Unnecessary imprecision
This article contains the following sentence:

McCain has won all of the state's 57 delegates, and the last primary before voters in more than 20 states head to the polls next Tuesday.

I'm not trying to pick on CTV here. A Google News search finds 42,000 instances of "more than 20", many of which could presumably be replaced with "26" or whatever. Well, I had originally written "most of which", but then I looked at some examples, and found that the situation is better than I thought it would be. Here are the first ten matches:

1. Australian Stocks Complete Worst Month in More Than 20 Years
2. It said the US air force committed more than 20 cases of aerial espionage by U-2 strategic espionage planes this month.
3. Farmland prices have climbed more than 20% over the past year in many Midwestern states...
4. "We have had record-breaking growth in our monthly shipments, as much as more than 20 percent improvements per month," said Christopher Larkins, President...
5. More than 20 people, including a district officer, were injured when two bombs exploded outside a stadium in the town yesterday...
6. By a vote of 14-7, the Senate Finance Committee last night voted to deliver $500 tax rebates to more than 20 million American senior citizens...
7. 9 killed, more than 20 injured in bus accident
8. While Tuesday's results may not lock up the nomination for either candidate, Democrats will have their say in more than 20 states...
9. Facing the potential anointment of his rival, John McCain, Romney has less than a week to convince voters in more than 20 states that...
10. More than 20 Aberdeen citizens qualified for elections as April ...

#2 may be legitimate, if the number of cases of aerial espionage is not known with certitude, or if the anonymous source really did say "more than 20". Similarly #4 is entirely off the hook since it is a quotation.

#3 may be legitimate if the price of farmland is uncertain and close to 20%. #5 is probably a loser. #7 is definitely a loser: it was the headline of an article that began "Nine people were killed and at least 22 injured when...". The headline could certainly have been "9 killed, 22 injured in bus accident".

#8 and #9 are losers, but they are the same example with which I began the article, so they don't count. #10 is a loser.

So I have, of eight examples (disregarding #8 and #9) three certain or near-certain failures (#5, #7, and #10), one certain non-failure (#4), and four cases to which I am willing to extend the benefit of the doubt. This is not as bad as I feared. I like when things turn out better than I thought they would.

But I really wonder what is going on with all these instances of "more than 20 states". Is it just sloppy writing? Or is there some benefit that I am failing to appreciate?

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Ramanujan's congruences
Let p(n) be the number of partitions of the integer n. For example, p(4) = 5 because there are 5 partitions of the integer 4, namely {4, 3+1, 2+2, 2+1+1, 1+1+1+1}.

Ramanujan's congruences state that:

p(5k+4)	=0	(mod 5)
p(7k+5)	=0	(mod 7)
p(11k+6)	=0	(mod 11)

Looking at this, anyone could conjecture that p(13k+7) = 0 (mod 13), but it isn't so; p(7) = 15 and p(20) = 48·13+3.

But there are other such congruences. For example, according to Partition Congruences and the Andrews-Garvan-Dyson Crank:

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More on risk
My article on risk was one of the more popular articles so far; it went to the top of Reddit, and was widely commented on. It wasn't the best article I've written. I confused a bunch of important things. But now I find I have more to say on the topic, so I'm back to screw up again.

One big problem with the Reddit posting is that the guy who posted it there titled the post on risk, or why poor people might not be stupid to play the lottery. So a lot of the Reddit comments complained that I had failed to prove that poor people must not be stupid to play the lottery, or that I was wrong on that point. They argued that the dollar cost of a lottery ticket is more valuable to a poor person than to a rich one, and so on. But I didn't say anything about poor people. People read this into the article based on the title someone else had attached to it, and they couldn't get rid of this association even after I pointed out that the article had nothing to say about poor people.

Something I do a lot, in this blog, and in life, is point out fallacious arguments. You get some argument that X is true, because of P and Q and therefore R, and then I'll come along point out that P is false and Q is irrelevant, and anyway they don't imply R, and even if they did, you can't conclude X from R, because if you could, then you could also conclude Y and Z which are obviously false. For example, in a recent article I addressed the argument that:

You can double your workforce participation from 27% to 51% of the population, as Singapore did; you can't double it again.

The "risk" article was one of those. I wanted to refute one specific argument, which is that (a) the expected return on a lottery ticket is negative, so therefore (b) it's stupid to buy lottery tickets. My counter-argument was to point out that (a) the expected return on fire insurance is negative, but that you can't conclude that therefore (b) it's stupid to buy fire insurance. It might be stupid to buy lottery tickets, but if it is, it's not because the expected return is negative. Or at least it's not only because the expected return is negative. There must be more to it than that.

I really like that pattern of argument, and I use it a lot: A can't imply B, because if it did, then it would also imply B', and B' is false, or at least B' is a belief held only by dumbasses.

None of this addresses the question of whether or not I think it's stupid to buy lottery tickets. I have not weighed in on that matter. My only argument is that the argument from expected value is insufficient to prove the point.

People have a lot of trouble with second-order arguments like this, though. If I argue "that argument against B is no good," they are likely to hear it as an argument in favor of B. Several of the Reddit people made this mistake. The converse mistake is to interpret "that argument against B is no good, because it can be converted into an argument against B'" as an argument against B'! Some of the Reddit people made this mistake too, and disdainfully explained to me why buying fire insurance is not stupid.

Another problem with the article was that it followed my usual pattern of meandering digression. Although the main point of the article was to refute the argument from expected value, I threw in a bunch of marginally related stuff that I thought was fun and interesting: the stuff about estimating the value one ascribes to one's own life; the stuff about the surprisingly high chance of being killed by a meteor strike. Email correspondents and Reddit commenters mistook both of these for arguments about the lottery, and tried to refute them as such. Well, I have nobody to blame but myself for that. If you present a muddled, miscellaneous article, you can't complain when other people are confused by it.

If I were going to do the article again, one thing I'd try to fix is the discussion of utility. I think my biggest screwup was to confuse two things that are not the same. One is the utility, which decreases for larger amounts of money; your second million dollars has less value than your first million. But another issue, which I didn't separate in my mind, was the administration cost of money. There must be a jargon term for this, but I don't know what it is.

Economists like to pretend that money is perfectly fungible, and this is a reasonable simplifying assumption in most cases. But it's easy to prove that money isn't perfectly fungible. Imagine you've just won a prize. You can have one thousand dollars paid in hundred-dollar bills, or you can have a thousand and one dollars, paid in pennies. Anyone who really believes that money is perfectly fungible will take the pennies, even though they weigh six hundred pounds, because that way they get the one-dollar bonus.

Money has a physical manifestation, even when it's just numerals written in a ledger somewhere, and managing the physical manifestation of money has an associated cost. The cost of managing a penny is a significant fraction of the value of the penny, to the point that many people throw away pennies or dump them in jars just to avoid the cost of dealing with them. In some circumstances, like the lottery ticket purchase, the non-fungibility of money is important. Blowing one dollar on a lottery that pays a thousand dollars is not the same as blowing a thousand dollars on a lottery that pays a million dollars, and it's not the same as blowing your whole paycheck on a big stack of lottery tickets. Partly it's the risk issue, and partly it's this other issue, that I don't know the name of, that a single dollar is worth less than one one-thousandth of a thousand dollars, because the cost to administer and manage it is proportionately higher. I didn't make this clear in the original article because it wasn't clear in my mind. Oh well, I'm not yet a perfect sage.

