Computer Moose

My younger son had some English homework where he was supposed to find all the errors in the given sentence. I see one error, but what's wrong with the moose?

My Head Cavorts on Dutch TV

Ionica Smeets of the website Wiskundemeisjes (Math Girls) has written to let me know that a Dutch TV program has featured my paper on optimal coin denominations. Probably only of interest if you are fluent in Dutch, or enjoy seeing my head being animated and doing strange things.

Local 9/11 Crackpots at it Again!

Not satisfied with their truly ignoble performance the last time around, our local 9/11 crackpots are holding another event this Thursday:



The misnamed "9/11 Truth" movement seems to be dying out almost everywhere, except in Canada, where it has a very strong strain of US-hatred to draw on. In the US, it seems the crackpots have moved on to "Obama is a Muslim Manchurian candidate, the secret love child of Malcolm X, who will become a dictator, take away everyone's rights, and turn the US into a socialist paradise."

As John Ray points out, "Today, the 9/11 conspiracy movement is a shell of what it once was. The website masquerading as an academic journal, Journal of 9/11 Studies, has dropped from a high of six articles in its August 2006 issue to one in March and its two most recent editions (it's supposed to be updated monthly) were simply skipped over, evidently for lack of a single article."

In case you can't read the poster, you can see a better version here. Global Outlook, the group sponsoring the Waterloo event, is also hosting a lecture series at the University of Toronto that looks just chock-full of all sorts of woo, including a bizarre focus on "natural medicine" and "out-of-place artifacts".

Blowhard of the Month: Wayne Eyre

There is no subject like evolution to bring out the blowhards, and Wayne Eyre is just the latest. Writing in the National Post, Eyre praises David Berlinski's latest screed, The Devil's Delusion.

Berlinski, as you probably know, is the poseur who somehow managed to get his anti-evolutionary blather published in venues such as Commentary. He was also recenty caught inventing bogus claims about John von Neumann's attitude towards evolution. A reliable source? I don't think so.

Nevertheless, Blowhard of the Month Eyre accepts Berlinski's claims about evolution at face value. If Berlinski says that the theory of evolution "makes little sense", Eyre believes it must be so. Somehow, Berlinski -- a man with no biological training -- knows more than actual biologists. Differential reproductive success coupled with a mechanism for genotypic/phenotypic change means evolution is inevitable. Any beginning biology student understands this. What about it is so difficult for Eyre?

If Berlinski says the theory of evolution "is supported by little evidence", it must be so. Never mind the painstaking case assembled by Darwin that convinced biologists a hundred years ago. Never mind the mounds and mounds of evidence assembled since then -- if Eyre has ever cracked open a biology textbook or Endler's Natural Selection in the Wild, I would be amazed. No: philosophy Ph. D. David Berlinski has said it, and so it must be true.

Eyre even resorts to the favorite ploy of the blowhard: if all the experts say I am wrong, that is proof I am right.

The fact that the National Post would publish this idea-free dreck is yet more proof that intellectual conservatism is dead.

Crackpots Advance Yet Another Obama Smear

This election has shown without a doubt that the American Right is totally bereft of any sensible ideas. So far they've produced:

• Obama is a terrorist
  
  
• Obama is not really an American citizen
  
  
• Michelle Obama refers to white people as "whitey"
  
  
• Obama is a communist mole
  
  

and many other similar claims that are jaw-dropping in their utter insanity. One McCain supporter even refused to give Halloween candy to the children of parents who supported Obama.

But this is one of the craziest yet. Now the claim is that Obama is secretly using hypnosis techniques to deceive the public. And what's the evidence? It's that Obama uses the hackneyed phrase, "As I stand here before you" in his speeches. Well, then I guess that McCain supporter Joe Lieberman must be using the same technique. After all, it was pioneered by baseball great Brooks Robinson, who apparently developed it to hypnotize pitchers.

It used to be that Republicans had some legitimate criticisms of the Dems. Now all they have is insanity.

Three Bloggers

On the left, yours truly. In the center, T. Ryan Gregory of Genomicron. On the right, the world's most famous science blogger, P. Z. Myers of Pharyngula. We were all in Guelph for P. Z.'s talk sponsored by CFI and the University of Guelph Skeptics.

