Recursivity

Well, the first episode of 'Watson' on Jeopardy was shown last night. I didn't see it live, but luckily it's available on Youtube, at least for a little while.

It's a great achievement. Question-answering systems are a hot topic now - my colleague Ming Li, for example, has created such a system, based on word associations it finds on the Internet. But Watson is much better than anything I've seen before. A system like Watson will be extremely useful for researchers and libraries. Instead of having to staff general inquiry telephone lines with a person, libraries can use a system like Watson to answer questions of patrons. And, of course, there will be applications like medical diagnoses and computer tech support, too.

I predict, however, that the reaction to Watson will be largely hostile, especially from Mysterian philosophers (like Chalmers), strong AI skeptics (like the Dreyfus brothers), and hardcore conservative theists firmly committed to the special status of humans (like David Gelernter). We'll also hear naysaying from jealous engineers (like this letter from Llewellyn C. Wall, who earns my nomination for Jerk of the Week).

Despite its impressive performance, we're going to hear lots of claims that Watson "doesn't really think". Critics will point gleefully to Watson stumbling on an answer, replying "finis" when the correct response was "terminus" or "terminal" -- as if humans never make a mistake on Jeopardy. We're going to hear columnists stating "But Watson can't smell a rose or compose a poem" - as if that is a cogent criticism of a system designed to answer questions.

I predict none of these naysayers will deal with the real issue: in what essential way does Watson really differ from the way people think? People make associations, too, and answer questions based on sometimes tenuous connections. Vague assertions like "Watson doesn't really think" or "Watson has no mental model of the world" or "Watson is just playing word games" aren't going to cut it, unless critics can come up with a really rigorous formulation of their argument.

Watson is just another nail in the coffin of Strong AI deniers like Dreyfus - even if they don't realize it yet.

Addendum: Ah, I see the moronic critiques are already dribbling in: from Gordon Haff we get typical boilerplate: "Watson is in no real sense thinking and the use of the term "understanding" in the context of Watson should be taken as anthropomorphism rather than a literal description." But without a formal definition of what means to "think" in a "real sense", Haff's claim is just so much chin music.

Mary Poplin, this year's Pascal lecturer at the University of Waterloo, returned for a second lecture, entitled "Is Anything Sacred?: A Conversation With Students". Like the first one, the second was poorly attended -- I'd estimate there were no more than about 15 people in the room, including some of the organizers.

Just as in the first lecture, she repeated her claims that Christianity is "under attack" at universities, and that Christians are unfairly excluded, censored, marginalized, etc.: "At the University every idea is engaged, but not Christianity" - a claim that would surprise the students enrolled in dozens of Waterloo courses with titles like History of Christianity, God and Philosphy, Jesus: Life and Legacy. Heck, if there's anything wrong with the way Christianity is treated at the University of Waterloo, it's that it's treated too seriously. There's also some sort of breathtaking irony involved in talking about how Christianity is "censored" while giving 3 invited 1-hour lectures with the sponsorship of a committee that sees its mandate as "challenging the university to a search for truth through personal faith and intellectual inquiry which focus on Jesus Christ." Why the heck is a public university sponsoring a lecture series that is clearly evangelical in nature?

She repeated her assertion that Christianity offers a useful standpoint from which to examine issues of the University, but she never really gave a single example how this could work. In response to a friendly question from someone on the committee who invited her, she could not come up with an example of how Christianity would be a useful perspective in physics, engineering, or mathematics. She did give a rather rambling and incoherent account of her work with teachers (work that, by the way, I fully support and think there should be more of) whose moral seemed to be that whatever religion you were, you came up with the same answers -- which seemed to completely undermine her point.

Personally, I reject her entire thesis. To the extent that Christianity is marginalized and excluded in academia, I see nothing wrong with it. Lots of bad ideas are rejected and marginalized: the idea that Zeus creates lightning, the idea that people have past lives, the idea that homeopathy is effective. In fact, the whole point of an intellectual enterprise like the university is that students need to be taught the intellectual tools they need to understand why some ideas are supported and others are not. Many Christian claims are rejected and marginalized because they have either been thoroughly refuted or because people have finally recognized that they do not represent serious knowledge claims. I wouldn't want a student citing the Bible on a biology exam as support for some supposedly scientific view.

Basically, Poplin wants her religious claims validated without doing the hard work she needs to do to convince others. She wants an intellectual free pass. And she wants this free pass solely on the basis of the fact that lots of people are Christians. She told me this on Thursday night, after the lecture, when she said that a good reason for treating the claims of Christianity seriously is that "a third of the world believes them". Well, worldwide there are lots of animists, too, but that doesn't mean we have to take their claims seriously.

Other things we heard about: before she became a Christian, Poplin was "not a nice person" and "slept with other people's husbands". She tried a succession of spiritual beliefs before settling on Christianity. She had encounters with "demonic spirits". I found her tale quite familiar: many people without a firm ethical compass drift from one religion to another, hoping to find something they lack internally.