One last point that has come up is that a couple of people have written to me to say that they would not take the Russian roulette bet for any amount of money at any odds. (Here's a blog post to that effect, for example.) One person even suggested that I only assumed he would take the bet at some odds because I'm an American, and I can't conceive of anyone refusing a big pot of money.

Well, maybe that's true, but I don't think that's why I assumed that everyone would take the bet for some amount of money. I assumed it because that is what I have observed people to do. I now know there are people who say that they would not play Russian roulette at any odds for any payoff. And I think those people are fooling themselves.

If you think you're one of those people, I have this question for you: Do you own a bicycle helmet? And if you do, did you buy the very top-of-the-line helmet? Or did you buy a mid-price model that might offer less protection? What, just to save money? I offered you a million dollars at million-to-one odds. Do you think that fifty dollars you saved on your bicycle helmet is paying you off for less risk than my million-to-one Russian roulette bet?

Well, maybe you don't own a bicycle, so you think you have no need of a helmet. But if the people who wrote to me were as risk-averse as some of them said they were, the lack of a bicycle wouldn't stop them from wearing helmets all the time anyway—another reason I think they are fooling themselves. I've met some of these people, and they don't go around in helmets and padded armor all the time.

Or maybe you do own the very safest helmet money can buy, since you have only one head, after all. But I bet you can find some other example? Have you ever flown in a plane? Did you refuse to fly anywhere not served by Qantas, like Raymond in Rain Man, because every other airline has had a crash? If you had a choice to pay double to fly with Qantas, would you take it? Or would you take the cheap flight and ignore the risk?

One comment that replies to the blog I cited above really hits the nail on the head, I think. It says: "you don't get paid a million dollars to get in your car and drive somewhere, but what are the chances you'll be killed in an auto accident?" My Russian roulette game is a much better deal than driving your car.

I'm going to end this article, as I did the last one, with an amusing anecdote about risk. My great-uncle Robert E. Machol was for a time the chief scientist of the Federal Aviation Administration. The regulations for infant travel were (and still are) that an infant may make an air trip on its parent's lap; parents do not need to buy a separate ticket and a seat for the infant.

In one air disaster, an infant that was being held on its parent's lap was thrown loose, hurtled to the end of the corridor, and died. The FAA was considering changing the rules for infants to require that they purchase a separate ticket, entitling them to their own seat, into which would be installed an FAA-approved safety car seat. Infants in their own restraint seats would be much safer than those held on their parents' laps.

Dr. Machol argued against this rule change, on the following grounds: If parents are required to buy separate tickets for their infants, air travel will be more expensive for them. As a result, some families will opt to take car trips instead of plane trips. Car trips are much more dangerous than plane trips; the fatalities per passenger per mile are something like twenty times higher. More babies can be expected to be killed in the resulting auto crashes than can be expected to be saved by the restraint seat requirement.

As before, this is not intended as an argument for or against anything in particular, except perhaps that the idea of risk is complex and hard to understand. Probably people will try to interpret it as an argument about the fungibility of money, or whatever the next Reddit person decides to put in the article title. You'd think I would have learned my lesson by now, but, as I said, I'm not yet a perfect sage.

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Nonstandard adjectives in mathematics
Ranjit Bhatnagar once propounded the notion of a "nonstandard" adjective. This is best explained by an example. "Red" is not usually a nonstandard adjective, because a red boat is still a boat, a red hat is still a hat, and a red flag is still a flag. But "fake" is typically nonstandard, because a fake diamond is not a diamond, a fake Gucci handbag is not a Gucci handbag.

The property is not really attached to the adjective itself. Red emeralds are not emeralds, so "red" is nonstandard when applied to emeralds. Fake expressions of sympathy are still expressions of sympathy, however insincere. "Toy" often goes both ways: a toy fire engine is not a fire engine, but a toy ball is a ball and a toy dog is a dog.

Adjectives in mathematics are rarely nonstandard. An Abelian group is a group, a second-countable topology is a topology, an odd integer is an integer, a partial derivative is a derivative, a well-founded order is an order, an open set is a set, and a limit ordinal is an ordinal.

When mathematicians want to express that a certain kind of entity is similar to some other kind of entity, but is not actually some other entity, they tend to use compound words. For example, a pseudometric is not (in general) a metric. The phrase "pseudo metric" would be misleading, because a "pseudo metric" sounds like some new kind of metric. But there is no such term.

But there is one glaring exception. A partial function is not (in general) a function. The containment is in the other direction: all functions are partial functions, but not all partial functions are functions. The terminology makes more sense if one imagines that "function" is shorthand for "total function", but that is not usually what people say.

If I were more quixotic, I would propose that partial functions be called "partialfunctions" instead. Or perhaps "pseudofunctions". Or one could go the other way and call them "normal relations", where "normal" can be replaced by whatever adjective you prefer—ejective relations, anyone?

I was about to write "any of these would be preferable to the current confusion", but actually I think it probably doesn't matter very much.

[ Addendum 20080201: Another example, and more discussion of "partial". ]

[ Addendum 20081205: A contravariant functor is not a functor. ]

[ Addendum 20090121: A hom-set is not a set. ]

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The Census Bureau's data file
Last week I posted an article about calculations with data provided by the U.S. Census Bureau. I'm thinking about writing that up in more detail, but today I learned something so astonishing that I couldn't wait to mention it.

The data is available from the Census Bureau's web site. It is a CSV file. Most of the file contains actual data, like this:

20220,,"Dubuque, IA",Metropolitan Statistical Area,"92,384","91,603","91,223","90,635","89,571","89,216","89,265","89,156","89,143"

table with row headers in column A and column headers in rows 3 through 4 (leading dots indicate sub-parts),,,,,,,,,,,,^M
"Table 1. Annual Estimates of the Population of Metropolitan and Micropolitan Statistical Areas: April 1, 2000 to July 1, 2006",,,,,,,,,,,,^M
CBSA Code,"Metro
Division
Code",Geographic area,"Legal/statistical
area description",Population estimates,,,,,,,"April 1, 2000",^M
,,,,"July 1, 
2006","July 1, 
2005","July 1, 
2004","July 1, 
2003","July 1, 
2002","July 1, 
2001","July 1, 
2000",Estimates base,Census^M
,,Metropolitan statistical areas,,,,,,,,,,^M

(I've translated ASCII CR characters to ^M sequences so that you can see that although the lines of the file are CR-LF terminated, some of the items contain extra LFs for no particular reason.)

Well, all this is minor. My real complaint is that some of the state name abbreviations are garbled:

19740,,"Denver-Aurora, CO1",Metropolitan Statistical Area,"2,408,750","2,361,778","2,326,126","2,299,879","2,276,592","2,245,030","2,193,737","2,179,320","2,179,240"

Then I sent email to an acquaintance who works for the Census Bureau (identity suppressed to protect the innocent), pointing out the errors so that they could be corrected.

My contact checked with the people who produced the data, and informed me that, according to them, CO1 was not an error. Rather, the 1 was a footnote mark, directing me to a footnote at the bottom of the file:

"1Broomfield, CO was formed from parts of Adams, Boulder, Jefferson, and Weld Counties, CO on November 15, 2001 and was coextensive with Broomfield city.",,,,,,,,,,,,^M
"For purposes of presenting data for metropolitan and micropolitan statistical areas for Census 2000, Broomfield is treated as if it were a county at the time of the 2000 census.",,,,,,,,,,,,^M

I would like to suggest the following as a basic principle of computerized data processing:

Data files should contain data.

