Saturday, December 20, 2008

My Genetic Journey

For my birthday, I got a kit from National Geographic's Genographic Project. For $99, you can submit a cheek swab and have the DNA of either your maternal or paternal lines analyzed. (Women will have to settle for just the maternal line.)

I had my paternal line done this year; next year, maybe I'll have the maternal line done.

The results are in, and they're not a surprise. I'm a member of Haplogroup E3b1, which, the project says, " is most heavily represented in Mediterranean populations. Approximately 10 percent of the men in Spain belong to this haplogroup, as do 12 percent of the men in northern Italy, and 13 percent of the men in central and southern Italy. Roughly 20 percent of the men in Sicily belong to this group. In the Balkans and Greece, between 20 to 30 percent of the men belong to E3b, as do nearly 75 percent of the men in North Africa. The haplogroup is rarely found in India or East Asia. Around 10 percent of all European men trace their descent to this line. For example, in Ireland, 3 to 4 percent of the men belong; in England, 4 to 5 percent; Hungary, 7 percent; and Poland, 8 to 9 percent. Nearly 25 percent of Jewish men belong to this haplogroup."

Here's how my ancestors are believed to have moved around from about 60,000 years ago to about 20,000 years ago.

Of course, since this data reflects only my father's father's father's .... father, it doesn't tell me about most of my ancestors. But it's still oddly moving to contemplate.

Sadly, some Native Americans are opposed to the Genographic Project, because learning about their ancestry "can clash with long-held beliefs".

Why We Never Lied to Our Kids About Santa

There are many things to dislike about Christmas: the bloated newspaper ads, the second-rate music repeated endlessly in shopping malls, the inane evangelical bleating that "Jesus is the reason for the season", and the pressure to conform lest you be labeled a Scrooge, or, even worse, a Grinch.

Of course, there are things to like about Christmas, too. Everybody enjoys giving presents, and some even like receiving them. A break from work is always appreciated -- even if, like me, you just use it to catch up on work left undone -- and a house that smells of roast turkey is one worth coming home to.

But there's one Christmas tradition that my wife and I have never shared: deceiving our kids about the real nature of Santa.

You know -- Santa Claus, Jolly St. Nick -- the man in the red suit who delivers the presents, as immortalized in the classic poem by Clement Clark Moore. (Shhh - don't tell the kids that Moore, a dour, humourless man who owned slaves and opposed abolition, probably stole the poem and its authorship from Henry Livingston.)

Ever year, Christmas offers adults the opportunity to participate in an absurd fraud against your own children: to pretend that Santa Claus is real, that he spookily monitors their behavior, that Santa won't bring them presents if they misbehave, and that he somehow manages to invade a billion houses in one night, aided by eight (or is it nine?) aviating ungulates.

I can already hear the howls of outrage. "It's a harmless fantasy," some will say. But it's not that harmless. Someday your Santa lie will be discovered. If you lied to them about Santa Claus, kids will wonder, what else did you lie to them about?

"It's only a little lie," others will say. But it's not so little. Once you lie about Santa's existence, you have to lie another time when your kids see Santa in two different stores. You have to lie once again when the kids leave Santa cookies before going to bed, and in the morning they're gone. It starts small, but it soon becomes an elaborate deception. We refused to play along.

I have nothing against fantasy stories. As a child, I loved the Lord of the Rings trilogy and read it over and over again. But it's important to know the difference between reality and fantasy. I never believed that Tolkien's Middle Earth was real, and my parents didn't lie to me that it was.

My wife and I never lied to our kids about Santa Claus. We treated him as a mythical figure, just like the the Easter Bunny and the Great Pumpkin.

Our kids don't seem to have been permanently harmed by our choice. Both like reading and telling stories, and they enjoy fantasy and role-playing games. The Narnia books are some of their favorites. They've even been known to wear Santa hats and play Christmas carols on their violins.

"You deprived them of a magical experience," some will say. I don't think so. Our kids know there is magic in the world, because they've looked through a microscope at a cell, and they've looked through a telescope at the rings of Saturn. They know that the tilt of the Earth's axis is the real reason for the season, but they also know the magic of their parents' love.

So no, Virginia -- Santa Claus isn't real. But there's nothing phony about human imagination, fantasy, the telling of tales, the complexity of our universe, the desire for a better world to live in, and our ability to achieve that world if we work hard enough and care about others. We told our kids the truth about those things, too.

Thursday, December 18, 2008

How to Handle Obama's Choice of Rick Warren to Give Inauguration Invocation

President-elect Obama has chosen Rick Warren, that clueless hypocrite and gay marriage opponent to deliver the invocation at his inauguration.

Well, I'm one Obama voter who thinks there shouldn't be a religious invocation at all. But if there is going to be one, I don't want a creep like Warren to be the one to deliver it.

Now, there's simply no way that Obama's going to go back on this choice. Once invited, the man stays invited.

But we can still express our displeasure.

So here's my solution: if you're going to the inauguration (and more than a million people may go), when Warren gets up to the podium, boo.

That's right, boo.

Boo loudly and lustfully. Boo more than once. Boo for more than just a few seconds. Drown out Warren's first sentence in a chorus of boos.

Boo Warren because you think he's an anti-gay bigot. Boo him again because he's prejudiced against atheists. Boo him once more because his book is a piece of crap.

At the inauguration, let Warren and Obama know what you think of this appalling choice.

They're So Predictable

When you read a theist's denunciation of atheism, one thing is certain: you are not likely to find any original criticisms. Instead you'll find the usual nonsense:

  • Atheists are "dogmatic" and their criticisms are "shrill".
  • Deep down, atheists really believe in a god.
  • Atheists have mental problems.
  • Atheists are hateful.
  • Atheists have no moral code.

etc., etc. For more along these lines, see my account of Tim Kenyon's talk last January.