We also learned that Poplin is a firm believer in the reality of miracle healing. She should read William Nolen's book Healing: a Doctor in Search of a Miracle. Nolen, a Christian, spent years looking for a legitimate example of faith healing. He found hucksters and fraud, but no actual examples.

Speaking of being "not a nice person", Poplin asserted that Christian students would be afraid to speak to me. (Ironically, in the audience was a former student of mine, a really bright guy who I never knew was religious. He had come to me for advice about graduate school just a few months earlier.) If so, that's bad. I never inquire about the religious beliefs of students and I try to treat all students fairly. But it never seemed to occur to her that, as an outspoken Christian, atheist students might be afraid to speak to her.

Altogether, this talk was even worse than the preceding one, if that's possible. Poplin rambled, failed to make any coherent point, and proved to be a sloppy thinker on the issues she spoke about. A waste of time. Let's hope the Pascal lecture series brings someone next year who might really have something to say - perhaps Ken Miller.

This is an oldie, but a goodie: Sam Harris versus David Wolpe:



I think Harris definitely gets the best of Wolpe, although Wolpe's no slouch. There are so many good lines by Harris it's hard to list them all. For example, "We need to cease to reward people for pretending to know things they do not know. And the only area of discourse where we do this is on the subject of God."

What interests me more, though, is Wolpe's utter confusion when it comes to understanding neuroscience (at 44:50):

"The reason that our minds can do something more than just operate on instinct is because we operate all the time with things that are not physical, right: ideas, words... I can say something and change the physiology of your brain. Now how is that unless there's something more to your brain than physiology?"

This is remarkably dim. Ideas and words are not physical? An idea is a certain pattern of our neurophysiology. Spoken words are vibrations of the air. The patterns thus formed are interpreted by the nerves in the ear and are transmitted to the brain as electrical signals. Calling these things "not physical" betrays an ignorant, pre-scientific view of the world.

I wonder where Wolpe thinks ideas reside, if not in the brains of humans and other animals? In some magical ethereal realm?

I can say something and change the physiology of my computer. Heck, if my toaster is hooked up to some voice recognition, I can say something and change the physiology of a piece of bread. How does that imply that there's "something more" to a piece of bread?

I remember seeing the B-52's give a free concert in Sproul Plaza back around 1980. But I think I like this version better.

It's time again for that excruciating annual exercise at my university called the "Pascal Lectures".

Inaugurated in 1978, the purpose is to "bring to the University of Waterloo outstanding individuals of international repute who have distinguished themselves in both an area of scholarly endeavor and an area of Christian thought or life. These individuals discourse with the university community on some aspect of its own world, its theories, its research, its leadership role in our society, challenging the university to a search for truth through personal faith and intellectual enquiry which focus on Jesus Christ."

From its very first speaker - Malcolm Muggeridge - this series has been an embarrassment. Muggeridge, you may recall, was the credulous journalist responsible for the Mother Teresa cult - and even claimed that the light used in the filming of a BBC documentary Mother Teresa's orphanage was miraculous: "In the processed film, the part taken inside was bathed in a particularly beautiful soft light, whereas the part taken outside was rather dim and confused.... I myself am absolutely convinced that the technically unaccountable light is, in fact, the Kindly Light [Cardinal] Newman refers to in his well-known exquisite hymn. ...[The love in the home is] luminous, like the haloes artists have seen and made visible around the heads of saints. I find it not at all surprising that the luminosity should register on a photographic film. ...I am personally persuaded that Ken recorded the first authentic photographic miracle."

But the cinematographer had something different to say: "And when we got back several weeks later, a month or two later, we are sitting in the rushes theatre at Ealing Studios and eventually up came the shots of the House of the Dying. And it was surprising. You could see every detail. And I said, 'That's amazing. That's extraordinary.' And I was going to on to say, three cheers for Kodak. I didn't get a chance to say that though, because Malcolm, sitting in the front row, spun round and said: 'It's divine light. It's Mother Teresa. You'll find that it's divine light, old boy.' And three or four days later I was being phoned by journalists who were saying things like: 'We hear you've just come back from India with Malcolm Muggeridge and you were the witness of a miracle.'"

To give you some idea of Muggeridge's intellectual acuity, here's a quote from What I Believe (Crossroad Publishing Co., 1984): "Nor, as far as I am concerned, is there any recompense in the so-called achievements of science. It is true that in my lifetime more progress has been made in unravelling the composition and the mechanism of the material universe than previously in the whole of recorded history. This does not at all excite my mind, or even my curiosity. The atom has been split; the universe has been discovered, and will soon be explored. Neither achievement has any bearing on what alone interests me -- which is why life exists, and what is the significance, if any, of my minute and so transitory part in it."

And in the first Pascal lecture, Muggeridge had this to say, in answer to a question: "I myself am convinced that the theory of evolution, especially the extent to which it's been applied, will be one of the great jokes in the history books in the future. Posterity will marvel that so very flimsy and dubious an hypothesis could be accepted with the incredible credulity that it has. I think I spoke to you before about this age as one of the most credulous in history, and I would include evolution as an example."