There's a larger issue here about confusing content and presentation. But "Data files should contain data" is simpler and easier to remember.

I suspect that this file was exported from a spreadsheet program, probably Excel. Spreadsheet programs desperately want you to confuse content and presentation. This is why one should not use a spreadsheet as a database.

I now recall another occasion when I had to deal with data that was exported from a spreadsheet that was pretending to be a database. It was a database of products made by a large cosmetics company. A typical record looked like this:

"Soft-Pressed Powder Blusher","618J-05","Warm, natural-looking powder colour for all skins.  Wide range of shades-subtle to vibrant.  With applicator brush.","Cheeks","Nudes","Chestnut Blush","All","","19951201","Yes","","14.5",""

"Water-Dissolve Cream Cleanser","6.61E+01","Creamy cleanser for drier, more sensitive skins.  Dissolves even the most tenacious makeups.","Cleansers","","","","Sub I, I, II","19951201","Yes","1","14.5",""

Back to the Census Bureau, which almost screwed me by putting a footnote on a state name. What if they had decided to put footnotes on the population figures? Then I would have been really screwed, because it would have been completely undetectable.

No, wait! It's all become clear. That's why they put the commas in the numerals!

[ Addendum 20080129: My Census Bureau contact tells me that the authors of the data file have seen the wisdom of my point of view, in spite of my unconstructive and unhelpful feedback (I said "Wow, that is an incredibly terrible idea") and are planning to address the issue in the next release of the data. Hooray for happy endings! ]

[ Addendum 20080129: My Census Bureau contact tells me that they do sometimes put footnotes on the data items, so don't laugh too hard at my remark about the commas. ]

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Smallest state capitals
I think it was James Kushner who first suggested that I consider the question of which U.S. state capital had the smallest population in relation to its state's largest city. For example, New York City is the largest city in the United States, but the state capital of New York State is Albany, with a population of about 850,000. The population of New York City exceeds that of Albany by a factor of around 20.

At the other end of the scale, of course, we have state capitals like Boston, Denver, Atlanta, and Honolulu that are their state's largest cities. For these states, the population quotient is 1, its theoretical minimum.

Well, James, it only took me thirty years, but here it is.

I tried to resolve the question manually a few weeks ago, by browsing Wikipedia for the populations of likely candidates. Today I took a more methodical approach, downloading the U.S. Census Bureau's July 2006 estimates for populations of metropolitan areas, and writing a couple of little programs to grovel the data.

I had to augment the Census Bureau's data with two items: Annapolis, MD, and Montpelier, VT are not large enough to be included in the metropolitan area data file. I used U.S. Census 2006 estimates for these cities as well.

I discarded one conurbation: the Census Bureau includes a "Metropolitan Division" in New Hampshire that consists of Rockingham and Strafford counties; this was the most populous identified area in New Hampshire. It didn't seem entirely germane to the question, so I took it out. On the other hand, including it doesn't change the results much: its population is 416,000, compared with Manchester-Nashua's 402,000.

The results follow.

State	Capital and its Population		Largest metropolitan area and its population		Quotient
MD	Annapolis	36,408	Baltimore-Towson	2,658,405	73	.02
IL	Springfield	206,112	Chicago-Naperville-Joliet	9,505,748	46	.12
NV	Carson City	55,289	Las Vegas-Paradise	1,777,539	32	.15
VT	Montpelier	7,954	Burlington-South Burlington	206,007	25	.90
NY	Albany	850,957	New York-Northern New Jersey-Long Island	18,818,536	22	.11
MO	Jefferson City	144,958	St. Louis	2,796,368	19	.29
KY	Frankfort	69,068	Louisville-Jefferson County	1,222,216	17	.70
FL	Tallahassee	336,502	Miami-Fort Lauderdale-Miami Beach	5,463,857	16	.24
WA	Olympia	234,670	Seattle-Tacoma-Bellevue	3,263,497	13	.91
AK	Juneau	30,737	Anchorage	359,180	11	.69
PA	Harrisburg	525,380	Philadelphia-Camden-Wilmington	5,826,742	11	.09
SD	Pierre	19,761	Sioux Falls	212,911	10	.77
MI	Lansing	454,044	Detroit-Warren-Livonia	4,468,966	9	.84
NJ	Trenton	367,605	Edison	2,308,777	6	.28
CA	Sacramento	2,067,117	Los Angeles-Long Beach-Santa Ana	12,950,129	6	.26
NM	Santa Fe	142,407	Albuquerque	816,811	5	.74
OR	Salem	384,600	Portland-Vancouver-Beaverton	2,137,565	5	.56
DE	Dover	147,601	Wilmington	691,688	4	.69
VA	Richmond	1,194,008	Washington-Arlington-Alexandria	5,290,400	4	.43
ME	Augusta	121,068	Portland-South Portland-Biddeford	513,667	4	.24
TX	Austin	1,513,565	Dallas-Fort Worth-Arlington	6,003,967	3	.97
AL	Montgomery	361,748	Birmingham-Hoover	1,100,019	3	.04
NE	Lincoln	283,970	Omaha-Council Bluffs	822,549	2	.90
WI	Madison	543,022	Milwaukee-Waukesha-West Allis	1,509,981	2	.78
NH	Concord	148,085	Manchester-Nashua	402,789	2	.72
KS	Topeka	228,894	Wichita	592,126	2	.59
MT	Helena	70,558	Billings	148,116	2	.10
ND	Bismarck	101,138	Fargo	187,001	1	.85
NC	Raleigh	994,551	Charlotte-Gastonia-Concord	1,583,016	1	.59
LA	Baton Rouge	766,514	New Orleans-Metairie-Kenner	1,024,678	1	.34
OH	Columbus	1,725,570	Cleveland-Elyria-Mentor	2,114,155	1	.23
AR	Little Rock	652,834	Little Rock-North Little Rock	652,834	1	.00
AZ	Phoenix	4,039,182	Phoenix-Mesa-Scottsdale	4,039,182	1	.00
CO	Denver	2,408,750	Denver-Aurora	2,408,750	1	.00
CT	Hartford	1,188,841	Hartford-West Hartford-East Hartford	1,188,841	1	.00
GA	Atlanta	5,138,223	Atlanta-Sandy Springs-Marietta	5,138,223	1	.00
HI	Honolulu	909,863	Honolulu	909,863	1	.00
IA	Des Moines	534,230	Des Moines-West Des Moines	534,230	1	.00
ID	Boise	567,640	Boise City-Nampa	567,640	1	.00
IN	Indianapolis	1,666,032	Indianapolis-Carmel	1,666,032	1	.00
MA	Boston	4,455,217	Boston-Cambridge-Quincy	4,455,217	1	.00
MN	St. Paul	3,175,041	Minneapolis-St. Paul-Bloomington	3,175,041	1	.00
MS	Jackson	529,456	Jackson	529,456	1	.00
OK	Oklahoma City	1,172,339	Oklahoma City	1,172,339	1	.00
RI	Providence	1,612,989	Providence-New Bedford-Fall River	1,612,989	1	.00
SC	Columbia	703,771	Columbia	703,771	1	.00
TN	Nashville	1,455,097	Nashville-Davidson--Murfreesboro	1,455,097	1	.00
UT	Salt Lake City	1,067,722	Salt Lake City	1,067,722	1	.00
WV	Charleston	305,526	Charleston	305,526	1	.00
WY	Cheyenne	85,384	Cheyenne	85,384	1	.00

Nineteen of fifty state capitals are their state's largest cities.