Now look at this silly opinion piece by Dow Marmur, a "rabbi emeritus" at Holy Blossom Temple in Toronto. How many of the atheism myths can you find?

The wonder is that the Toronto Star found this drivel suitable for publication. At least the letters published in response, including one from Larry Moran, uniformly disagree with the good rabbi emeritus.

Hat tip: Ed Barsalou.

Sunday, December 07, 2008

Blowhard of the Month: Joseph Epstein

Academia is one of the few places in American society where accepted truths get questioned. Ronald Reagan was a great president? The general public may think so, but historians definitely don't. Religion is a positive force in American society, and believers are more moral than non-believers? Sociologists might beg to differ.

Conservatives, however, like accepted truths -- and the older the truth, the better. This produces a certain kind of academic who yearns for an earlier time and, secretly or not-so-secretly, despises his students. Such a man (and it is nearly always a man) has little or no understanding of any discipline outside his own, and labels his colleagues as "sour" or "depressed" or "overpaid". He is almost always to be found in an English or philosophy department, and distrusts science because its achievements are beyond him and its practitioners are too excited by the joy of learning and discovery to be encapsulated by his thesis.

Allan Bloom was that kind of academic. In his screed, The Closing of the American Mind, Bloom claimed that what American universities really needed was a healthy dose of the Great Books. Reading Plato, Bloom said, would cure the University's ills, while modern science was not to be trusted.

And here's another: Joseph Epstein. In this egregious 2005 piece from the Weekly Standard, he calls university teaching a "racket", describes university working conditions as "complete freedom", and claims academics work "fewer than six months a year". His colleagues are "obviously disappointed, depressed, and generally demoralized". They are "dour". He wonders why no one has done a study on academic unhappiness. Well, someone has.

For example, in 1999 Melanie E. Ward-Warmedinger and Peter J. Sloane studied job satisfaction among Scottish academics. They concluded that "levels of overall job satisfaction among academics are high, though not with pay and promotion". By the standards of the study, 41.5% of respondents found their jobs highly satisfying, while only 5.9% reported being highly dissatisfied.

A 1997 study by Lacy and Sheehan, published in Higher Education in 1997, found that about 60% of academics in Sweden and the US were satisfied with their jobs. Job satisfaction was lower in the UK, Australia, and some other countries.

A 2007 NORC report found that teachers were among the most satisfied of all professions, with 69.2% "very satisfied", compared with 47% for all workers (but the survey report seems to have lumped together all teachers with college and university professors).

Yale Law School surveyed its graduates from 1996 to 2000 and found that academics were the most satisfied of all its graduates, with 75% reporting that they are "very satisfied". (By contrast, only 24% of those working at private law firms said they were "very satisfied".)

Finding these sources took me about half an hour. Why couldn't Epstein find them? Because he is not interested in the truth; he is, in the words of William James, only interested in rearranging his own prejudices. And prejudices abound: when discussing a black female English professor he met at Denison University, he feels it necessary to condescend parenthetically that she was "very nice, by the way".

Epstein's conception of academia seems entirely limited to English. He shows no awareness of the existence of other departments. He maunders on about "feminism, Marxism, and queer theory", but says nothing at all about quantum cryptography or string theory. Joe: there's an exciting world out there in other academic departments; maybe you should make an effort to learn what's going on.

When he says that aging professors "discover the students aren't sufficiently appreciative; the books don't get written; the teaching begins to feel repetitive", he's not describing anything in my experience. My students are absolutely terrific, and I don't waste time thinking about whether I am unappreciated. My books do get written, and so do those of my colleagues. While some teaching is repetitive, it is easy to enliven it by covering new topics. And when he labels academics as jealous of the success of others ("Meanwhile, people who got lots of B's in school seem to be driving around in Mercedes, buying million-dollar apartments, enjoying freedom and prosperity in a manner that strikes the former good students, now professors, as not only unseemly but of a kind a just society surely would never permit.") it gives you some idea of what Epstein himself thinks is valuable.

All this is typical blowhard fodder. But wait, there's more.

In his most recent piece in the Weekly Standard, Epstein criticizes Obama's administration because (wait for it) it has too many people who attended schools like Harvard, Princeton, Stanford, Oxford, and Yale. Epstein dismisses such people because they "[work] hard in high school and [pile] up lots of activities, and [score] high on [their] SAT's". He seems to have no conception that good students might do well because they actually enjoy learning.

Epstein justifies his criticism by saying that "some of the worst people in the United States have gone to the Harvard or Yale Law Schools: Mr. and Mrs. Eliot Spitzer, Mr. and Mrs. William Clinton, and countless -others [sic]". Whatever you think of Hillary and Bill Clinton, labelling them as "the worst people in the United States" is ridiculous rhetorical excess. (If he gets to mention the Clintons as examples of bad people who attended elite schools, then I get to mention George W. Bush, Pat Robertson, and Phyllis Schlafly. I think I win.) As for Mrs. Spitzer -- that is, Silda Alice Wall Spitzer -- it's not clear why Epstein despises her. Was it her founding of Project Cicero, which works to improve classroom libraries? Or her founding of Children for Children?

Epstein clearly doesn't believe in government by educated, knowledgeable people who attended good schools. What we need, he says, is someone who attended a second-rate religious school like Eureka College: Ronald Reagan. Reagan, Epstein tells us, was one of the two greatest presidents of the 20th century. Reagan, that most conventional of small-minded men, is, in Epstein's view, "without the least trace of conformity or hostage to received opinion or conventional wisdom." I guess that explains why Reagan believed that evolution is a "theory only, and it has in recent years been challenged in the world of science and is not yet believed in the scientific community to be as infallible as it once was believed. But if it was going to be taught in the schools, then I think that also the biblical theory of creation, which is not a theory but the biblical story of creation, should also be taught." Yup, it sure looks like a Eureka College education made Reagan challenge conventional wisdom there. If this passes for intellectual conservative commentary, it is yet more proof that intellectual conservatism is dead.