Isn't there something perversely fascinating about a man who can dismiss one of the best-supported scientific theories -- evolution -- while railing about credulity AND also jumping to the conclusion that good photographic film is a Christian miracle?

This drivel is what the Pascal committee apparently thinks is a good example of "challenging the university to a search for truth".

Not every Pascal lecture was as bad as Muggeridge. Howard J. Van Till, who spoke in 1999, was a physics professor from Calvin College, and is one of the few evangelicals I know who can approach evolution with something resembling intellectual honesty. And - no surprise - he was investigated by his own university for heresy simply for being honest. And Donald Knuth, a personal hero of mine, spoke in 2000.

In 2007, MIT computer scientist Rosalind Picard spoke. She's infamous as one of the signers of the Discovery Institute's A Scientific Dissent from Darwinism letter -- despite having, as far as I can tell, no advanced biological training. This didn't prevent her from using her professional affiliation at MIT to sign. I once asked her if she thought this was ethical, but she didn't reply.

This year's speaker was Mary Poplin, a professor at the Claremont Graduate School. I knew what to expect, since I had already watched one of her videos. I got exactly what I expected. Speaking in a nearly empty hall that could hold over 700 people but probably held about 50, she provided

* a phony quote in support of Christianity
* slurs directed towards atheists and Christopher Hitchens
* vague complaints that Christianity is "suppressed" or "censored"
* crackpot claims that the Bible holds important medical knowledge
* a conversion story based on emotions and dreams rather than any evidence

The quote story is rather interesting. Jürgen Habermas is an elderly German philosopher who Poplin quoted as follows: "Christianity, and nothing else is the ultimate foundation of liberty, conscience, human rights, and democracy, the benchmarks of western civilization. To this day, we have no other options [to Christianity]. We continue to nourish ourselves from this source. Everything else is postmodern chatter."

This quotation is phony, but is very popular among Christians.

Its origins have been carefully traced by Thomas Gregersen, who writes:

But this is a misquotation! The reference is an interview with Jürgen Habermas that Eduardo Mendieta made in 1999. It is published in English with the title "A Conversation About God and the World" in Habermas's book "Time of Transitions" (Polity Press, 2006).

What Habermas actually says in this interview is:

"Egalitarian universalism, from which sprang the ideas of freedom and social solidarity, of an auonomous conduct of life and emancipation, of the individual morality of conscience, human rights and democracy, is the direct heir of the Judaic ethic of justice and the Christian ethic of love. This legacy, substantially unchanged, has been the object of continual critical appropriation and reinterpretation. To this day, there is no alternative to it. And in light of the current challenges of a postnational constellation, we continue to draw on the substance of this heritage. Everything else is just idle postmodern talk (p. 150f)."

The misquote rewrites Habermas's statement and changes its meaning:
(1) Habermas talks about the historical origin of egalitarian universalism - not the foundation of human rights today.
(2) Habermas mentions both Judaism and Christianity - not only Christianity.
(3) Habermas says that there is no alternative to this legacy ("Erbe" in German) - not that we have no alternative to Christianity.


In the question-and-answer-session after the talk, I informed Poplin of the phony quote and asked her to withdraw it. In response, she claimed that Habermas had been asked about the quote at a lecture and did not deny it! So she knew the quote was dubious, she knew there was no actual original source confirming the phony quote, but she proffered it anyway with no disclaimers. In my opinion, this constitutes serious scholarly misconduct.

Later, I discussed the quote again with Poplin. She admitted she had no source for the quote, but she insisted it was legitimate because it accurately reflected Habermas' ideas, even if it was not his actual words. She again referred to this video, claiming that Habermas was asked about the quote and did not deny it. Watch the video, and see if it supports Poplin's interpretation. I don't think it does.

Here are some other aspects of Poplin's talk, with brief commentary:

- She claimed that "arch-atheist" Hitchens was practically the only author taking issue with Mother Teresa's career. This is simply untrue; authors such as Michael Parenti, Aroup Chatterjee, and others have criticized Agnes Bojaxhiu.

- Like many Christians, she seemed really disturbed that university students sometimes have sex with each other, and she claimed this was due to the loss of "ability to have a moral conversation" about anything. (I don't have any idea what she's talking about: questions of ethics routinely come up even in our computer science curriculum.)

- She dismissed the Christian pastor who wanted to burn a Koran as unrepresentative of North American Christianity

- She claimed "advocates of secularism try to keep orthodox Christianity a secret". Not so - I'd like it to be exposed in all its silliness.

- Secularism has "diminished the Academy"

- the University is hostile to "God, Jesus, and the Holy Spirit". Yes, but in exactly the same way it is hostile to any claim presented without evidence, such as Bigfoot, UFO's, and homeopathy.

- She approvingly quoted C. S. Lewis, from Mere Christianity, claiming "If Christianity is true then it ought to follow (a) That any Christian will be nicer than the same person would be if he were not a Christian. (b) That any man who becomes a Christian will be nicer than he was before." (I wonder what a non-Christian David Bahati might be like.)