Vermont is an interesting outlier here. It makes fourth place not because it has a large city, but because its capital, Montpelier, is so very small. I tried doing some scatter plots, to see if anything else jumped out, but they weren't very illuminating. If anything, the data is suprisingly evenly distributed. Here's an example:

[ Addendum 20080129: Some remarks about the format of the Census Bureau's data file. ]

[ Addendum 20090217: A comparison of the relative sizes of each state's largest and second-largest cities. ]

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Utterly Useless Book Reviews (#1 in a series?)
This month I'm reading Robert Graves' awesome novel King Jesus. Here's the utterly useless review I wanted to write: It does for the Bible what I, Claudius did for Suetonius. And yeah, if you've read I, Claudius and Suetonius, then that's all you need to know about King Jesus, and you'll rush out to read it. But how many of you have read I, Claudius and Suetonius? Hands? Anyone? Yeah, I didn't think so.

Order I, Claudius with kickback no kickback

Graves was a classical scholar, and based his novel on the historical accounts available, principally The Twelve Caesars of Suetonius. Suetonius wrote his history after all the people involved were dead, and his book reads like a collection of anecdotes placed in approximately chronological order. Suetonius seems to have dug up and recorded as fact every scurrilous rumor he could find. Some of the rumors are contradictory, and some merely implausible. When Graves turned The Twelve Caesars into I, Claudius, he resolved this mass of unprocessed material into a coherent product. The puzzling trivialities are explained. The contradictions are cleared up. Sometimes the scurrilous rumors are explained as scurrilous rumors; sometimes Claudius explains the grain of truth that lies at their center. Other times the true story, as related by Claudius, is even worse than the watered-down version that came to Suetonius's ears. Suetonius mentions that, as emperor, Claudius tried to introduce three new letters into the alphabet. Huh? In Graves' novel, this is foreshadowed early, and when it finally happens, it makes sense.

Order King Jesus with kickback no kickback

There is a story that Borges tells about the miracles performed by the Buddha, who generally eschewed miracles as being too showy. But Borges tells the story that one day the Buddha had to cross a desert, and seven different gods each gave him a parasol to shade his head. The Buddha did not want to offend any of the gods, so he split himself into seven Buddhas, and each one crossed the desert using a different parasol. He performed a miracle of politeness.

(The trouble with Borges's stories is that you never know which ones he read in some obscure 17th-century book, and which ones he made up himself. I spent a whole year thinking how clever Borges had been to have invented the novelist Adolfo Bioy Casares, with his alphabetical initials, and then one day I was in the bookstore and came upon the Adolfo Bioy Casares section. Oops.)

Anyway, Graves lets Jesus have the miracles, and they are indeed miraculous, but they are miracles of kindness and insight, not miracles of stage magic. When Graves explains the miracles, you say "oh, of course", without then saying "is that all?" I have not yet gotten to the part where Jesus silences the storm and walks on water, but I am looking forward to it. I did get to the loaves and fishes, and it was quite satisfactory. I am not going to spoil the surprise.

I recommend it. Check it out.

[ Addendum 20080201: James Russell has read both I, Claudius and Twelve Caesars. ]

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Help, help!
(Readers of Planet Haskell may want to avert their eyes from this compendium of Perl introspection techniques. Moreover, a very naughty four-letter word appears, a word that begins with "g" and ends with "o". Let's just leave it at that.)

Przemek Klosowski wrote to offer me physics help, and also to ask about introspection on Perl objects. Specifically, he said that if you called a nonexistent method on a TCL object, the error message would include the names of all the methods that would have worked. He wanted to know if there was a way to get Perl to do something similar.

There isn't, precisely, because Perl has only a conventional distinction between methods and subroutines, and you Just Have To Know which is which, and avoid calling the subroutines as methods, because the Perl interpreter has no idea which is which. But it does have enough introspection features that you can get something like what you want. This article will explain how to do that.

Here is a trivial program that invokes an undefined method on an object:

        use YAML;

        my $obj = YAML->new;
        $obj->nosuchmethod;

        Can't locate object method "nosuchmethod" via package "YAML" at test.pl line 4.

Now consider the following program instead:

        use YAML;
        use Help 'YAML';
        
        my $obj = YAML->new;
        $obj->nosuchmethod;

        Unknown method 'nosuchmethod' called on object of class YAML
        Perhaps try:
          Bless 
          Blessed 
          Dump 
          DumpFile 
          Load 
          LoadFile 
          VALUE 
          XXX 
          as_heavy (inherited from Exporter)
          die (inherited from YAML::Base)
          dumper_class 
          dumper_object 
          export (inherited from Exporter)
          export_fail (inherited from Exporter)
          export_ok_tags (inherited from Exporter)
          export_tags (inherited from Exporter)
          export_to_level (inherited from Exporter)
          field 
          freeze 
          global_object 
          import (inherited from Exporter)
          init_action_object 
          loader_class 
          loader_object 
          new (inherited from YAML::Base)
          node_info (inherited from YAML::Base)
          require_version (inherited from Exporter)
          thaw 
          warn (inherited from YAML::Base)
          ynode 
        Aborting at test.pl line 5

Some of the items may be intended to be called as functions, and not as methods. Some may be functions imported from some other module. A common offender here is Carp, which places a carp function into another module's namespace; this function will show up in a list like the one above, without even an "inherited from" note, even though it is not a method and it does not make sense to call it on an object at all.

Even when the items in the list really are methods, they may be undocumented, internal-use-only methods, and may disappear in future versions of the YAML module.

But even with all these warnings, Help is at least a partial solution to the problem.

The real reason for this article is to present the code for Help.pm, not because the module is so intrinsically useful itself, but because it is almost a catalog of weird-but-useful Perl module hackery techniques. A full and detailed tour of this module's 30 lines of code would probably make a decent 60- or 90-minute class for intermediate Perl programmers who want to become wizards. (I have given many classes on exactly that topic.)

Here's the code:

        package Help;

        use Carp 'croak';

        sub import {
          my ($selfclass, @classes) = @_;
          for my $class (@classes) {
            push @{"$class\::ISA"}, $selfclass;
          }
        }

        sub AUTOLOAD {
          my ($bottom_class, $method) = $AUTOLOAD =~ /(.*)::(.*)/;
          my %known_method;

          my @classes = ($bottom_class);
          while (@classes) {
            my $class = shift @classes;
            next if $class eq __PACKAGE__;
            unshift @classes, @{"$class\::ISA"};
            for my $name (keys %{"$class\::"}) {
              next unless defined &{"$class\::$name"};
              $known_method{$name} ||= $class;
            }
          }

          warn "Unknown method '$method' called on object of class $bottom_class\n";
          warn "Perhaps try:\n";
          for my $name (sort keys %known_method) {
            warn "  $name " . 
              ($known_method{$name} eq $bottom_class 
               ? "" 
               : "(inherited from $known_method{$name})") . 
                "\n";
          }
          croak "Aborting";
        }

        sub help {
          $AUTOLOAD = ref($_[0]) . '::(none)';
          goto &AUTOLOAD;
        }

        sub DESTROY {} 

        1;

use Help 'Foo'

Typically, a module's import method is inherited from Exporter, which gets control at this point and arranges to make some of the module's functions available in the caller's namespace. So, for example, when you invoke use YAML 'freeze' in your module, Exporter's import method gets control and puts YAML's "freeze" function into your module's namespace. But that is not what we are doing here. Instead, Help has its own import method:

        sub import {
          my ($selfclass, @classes) = @_;
          for my $class (@classes) {
            push @{"$class\::ISA"}, $selfclass;
          }
        }

@Foo::ISA is the array that is searched whenever a method call on a Foo objects fails because the method doesn't exist. Perl will search the classes named in @Foo::ISA, in order. It will search the Help class last. That's important, because we don't want Help to interfere with Foo's ordinary inheritance.