Or maybe, what we need is government by second-rate hacks who achieve their positions by being born to achieving fathers. You know, like George Bush and Epstein's employer, William Kristol?

Maybe Epstein thinks academics are "sour" and "unhappy" because he is, I don't know. Maybe Epstein is unhappy because his fellow academics don't put up with the kind of fact-free claptrap he displayed in these two articles, I don't know. But I do know that Joseph Epstein is December's Blowhard of the Month.

Postscript: It might be objected that I addressed job satisfaction, not happiness. So I went to the NORC survey website and, based on the interface at, I tabulated the happiness of "teachers, college and university" for the years 1972-2006. The cumulative results are: 37.95% report being "very happy"; 54.8% report being "pretty happy", and only 7.3% report being "not too happy". By contrast, for all professions the results are 34.1% report being "very happy", 54.6% report being "pretty happy", and 11.25% report being "not too happy". I conclude that academics are, on the whole, slightly happier than the average person.

Tuesday, December 02, 2008

Great Guitar Performance

Here's a YouTube video of a terrific guitar performance. José Antonio López plays an arrangement of Fernando Bustamante's guitar solo piece, "Misionera". This piece has it all: dramatic changes in dynamics, some flamenco strumming, sul ponticello, sul tasto, tremolo, and virtuoso runs. Just the thing to warm you up on a cold fall day here in Canada.

Monday, November 17, 2008

I Didn't Get Elected President

The one really surprising fact about the US presidential election is how few people voted for me.

After all, I have international experience, having lived in Canada since 1990. And I know more about economics than John McCain, and more about geography than Sarah Palin. Why not me?

I've been training for the job since 1963. In the photo, that's me in the White House cabinet room, waiting for the rest of the cabinet to assemble for our meeting. I was only 5 at the time, but they still gave me the seat of honor.

[My father knew Myer Feldman, the deputy special counsel to President Kennedy, because they both grew up in Philadelphia, so we got a special tour of the White House on May 11, 1963. Kennedy was away in Massachusetts meeting with the Prime Minister of Canada, so we didn't get to meet him.]

Sunday, November 16, 2008

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?

Friday, November 14, 2008

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.

Tuesday, November 11, 2008

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".

Sunday, November 02, 2008

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:

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.

Saturday, November 01, 2008

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.

Friday, October 31, 2008

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.

Monday, October 20, 2008

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".

Sunday, October 19, 2008

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.

Sunday, October 05, 2008

Best Newspaper Headline

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

Early birds enjoy undead, ducks.

Thursday, September 25, 2008

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 pn / qn .

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 pn and qn 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.

Wednesday, September 17, 2008

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?

Wednesday, September 03, 2008

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.

Sunday, August 24, 2008

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:

CountryJohnson's predictionActual 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.

Monday, August 18, 2008

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.

Wednesday, August 06, 2008

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.

Tuesday, August 05, 2008

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

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

Wednesday, July 30, 2008

"Institute of Advanced Scientific Researches" Changes Name, Threatens Me

I previously commented on the odd solicitation I received from the "Institute of Advanced Scientific Researches". I observed in passing that the name was odd, as most North Americans would be more likely to use "research" instead of "researches".

Over the past couple of days, the Institute has apparently changed its name to the "Institute of Advanced Scientific Research". But instead of thanking me for correcting their English, they are now threatening me.

I have now received several incoherent e-mail messages from "Zahra K. Khalafi" who claims to be the "Director of Institute of Advanced Scientific Research" and accuses me of writing "fake" and "counterfeit" messages. He states he will "take action by the law and we will see you in court in USA or CANAD" [sic] and asks if I am a "Canadian government agent". Really, I have no idea what he is complaining about. I found his institute's solicitation odd, and I said so. I found his Institute's name odd, and he apparently changed it. It seems to me he should be grateful.

If Mr. Khalafi wants to encourage other researchers to join his efforts, inviting people to join editorial boards and then threatening to sue them is probably not the optimal way to go about it.

Saturday, July 26, 2008

Another Healie-Feelie Book

The recent flood in my basement ruined a perfectly good book. Actually, the book was perfectly awful: it is Healing Crystals and Gemstones: From Amethyst to Zircon by Flora Peschek-Böhmer and Gisela Schreiber. (I won't say how it came to be in my basement, but I will say that I don't own it.)

This book is typical of the "healing crystal" literature: a lack of understanding of basic geology and chemistry, combined with healing claims that are not substantiated in any way, resulting in dangerous advice for people with serious health conditions.

The book is littered with errors. Even the very first sentence is incorrect, when it claims that all gemstones originate from hot magma. (Opal, for example, can be sedimentary.) The authors claim "jasper ... always has a trigonal structure", when in fact jasper essentially doesn't form crystals at all. On page 150, the authors claim that fluorite is "also known as feldspar", when in fact feldspar is an entirely different mineral. On page 75, the authors confuse native antimony with the mineral stibnite, which is actually antimony sulfide. On page 85 the authors claim that that aragonite is silicon dioxide, not calcium carbonate. The mineral Charoite is consistently misspelled as "Chaorite". They claim that the crystal structure of Herkimer diamonds is similar to that of real diamond, when in fact they crystallize in completely different systems. They claim that kunzite is "aluminum acetate-lithium", when in fact it is a lithium aluminum silicate; no acetate at all is contained in it. They claim that Magnesite "consists almost entirely of pure magnesium", when in fact it is just magnesium carbonate. They claim that Magnesite "was first discovered in Africa", when in fact its co-type localities are in Greece and Italy.