The talk was well-attended, as P. Z. and his daughter discussed a variety of different subjects, including science education, the upcoming election, and strategies for fighting the foolishness of creationism and intelligent design.

The highlight for me, however, had to be the fellow who during question period insisted that there had to be something outside scientific inquiry, and gave as his prime example (and no, I am not making this up) the 2004 World Series victory by the Boston Red Sox. He claimed that the Sox's improbable finish, including victory during a total lunar eclipse, was proof of supernatural intervention. The majority of the audience laughed, because I suspect they know what I know: that the 2008 World Series Victory by the Phillies is the ultimate, unquestionable proof of a deity.

Poem Banned from British Exam Syllabus

From the Manifesto Club comes this news of a poem removed by the AQA (the awarding body for A-level exams and GCSE's) from the GCSE (General certificate of secondary education) syllabus in Great Britain.

The poem is entitled "Education for Leisure" and was written by the award-winning poet, Carol Ann Duffy. It can be found here.

Syllabi change all the time, but this case is special, since the decision to remove it was spurred by an exam invigilator, Pat Schofield, who apparently felt the poem glorified knife crime. She is quoted as saying, "I think it is absolutely horrendous - what sort of message is that to give to kids who are reading it as part of their GCSE syllabus?"

What's next, banning The Charge of the Light Brigade because it glorifies suicidal military exploits?

The AQA itself responded with these weasel words: "The decision to withdraw the poem was not taken lightly and only after due consideration of the issues involved. We believe the decision underlines the often difficult balance that exists between encouraging and facilitating young people to think critically about difficult but important topics and the need to do this in a way which is sensitive to social issues and public concern."

It looks like Carol Ann Duffy got the last laugh, however. She's written a response entitled Mrs. Schofield's GCSE. How fitting that Schofield, like Bowdler, will pass into the language as a synonym for small-minded censorship.

Mrs Schofield's GCSE

Carol Ann Duffy

You must prepare your bosom for his knife,

said Portia to Antonio in which

of Shakespeare's Comedies? Who killed his wife,

insane with jealousy? And which Scots witch

knew Something wicked this way comes? Who said

Is this a dagger which I see? Which Tragedy?

Whose blade was drawn which led to Tybalt's death?

To whom did dying Caesar say Et tu? And why?

Something is rotten in the state of Denmark - do you

know what this means? Explain how poetry

pursues the human like the smitten moon

above the weeping, laughing earth; how we

make prayers of it. Nothing will come of nothing:

speak again. Said by which King? You may begin.

McCain Mangles English Again

I wrote about this before. John McCain mangles English almost as much as George Bush. On two occasions he's used the nonexistent word "epitat" instead of "epithet", and now a report from the Boston Globe has him saying "predicate" instead of "precedent".

Guitarist Tony McManus in Elora

One of the nicest things about having a blog is meeting interesting people online, and then in real life. (Of course, you also meet some unpleasant loonies, but that's fodder for another post.)

Last May Recursivity got some fan mail from Tony McManus, a guitarist who lives in nearby Elora, Ontario. Actually, calling him a "guitarist" is somewhat of an understatement; he has been called "the best Celtic guitarist in the world". Tony studied ring theory under Peter Vámos at the University of Exeter before giving up mathematics for music.

Tony was kind enough to leave tickets for me and my family to attend his concert in Elora, and last night we all went. Tony's music was phenomenal, combining an intense virtuosity with a percussive style that left the audience breathless. He predominantly played Celtic tunes, but there was quite a lot of variety (including a Bulgarian piece and two pieces played on a special guitar, designed by a Toronto guitar maker, that sounds like a sitar). The variety of sounds he can get from a guitar made me really envious. In between tunes, Tony told us a lot of great stories about drunk Celtic musicians. We all had a terrific time.

Tony was accompanied by Rolly Brown, a fingerpicker now living in Bucks County, Pennsylvania, near where I grew up. In addition to guitar, Rolly is an acupuncturist, a Tai Chi instructor, and he raises Australian dogs. Rolly played some Reverend Gary Davis, Steve Mann, and he closed with a take-off on Julie Gold's "From a Distance" (made famous by Nanci Griffith) written by Jay Mankita in 1992: "From a Dog's Stance". The audience was in stitches.