Notice the way the variable name Foo::ISA is generated dynamically by concatenating the value of $class with the literal string ::ISA. This is how you access a variable whose name is not known at compile time in Perl. We will see this technique over and over again in this module.

The backslash in @{"$class\::ISA"} is necessary, because if we wrote @{"$class::ISA"} instead, Perl would try to interpolate the value of $ISA variable from the package named class. We could get around this by writing something like @{$class . '::ISA'}, but the backslash is easier to read.

AUTOLOAD

But when method search fails, Perl doesn't give up right away. Instead, it tries the method search a second time, this time looking for a method named AUTOLOAD. If it finds one, it calls it. It only throws an exception of there is no AUTOLOAD.

The Help class doesn't have a nosuchmethod method either, but it does have AUTOLOAD. If Foo or one of its other parent classes defines an AUTOLOAD, one of those will be called instead. But if there's no other AUTOLOAD, then Help's AUTOLOAD will be called as a last resort.

$AUTOLOAD

This pattern match dismantles the contents of $AUTOLOAD into a class name and a method name:

        sub AUTOLOAD {
          my ($bottom_class, $method) = $AUTOLOAD =~ /(.*)::(.*)/;

The AUTOLOAD function is now going to accumulate a table of all the methods that could have been called on the target object, print out a report, and throw a fatal exception.

The accumulated table will reside in the private hash %known_method. Keys in this hash will be method names. Values will be the classes in which the names were found.

Accumulating the table of method names

          my @classes = ($bottom_class);

          while (@classes) {
            my $class = shift @classes;

            next if $class eq __PACKAGE__;

Before the loop actually looks at the methods in the current class it's searching, it looks to see if the class has any base classes. If there are any, it pushes them onto the stack to be searched next:

            unshift @classes, @{"$class\::ISA"};

To find out if a name denotes a subroutine, we use defined(&{subroutine_name}) for each name in the package symbol table. If there is a subroutine by that name, the program inserts it and the class name into %known_method. Otherwise, the name is a variable or filehandle name and is ignored:

            for my $name (keys %{"$class\::"}) {
              next unless defined &{"$class\::$name"};
              $known_method{$name} ||= $class;
            }
          }

If you have any clever techniques for identifying other stuff that should be omitted from the output, this is where you would put them. For example, many authors use the convention that functions whose names have a leading underscore are private to the implementation, and should not be called by outsiders. We might omit such items from the output by adding a line here:

              next if $name =~ /^_/;

    (
        this => Foo,
        that => Foo,
        new => Base,
        blookus => Mixin::Blookus,
        other => Foo
    )

Printing the report

          warn "Unknown method '$method' called on object of class $bottom_class\n";
          warn "Perhaps try:\n";

          for my $name (sort keys %known_method) {
            warn "  $name " . 
              ($known_method{$name} eq $bottom_class 
               ? "" 
               : "(inherited from $known_method{$name})") . 
                "\n";
          }
          croak "Aborting";
        }

The output for my example would look like this:

        Unknown method 'nosuchmethod' called on object of class Foo:
        Perhaps try:
          blookus (inherited from Mixin::Blookus)
          new (inherited from Base)
          other
          that
          this
        Aborting at YourErroneousModule.pm line 679

Synthetic calls

You can always force the help message by calling $object->Help::help. This calls a method named help, and it starts the inheritance search in the Help package. Control is transferred to the following help method:

        sub help {
          $AUTOLOAD = ref($_[0]) . '::(none)';
          goto &AUTOLOAD;
        }

Calling AUTOLOAD in the normal way, without goto, would have worked also. I did it this way just to be a fusspot.

DESTROY

It is very common for objects to lack a DESTROY method; usually nothing additional needs to be done when the object's lifetime is over. But we do not want the Help::AUTOLOAD function to be invoked automatically whenever such an object is destroyed! So Help defines a last-resort DESTROY method that is called instead; this prevents Perl from trying the AUTOLOAD search when an object with no DESTROY method is destroyed:

        sub DESTROY {} 

Living dangerously

        use Help 'UNIVERSAL';

About use strict

Well, this code will not run with "use strict". It does a lot of stuff on purpose that "strict" was put in specifically to keep you from doing by accident.

At some point you have to take off the training wheels, kiddies.

License

Share and enjoy.

[Other articles in category /prog/perl] permanent link

Clubbing someone to death with a loaded Uzi
I once had an intern who wrote wrote the following code to process a web survey form. The form input widgets were named q1, q2, and so forth:

    foreach $k (keys %in) {
            if ($k eq q1) {
                    if ($in{$k} eq agree) {
                            $count{q10} = $count{q10} + 1;
                    }
                    if ($in{$k} eq disaagree) {
                            $count{q11} = $count{q11} + 1;
                    }
            }
            if ($k eq q2) {
                    @q2split = split(/\0/, $in{$k});
                    foreach (@q2split) {
                            $count{$_} = $count{$_} + 1;
                    }
            }
            if ($k eq q3) {
                    $count{$in{$k}} = $count{$in{$k}} + 1;
            }

            ...
     }   

    if ($in{q1} eq agree) {
            $count{q10} = $count{q10} + 1;
    }
    if ($in{q1} eq disaagree) {
            $count{q11} = $count{q11} + 1;
    }

    @q2split = split(/\0/, $in{q2});
    foreach (@q2split) {
            $count{$_} = $count{$_} + 1;
    }

    $count{$in{q3}} = $count{$in{q3}} + 1;
    ...

This is the sort of mistake you expect from an intern. I chuckled and corrected him. But I've seen it several times since from non-interns.

Here's another example. I am not making this up. Whether it's more or less odious than the intern code is up to you to decide:

         foreach $location_name (%LOCATION ) {
                $location_code = $LOCATION{$location_name};

                if ($location_name eq $location ) {

                    printf FILE "$location_code\,";
                        printf FILE "%4s", "$min3\,";
                        printf FILE "%4s", "$max3\,";
                        printf FILE "%1s", "$wx3\n";

                }      

        } 

        printf FILE "$LOCATION{$location}\,";
            printf FILE "%4s", "$min3\,";
            printf FILE "%4s", "$max3\,";
            printf FILE "%1s", "$wx3\n";

        for my $k (keys %hash) {
          if ($k eq "name") {
            $hash{$k}++;
          }
        }

It's appalling how many supposedly professional programmers see nothing wrong here. They squint at the code, and say "I think you need parentheses around %hash there", or they criticize the choice of variable names.

I first used this as an interview question because the Python code sample submitted by a job applicant contained an example of it. "Weird," I thought, "but maybe she's outgrown that." Since she claimed to be an expert Perl user, I asked her about it in Perl, using code like the example above. After she made a syntactic suggestion, I said "It's not a syntax problem, and it's not a trick question." She criticized the syntax some more. Finally I told her the answer: "Couldn't you just use $hash{name}++?"