The authors recommend the use of various minerals without noting health problems associated with them. For example, the authors recommend actinolite to stimulate "the inner organs such as the liver and the kidneys", but fail to note that the tiny fibers of actinolite have been associated with severe and potentially life-threatening respiratory disorders. They recommend using orpiment "externally as a powder to treat sexual disorders", but this is not a good idea, as orpiment is arsenic sulfide.

But the most serious problem with the book is the repeated and unsubstantiated health claims, all made without a single reference to any study in support of them. Someone with serious health problems might be persuaded to use the entirely ineffective remedies suggested in this book instead of seeking effective medical treatment. Cancer is unlikely to be helped by toumaline, sugilite, or lapis lazuli. High blood pressure cannot be improved with sodalite, lapis, or chrysoprase. Diabetes sufferers will find no relief with citrine or pyrite. Kidney ailments will not be improved with jade. For ulcers you should see your family doctor, not wear jasper or topaz.

Ahh, well, I doubt any of this will convince the healie-feelie crowd. When they're done with this, they can move on to the other immortal works of Flora Peschek-Böhmer, such as Urine Therapy: Nature's Elixir for Good Health. Urine therapy, in case you didn't know, consists of drinking your own urine. Great idea! You can use it to wash down some crystals of orpiment.

Strange Solicitation

Today I received an odd solicitation to join the editorial board of a journal I've never heard of, the Journal of Advanced Researches on Computer Science. It is published by an institute I've never heard of, the "Institute of Advanced Scientific Researches".

The solicitation was strange for a number of reasons. First, this "Institute" seems to publish (or want to publish) 16 different journals; yet as I write this, many of them seem to have no editorial board listed. Second, the name of the Institute itself is odd; no native English speaker would be likely refer to "researches", as "research" is typically a mass noun, like "information". Also, the solicitation letter was filled with grammatical errors. Third, I can find no information about this "Institute" online, nor any of the people associated with it, except for the person who wrote the solicitation letter, "Kavin Kalfi".

So, does anyone else know about this "Institute"?

Friday, July 25, 2008

Friday Moose Blogging

Here are some photos by my colleague Doug Payne, taken during his recent trip to Algonquin Park. No surprise, there's a moose or two. Moose twins, too.

Thursday, July 24, 2008

SIGAPL dissolved

A sad day for the APL community: SIGAPL, the ACM special interest group on APL, has been dissolved by the ACM SIG governing board.

I first learned APL in 1973 at the IBM Scientific Center in Philadelphia (long gone). At the insistence of my father, I had written to several large computing companies, asking for a summer job. Only IBM replied favorably, and I had a rather intimidating interview with Ken Iverson and Adin Falkoff in their offices on Market Street. To my delight, they hired me for a vague project about whether it was better to learn APL by reading other people's programs first, or writing one's own.

I remember going home with a copy of the APL\360 user's manual, which was initially very mysterious to me, and had an exotic smell like bacon. I had learned programming from Kemeny's book on BASIC, and APL was a revelation. I immediately took to the language and ended up spending the next few years of my life involved in APL in various ways: coding in APL for financial institutions, writing my own extended precision arithmetic package and selling it to IBM, etc. I was programming on IBM machines, using a printing terminal with an APL typeball.

I soon discovered the newsletter of SIGAPL, called "Quote-Quad". (The unusual name comes from the special APL symbol for character input, which was formed by typing a "quad" (shift-L) and overstriking it with a quote (shift-K).) At that time I eagerly awaited every issue, filled with incredible one-liners that accomplished results you would need hundreds of lines in BASIC to duplicate, puzzles like the self-replicating APL expression puzzle (type it in and you get exactly the same result back), and proposals to extend APL in bizarre and mind-expanding ways. It was really the golden age of APL.

It's clear that the passion and excitement about APL has decreased since then, although I still use APL on at least a weekly basis to do experimental mathematics: Dyalog APL on my Sun workstation, and APLX on my Macintosh. In many ways it is far superior to Maple and Mathematica, although the lack of easy availability of extended precision and symbolic arithmetic is a pain. I can code a quick-and-dirty solution to a problem faster in APL than I can in any other language. People who see it always stare open-mouthed: what is that? they say, and they want to borrow a manual.

The dissolution of SIGAPL is the passing of an age.

Wednesday, July 23, 2008

Christian Compassion

From the Toronto Sun comes this heartwarming story of Christian compassion.

Sex offender Patrick White is really, really sorry that he committed fraud and sex-related offenses in the US and Canada. He's really, really sorry that he sexually abused mentally retarded men. In fact, he's so sorry that he will pay for counselling for his victims, but only if it's "Christian counselling".

How generous!

Never fear, White is assured of a place in his Christian heaven, because, as he says, "God has forgiven me".

Mark Shea Thinks Scientists Are Stupid, Makes Gaffe

Over at Catholic Exchange, Mark Shea relates an anecdote that demonstrates, for him, that scientists are sadly lacking in emotional intelligence:

Long ago, I remember watching some film about human evolution narrated by Richard Leakey, Jr. It was interesting as such films go, but you got the sense as it went along that it explained everything at the cost of leaving everything out—like scientists in a Far Side cartoon analyzing humor.

The crowning moment of the film, for me, was when Leakey stood in front of the gorgeous twenty-thousand-year-old cave paintings in Lascaux, France and, with genuine puzzlement in his voice, wondered aloud “Why did they do this? What was the purpose?”