If you ever get a chance to see Tony McManus or Rolly Brown, take it! Tony gives concerts and workshops all across the world. I guarantee you'll have a great time.

Best Newspaper Headline

Here is my nomination for the best newspaper headline of the year:

Early birds enjoy undead, ducks.

My Favorite Living Mathematician

Ionica Smeets, of the Dutch website Wiskundemeisjes (Math girls), recently asked me to name my favorite living mathematician. Her version of my answer, and some additional text, can be found (in Dutch) here.

Smeets also kindly allowed me to post my response here.

1. Who is your favorite still living mathematician?

I have many favorites, and it's hard to choose: Alf van der Poorten, Carl Pomerance, Michel Mendès France, Donald Knuth, Adi Shamir, Manuel Blum, just to name a few. But if you force me to choose, I think I would have to say that my favorite is the Dutch mathematician Hendrik W. Lenstra, Jr.

2. Why do you admire him/her?

I admire the beauty of his results and his talent for exposition. To list just two of his famous results:

- the Lenstra-Lenstra-Lovász algorithm for lattice basis reduction, which led to a fast algorithm for factoring polynomials with integer coefficients, and has also given us new ways to attack cryptosystems

- the Lenstra elliptic curve factoring algorithm, which allows us to efficiently find small factors of very large numbers

3. What is special about his/her work?

First, Hendrik Lenstra has a really deep understanding of algebra, so intimate that he can see almost instantly how to solve problems that would take others hours or days.

Second, his exposition is always precise. Unlike some other top-flight mathematicians, who are often a little too casual in their proofs, Hendrik doesn't feel it is beneath his dignity to provide details. When you read one of his papers, you get the feeling that every sentence has been chosen with economy and clarity in mind.

Third, Lenstra has a wide variety of interests, and doesn't hesitate to think seriously about things that others might dismiss as 'recreational'. I point in particular to his work on the mathematics of the Dutch artist M. C. Escher and his delightful paper on profinite Fibonacci numbers.

4. Have you ever worked together?

Yes, we wrote one paper together, "Continued fractions and linear recurrences", which appeared in the journal Mathematics of Computation in 1993. To explain what we did, I have to remind your readers about the two subjects of the title.

Every real number has an essentially unique expansion as a continued fraction, that is, an expression of the form x = a+1/(b+1/(c+ ....)), where all the terms, except possibly the first, are positive integers. For example, π = 3+1/(7+1/(15+ 1/(1 + ...))). When you truncate a continued fraction after n terms, you get better and better rational approximations to the original number. For example, one term of the continued fraction for π gives 3, two terms gives 22/7, three terms gives 333/106, four terms gives 355/113, etc. These fractions are called the convergents and are usually written as p_n / q_n .

Another thing your readers probably know about is linear recurrences. A simple example of a linear recurrence is the recurrence that gives the Fibonacci numbers: each term of the Fibonacci sequence is the sum of the two previous. When we generalize this to "each term is a linear combination of a fixed number of previous terms", we get the sequences defined by linear recurrences with constant coefficients.

In our paper we combined these two ideas, and asked, "When are the sequences p_n and q_n linear recurrences?" The answer is not unexpected: this situation can occur if and only if the original number is the root of a quadratic equation, such as the square root of 2, or the golden ratio. However, the proof was unexpectedly hard, and we had to rely on a very deep theorem, the Hadamard quotient theorem of Alf van der Poorten. Later, Andrew Granville found a simpler argument that avoided the need for this difficult theorem.

5. What kind of person is he/she?

Hendrik Lenstra is very much a picture of the traditional European intellectual: always impeccably dressed in a suit and tie, knowledgeable in many fields, and not afraid to show it, sometimes at the expense of those who know less. (I remember once him laughing at me because I did not know whether the root of a word was Latin or Greek.) But he is also extremely kind. Once, when I was hospitalized in the Netherlands following a talk in Leiden, he came to visit me each day in the hospital, bringing me excellent things to read, including The Assault by Dutch author Harry Mulisch.

Hendrik exhibits a playful sense of humor and appreciates a good pun. It was he who once told me about the longest "square" in English: hotshots, which can be written as (hots)² . (The longest squares I know in Dutch are tenten and kerker .) I also remember him quipping that "Shakespeare's plays weren't written by Shakespeare, but by another man with the same name." (It gets more profound the more you think about it!)