- And, in a stunning display of hypocrisy, she both praised the Roman Catholic church for helping the poor and sick in the 15th century, and dismissed its role in genocide in the New World and its role in the Crusades as complaints by ignorant critics.

Overall, this was probably the shallowest, most anti-intellectual Pascal lecture I've attended.

This is the word-salad recently received from a spammer-scammer:

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Man, this guy needs to take a course in English composition.

The Fibonacci Quarterly has gone electronic! And they've put all their articles before 2006 online for free.

When I was a teenager, this was one of my favorite journals - because, unlike most math journals, I could actually understand most of the articles in it. My parents thought it was weird, but they were very understanding, and even got me a subscription.

I remember one of the articles that blew my mind was Aho and Sloane's Some Doubly Exponential Sequences. The authors found beautiful analyses of some nonlinear recurrences, including one of my favorites:

y₁ = 5; y_n+1 = (y_n - 2)².

The first few values are y₂ = 9; y₃ = 49; y₄ = 2209; and it is not hard to prove that y_n = L_2ⁿ + 2, where L_i is the i'th Lucas number.

It's still a good and worthwhile journal, even if it doesn't usually get much praise from the kind of people who publish in Inventiones. It struggles from time to time with quality issues, and I really dislike the typesetting, but there's often something interesting in it.

So, congrats to the Fibonacci Quarterly for taking this step. If only they'd put in a search function for titles and authors...

From recent e-mail from a fundamentalist:

"Cursed be all that learning that is contrary to the cross of Christ."
-James Madison, America's Providential History, p. 93.

Now, anyone who knows anything about Madison should be very suspicious of this quote. Madison was not a traditional Christian, and said things like "Religious bondage shackles and debilitates the mind and unfits it for every noble enterprize, every expanded prospect." (letter by Madison to William Bradford, April 1, 1774).

Second, as Chris Rodda has shown, America's Providential History is thoroughly unreliable when it comes to quotations.

Third, this quotation is attributed in Popular Science, February 1887, to John Witherspoon, the president of Princeton University, not Madison. I haven't found it in Witherspoon's writings, but it sounds much more like Witherspoon than Madison. Confusingly, it has also been attributed to Jonathan Dickinson, another of Princeton's presidents. It sounds consistent with him, too.

So I am calling bogus on this quote. Not surprisingly, it is found on many Christian websites, with attributions to Madison. We see here a good example of the fundamentalist devotion to truth.

I wish I had a little more time to discuss all the stoopid that's been in the news lately! But I don't, so here's a few links:

What to do if you're a glorified librarian who can't get his book on Alfred Russel Wallace published with a real publisher? Why, get the Discovery Institute's own vanity press to publish it for you! (It helps if you have friends claim the story has been "embarrassing Darwinians ... for almost a century and a half".)

What to do if you're a moron hockey coach? Why, refuse to play one of your players because he's Jewish.

What to do if you're a faux science journalist who spends most of her time denying evolution? Why, incoherently praise a creationist book and wonder why "so few career Darwinists have brayed against it." (Hint: real biologists have better things to do with their time than to read every vanity press book that comes along.)

What to do if you're a religious crackpot? Why, file a lawsuit claiming that evolution is a religion and so can't be legally taught in US schools.

What to do if you're a math professor who gets in a fight with a colleague? Why, go piss on his door, of course! I always thought there was something odd about algebraic geometers.

What to do if you're a Discovery Institute flunkey who can't answer our criticisms of intelligent design? Why, simply object that we didn't mention articles that appeared after our publication.

What to do if you're a philosopher who doesn't know a damn thing about mathematics? Why, publish a piece in the Times Higher Education claiming"But there is only an infinity of mathematical objects, not a super-infinite (transfinite) totality.

So how has it happened that for a hundred years, the mathematical establishment has swallowed the idea of transfinite sets? Georg Cantor produced an argument that seemed to point to transfinite immensities, but that was before we realised that mathematics was incompletable. In effect Cantor's argument showed that the set of real numbers was incompletable. It did not (could not) show that there were more mathematical objects than an ordinary infinity...

Once installed, blind faith ensured that the transfinite would continue to thrill and amaze generations of students - in spite of the inconvenient fact of its mathematical impossibility."

Yup, he really seems to be claiming that the real numbers are a "mathematical impossibility". That's ok with me, I never liked real analysis very much anyway.

So much stoopid, so little time!

Now, as a relief from all that stoopid, look at this: the earth (and moon - wait for it) from 31 million miles away:



Ahh, now that's a relief.

Here is a commentary with equal parts smugness, lies, and ignorance, delivered by Andrew Klavan:



It's truly fascinating how moronic it is, and how un-self-aware. One minute he's saying that liberals are evil because they call the far-right "fascist" or "worse than Hitler"; the next minute he's displaying the term "net neutrality" written in pseudo-cyrillic script, with the clear implication that somehow it is Communist.

He also makes the claim that bailing out banks and big corporations is a "radical attempt to destroy our free-market system". I wonder what a real attempt to destroy it would look like?