I had the distinct impression he would have expressed equal bafflement were he standing in the Louvre. There seemed to be a gene missing somewhere. He was a man who knew a great deal about human origins and yet, however smart he was, there was something about him that was radically out of touch with, well, what it meant to be human. You felt he needed tape on his glasses, a pocket protector, high water trousers and D&D dice in his pocket to complete the image he seemed to project with such earnest unconsciousness.

I'm a little skeptical that the film went exactly as Shea claims it did. People's memories are notoriously unreliable, and events are rewritten in brains to conform to a person's individual narrative: in this case, Shea's commitment to the Catholic faith as the essential guide to understanding the world.

But assuming Shea's memory was correct, he seems to have entirely missed the point of Leakey's question. Shea doesn't seem to have any awareness that there is a debate among archaeologists about Lascaux's purpose. Was it continuously occupied, or only visited periodically? Was it part of a shaman's ritual to improve chances during the hunt, a record of previous successful hunts, or simply a decoration? Why are there no images of reindeer, which formed a major part of the diet of the artists? Do the painted dots really represent an accurate map of the night sky, as suggested by Michael Rappenglueck?

If you have scientific training, then questions like these seem natural and interesting. If you don't, and are immersed in dogma that preaches simple answers to difficult questions, then even asking this kind of question demonstrates some moral failing. I'd wager that Leakey knows a lot more about people, and their goals, desires, and questions, than Mark Shea does.

Sunday, July 20, 2008

Rutgers Graduate Student Finds New Prime-Generating Formula

Studying prime numbers is like playing the guitar. No, really, let me explain.

The guitar is a simple instrument: six strings, some frets, a sound hole. You strum with the right hand, and form chords with the left. What could be simpler? Any reasonably coordinated person can learn to play a simple song, such as "Heart of Gold", passably in a few hours.

In the same way, the prime numbers have a simple definition: the integers greater than 1 that are divisible only by themselves and 1. Any reasonably intelligent person can learn to test a small number for primality, or understand Euclid's proof that there are infinitely many prime numbers, in a short amount of time.

Yet the guitar is also fiendishly difficult. Those studying classical guitar know well how some pieces take hundreds of hours to master. Techniques such as tremolo might take years, especially if you start learning as an adult.

In the same way, the prime numbers contain within them enough subtlety that many problems remain unsolved after hundreds of years. Goldbach conjectured in 1742 that every even number greater than 2 is the sum of two primes, and today this conjecture is still unsolved. (It is known to hold for every even number less than 1018.) And a proof of the Riemann hypothesis, which would have extremely important consequences for the distribution of primes, will net you a million dollars from the Clay Mathematics Institute -- probably more than you'll get from appearing on American Idol.

For a long time mathematicians have sought a simple formula that would generate all the prime numbers, or even infinitely many distinct prime numbers. Some have even gone so far as to claim that no such formula exists -- a statement of very questionable veracity that depends entirely on one's definition of "formula". If you define formula to mean "polynomial with integer coefficients", then it's not hard (and I leave it as a challenge to the reader) to prove that no such polynomial can generate only primes, other than the trivial example of a constant polynomial. Euler's polynomial x2 + x + 41 comes close: it generates primes for x = 0, 1, 2, ..., 39, but fails at x = 40.

A slight variation, though, leads to a genuine prime-generating polynomial. It is a consequence of the Davis-Matiyasevich-Putnam-Robinson work on Hilbert's 10th problem that there exists a multivariate polynomial with integer coefficients that takes on only negative and prime values when integers are substituted for the variables, and every prime is generated by some choice of the variables. In 1976, Jones, Sato, Wada, and Wiens actually wrote down such a polynomial. It has 26 variables.

Another prime-generating formula comes from a 1947 paper of W. H. Mills. Mills proved that there exists a real number A such that [ A3n ] is a prime number for all integers n ≥ 1. Here [ x ] is the greatest integer function, the greatest integer ≤ x. Unfortunately, nobody knows a good way to calculate A other than testing the numbers the formula is supposed to generate for primality, and then constructing A by working backwards.

So many people have worked on the prime numbers that it seems unlikely that there could be a simple prime-generating function that has been overlooked until now.

Rutgers graduate student Eric Rowland has defied the odds, however, and has found a new one. In a paper just published in a journal I edit, the Journal of Integer Sequences, Rowland defines his formula and proves it generates only 1's and primes. (1 is generally not accepted as a prime number, for a variety of reasons. For one thing, if 1 were a prime, then positive integers would not have a unique factorization into primes.) To be precise, I should say that the unusual property of the formula was originally conjectured by a team led by Matt Frank at a mathematics summer school in 2003 where Rowland was attending, but it was not proved until now.

Here is Rowland's formula. We define a(1) = 7, and for n ≥ 2 we set

a(n) = a(n-1) + gcd(n,a(n-1)).

Here "gcd" means the greatest common divisor. So, for example, we find a(2) = a(1) + gcd(2,7) = 8. The prime generator is then a(n) - a(n-1), the so-called first differences of the original sequence.

For example, here are the first 23 values of the a sequence:
7, 8, 9, 10, 15, 18, 19, 20, 21, 22, 33, 36, 37, 38, 39, 40, 41, 42, 43, 44, 45, 46, 69

and here are the first differences of these values:
1, 1, 1, 5, 3, 1, 1, 1, 1, 11, 3, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 23

If we ignore the 1's, then, the Rowland formula starts by generating the primes 5, 3, 11, 3 (again), and 23. The reader can easily program up the formula and find lots more primes. Removing duplicates, the first few are
5, 3, 11, 23, 47, 101, 7, 13, 233, 467, 941, 1889, 3779, 7559, 15131, 53, 30323, ...

Why does it work? The proof is too involved to give here, but it is not that difficult. The interested reader can go to Rowland's paper for the details.