Hendrik is a collector of unusual and antiquarian books. He has a fondness for the Greek poet Homer. Knowing my interest in the crank mathematical literature, he once gave me a copy of the crackpot work The Life-Romance of an Algebraist by George Winslow Pierce, a book I still treasure in my personal collection.


6. Is there a nice story you know about him/her?

One of my nicest memories of time spent with Hendrik was our trip to watch the annular solar eclipse visible from southern Ontario on May 10, 1994. An annular eclipse occurs when the Moon comes between the Sun and the Earth, but is farther away than normal, so that all but a tiny outer ring of the Sun is covered. The sky took on a very unusual appearance, and you could see images of the sun in the diffraction patterns made by the leaves on the trees.

Hendrik wrote a paper called "Mathematics and misunderstanding" which I have not been able to read, since it has appeared only in Dutch. But a reviewer of the paper summed up the argument as follows: "It is the author's contention that the true motivation for doing mathematical research is insight into one's own lack of understanding. The hallmark of the true researcher is his or her ability to recognize, in a seemingly wholly satisfactory theory, points which on closer inspection appear to be not fully understood and hence need further clarification."

Hendrik does not like saying in a paper that something "must be true". He once wrote to me as follows:

"I am not as dogmatic about this as X, who used to ask me when I was a student: if something MUST be true, then IS it true? I think the answer is yes, but X apparently had a supernatural fear that if you FORCE something it may become recalcitrant and misbehave."

For some other quotes of Hendrik Lenstra, see here.

I Won't Be Attending Graduation at the University of Alberta Any Time Soon

...and here's why.

A publicly-funded university shouldn't be instructing its students to do something "for the glory of God".

You can write the President of the University of Alberta, Indira V. Samarasekera, to express your displeasure with her university's actions.

City Puzzle

What country's current capital city has a name that can be cyclically shifted some number of letters to get the name of its former capital?

My New Book is Out!

My new book, A Second Course in Formal Languages and Automata Theory, is out!



Here's a web page that tells you a little more about the book. And, if you absolutely have to have your own copy, you can buy it at Amazon or Barnes and Noble.

Failed Olympic Medal Predictions

Leading up to the Olympics, there was a lot of hype about the work of Colorado College economist Daniel K. N. Johnson and his predictions about the Olympic medal count. For example, he was interviewed on NPR and featured in the Wall Street Journal. Prof. Johnson's method was based on five factors only: GDP per capita, total population, political structure, climate, and home-nation bias, and was touted as "remarkably accurate".

Now the results are in. Here are Johnson's predictions of the top ten medal winners, compared to the actual total these countries won:

Country	Johnson's prediction	Actual result
USA	103	110
Russia	95	72
China	89	100
Germany	66	41
Japan	37	25
Hungary	31	10
Italy	29	28
Great Britain	28	47
France	27	40
Australia	26	46

Rating a prediction p as good if .75r ≤ p ≤ 1.25r, where r is the actual result, I'd say Johnson made 3 good predictions out of his top 10: China, USA, and Italy. And he made some really bad ones, including Hungary, Great Britain, and Australia. Altogether, Johnson's predictions don't deserve a place at the podium.

Extraordinary Sports Events

Watching the Olympics this week reminds me of some of my favorite extraordinary events in sports:

1. Dorando Pietri's Marathon: Pietri, an unknown entrant in the 1908 London marathon, led the field as the race entered the final segment in the stadium, but was so exhausted and confused that he started going the wrong way around the track. Within sight of the finish line, he collapsed multiple times and had to be helped over the line by race officials. Although apparently the winner, he was later disqualified because of the help he received.

2. Emil Zátopek's Marathon: Having already won the 5K and 10K races at the 1952 Olympics in Helsinki, Zátopek decided at the last minute to enter the marathon, despite having never run the race before. He won.



3. Tom Dempsey's 63-yard field goal: Dempsey, born without a right foot and right hand, kicked a 63-yard field goal, the longest in NFL history, to give the New Orleans Saints a 19-17 win over the Detroit Lions. I think this is one of the most exciting moments in professional football.