There are good arguments both for and against net neutrality (and the Fairness Doctrine, for that matter). But they're not even remotely related. One is about a national public resource with very limited access and bandwidth, controlled largely by corporate interests. The other is about a global network and peer-to-peer communication with near-universal access in North America, and essentially unlimited bandwidth. There's simply no way that net neutrality could "force conservatives to shut up online as well".

Klavan claims "leftism has failed everywhere". Yet in the European social democracies, such as Sweden, Norway, and Denmark, people live longer, healthier lives, and they have less crime. Furthermore, "leftist" policies like the minimum wage and Medicare haven't failed -- they have become standard practice in democracies.

I wonder if Klavan is more or less stupid than his audience? Is he a moron, or actively dishonest?

Check out this letter in our local paper, the Waterloo Region Record.

It's got all the usual stupidities: "scientists have not been able to find even one provable fact to back up the theory of “goo-to-you” evolution" -- as if the letter writer spends all his spare time reading the evolutionary biology literature.

"Yes, we have evolution within kinds, as God programmed." -- the usual creationist invention of terms -- "kinds" - that no actual biologist uses. I suppose we can be grateful he didn't say "baramin".

"There were probably two dogs on Noah’s Ark" -- as if Noah's ark were an actual historical event.

"there is any evidence to show that any of them changed into a cat or a small horse or any other animal" -- as if dogs changing into cats or horses is a prediction of evolution.

"My definition of the word “theory” is “imagination.”" -- Well, he'd better get a better dictionary!

And this guy is a financial planner at a local "wealth management" company!

Back in 2003, I sent this guy a list of examples of speciation, but here he is again, 8 years later, repeating the same falsehoods.

Thankfully our residents with connected brain cells have already responded to this nonsense here and here.

This is fun.

Two men in Newfoundland who experienced car collisions with moose are suing the provincial government, arguing their collisions were the government's fault because the introduced moose to the province 100 years ago.

And - since you asked - yes, there have been several other moose-related lawsuits.

I wonder if we could sue the state of Washington for facilitating the existence of Glenn Beck?

Of all the commenters at Uncommon Descent, "Kairosfocus/GEM of TKI" (actually Gordon Mullings) is the one with the second largest stupidity-verbosity product.

Here he is citing science "journalist" Richard Milton to argue against radiometric dating. Quoting Milton, he says radioactive dates cannot be falsified, that any scientist debating a date would be regarded as a crackpot, that errors are corrected to the currently accepted value, and only dates conforming to current understanding will get published.

Mullings and Milton don't understand how science works. With radiometric dating, the essential point is that we have multiple, independent analyses all leading to essentially the same estimates for, e.g., the age of the earth. (Read, for example, Dalrymple's book with that title.) It is the consilience of our estimates that give us confidence. The evidence is now so strong that a single discordant result will not cause scientists to throw away all previous results; rather, someone disputing the age of the earth will have to amass evidence that is roughly equal in strength (or stronger) to the case for our current estimate. Not only that, anyone calling the age of the earth into question is going to have to explain what, precisely, has gone wrong with all the evidence we have -- why, precisely, do all those dates obtained by independent investigators match up so well?

And that's the way it should be. Science is not mathematics, where a single counterexample can invalidate a theorem (but even there, not always! -- the message of Lakatos' Proofs and Refutations). In science, a very strong evidentiary case doesn't get overthrown by a few isolated results that suggest another conclusion. There are simply too many possibilities for error in scientific experiments for that.

Let's apply Milton's four objections to, for example, the distance from the earth to Alpha Centauri. Just like radiometric dating, we have no direct experience of this distance; any scientist claiming a substantially different distance from 4.37 light years would be regarded as a crackpot; an experiment giving a substantially different distance would be scrutinized carefully for sources of error; and it is unlikely (unless the evidence case were extremely strong) that another distance would get published.

In fact, we have an example of this from the history of Alpha Centauri itself: James Henderson studied the distance to Alpha Centauri using parallax in 1832-3, but he didn't publish his results because the great distance he obtained made him suspect an error. Only after Bessel determined the distance to 61 Cygni in 1838 did Henderson change his mind. Once again, the consilience of the two independent experiments increased our confidence in the results.

So the Mullins-Milton objections apply to all of science, not just evolution. Were we to accept them as definitive, all of science would disappear.

The Manifesto Club has the interesting story of a flower arranger at a church in England who refused to undergo a criminal records check so she could continue with her work. This is just one example of the continuing intrusion of the State into daily life where no reasonable cost-benefit analysis is done.

I had to undergo a costly criminal record check and fingerprinting just to accompany my sons on a school outing canoe trip down a local river, so I'm sympathetic to Annabel Hayter and others standing up to this nonsense.

Here's a silly letter to the editor from a local theist.

How many examples of bogus reasoning can you find? It's practically a classroom exercise in shoddy thinking.

