Sa   Su Mo Tu We Th Fr Sa 
                  1  2  3  4                   1  2       1  2  3  4  5  6
         5  6  7  8  9 10 11    3  4  5  6  7  8  9    7  8  9 10 11 12 13
        12 13 14 15 16 17 18   10 11 12 13 14 15 16   14 15 16 17 18 19 20
        19 20 21 22 23 24 25   17 18 19 20 21 22 23   21 22 23 24 25 26 27
        26 27 28 29 30         24 25 26 27 28 29 30   28 29 30
                               31
                July                  August                September      
        Su Mo Tu We Th Fr Sa   Su Mo Tu We Th Fr Sa   Su Mo Tu We Th Fr Sa 
                  1  2  3  4                      1          1  2 14 15 16
         5  6  7  8  9 10 11    2  3  4  5  6  7  8   17 18 19 20 21 22 23
        12 13 14 15 16 17 18    9 10 11 12 13 14 15   24 25 26 27 28 29 30
        19 20 21 22 23 24 25   16 17 18 19 20 21 22
        26 27 28 29 30 31      23 24 25 26 27 28 29
                               30 31
               October               November               December       
        Su Mo Tu We Th Fr Sa   Su Mo Tu We Th Fr Sa   Su Mo Tu We Th Fr Sa 
         1  2  3  4  5  6  7             1  2  3  4                   1  2
         8  9 10 11 12 13 14    5  6  7  8  9 10 11    3  4  5  6  7  8  9
        15 16 17 18 19 20 21   12 13 14 15 16 17 18   10 11 12 13 14 15 16
        22 23 24 25 26 27 28   19 20 21 22 23 24 25   17 18 19 20 21 22 23
        29 30 31               26 27 28 29 30         24 25 26 27 28 29 30
                                                      31

        % cal 1751
                                       1751                                

               January               February                 March        
        Su Mo Tu We Th Fr Sa   Su Mo Tu We Th Fr Sa   Su Mo Tu We Th Fr Sa 
               1  2  3  4  5                   1  2                   1  2
         6  7  8  9 10 11 12    3  4  5  6  7  8  9    3  4  5  6  7  8  9
        13 14 15 16 17 18 19   10 11 12 13 14 15 16   10 11 12 13 14 15 16
        20 21 22 23 24 25 26   17 18 19 20 21 22 23   17 18 19 20 21 22 23
        27 28 29 30 31         24 25 26 27 28         24 25 26 27 28 29 30
                                                      31
                April                   May                   June         
        Su Mo Tu We Th Fr Sa   Su Mo Tu We Th Fr Sa   Su Mo Tu We Th Fr Sa 
            1  2  3  4  5  6             1  2  3  4                      1
         7  8  9 10 11 12 13    5  6  7  8  9 10 11    2  3  4  5  6  7  8
        14 15 16 17 18 19 20   12 13 14 15 16 17 18    9 10 11 12 13 14 15
        21 22 23 24 25 26 27   19 20 21 22 23 24 25   16 17 18 19 20 21 22
        28 29 30               26 27 28 29 30 31      23 24 25 26 27 28 29
                                                      30
                July                  August                September      
        Su Mo Tu We Th Fr Sa   Su Mo Tu We Th Fr Sa   Su Mo Tu We Th Fr Sa 
            1  2  3  4  5  6                1  2  3    1  2  3  4  5  6  7
         7  8  9 10 11 12 13    4  5  6  7  8  9 10    8  9 10 11 12 13 14
        14 15 16 17 18 19 20   11 12 13 14 15 16 17   15 16 17 18 19 20 21
        21 22 23 24 25 26 27   18 19 20 21 22 23 24   22 23 24 25 26 27 28
        28 29 30 31            25 26 27 28 29 30 31   29 30

               October               November               December       
        Su Mo Tu We Th Fr Sa   Su Mo Tu We Th Fr Sa   Su Mo Tu We Th Fr Sa 
               1  2  3  4  5                   1  2    1  2  3  4  5  6  7
         6  7  8  9 10 11 12    3  4  5  6  7  8  9    8  9 10 11 12 13 14
        13 14 15 16 17 18 19   10 11 12 13 14 15 16   15 16 17 18 19 20 21
        20 21 22 23 24 25 26   17 18 19 20 21 22 23   22 23 24 25 26 27 28
        27 28 29 30 31         24 25 26 27 28 29 30   29 30 31