"Oh, yeah, I guess so," she said.

A few minutes later we were going over her Python code sample and I pointed out the place where she had done the exact same thing, and asked if she was happy with that loop and wanted to change it. No, she thought it was just fine.

"Doesn't this look like the example I showed you on the whiteboard a little while ago?"

"Oh, I guess it does."

We didn't hire her.

Larry Wall once said that iterating over the keys of a hash is like clubbing someone to death with a loaded Uzi.

I had already realized that you could, in principle, commit this error with a regular array instead of with a hash, but I had never seen an example until today's episode of the Daily WTF. The Daily WTF code is so awful, all the way through, that I was afraid that people might miss this slightly-more subtle gem lurking in the middle, and that was what motivated me to write this article in the first place. Here's the gem:

        // Java
        for (int a=1;a<=params.size();a++) switch (a)
            {
              case 1 : if (params.get(0) != null) 
                this.one=params.get(0).toString();
                break;
              case 2 : if (params.get(1) != null)
                this.two=params.get(1).toString();
                break;
              ...
              case 14 : if (params.get(13) != null)
                this.fourteen=params.get(13).toString();
                break;
            }
          }

[ Addendum 20080201: A bit more. ]

[ Addendum 20090213: A counterexample. ]

[Other articles in category /prog] permanent link

Squillions
A while back I looked up "zillion" in Wikipedia, which is an alias for the Wikipedia article about "Indefinite and fictitious numbers". The article includes a large number of synonyms for "zillion", such as bajillion, kajillion, gazillion, and so forth. For some reason the word "squillion" caught my eye, and I noticed that the citation was from Terry Pratchett: "And you owe me a million billion trillion zillion squillion dollars." This suggested to me that "squillion" might be a nonce-word, one made up on the spot by Pratchett for that one sentence, in which case it should not be in the Wikipedia article.

Google book search is a good way to answer questions like that, because if "squillion" is widely used, you will find a lot of examples of it. And indeed it is widely used, and I did find a lot of examples of it. So there was no need to remove it from the article.

One of the Google hits was from the Cormac Ó Cuilleanáin translation of Giovanni Boccaccio's Decameron. The Decameron is a great classic of Italian Renaissance literature, probably the greatest classic that Italian has, after Dante's Divine Comedy. It was written around 1350. In this particular chapter (the tenth story on the sixth day, if you want to look it up) Guccio, a priest, is trying to seduce a hideous kitchen-maid:

He sat himself down by the fire—although this was August—and struck up a conversation with the wench in question (Nuta by name), informing her that he was by rights a member of the gentry and had more than a squillion florins in the bank, not counting those he had to give to other people...

The kitchen-maid, by the way, is described as having "a pair of tits like two baskets of manure".

This was amusing, and as I had never read the Decameron, I wanted to read more, and learn how it turned out. But the Google excerpt was limited, so I asked the library to get me a copy of that version of the Decameron. Of course they have many copies on the shelf, but not that particular translation. So I asked the interlibrary loan people for it, and they got it for me.

When it arrived, I was rather dismayed. The ILL people get the book from the most convenient place, and that means that it often comes from the Drexel library, up the street, or the Temple library, across town, or the West Chester Community College library, or Lehigh University, about an hour away in Bethlehem. (Steel Bethlehem, of course, not Jesus Bethlehem.) The farthest I had ever gotten a book from was an extremely obscure quilting manual that Lorrie asked for; it eventually arrived from the Sno-Isles regional library system of Marysville, Washington.

But this copy of the Decameron came from the Sloman library of the University of Essex. I was so shocked that I had to look it up online to make sure that it was not Essex, New Jersey, or something like that. I was not. It was East Saxony. I was upset because I felt that the trouble and effort had been wasted. If I had known that the nearest available copy of Cormac Ó Cuilleanáin's translation was in Essex, I would have been happy to take a different version that was on the shelf. And then to top it off, I had hardly begun to read it before it came due and had to be sent back to Essex.

So I went to the library and got another Decameron, this one translated by Mark Musa and Peter Bondanella. Here is the corresponding passage:

Although it was still August, he took a seat near the fire and began to talk with the girl, whose name was Nuta, telling her that he was a gentleman by procuration, that he had more than a thousand hundreds of florins (not counting those he had to give away to others), ...

And there is a footnote on "thousand hundreds" explaining "Guccio invents this amount, as well as the previous phrase 'by procuration,' in order to impress his lady." By the way, in this version, Nuta has "a pair of tits that looked like two clumps of cowshit".

Anyway, I think I liked "squillions" better than "thousand hundreds", although I suppose "thousand hundreds" is probably a more literal translation.

Well, I can find this out. Of course, one can find the Decameron online in Italian; the copyright expired about five hundred years ago. Here it is in Italian, courtesy of Brown University:

E ancora che d'agosto fosse, postosi presso al fuoco a sedere, cominciò con costei, che Nuta aveva nome, a entrare in parole e dirle che egli era gentile uomo per procuratore e che egli aveva de' fiorini piú di millantanove, senza quegli che egli aveva a dare altrui,...

The 1903 translation that Brown University provides is "more florins than could be reckoned", which does not seem to me to capture the flavor of the original, and does not seem to be a literal translation either. "Millantanove" seems to me to be a made-up word resembling "mille" = "thousand". But as I said, I don't know Italian.

Nuta in this version has "a pair of breasts that shewed as two buckets of muck". Feh. The Italian is "con un paio di poppe che parean due ceston da letame". The operative phrase here seems to be "ceston da letame". I don't know what those words mean, but, happily, Italian Wikipedia has an article about letame, and as the picture makes clear, it is indeed manure.

Oh, did you want this article to have a point? Too bad.

I recommend the Decameron. It is funny and salacious. There are a lot of stories about women cheating on their husbands, and then getting away with it through some clever trick, and then everyone who hears the story laughs and admires the cleverness of the ladies. (The counterpoint to this is that there are a number of stories of wife-beating, in which everyone who hears the story laughs and admires the wisdom of the husbands. I don't like that so much.)

There are farcical stories of bed-swapping and wife-swapping, and one story about an abbess who comes out of her cell to berate a nun for having her lover in to visit, but the abbess is wearing a pair of men's trousers on her head instead of her wimple. Oops.

This reminds me of when I was in high school, I was talking to one of my friends, who opted to study French, and this friend told me studying French is fun, because when you get to the third year and start reading real French literature, you read that great classic of French Literature, La Vie de Gargantua et de Pantagruel. If you have not read this master treasure of French culture, I should explain that the first chapter is mainly taken up with Gargantua and Pantagruel having a discussion about what is the best sort of thing to wipe your ass with, and it goes on from there.

I took Latin, and in third-year Latin we read the orations of Cicero against Cataline. Fun stuff, but not the sort of thing that has you rushing to translate the next word.

I was going to write an article about symmetries of the dodecahedron, and an interesting problem suggested to me by these balloon displays that I saw at the local Mazda dealership, but eh, this was a lot easier.

Gargantua and Pantagruel eventually agree that the answer is a live goose.

[ Addendum 20080201: More about 'milliantanove'. ]

[Other articles in category /lang] permanent link

Pepys' footballs explained
Walt Mankowski wrote to me with the explanation of Samuel Pepys' footballs: They are not clods of mud, as I guessed, nor horse droppings, as another correspondent suggested, but... footballs.