Responding to the assertion that we can be good without a god, the writer claims "this has been tried in a number of countries with disastrous results". Let's look at homicide rate as a proxy for "goodness". Notice anything? The US's homicide rate (5.0 per 100,000) and Canada's (1.81) are both distinctly higher than many countries that are largely secular, such as the Czech Republic (1.33), Sweden (1.25), and France (1.60). Similarly, religious states such as South Carolina and Florida have high homicide rates, while more secular states such as Oregon and Maine have much lower rates. So belief in a god is not a controlling factor for the goodness of a society.

The writer goes to say "Without biblical guidelines, countries such as Russia descended into moral chaos." Now I'm not going to defend the totalitarian regimes of Stalin et al., but one can hardly say that Christian Russia before communism was a moral paragon. Has the writer never heard of the Massacre of Novgorod? Or the word "pogrom"? And now that Christianity is practiced openly in Russia, has the country's moral tone improved? Hardly.

The next paragraph begins "Just look at has happened in our own schools since they took out prayer and Bible readings and instruction in moral behaviour. There has been an increase in violence, drug problems, teen pregnancy and defiance against authorities". (But evidently a decrease in commas.)

This is a good example of the "post hoc, ergo propter hoc" fallacy. There is no evidence that either prayer or Bible readings has much effect on crime. In the US today, for example, the homicide rate is at the rate it was back in 1965, in the good old days envisioned by the letter writer. Yet prayer and Bible readings have not returned. What is responsible for the change?

Crime is a multifactorial problem, and it's not easy to simplistically assign causes. (Read Walker's Sense and Nonsense About Crime if you want pretty much everything you knew about crime to be overturned.) Some changes in the crime rate are due to simple demographics: the change in the number of males aged 15-24 in the population. Others may be due to changes in abortion law. No serious analyst of crime, however, thinks changes in the crime rate are simply linked to policies like prayer in the schools.

The shoddy journalism of David Warren, Ottawa Citizen columnist and perennial candidate for Canada's Worst Journalist, has finally been exposed.

Thanks to Carol Wainio, the Ontario Press Council has ruled that Warren "failed to meet generally accepted journalistic attribution standards".

Even though the OPC clearly ruled against Warren, the decision has been criticized for not being sufficiently strong.

How has Warren responded? Exactly as you might expect: instead of 'fessing up that he's a crappy member of his profession, he's been whining and portraying himself as a victim.

Three cheers for Carol Wainio! And three raspberries for David Warren and the Citizen.

From The Weather Network website today:

Spotted on Queen Street in Kitchener, Ontario:

I like the unintentional coinage very much.

Homeoapathy: The selling of quack medical remedies while being unconcerned about their lack of effectiveness.

Now that the offensive and moronic DADT policy has been repealed, it's time to revisit a Salon panel discussion held ten years ago.

Charles Moskos, the late Northwestern sociologist, tried to defend DADT by saying things like "That's just asking for trouble. How do we do it with men and women? It doesn't work there. We're having all kinds of cases, including as the women say, too many false accusations. Let's just muddle through the way we are with "don't ask, don't tell." It's much easier. I think the gender stuff is hard enough to deal with and to replicate that with sexual orientation just makes life too much trouble."

He also said, in Lingua Franca, that "I should not be forced to shower with a woman. I should not be forced to shower with a gay."

Here is the comment I left ten years ago, which is still visible:

Your panel discussion on gays in the military was remarkable in that it did not even mention the experiences of other countries. Canada, for example, successfully integrated gays in the military some years ago, and the UK is now slated to follow the same path. Brigadier General Daniel E. Munro, the director general for personnel policy in the Canadian Forces, was quoted in the Washington Post as saying, "We would not have been able to prove that [homosexuality] had that deleterious effect on cohesion and morale that everyone talked about. Basically, we realized that we didn't have the evidentiary foundation ... It just wasn't there, I mean, you can't use the old cohesion and morale arguments just based on folklore. You have to be able to prove this stuff." If only U.S. military officials could speak with such honesty!

I have been having some of the strangest interactions I have ever had, with both Charles Lewis, religion columnist of the National Post, and Stephen Meurice, the Post's editor-in-chief. They resulted from my blog post reacting to Lewis's column, entitled Dear atheists: most of us don't care what you think.

First, Meurice. I asked him why it was acceptable to have Lewis's headline, but not acceptable to have the analogous headline with (say) "Jews" replacing "atheists".

I found his reply rather surprising. He thinks the distinction is that most Jews are born into their faith, while atheism is just "an opinion".

One great feature of both American and Canadian democracies is that we find discrimination against people for irrelevant attributes to be unacceptable. This principle is behind laws against employment discrimination, and the recent repeal of DADT. (Canada, I'm glad to say, ended discrimination against gays in the military long ago.)

But it is quite strange to suggest that discrimination against irrelevant attributes becomes unacceptable only when those attributes arise from the circumstances of one's birth.

If Meurice's view is correct, then we should be free to discriminate against adult converts to any religion. After all, the Jew who converts to Christianity was not born into his faith; he chose it, presumably after some intellectual struggle, and therefore, pace Meurice, it is just "an opinion". Similarly, we should be free to discriminate against adherents of new religions, such as Scientology or Branch Davidianism, since many adherents were not born into those faiths. This is clearly ridiculous.