When you excise eleven days from the calendar, you have a lot of puzzles. For any event that was previously scheduled to occur on or after 14 September, 1752, you now need to ask the question: should you leave its nominal date unchanged, so that the event actually occurs 11 days sooner than it would have, or do you advance its nominal date 11 days forward? The Calendar Act deals with this in some detail. Certain court dates and ecclesiastical feasts, including corporate elections, are moved forward by 11 real days, so that their nominal dates remain the same; other events are adjusted so that the occur at the same real times as they would have without the tamperings of the calendar act. Private functions are not addressed; I suppose the details were left up to the convenience of the participants.

Historians of that period have to suffer all sorts of annoyances in dealing with the dates, since, for example, you find English accounts of the Battle of Gravelines occurring on 28 July, but Spanish accounts that their Armada wasn't even in sight of Cornwall until 29 July. Sometimes the histories will use a notation like "11/21 July" to mean that it was the day known as 11 July in England and 21 July in Spain. I find this clear, but the historians mostly seem to hate this notation. ("Fractions! If I wanted to deal in fractions, I would have become a grocer, not a historian!")

You sometimes hear that there were riots by tenants, angry to be paying a full month's rent for only 19 days of tenancy in September 1752. I think this is a myth. The act says quite clearly:

. . . nothing in this present Act contained shall extend, or be construed to extend, to accelerate or anticipate the Time of Payment of any Rent or Rents, Annuity or Annuities, or Sum or Sums of Money whatsoever. . . or the Time of doing any Matter or Thing directed or required by any such Act or Acts of Parliament to be done in relation thereto; or to accelerate the Payment of, or increase the Interest of, any such Sum of Money which shall become payable as aforesaid; or to accelerate the Time of the Delivery of any Goods, Chattles, Wares, Merchandize or other Things whatsoever . . .

I first brought this up in connection with Benjamin Franklin's 300th birthday, saying that although Franklin had been born on 6 January, 1706, his birthday had been moved up 11 days by the Act. But things seem less clear to me now that I have reread the act. I thought there was a clause that specifically moved birthdays forward, but there isn't. There is the clause that says that Franklin cannot be said to be 300 years old until 17 January, and it also says that dates of delivery of merchandise should remain on the same real days. If you had contracted for flowers and cake to be delivered to a birthday party to be held on 6 January 2006, the date of delivery is advanced so that the florist and the baker have the same real amount of time to make delivery, and are now required to deliver on 17 January 2006.

But there is the additional confusion I had forgotten, which is that Franklin was born on 6 January 1706, and there was no 6 January 1751. What would have been 6 January 1751 was renominated to be 6 January 1752 instead, and then the old 6 January 1752 was renominated as 17 January 1753.

To make the problem more explicit, consider John Smith, born 1 January 1750. The previous day was 31 December 1750, not 1749, because 1749 ended nine months earlier, on March 24. Similarly, 1751 will not begin until 25 March, when John is 84 days old. 1751 is an oddity, and ends on December 31, when John is 364 days old. The following day is 1 January 1752, and John is now one year old. Did you catch that? John was born on 1 January 1750, but he is one year old on 1 January 1752. Similarly, he is two years old on 1 January 1753.

The same thing happens with Benjamin Franklin. Franklin was born on 6 January 1706, so he will be 300 years old (that is, 365 × 300 + 73 = 109573 days old) on 17 January 2007.

So I conclude that the cake and flowers for Franklin's 300th birthday celebration are being delivered a year early!

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Happy Birthday Benjamin Franklin!

Today is Benjamin Franklin's 300th birthday.

Franklin was born on 6 January, 1706. When they switched to the Gregorian calendar in 1752, everyone had their birthday moved forward eleven days, so Franklin's moved up to 17 January. (You need to do this so that, for example, someone who is entitled to receive a trust fund when he is thirty years old does not get access to it eleven days before he should. This adjustment is also why George Washington's birthday is on 22 February even though he was born 11 February 1732.)

(You sometimes hear claims that there were riots when the calendar was changed, from tenants who were angry at paying a month's rent for only 19 days of tenancy. It's not true. The English weren't stupid. The law that adjusted the calendar specified that monthly rents and such like would be pro-rated for the actual number of days.)