Walt found a reference in Montague Shearman's 1887 book on the history of football in England that specifically mentions this. Folks were playing football in the street, and because of this, Pepys took his coach to Sir Philip Warwicke's, rather than walking.

I didn't ask, but I presume Walt found this by doing some straightforward Google search for "pepys footballs" or something of the sort. For some reason, this did not even occur to me. Once Big Dictionary failed me, I was stumped. Perhaps this marks me as a member of the pre-Internet generation. I imagined this morning that this episode would be repeated, with my daughter Iris in place of Walt. "Oh, Daddy! You're so old-fashioned. Just use a Google search."

Anyway, inspired by Walt's example, or by what I imagined Walt's example to be, I did the search myself, and found the Shearman reference, as well as the following discussion in William Carew Hazlitt's Faiths and Folklore of 1905:

Mission, writing about 1690, says: "In winter foot-ball is a useful and charming exercise. It is a leather ball about as big as one's head, fill'd with wind. This is kick'd about from one to t'other in the streets, by him that can get at it, and that is all the art of it."

Thanks very much, Walt.

[Other articles in category /lang] permanent link

Your age as a fraction
Little kids often report their ages as "two and a half" or sometimes even "three and three quarters". These evaluations are usually based on whole months: if you were born on April 2, 1969, then on October 2, 1971 you start reporting your age as "two and a half", and, if you choose to report your age as "three and three quarters", you conventionally may begin on January 2, 1973.

However, these reports are not quite accurate. On January 2, 1973, exactly 3 years and 9 months from your birthday, you would be 1,371 days old, or 3 years plus 275 days. 275/365 = 0.7534. On January 1, you were only 3 + 274/365 days old, which is 3.7507 years, and so January 1 is the day on which you should have been allowed to start reporting your age as "three and three quarters". This slippage between days and months occurs in the other direction as well, so there may be kids wandering around declaring themselves as "three and a half" a full day before they actually reach that age.

Clearly this is one of the major problems facing our society, so I wanted to make up a table showing, for each number of days d from 1 to 365, what is the simplest fraction a/b such that when it is d days after your birthday, you are (some whole number and) a/b years. That is, I wanted a/b such that d/365 ≤ a/b < (d+1)/365.

Then, by consulting the table each day, anyone could find out what new fraction they might have qualified for, and, if they preferred the new fraction to the old, they might start reporting their age with that fraction.

There is a well-developed branch of mathematics that deals with this problem. To find simple fractions that approximate any given rational number, or lie in any range, you first expand the bounds of the range in continued fraction form. For example, suppose it has been 208 days since your birthday. Then today your age will range from (y years and) 208/365 days up to (y years and) 209/365 days.

Then we expand 208/365 and 209/365 as continued fractions:

208/365 = [0; 1, 1, 3, 12, 1, 3]
209/365 = [0; 1, 1, 2, 1, 16, 1, 2]

Then you need to find a continued fraction that lies numerically in between these two but is as short as possible. (Shortness of continued fractions corresponds directly to simplicity of the rational numbers they represent.) To do this, take the common initial segment, which is [0; 1, 1], and then apply an appropriate rule for the next place, which depends on whether the numbers in the next place differ by 1 or by more than 1, whether the first difference occurs in an even position or an odd one, mumble mumble mumble; in this case the rules say we should append 3. The result is [0; 1, 1, 3], or, in conventional notation:

Since I already had a library for calculating with continued fractions, I started extending it with functions to handle this problem, to apply all the fussy little rules for truncating the continued fraction in the right place, and so on.

Then I came to my senses, and realized there was a better way, at least for the cases I wanted to calculate. Given d, we want to find the simplest fraction a/b such that d/365 ≤ a/b < (d+1)/365. Equivalently, we want the smallest integer b such that there is some integer a with db/365 ≤ a < (d+1)b/365. But b must be in the range (2 .. 365), so we can easily calculate this just by trying every possible value of b, from 2 on up:

        use POSIX 'ceil', 'floor';

        sub approx_frac {
          my ($n, $d) = @_;
          for my $b (1 .. $d) {
            my ($lb, $ub) = ($n*$b/$d, ($n+1)*$b/$d);
            if (ceil($lb) < ceil($ub) && ceil($ub) > $ub) {
              return (int($ub), $b);
            }
          }
          return ($n, $d);
        }

        my $N = shift || 365;

        for my $i (1..($N-1)) {
          my ($a, $b) = approx_frac($i, $N);
          print "$i/$N: $a/$b\n";
        }

1/10 ≤	1/6	< 2/10	(0.1667)
2/10 ≤	1/4	< 3/10	(0.2500)
3/10 ≤	1/3	< 4/10	(0.3333)
4/10 ≤	2/5	< 5/10	(0.4000)
5/10 ≤	1/2	< 6/10	(0.5000)
6/10 ≤	2/3	< 7/10	(0.6667)
7/10 ≤	3/4	< 8/10	(0.7500)
8/10 ≤	4/5	< 9/10	(0.8000)
9/10 ≤	9/10	< 10/10	(0.9000)

The simplest fractions that are missing from this table are 1/5, which is in the [2/10, 3/10) range and is beaten out by 1/4, and 3/5, which is in the [6/10, 7/10) range and is beaten out by 2/3.

This works fine, and it is a heck of a lot simpler than all the continued fraction stuff. The more so because the continued fraction library is written in C.

For the application at hand, an alternative algorithm is to go through all fractions, starting with the simplest, placing each one into the appropriate d/365 slot, unless that slot is already filled by a simpler fraction:

        my $N = shift || 365;
        my $unfilled = $N;

        DEN:
        for my $d (2 .. $N) {
          for my $n (1 .. $d-1) {
            my $a = int($n * $N / $d);
            unless (defined $simple[$a]) {
              $simple[$a] = [$n, $d];
              last DEN if --$unfilled == 0;
            }
          }
        }

        for (1 .. $N-1) {
          print "$_/$N: $simple[$_][0]/$simple[$_][1]\n";
        }

(It might also be that you could optimize the algorithms to go faster: you can skip the body of the loop in the slot-filling algorithm whenever $n and $d have a common factor, which means you are executing the body only n log n times. But testing for common factors takes time too...)

I was going to paste in a bunch of tabulations, but once again I remembered that it makes more sense to just let you run the program for yourself. Here is a form that will generate the table for all the fractions 1/N .. (N-1)/N; use N=365 to generate a table of year fractions for common years, and N=366 to generate the table for leap years:

Here's a program that will take your birthday and calculate your age in fractional years. Put in your birthday in ISO standard format: 2 April, 1969 is 19690402.

[ Addendum 20070429: There is a followup to this article. ]

[Other articles in category /math] permanent link

Footballs?
The diary of Samuel Pepys for Tuesday, 3 January 1664/5 says:

Up, and by coach to Sir Ph. Warwicke's, the streete being full of footballs, it being a great frost, and found him and Mr. Coventry walking in St. James's Parke.

My best guess is that it's big chunks of frozen mud that you have to kick out of the way. Do any gentle readers know for sure?

The Diary of Samuel Pepys has a syndication feed you can subscribe to. You get a diary entry every day or so, with all the names and places linked to a glossary. It's fun reading.