Meurice's view also implies that if atheism becomes more mainstream - to the point, let's say, where most adherents are born atheists - then suddenly it would become unacceptable to discriminate against it. But isn't this the opposite of what should be the case? Established viewpoints don't need much protection; it's the more unfamiliar that routinely gets discriminated against.

So I don't think Meurice's distinction makes much sense.

Charles Lewis has also been corresponding with me - but in the oddest, passive-aggressive sort of way. At one point he wrote "I will never think of you again", but a few days later he was badgering me to publish this response on my blog. At another point he said he would call me to discuss a misunderstanding; when he finally did, he wouldn't let me speak, called me "weak-minded", and hung up in a huff.

The misunderstanding came about when I wrote a long response to some of his points, and even offered to buy him a coffee if he were ever in town. But he apparently didn't see that response, because he wrote back "you could have answered and created a dialogue". I've tried to resolve that, but he doesn't seem to want to listen.

If this is representative of the state of journalism in Canada, we're in deep trouble.

I hadn't heard about convicted criminal Bob Enyart before, but based on yesterday's posting, I haven't missed much.

He gives a list of what he calls "typical atheist clichés" and then refutes them in a single line. Unfortunately, most of his "clichés" are straw men -- arguments that I've never heard, or rarely heard, anyone put forward, let alone atheists.

Let's take #1: "There is no truth!" Who ever said that, and what is it even supposed to mean?

Other of his "clichés" make sense, but only if you interpret them in a reasonable way. For example, #2 is "Truth is unknowable!" But the only sensible interpretations of that statement are (for example) that some truths are unknowable (which we know to be true from Gödel), and that other statements that we believe we know with certainty (such as our own birthdate) are, in fact, only held with justifiable and strong certainty, not irrefutable knowledge. Enyart's proposed rebuttal "How do you know?" is just nonsensical.

Enyart says "If your worldview can be dismantled within eight seconds, then get a better one." I'd say, if you think you have dismantled someone else's worldview in 8 seconds, you're just fooling yourself.

I wrote to Gordon Fisher, President of the National Post; Douglas Kelly, the Publisher; Jonathan Harris, VP of Digital Media; Stephen Meurice, the Editor-in-Chief; and Jonathan Kay, Managing Editor, Comment.

I asked them all the same thing: if it would not be acceptable for someone at the National Post to write a piece entitled "Dear Jews: Most of us don't care what you think", why is it acceptable for Charles Lewis to do so with "Jews" replaced by "atheists"?

Not a single person at the National Post was courageous enough to reply.

It speaks volumes, doesn't it, about the double standard that allows atheists to be criticized in the most vituperative and bigoted ways, with no uproar?

Addendum: (December 20). Stephen Meurice responded to me on December 17. Here is my response.

I don't get that many creationists writing me, but I am indebted to a certain J. M. of Massachusetts, who has recently written to send me a copy of the November 2010 Jehovah's Witness publication, Awake!. He claims "This magazine points out some flaws in the atheists' reasoning."

Well, no, it doesn't.

The first article is entitled "Atheists on a Crusade", and is just one in a long line of articles by theists using religious language to denigrate atheism and evolution. "Called the new atheists," the article says, "they are not content to keep their views to themselves".

This just cracks me up. The Jehovah's Witnesses - you know, the folks who go door-to-door to spread their religion - are complaining because atheists are not content to keep their views to themselves. My irony meter just broke.

Another article, "Has Science Done Away with God?" repeats the canard that "everyday experience tells us that design -- especially highly sophisticated design -- calls for a designer". Well, no, it doesn't. That was resolved 150 years ago, when Darwin published The Origin of Species. We know now that mechanisms like mutation and natural selection can produce complexity and the appearance of design. The article goes on to ask, "What is the only source of information that we know of? In a word, intelligence". But anyone taking an introductory course in information theory at my university knows this is a lie.

It's a shame that creationists have to resort to untruths like this, but it's all they have.

If you can stomach it, read this appalling piece of dreck by Charles Lewis, religion writer for the National Post.

It's hard to know what to make of it, other than that Lewis is terribly, terribly threatened by the rising popularity of atheism and atheist writers. He doesn't seem to know a damn thing about atheists, but believes they are all horrible, boring utopians.

As evidence of this, he trots out Christopher Hitchens and Richard Dawkins, and labels them "dreary". Hitchens, dreary? Lewis must be living in some bizarro universe where dreary means "vastly entertaining".

If I had to name a single famous person I'd love to have dinner with, it would be Hitchens, who knows much more about politics and history than I do, and is witty to boot. Dawkins would be a close second. Come to think of it, having them both for dinner would be perfect: Hitchens can talk about art, history, and politics, and Dawkins can talk about science.

I understand perfectly well why Lewis feels threatened by Hitchens. It was Hitchens who wrote The Missionary Position, exposing Mother Teresa as a pious fraud who loved poverty and suffering for everyone except herself. Lewis, who himself wrote on Mother Teresa, can't accept that characterization. But it is difficult to get a man to understand something when his salary depends on him not understanding it.