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Since I live in Philadelphia, Franklin is often in my thoughts. In the 18th century, Franklin was Philadelphia's most important citizen. (When I first moved here, my girlfriend of the time sourly observed that he was still Philadelphia's most important citizen. Philadelphia's importance has faded since the 18th century, leaving it with a forlorn nostalgia for Colonial days.) When you read Franklin's Autobiography, you hear him discussing places in the city that are still there:

So not considering or knowing the difference of money, and the greater cheapness nor the names of his bread, I made him give me three-penny worth of any sort. He gave me, accordingly, three great puffy rolls. I was surpriz'd at the quantity, but took it, and, having no room in my pockets, walk'd off with a roll under each arm, and eating the other.

Thus I went up Market-street as far as Fourth-street, passing by the door of Mr. Read, my future wife's father; when she, standing at the door, saw me, and thought I made, as I certainly did, a most awkward, ridiculous appearance.

Heck, I was down at Fourth and Market just last month.

Franklin's personality comes across so clearly in his Autobiography and other writings that it's easy to imagine what he might have been like to talk to. I sometimes like to pretend that Franklin and I are walking around Philadelphia together. Wouldn't he be surprised at what Philadelphia looks like, 250 years on! What questions does Franklin have? I spend a lot of time explaining to Franklin how the technology works. (People who pass me in the street probably think I'm insane, or else that I'm on the phone.) Some of the explaining is easy, some less so. Explaining how cars work is easy. Explaining how cell phones work is much harder.

Here's my favorite quotation from Franklin:

I believe I have omitted mentioning that, in my first voyage from Boston, being becalm'd off Block Island, our people set about catching cod, and hauled up a great many. Hitherto I had stuck to my resolution of not eating animal food, and on this occasion consider'd, with my master Tryon, the taking every fish as a kind of unprovoked murder, since none of them had, or ever could do us any injury that might justify the slaughter. All this seemed very reasonable. But I had formerly been a great lover of fish, and, when this came hot out of the frying-pan, it smelt admirably well. I balanc'd some time between principle and inclination, till I recollected that, when the fish were opened, I saw smaller fish taken out of their stomachs; then thought I, "If you eat one another, I don't see why we mayn't eat you." So I din'd upon cod very heartily, and continued to eat with other people, returning only now and then occasionally to a vegetable diet. So convenient a thing it is to be a reasonable creature, since it enables one to find or make a reason for everything one has a mind to do.

Happy birthday, Dr. Franklin.

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Happy Birthday Universe of Discourse
Today is the 12th anniversary of my web site. Early attractions included a CGI version of the venerable "Guess-the-Animal" game and what I believe was the first "guestbook" application on the web.

It's been a wild ride! I hope the next twelve years are as much fun.

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Medieval Chinese typesetting technique
One of my longtime fantasies has been to write a book called Quipus and Abacuses: Digital Information Processing Before 1946. The point being that digital information processing did exist well before 1946, when large-scale general-purpose electronic digital computers first appeared. (Abacuses you already know about, and a future blog posting may discuss the use of abacuses in Roman times and in medieval Europe. Quipus are bunches of knotted cords used in Peru to record numbers.) There are all sorts of interesting questions to be answered. For instance, who first invented alphabetization? (Answer: the scribes at the Great Library in Alexandria, around 200 CE.) And how did they do it? (Answer to come in a future blog posting.) How were secret messages sent? (Answer: lots of steganography.) How did people do simple arithmetic with crappy Roman numerals? (Answer: abacuses.) How were large quantities of records kept, indexed, and searched? How were receipts made when the recipients were illiterate?

Here's a nice example. You may have heard that the Koreans and the Chinese had printing presses with movable type before Gutenberg invented it in Europe. How did they organize the types?

In Europe, there is no problem to solve. You have 26 different types for capital letters and 26 for small letters, so you make two type cases, each divided into 26 compartments. You put the capital letter types in the upper case and the small letter types in the lower case. (Hence the names "uppercase letter" and "lowercase letter".) You put some extra compartments into the cases for digits, punctuation symbols, and blank spaces. When you break down a page, you sort the types into the appropriate compartments. There are only about 100 different types, so whatever you do will be pretty easy.