Rowland has been involved with mathematics for some time. He attended UC Santa Cruz and graduated with highest honors in math in 2003. Since then he has been a graduate student at Rutgers University, studying with Doron Zeilberger. Rowland describes himself as an "experimental mathematician", and uses the computer algebra system Mathematica for his experiments. Rowland tells me that he tried to prove the formula from time to time over a four-year period, but once the crucial insight was found, "I had an outline of the proof within a few days and all the details within a few weeks."

Are there any other formulas like Rowland's? Apparently yes. Benoit Cloitre, a French mathematician, recently proved that if you set b(1) = 1 and

b(n) = b(n-1) + lcm(n,b(n-1)) for n ≥ 2,

then b(n)/b(n-1)-1 is either 1 or prime for all n ≥ 2.

Will Rowland's formula lead to more efficient ways to generate large primes? If so, cryptographers would love it. But it seems unlikely. As Rowland explains in his paper, his formula only produces the prime p after first generating (p-3)/2 1's, so it takes a really long time to generate a large prime. He has a method for skipping over those useless 1's, but doing so essentially requires an independent test for primality.

Are there still unsolved properties of Rowland's prime generator? Yes. For example, is there anything special about the choice a(1) = 7? Other choices, such as a(1) = 8, always generate primes and 1's, but others, such as a(1) = 532, do not. (This choice generates 9 after less than 20 steps.) However, Rowland conjectures that for each starting value of a(1), there exists a point after which the first differences are always either 1 or prime. Rowland also doesn't know if his formula eventually generates all odd primes, although he believes it probably does.

Rowland has a number of other projects in the works. He told me, "I'm working on several things, mostly trying to finish up a backlog of papers. But one newer project is putting bounds on the frequency of 1's in the Kolakoski word. Another is something I'm not ready to fully divulge, but it has to do with values of the p-adic logarithm. A longer term project of mine is extending what is known about the arithmetic of Pascal's triangle modulo m and, generally, additive cellular automata."

What problem would Rowland most like to solve? "I'd really like to solve the 3n+1 problem, because I think it would tell us something very interesting about representations of integers. Dividing by 2 in base 2 just means dropping the last 0, and mapping n -> 3n+1 in base 3 just means appending 1. The problem is that we don't know how to get these two bases to talk to each other -- and of course perhaps there isn't a way -- but a solution to the 3n+1 problem might show us how to do this."

Solving the 3n+1 problem would indeed be a great achievement. In the meantime, however, he can take pleasure in his prime formula. Blending simplicity and mystery, Eric Rowland's formula is a delightful composition in the music of the primes, one everyone can enjoy.

Update, July 31 2008: Rowland has his own post describing his discovery.

Friday, July 18, 2008

Friday Moose Blogging

Here's a great youtube video of 2 baby moose and their mother playing in a sprinkler in an Alaskan backyard.

When a Creationist Says the Sky is Blue...

When a creationist says the sky is blue...

go outside and check.

That's the wise advice of my friend and co-author, Wesley Elsberry.

It seems particularly apt this week, with yet another outbreak of creationist misrepresentation:

  1. Over at Uncommon Descent, William Dembski claims, citing Michael Asher, that "The American Physical Society, an organization representing nearly 50,000 physicists, has reversed its stance on climate change and is now proclaiming that many of its members disbelieve in human-induced global warming." Only problem is, the American Physical Society has done nothing of the sort. Instead, the APS's Forum on Physics & Society has published an issue with two opposing articles, one in favor of the human-caused global warming theory and one attempting to cast doubt on it. The latter article was written by Christopher Monckton, a man with apparently no scientific training who has a history of statements of debatable veracity.

    Even Asher himself has been forced to concede that his description of the Forum on Physics & Society's issue was incorrect, admitting in an update at the bottom in a much smaller typeface that "After publication of this story, the APS responded with a statement that its Physics and Society Forum is merely one unit within the APS, and its views do not reflect those of the Society at large."

  2. Next, at The Panda's Thumb, Nick Matzke points out that Casey Luskin gets nearly everything wrong when describing the Alternberg meeting. Luskin claims the NCSE opposed the meeting for political reasons (false; it didn't oppose it at all) and that Rutgers philosopher Jerry Fodor was one of the Alternberg 16 (false, as one can easily check here). Even more importantly, Luskin imagines the meeting as some sort of significant challenge to the theory of evolution, when in fact the participants claim just the opposite.

  3. Finally, I've been contacted by some cretin named Bill Crofut, who proclaims himself a "an unlettered Traditional Roman Catholic, militant young-Earth Biblical creationist and geocentrist". Crofut proffered a quote by Birch and Ehrlich from a 1967 Nature article as evidence against evolution. Only problem is, the quote was stripped of context and is a well-known quote mine. When confronted with the evidence of his misrepresentation, Crofut told me he was "a son of Satan".

I don't think creationists are always dishonest, but (1) they uncritically accept anything that supports their view instead of examining it critically and (2) they are not particularly concerned with making sure that their sources are correct.

Thursday, July 17, 2008

World Religious Leaders Praise Saudi King's Anti-Atheist Bigotry

Saudi King Abdullah spoke at a Madrid conference sponsored by the Muslim World League, and spoke against religious extremism. Good, as far as it goes.

Unfortunately, he whitewashed the role of religion in the world's problems. According to King Abdullah, religion (especially his) is blameless, claiming that "Islam is a religion of moderation and tolerance". Ironically, the conference apparently took place in Spain instead of Saudi Arabia, because Saudi Arabia is "the only Arab Muslim country to ban all non-Islamic religious practices on its soil, even though it has a large community of expatriates professing other faiths."