4. Berkeley-Stanford football game, 1982: I was listening to this game on the radio, and couldn't believe my ears. With 4 seconds left, and Berkeley trailing 20-19 on a last-minute Stanford field goal, Berkeley returned the kick-off 55 yards to win 25-20. What made the return special was the use of 5 laterals and the fact that the Stanford band, believing the game won, went onto the field and created additional chaos, with the trombone player getting flattened at the conclusion. This event is so special that among Cal alumni it is simply known as "The Play". The next week, Berkeley street vendors were selling a t-shirt with a diagram of the play, ending in a music note representing the trombone.



5. Jordan Snipes' 2005 shot: With 0.6 seconds left in overtime and Guilford College trailing Randolph-Macon 89-88, Jordan Snipes rebounded the ball and launched a full-court shot that swished the hoop at the other hand, giving his team a 91-89 victory. Then a news team asked him to re-enact the shot, and he made it again.



6. Bonnie Richardson, a Texas high school student, won the state's team championship -- all by herself. Richardson, the only student from her school, Rochelle High, to compete, won the high jump and 200 meters, placed second in the long jump and and 100 meters, and finished 3rd in the discus, for a total of 42 team points.

7. Cliff Young's Ultramarathon: Young, a 61-year-old sheep farmer, entered the Sydney-to-Melbourne footrace (a distance of 875 kilometers) in 1983. Despite wearing work boots, Young outran the world-class athletes by not sleeping, finishing 9 hours in front of his closest competitor. He then split the $10,000 first prize among 5 other runners and didn't keep a cent for himself.

8. Jennifer Jones' curling shot: I don't know anything at all about curling, despite having lived in Canada since 1990. But this shot by Jennifer Jones in the 2005 Scott Tournament of Hearts is so spectacular, one can enjoy it just for the geometry.



9. Dave Wottle's 800 m Finish: Wottle, known for wearing a golf cap while running, had an unbelievable kick in the 1972 Olympics to come from behind to win the 800 meters.

Little League's Not For Atheists

When I was a kid, I desperately wanted to play in Little League baseball. I never did, although exactly why is lost in time. Was it because there was no Little League where I lived, or because I wasn't good enough, or some other reason? I can't remember. But maybe it was all for the best, because the Little League thinks that atheists can't be good baseball players.

Want proof? Look at the Little League Pledge, which is


I trust in God
I love my country
And will respect its laws
I will play fair
And strive to win
But win or lose
I will always do my best


Despite protests, Little League refuses to change or modify its pledge. When criticized, LL hides behind the claim that "it is not, and has never been, required to be recited by any person involved with Little League Baseball or Softball". But you can be damn sure if the Pledge said, "I trust in Allah", they'd be really quick to change it.

I don't understand why belief in magical beings has anything to do with playing baseball, and it's too bad that Little League does.

Update: Jerry K. reminds me about this column by my colleague Josh Benaloh.

Our Moral Intuition Says Abortion is not the Same as Murder

This is an very interesting video that demonstrates how our moral intuition about abortion denies its equivalence to murder. Even the video's committed anti-abortion activists could not bring themselves to say that, were abortion made illegal again, women who abort their fetuses should receive a prison term commensurate with murder. Perhaps more surprisingly, most of these anti-abortion activists seemed to think there should be no penalty at all. The interviewer tries to get them to think more deeply about this contradiction, but without much success.

The lesson is that most people do not regard abortion as equivalent to murder, despite the rhetoric of the anti-abortion movement.

Danish Hospital Hosts Wacko Medical Meeting

From the Copenhagen Post comes this article about how the Copenhagen University Hospital agreed to host the woo-fest called the European Quantum Energy Medicine Conference, to the disgust of Danish medical professionals. One is quoted as saying, "It's an extremely unfortunate signal to send when we're talking about a conference that primarily consists of completely undocumented claims, and products that don't have a shred of evidence supporting their effectiveness".

I wonder why they didn't get Radovan Karadzic to speak.

Hat-tip: Terry Polevoy.

I Was Doing It Right All Along

When I was a kid, I used to sneeze and use my shirtsleeve to wipe it off. My teachers and classmates were usually horrified by this practice, but now I learn, to my surprise, that I was right all along. Well, sort of.

My pharmacy was displaying this extremely weird large poster, which is available from www.coughsafe.com:



At the same website, you can even watch a movie that teaches you how to cough and sneeze properly. Four stars!