However, if you are typesetting Chinese, you have a much bigger problem on your hands. You need to prepare several thousand types just for the common characters. You need to store them somehow, and when you are making up a page to be printed you need to find the required types efficiently. The page may require some rare characters, and you either need to have up to 30,000 rarely-used types made up in advance or some way to quickly make new types as needed. And you need a way to sort out the types and put them away in order when the page is complete.

(I'm sure some reader is itching to point out that Korean is written with a phonetic alphabet, hangul, which avoids the problem by having only 28 letters. But in fact that is wrong for two reasons. First, the layout of Korean writing requires that a type be made for each two- or three-letter syllable. And second, perhaps more to the point, moveable type presses were used in Korea before the invention of hangul, before Korean even had a written form. Movable type was invented in Korea around 1234 CE; hangul was first promulgated by Sejong the Great in 1443 or 1444. The first Korean moveable type presses were used to typeset documents in Chinese, which was the language of scholarship and culture in Korea until the 19th century.)

In fact, several different solutions were adopted. The earliest movable types in China were made of clay mixed with glue. These had the benefit of being cheap. Copper types were made later, but had two serious disadvantages. First, they were very expensive. And second, since much of their value could be recovered by melting them down, the government was always tempted to destroy them to recover the copper, which did indeed happen.

Wang Chen, in 1313, writes that the types were organized as follows: There were two circular bamboo tables, each seven feet across and with one leg in the middle; the tabletops were mounted on the legs so that they could rotate. One table was for common types and the other for the rare, one-off types. The top of each table was divided into eight sections, and in each section, types were arranged in their numerical order according to their listing in the Book of Rhymes, an early Chinese dictionary that organized the characters by their sounds.

To set the type for a page, the compositors would go through the proof and number each character with a code indicating its code number from the Book of Rhymes. One compositor would then read from the list of numbers while the other, perched on a seat between the two rotating tables, would select the types from the tables. Wang doesn't say, but one supposes that the compositors would first put the code numbers into increasing order before starting the search for the right types. This would have two benefits: First, it would enable a single pass to be made over the two tables, and second, if a certain character appeared multiple times on the page, it would allow all the types needed for that character to be picked up at once.

The types would then be inserted into the composition frame. If a character was needed for which there was no type, one was made on the spot. Wang Chen's types were made of wood. The character was carefully written on very thin paper, which was then pasted upside-down onto a blank type slug. A wood carver with a delicate chisel would then cut around the character into the wood.

(Source: Invention of printing in China and its spread westward. Thomas Francis Carter, 1925.)

In 1776 a great printing project was overseen by Jian Jin (Chin Ch'ien), also using wooden types. Jin left detailed instructions about how the whole thing was accomplished. By this time the Book of Rhymes had been superseded.

The Imperial K'ang Hsi Dictionary (K'ang-hsi tzu-tien), written between 1710 and 1716, was the gold standard for Chinese dictionaries at the time, and to some extent, still is, since it set the pattern for the organization of Chinese characters that is still followed today. If you go into a store and buy a Chinese dictionary (or a Chinese-English dictionary) that was published last week, its organization will be essentially the same as that of the Imperial K'ang Hsi Dictionary. Since readers may be unfamiliar with the organization of Chinese dictionaries, I will try to explain.

Characters are organized primarily by a "classifier", more usually called a "radical" today. The typical Chinese character incorporates some subcharacters. For example, the character for "bright" is clearly made up of the characters for "sun" and "moon"; the character for "sweat" is made up of "water" and "shield". (The "shield" part is not because of anything relating to a shield, but because it sounds like the word for "shield".) Part of each character is designated its radical. For "sweat", the radical is "water"; for "bright" it is "sun". How do you know that the radical for "bright" is "sun" and not "moon"? You just have to know.

What about characters that are not so clearly divisible? They have radicals too, some of which were arbitrarily designated long ago, and some of which were designated based on incorrect theories of etymology. So some of it is arbitrary. But all ordering of words is arbitrary to some extent or another. Why does "D" come before "N"? No reason; you just have to know. And if you have ever seen a first-grader trying to look up "scissors" in the dictionary, you know how difficult it can be. How do you know it has a "c"? You just have to know.