Instead, he chose to blame the world's problems on "secularism" and atheists: "If we wish this historic meeting to succeed, we must focus on the common denominators that unite us, namely, deep faith in God, noble principles, and lofty moral values, which constitute the essence of religion" and that the world's problems are "a consequence of the spiritual void from which people suffer when they forget God, and God causes them to forget themselves." Despite blaming the world's problems on atheists, he also denied their existence, claiming that "we all believe in one God, who sent messengers for the good of humanity in this world and the hereafter".

Did any of the 200 religious and political leaders present speak against this anti-atheist bigotry? Nope. Instead, they fell over themselves to praise King Abdulalh. Ronald Lauder, president of the World Jewish Congress, "said the conference was a 'significant and timely development.'" Catholic Cardinal Tauran called it "an act of great courage". Jesse Jackson apparently called the speech "a distinguished one in its contents and noble message" (may not be an exact quote). Abdullah Tariq said, "It is a great beginning of a valuable call from a generous King."

I'm really sick of hypocritical religious leaders telling me that not accepting their wild and unsupported claims about their deities is some sort of moral failing. It's religion that is to blame for Saudi Arabia's medieval treatment of women. It's religion that is to largely blame for the Saudi hijackers who crashed planes into the World Trade towers on September 11. It's religion that is largely to blame for overpopulation and our worsening ecological crisis. Let's have some religious leaders forthrightly admit this, and then we can have some dialogue.

Sunday, July 06, 2008

All People of Good Will Agree With Me

Dr. Henry Morgentaler, the single person most responsible for making abortion safe and legal in Canada, was recently given a national award, the Order of Canada. Not surprisingly, the Catholic hierarchy is outraged. But their outrage took a pernicious dimension when Archbishop Thomas Collins of the Toronto archdiocese said in interview that he called on "all people of good will, to protest this act of dishonour".

Archbishop Collins evidently believes that one cannot be a person of good will and still support the right to abortion. I've met a lot of anti-abortion activists. Most are sincere people who, though misguided, honestly believe that they are acting ethically. But so do people who argue for the right to abortion. It is really offensive for the Archbishop to suggest that the only way you can be a "person of good will" is to agree with the Catholic Church's position.

Thursday, July 03, 2008

William Carlos Williams with a Handtruck

From my niece Rachel comes this inspired bit of silliness: an English professor couldn't find the departmental handtruck, so he put out a request on the local listserv. In response, he got 12 odes to the missing handtruck, done in the style of William Carlos Williams, John Donne, and other famous poets. I particularly like this one, by Carl Rapp.

This Is Just to Say

I have pinched
the hand truck
that I happened to run across in
a convenient location

and which
you were probably
for your own future toils

Forgive me
it was so “dependable”
so red
and so obviously up for grabs

Can't you just hear Garrison Keillor reciting it?

Monday, June 30, 2008

Journalistic Credulity

Continuing with the theme of crappy journalism, this weekend on Wait Wait ... Don't Tell Me!, I learned about a hoax perpetrated on the New York Times back in 1992.

Rick Marin wrote an article about "grunge music" and the Seattle alternative music scene that appeared in the "Styles" section on November 15. Apparently he wanted a lexicon of slang, and so he turned to Seattle-based Sub Pop Records for advice. Sales rep Megan Jasper reportedly just made up a bunch of phrases on the spot, such as

Swingin' on the flippity-flop: hanging out

Harsh realm: bummer

Cob nobbler: loser

Lamestain: uncool person

This made-up lexicon was swallowed whole by Marin, and the Times apparently printed it without any fact-checking.

Maybe Marin isn't representative of journalism as a whole, but the lesson still is that a good journalist ought to be skeptical of all claims, and make a serious effort to fact-check. Rick Marin: what a lamestain!

Friday, June 27, 2008

Science Unites - Religion Divides

Here's an article about my friend Mark Gluck, a Rutgers neuroscientist who organized a joint Israeli-Palestinian conference on Alzheimer's disease. It's a good example of the best science can offer: people of different backgrounds, politics, and religion joining together to solve real problems in a spirit of scientific inquiry.

Religion and ancient animosities would have kept these scientists apart. Rational and skeptical inquiry can unite them.

Thursday, June 26, 2008

Peter McKnight Not Confused by Expelled

Peter McKnight, writing in the Vancouver Sun, gives a clear-headed appraisal of the crackpot documentary Expelled, which has just opened in Canada. Among the best tidbits, Ben Stein is reported to have replied, "It's none of their f---ing business" when McKnight asked him about the ADL statement on Expelled.

I predict that Expelled will flop even more egregiously in Canada than it did in the US. Reasons: there are not as many far-right religious crackpots in Canada; Canadians don't really care so much about US church-state battles; it's only playing in a relatively small number of theatres; and the producers are so desperate they're giving tickets away to a freethought group.

Sunday, June 22, 2008

Oh, the Inanity! Slack in The Scientist

I've never read anything by Gordy Slack before, but based on this opinion piece in The Scientist, I'm not likely to in the future. Slack tries to defend the ID crowd, but all he comes up with is a confused mess.

Slack claims that ID advocates "make a few worthy points". But his examples demonstrate nothing of the sort.

1. Slack says, "While there is important work going on in the area of biogenesis, for instance, I think it's fair to say that science is still in the dark about this fundamental question." (Judging from the context, it seems that Slack really means abiogenesis.) He continues, "I think it is disingenuous to argue that the origin of life is irrelevant to evolution. It is no less relevant than the Big Bang is to physics or cosmology." This is just idiotic. Evolution is, by definition, what happens after there is a replicator to replicate. What came before is certainly relevant to biology, but it is not, strictly speaking, part of evolution itself. Even if some magical sky fairy created the first replicator, it wouldn't change all we know about the mechanisms of evolution today. Slack compares the Big Bang to physics, but then he doesn't compare the origin of life to biology, but rather to evolution. Isn't it clear that the analogy is faulty?