[ Addendum 20080105: The answer. ]

[Other articles in category /lang] permanent link

Iris is not a vegetarian
I just had a long vacation and got to spend a lot of time with Iris, which is why she's popping up so much all of a sudden. I seem to have gotten into Mimi Smartypants mode. I will return to the regularly-scheduled discussions of programming and mathematics shortly. But since I seem to have written two articles in a row ([1] [2]) on the subject of telling kids the difficult truth, I thought I'd try to finish up this one, which has been mostly done for months now. Also there was a recent episode that got me thinking about it again.

I went to visit Iris at school last week, and stayed for lunch. I was seated with Iris and three other little girls. As the food was served, one of the girls, Riley, made some joke about how the food cart contained guinea pigs instead. This sort of joke is very funny to preschoolers.

My sense of humor is very close to a preschooler's, and I would have thought that this was funny if she had said that the food cart contained clocks, or nose hairs, or a speech in defense of the Corn Laws, or the Trans-Siberian Railroad, or fish-shaped solid waste. But she said guinea pigs, and instead of laughing, I mused aloud that I had never eaten a guinea pig.

Riley informed me that "You can't eat guinea pigs! They're animals, not food."

"Sure you can," I said. "Meat is made from animals."

Riley got this big grin on her face, the one that preschoolers get when they know that the adults are teasing them, and said "Nawww!"

"Yes," I said. "Meat comes from animals."

Riley shook her head. She knew I was joking. A general discussion ensued, with Iris taking my side, and another girl, Flora, taking Riley's. In the end, I did not convince them.

"Well," I said, mostly to myself, at the end, "you girls are in for a rude awakening someday."

Now, I know that not everyone is as direct as I am. And I know that not all non-vegetarians are as concerned as I am about the ethics of eating meat. But wow. I would have thought that someone would have explained to these girls where meat came from, just as a point of interest if nothing else. Or maybe they would have made the connection between chicken-the-food and chicken-the-farm-animal. I mean, they are constantly getting all these stories set on farms. Since three-year-olds ask about a billion questions a day. they must ask around a thousand questions a day about the farms, so how is it that the subject never came up?

Iris was accidentally exposed to a movie version of Charlotte's Web on an airplane, and the plot of Charlotte's Web is that Charlotte is trying to save Wilbur from being turned into smoked ham. Left to myself I wouldn't have exposed Iris to Charlotte's Web so soon—it is too long for her, for one thing—but my point here is that the world is full of reminders of the true nature of meat, and they can be hard to avoid. So I was very surprised when it turned out that these two age-mates of Iris's were so completely unaware of it.

Anyway, Iris has known from a very early age where meat comes from. Early in her meat-eating career, probably before she was two years old, I specifically explained it to her. I wanted to make sure that she understood that meat comes from animals. Because there are serious ethical issues involved when one eats animals, and I think they must be considered. We may choose to kill and destroy thinking beings to make food, but we should at least be aware that that is what is happening. I'm not sure I think it is evil, but I want to at least be aware of the possibility.

I have never been a vegetarian, but I want to try to face the ethical results of that choice head on, and not pretend that they are not there. I did not want Iris growing up to identify meat with sterile packages in the supermarket. Meat was once alive, moving around with its own agenda, and I think it is important to understand this.

So I made an effort to bring up the subject at home, and then one day when Iris was around twenty months old we went to a Chinese restaurant that has live fish in tanks at the front of the restaurant, and you can ask them to take one of these fish into the kitchen to be cooked for your dinner. Iris has loved to eat fish since she was a tiny baby.

We ordered a striped bass, and then I took Iris to look at the fish in the tanks. I explained to her that these fish swimming in the tanks were for people to eat, and that when we ordered our fish for dinner, a waiter came out and caught one of the fish in a net, took it back to the kitchen, and they killed it and were cooking it for us.

As I said, I had made the point before, but never so directly. We had never before seen the live animals that were turned into food for us. I really did not know how Iris would respond to this. Some people have a very strong negative response when they first learn that meat comes from animals, so negative that they never eat meat again. But I thought Iris should know the truth and make her own decision about how to respond.

Iris's response was to point at one of the striped bass and say "I want to eat that one."

Then she took me to each tank in turn, and told me me which kind of fish she wanted to eat and which ones she did not want to eat. (She favored the fish-looking fish, and rejected the crabs, shrimp, and eels.)

Then when the fish arrived on our table Iris asked if it had been swimming in the tank, and I said it had. "Yum yum," said Iris, and dug in.

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Santa Claus
A few years ago I was talking to a woman I worked with, who told me that she told her kids that Santa Claus was real, "because how could you not?". She thought she would have been depriving her kids by not telling them the story. And maybe she would have been; I honestly don't know. I don't remember what it was like to believe literally in Santa Claus or how I felt when I learned the truth.

My vocabulary here is failing me. "Telling them the story" is not what I want, because the Santa Claus thing is deceptive, and telling stories is not normally deceptive: "fiction" and "lies" mean different things. When I tell Iris the story of the Little Red Hen, there is no presumption that there is an actual, literal Red Hen. Iris might think there is, or not, or might not think about it at all; I don't know which. Ditto Cinderella, or Olivia the Pig, or any other story I tell or read to her. But when people tell their kids about Santa Claus, they present it not as a story, but as a literal truth. They present it in a way that is calculated to make the kids believe there is actually a fat, benevolent, white-bearded immortal, manufacturing toys in a secret arctic workshop. This is no longer mere fiction; it is a lie. So what I want to say is that this lady thought she would be depriving her kids of the magic of Santa Claus by not telling them this lie.

But I really don't want to use the word "lie" here, because it's so pejorative. It makes it sound as though I think badly of this good woman for telling her kids that Santa Claus was real. But I don't, at all. She is generally wise and honest and I respect her. Parents tell their kids all sorts of awful, appalling lies, which upsets me a lot, but this lie is quite benign by comparison, and bothers me not at all.

Let me be perfectly clear: I have nothing, absolutely nothing, against the Santa Claus story. I have an article in progress about how much I hate the way parents routinely lie to their kids, to manipulate them, and this one isn't in the article, because it doesn't even register. It's just for fun, or nearly so.

Santa Claus seems pretty harmless to me. Unlike many of the pernicious lies children are told, Santa Claus is a great story. It would be really wonderful to believe that I would get presents every year because there was a fat guy manufacturing toys at the North Pole. Delightful! And the only thing wrong with it is that it isn't true. Oh well. There are a lot of pretty stories that aren't true.

Anyway, at the time I had this conversation about Santa Claus, Iris was too young to have heard about Santa Claus anyway, and my co-worker asked if I was planning to tell Iris the Santa Claus story.

Now that I've written this article, it occurs to me what she meant to ask, was not whether I was going to tell Iris the story, but whether I was going to tell her that it was true. Having realized that now, my reply seems a lot more obvious in retrospect than it did at the time.

I hadn't thought about it before, but I said I didn't think I would.

"But what are you going to tell her?"

"The truth, I guess."

The truth, though, is pretty wonderful, although less astonishing. You don't get presents because of the fat guy in the red suit, which is a shame, because wouldn't it be fun if it were true? But you do get them anyway, and it's because your family loves you. As consolation prizes go, that one's pretty good.

So we did tell her the truth. Santa Claus is just a story. Iris will have to grow up without that piece of childhood delight. Sorry, Iris. But she'll also grow up knowing that her parents respect her enough to tell her the truth instead of a pretty lie, and maybe that will be enough of a consolation prize to make up for it.

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