Anyway, a character has a radical, which you can usually guess in at most two or three tries if you don't already know it. There are probably a couple of hundred radicals in all, and they are ordered first by number of strokes, and then in an arbitrary but standard order among the ones with the same number of strokes. The characters in the dictionary are listed in order by their radical. Then, among all the characters with a particular radical, the characters are ordered by the number of strokes used in writing them, from least to most. This you can tell just by looking at the characters. Finally, among characters with the same number of strokes and the same radical, the order is arbitrary. But it is still standardized, because it is the order used by the Imperial K'ang Hsi Dictionary.

So if you want to look up some character like "sweat", you first identify the radical, which is "water", and has four strokes. You look in the radical index among the four-stroke radicals, of which there are no more than a couple dozen, until you find "water", and this refers you to the section of the dictionary where all the characters with the "water" radical are listed. You turn to this section, and look through it for the subsection for characters that have seven strokes. Among these characters, you search until you find the one you want.

This is the solution to the problem of devising an ordering for the characters in the dictionary. Since this ordering was (and is) well-known, Jin used it to organize his type cases. He writes:

Label and arrange twelve wooden cabinets according to the names of the twelve divisions of the Imperial K'ang Hsi Dictionary. The cabinets are 5'7" high, 5'1" wide, 2'2" deep with legs 1'5" high. Before each one place a wooden bench of the same height as the cabinet's legs; they are convenient to stand on when selecting type. Each case has 200 sliding drawers, and each drawer is divided into eight large and eight small compartments, each containing four large or four small type. Write the characters, with their classifiers and number of strokes, on labels on the front of each drawer.

When selecting type, first examine the make-up of the character for its corresponding classifier, and then you will know in which case it is stored. Next, count the number of strokes, and then you will know in which drawer it is. If one is experienced in this method, the hand will not err in its movements.

There are some rare characters that are seldom used, and for which few type will have been prepared. Arrange small separate cabinets for them, according to the twelve divisions mentioned above, and place them on top of each type case where they may be seen at a glance.

The size measurements here are misleading. The translator says that the "inch" used here is the Chinese inch of the time, which is about 32.5 mm, not the 25.4 mm of the modern inch. He does not say what is meant by "foot"; I assume 12 inches. That means that the type cases are actually 7'2" high, 6'6" wide, 2'9" deep, (218 cm × 198 cm × 84 cm) with legs 1'10" high (55 cm), in modern units.

(Addendum 20060116: The quote doesn't say, but the illustration in Jin's book shows that the cabinets have 20 rows of 10 drawers each.)

One puzzle I have not resolved is that there do not appear to be enough type drawers. Jin writes that there are twelve cabinets with 200 drawers each; each drawer contains 16 compartments, and each compartment four type. This is enough space for 153,600 types (remember that you need multiples of the common characters), but Jin reports that 250,000 types were cut for his project. Still, it seems clear that the technique is feasible.

Another puzzle is that I still don't know what the "twelve divisions" of the Imperial K'ang Hsi Dictionary are. I examined a copy in the library and I didn't see any twelve divisions. Perhaps some reader can enlighten me.

As in Wang's project, one compositor would first go over the proof page, making a list of which types needed to be selected, and how many; new types were cut from wood as needed. Then compositors would visit the appropriate cases to select the types as necessary; another compositor would set the type, and then the page would be printed, and the type broken down. These activities were always going on in parallel, so that page n was being printed while page n+1 was being typeset, the types for page n+2 were being selected, and page n-1 was being broken down and its types returned to the cabinet.

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Typographic conventions in computer books

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I don't remember what (if any) conclusion Peter drew from this, but I was struck by it, because I had been thinking about that myself for a couple of days. Really, what is this section for? Does anyone really need it? Here, for example, is the corresponding section from Mastering Algorithms with Perl, because it is the first book I pulled off my shelf:

Conventions Used in This Book

Italic

Used for filenames, directory names, URLs, and occasional emphasis.

Constant width

Used for elements of programming languages, text manipulated by programs, code examples, and output.

Constant width bold

Used for use input and for emphasis in code

Constant width italic

Used for replaceable values

Several questions came to my mind as I transcribed that, even though it was 4 AM.