I disagree with Slack that we've made little progress in understanding abiogenesis. (What is this paper, chopped liver?) But even if mainstream science has made little progress, what progress has ID made? Nothing. No scientific papers, no testable models, no predictions. Nada. Zilch.

2. Slack says, "Second, IDers also argue that the cell is far more complex than Darwin could have imagined 149 years ago when he published On the Origin of Species." And so what? ID advocates weren't the ones to discover the cell's complexity, and they weren't the first to observe it was more complex than originally thought. (Darwin, by the way, knew well that the cell was not an undifferentiated blob of protoplasm; the nucleus was discovered in 1833.) And Darwin got lots of things wrong, so why is it even relevant to modern evolutionary biology what Darwin thought 149 years ago? The ID advocates would only have a worthwhile point if mainstream biologists were denying the complexity of cellular processes. But they don't. Mainstream biologists discovered the complexity. So what's the point?

3. Slack says, "Millions of people believe they directly experience the reality of a Creator every day, and to them it seems like nonsense to insist that He does not exist. Unless they are lying, God's existence is to them an observable fact. Denying it would be like insisting that my love for my children was an illusion created by neurotransmitters." I don't understand why something should be considered true simply because millions of peeople believe it. After all, there are probably millions of people who believe in witches, or that Elvis is still alive, or that 9/11 was a vast government conspiracy. But without evidence to support these claims, there's no reason why I need to take them seriously. Slack's comparison to "love for my children" being an "illusion" is remarkably inapposite. As a materialist, my guess is that love is, indeed, a product of neurotransmitters. But that doesn't mean that the experience of love is an "illusion". The neurotransmitters create the experience, but that doesn't mean the experience doesn't exist. Belief in a deity, however, is different. You can have the experience of a supernatural presence, but that doesn't mean the experience corresponds to anything outside your head. I don't see why Slack doesn't understand the difference.

4. Finally, Slack says that those who accept evolution can be dogmatic followers, too. "I met dozens of people there who were dead sure that evolutionary theory was correct though they didn't know a thing about adaptive radiation, genetic drift, or even plain old natural selection." Any field has dogmatic followers. But this has nothing to do whether ID is correct, is science, or has anything useful to say.

The really big point, the one that Slack misses completely, is the transparent dishonesty of nearly everything about intelligent design. ID advocates have to lie, because the evidence for evolution is so strong that they have no choice. That's something that even John Derbyshire understands, but Slack doesn't display any awareness of it.

All in all, this is one of the lamest defenses of ID I've ever seen.

Thursday, June 19, 2008

Psychic's Report Basis for Child Abuse Investigation

An appalling story out of Barrie: the Simcoe County District School Board reportedly started an investigation into sexual abuse of a child after receiving a report from a psychic consulted by the child's educational assistant at the school.

As reported by Canadian Press, the psychic claimed "a youngster whose name started with "V" was being sexually abused by a man between 23 and 26 years old" and so the Children's Aid Society was called to investigate.

If the facts are as reported, this is a horrifying and ridiculous intrusion into family life based on utter nonsense. The Simcoe County District School Board owes the parent and child an apology.

Tuesday, June 17, 2008

The Davis-Weller Study on HIV Transmission Misrepresented Again

In 1999, Davis and Weller published a paper in Family Planning Perspectives entitled "The Effectiveness of Condoms in Reducing Heterosexual Transmission of HIV". Their meta-study combined results from other studies about couples where one partner was HIV-positive and the other not, with respect to how often a condom was used. Unfortunately, their conclusions (and the conclusions of an earlier study by Weller alone) have been systematically misrepresented by conservative Christian activists.

I've written about this misrepresentation before. In 1993, Harold Albrecht, a local MP, misrepresented the earlier study by claiming that "An analysis by researchers at the University of Texas estimates that when condoms are used, the risk of acquiring HIV from an infected partner is 31 per cent over a year's time."

Now the work of Davis and Weller has been misrepresented again. Our local paper, the Kitchener-Waterloo Record, has a "Community Editorial Board", where local residents are tapped to write a series of opinion pieces. (I was on the Board in 2000, and you can see my columns here.) Yesterday the Record carried this column by Harriette Mostert, who is described as a "part-time teacher and a longtime community volunteer".

Mostert claimed that this NIH report says that "HIV/AIDS carries a 15 per cent risk of transmission even with a condom". However, the NIH report was referring to the Davis-Weller study, and it is being misrepresented again.

The Davis-Weller study found that using a condom reduces the risk of HIV transmission by 85%. Now, you might think that Mostert's 15% figure is just 100%-85%, and so she's correct. But you would be wrong.

Davis and Weller were studying the reduction in risk obtained when using a condom; Mostert incorrectly labels this the "risk of transmission". They're not the same at all. I think most people would interpret "risk of transmission" as meaning "the chances that you will get the disease in a single encounter", and indeed, that's the interpretation I got when I asked several people what they thought it means. Or maybe it means "the chances that you will get the disease in a year"? The lack of units should raise warning bells in the mind of any educated person.

The answer is that Davis and Weller found that in one year, 6.7 infections per 100 person-years occurred when a condom is not used, and 0.9 infections per 100 person-years occurred when a condom is always used. The reduction in risk is therefore (6.7-0.9)/6.7, or approximately 85%. Contrary to Mostert, the "risk of transmission" when using a condom is less than 1 infection in 100 person years. There's no way this can be characterized as "15%".

Mostert uses this bogus figure to argue for "chastity or monogamy", and smugly concludes "Interestingly, this is also consistent with the ideals set out in many faith communities." She fails to note that the very study she cites concludes "These data provide strong evidence for the effectiveness of condoms for reducing sexually transmitted HIV."