First, does anyone really read this section and pay attention to it, making a careful note that italic font is used for filenames, directory names, URLs, and occasional emphasis? Does anyone, reading the book, and encountering italic text, say to themselves "I wonder what the funny font is about? Oh! I remember that note in the preface that italic font would be used for filenames, directory names, URLs, and occasional emphasis. I guess this must be one of those."

Second, does anyone really need such an explanation? Wouldn't absolutely everyone be able to identify filenames, directory names, URLs, and occasonal emphasis, since these are in italics, without the explicit directions?

I wonder, if anyone really needed these instructions, wouldn't they be confused by the reference to "constant-width italic", which isn't italic at all? (It's slanted, not italic.)

Even if someone needs to be told that constant-width fonts are used for code, do they really need to be told that constant-width bold fonts are used for emphasis in code? If so, shouldn't they also be told that bold roman fonts are used for emphasis in running text?

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Some books, like Common Lisp: The Language, have extensive introductions explaining their complex notational conventions. For example, pages 4--11 include the following notices:

The symbol "⇒" is used in examples to indicate evaluation. For example,

        (+ 4 5) ⇒ 9

means "the result of evaluating the code (+ 4 5) is (or would be, or would have been) 9."

The symbol "→" is used in examples to indicate macro expansions. ...

Explanation of this sort of unusual notation does seem to me to be valuable. But really the explanations in most computer books make me think of long-playing record albums that have a recorded voice at the end of the first side that instructs the listener "Now turn the record over and listen to the other side."

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I don't think omitted this section from HOP on purpose; it simply never occurred to me to put one in. Had MK asked me about it, I don't know what I would have said; they didn't ask.

HOP does have at least one unusual typographic convention: when two versions of the same code are shown, the code in the second version that was modified or changed has been set in boldface. I had been wondering for a couple of weeks before OSCON if I had actually explained that; after running into Peter I finally remembed to check. The answer: no, there is no explanation. And I don't think it's a common convention.

But of all the people who have seen it, including a bunch of official technical reviewers, a few hundred casual readers on the mailing list, and now a few thousand customers, nobody suggested than an explanation was needed, and nobody has reported being puzzled. People seem to understand it right away.

I don't know what to conclude from this yet, although I suspect it will be something like:

(a) the typographic conventions in typical computer books are sufficiently well-established, sufficiently obvious, or both, that you don't have to bother explaining them unles they're really bizarre,

or:

(b) readers are smarter and more resilient than a lot of people give them credit for.

Explanation (b) reminds me of a related topic, which is that conference tutorial attendees are smarter and more resilient than a lot of conference tutorial speakers give them credit for. I suppose that is a topic for a future blog entry.

(Consensus on my mailing list, where this was originally posted, was that the ubiquitous explanations of typographic conventions are not useful. Of course, people for whom they would have been useful were unlikely to be subscribers to my mailing list, so I'm not sure we can conclude anything useful from this.)

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Book economics

[I sent this out to my book discussion mailing list back in November, but it seems like it might be of general interest, so I'm reposting it. - MJD]

People I talk to often don't understand how authors get paid. It's interesting, so I thought I'd send out a note about it.

Basically, the deal is that you get a percentage of the publisher's net revenues. This percentage is called "royalties". So you're getting a percentage of every book sold. Typical royalties seem to be around 15%. O'Reilly's are usually closer to 10%. If there are multiple authors, they split the royalty between them.

Every three or six months your publisher will send you a statement that says how many copies sold and at what price, and what your royalties are. If the publisher owes you money, the statement will be accompanied by a check.

The 15% royalty is a percentage of the net receipts. The publisher never sees a lot of the money you pay for the book in a store. Say you buy a book for $60 in a bookstore. About half of that goes to the store and the book distributor. The publisher gets the other half. So the publisher has sold the book to the distributor for $30, and the distributor sold it to the store for perhaps $45. This is why companies like Amazon can offer such a large discount: there's no store and no distributor.

So let's apply this information to a practical example and snoop into someone else's finances. Perl Cookbook sells for $50. Of that $50, O'Reilly probably sees about $25. Of that $25, about $2.50 is authors' royalties. Assuming that Tom and Nat split the royalties evenly (which perhaps they didn't; Tom was more important than Nat) each of them gets about $1.25 per copy sold. Since O'Reilly claims to have sold 150,000 copies of this book, we can guess that Tom has made around $187,500 from this book. Maybe. It might be more (if Tom got more than 50%) and it might be less (that 150,000 might include foreign sales, for which the royalty might be different, or bulk sales, for which the publisher might discount the cover price; also, a lot of those 150,000 copies were the first edition, and I forget the price of that.) But we can figure that Tom and Nat did pretty well from this book. On the other hand, if $187,500 sounds like a lot, recall that that's the total for 8 years, averaging about $23,500 per year, and also recall that, as Nat says, writing a book involves staring at the blank page until blood starts to ooze from your pores.

Here's a more complicated example. The book Best of The Perl Journal vol. 1 is a collection of articles by many people. The deal these people were offered was that if they contributed less than X amount, they would get a flat $150, and if they contributed more than X amount, they would get royalties in proportion to the number of pages they contributed. (I forget what X was.) I was by far the contributor of the largest number of pages, about 14% of the entire book. The book has a cover price of $40, so O'Reilly's net revenues are about $20 per copy and the royalties are about $2 per copy. Of that $2, I get about 14%, or $0.28 per copy. But for Best of the Perl Journal, vol. 2, I contributed only one article and got the flat $150. Which one was worth more for me? I think it was probably volume 1, but it's closer than you might think. There was a biggish check of a hundred and some dollars when the book was first published, and then a smaller check, and by now the checks are coming in amounts like $20.55 and $12.83.

The author only gets the 15% on the publisher's net receipts. If the books in the stores aren't selling, the bookstore gets to return them to the publisher for a credit. The publisher subtracts these copies from the number of copies sold to arrive at the royalty. If more copies come back than are sold, the author ends up owing the publisher money! Sometimes when the book is a mass-market paperback, the publisher doesn't want the returned copies; in this case the store is supposed to destroy the books, tear off the covers, and send the covers back to the publisher to prove that the copies didn't sell. This saves on postage and trouble. Sometimes you see these coverless books appear for sale anyway.

When you sign the contract to write the book, you usually get an "advance". This is a chunk of money that the publisher pays you in advance to help support you while you're writing. When you hear about authors like Stephen King getting a one-million-dollar advance, this is what they are talking about. But the advance is really a loan; you pay it back out of your royalties, and until the advance is repaid, you don't see any royalty checks. If you write the book and then it doesn't sell, you don't get any royalties, but you still get to keep the advance. But if you don't write the book, you usually have to return the advance, or most of the advance. I've known authors who declined to take an advance, but it seems to me that there is no downside to getting as big an advance as possible. In the worst case, the book doesn't sell, and then you have more money than you would have gotten from the royalties. If the book does sell, you have the same amount of money, but you have it sooner. I got a big advance for HOP. My advance will be paid back after 4,836 copies are sold. Exercise: estimate the size of my advance. (Actually, the 4,836 is not quite correct, because of variations in revenues from overseas sales, discounted copies, and such like. When the publisher sells a copy of the book from their web site, it costs the buyer $51 instead of $60, but the publisher gets the whole $51, and pays royalties on the full amount.)

If the publisher manages to exploit the book in other ways, the author gets various percentages. If Morgan Kaufmann produces a Chinese translation of HOP, I get 5% of the revenues for each copy; if instead they sell to a Chinese publisher the rights to produce and sell a Chinese translation, I get 50% of whatever the Chinese publisher paid them. If Universal pictures were to pay my publisher a million dollars for the rights to make HOP into a movie starring Kevin Bacon, I would get $50,000 of that. (Wouldn't it be cool to live in that universe? I hear that 119 is a prime number over there.)

If you find this kind of thing interesting, O'Reilly has an annotated version of their standard publishing contract online.

[ Addendum 20060109: I was inspired to repost this by the arrival in the mail today of my O'Reilly quarterly royalty statement. I thought I'd share the numbers. Since the last statement, 31 copies of Computer Science & Perl Programming were sold: 16 copies domestically and 15 foreign. The cover price is $39.95, so we would expect that O'Reilly's revenues would be close to $619.22; in fact, they reported revenues of $602.89. My royalty is 1.704 percent. The statement was therefore accompanied by a check for $10.27. Who says writing doesn't pay? ]

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