Lewis claims "most atheists do not have a clue what religion is about". Like most bigots, though, he doesn't present a shred of evidence for this claim. If he bothered to look at the evidence, though, he'd conclude just the opposite: atheists know more about religion than Protestants and Catholics.

Lewis gives North Korea as an example of a "godless society". But he doesn't dare mention the European social democracies, such as Denmark, Norway, and Sweden, all of which are good examples of peaceful, prosperous societies with significantly lower levels of religious belief than either Canada or the US. Nor does Lewis mention the behavior of officially religious societies, such as Afghanistan. That's simple dishonesty. Perhaps Lewis should review the Ten Commandments -- as I recall, there was this prohibition against "bear[ing] false witness".

Lewis claims "Atheists are under the ridiculous illusion that religious people think that all they have to do is call out to God and help will be on the way". Well, no. Atheists know that there is a huge variety of religious belief, and we also know that many Christians do believe exactly what Lewis says they don't. Pretending that this is not a large strain of North American religious belief is, simply, dishonest.

Lewis says "Faith is not up for debate". Well, I've got news for you, Chuck: you're wrong. In a free society, you don't get a pass because you call your beliefs "faith" and pronounce them off limits. Can't justify them? Fine with me. Just don't expect me, or anyone else to take you seriously.

I can just imagine the reaction if Lewis wrote a column entitled "Dear Jews: most of us don't care what you think". No doubt he'd be fired in a minute. But criticizing atheists is just fine.

Why on earth is the National Post employing this ignorant bigot?

Loren Graham, an American historian of science, and Jean-Michel Kantor, a French mathematician, have collaborated on a recent book, Naming Infinity: A True Story of Religious Mysticism and Mathematical Creativity (Harvard University Press, 2009).

Graham and Kantor's thesis is that a Russian religious cult, "name worshipping", was partly responsible for advances in set theory made by Russian mathematicians in the early 1900's, whereas the French "rationalistic, Cartesian" approach prevented similar breakthroughs. Indeed, on p. 189 they claim "under the influence of their [Borel, Baire, Lebesgue's] ultra-rationalistic traditions, they lost their nerve". (However, this supposed "loss of nerve" is not supported by any documentation.)

I found it an interesting book, but one that did not successfully support its thesis. After all, placing the responsibility for an historical event on some other single event or belief is highly problematic: consider that there are still people who debate the conclusion that slavery was a primary cause of the American civil war. Why one group solved a mathematical problem, while another failed, is not always so simple to determine. It can be a matter of pure intellectual ability, or a desire to focus on one area rather than other, or something entirely random, like a conversation in a café. Graham and Kantor hedge a bit on p. 100, where they write, "when we emphasize the importance of Name Worshipping to men like Luzin, Egorov, and Florensky, we are not claiming a unique or necessary relationship. We are simply saying that in the cases of these thinkers, a religious heresy being talked about at the time when creative work was being done in set theory played a role in their conceptions. It could have happened another way; but it did not." But if this all they were saying, then so what?

Srinivasan Ramanujan believed that his family's deity, Namagiri, whispered equations in his ear. But it doesn't necessarily follow that without a belief in Namagiri, he would not have created the mathematics he did. Maybe he would have been an even better mathematician had he not been imbued with his Hindu superstitions.

Similarly, it's not clear to me that Russian mathematicians like Egorov, Luzin, Florensky, and others could not have been just as successful -- or even more so -- had they not subscribed to their bizarre Christian cult. It even seems that their cult could induce ridiculous statements like the one the quote from Bely: "When I name an object with a word, I thereby assert its existence." That will certainly be news to unicorns and the set of all sets. Similarly, Luzin wrote that he "consider[ed] the totality of all natural numbers objectively existing" (italics in original), which raises the question, what precisely does it mean for a number to "exist"? This point is not really discussed by the authors. But it seems to me that, for example, that the number ℵ₀ "exists" in exactly the same way that the number 4 "exists".

The book is generally well-presented, although I found a couple of things to quibble about. On page 58, for example, the authors claim that "explicit namings of even one of them [normal numbers in base 10] have been very difficult to obtain". But this is not true. For example, Champernowne's number .123456789101112 ..., which consists of the decimal expansions of the integers concatenated in increasing order, has a very simple proof of normality found by Pillai in 1939. Many, many other examples are known, such as the result of Davenport and Erdős in 1952 that .f(1)f(2)f(3)... is normal if f is any polynomial taking positive integer values at the positive integers. And I was also annoyed by the misspelling "Riemanian surfaces" on p. 113 --- "Riemann" has two n's, not one --- and the failure to put the proper accents on Wacław Sierpiński on p. 118.

Nevertheless, this is a little book worth reading, even if its main thesis is poorly supported. For me, the best part of the book was the history of Soviet mathematics in Chapters 7 and 8. Although I knew the names of most of the Russian mathematicians discussed, I had not explicitly realized the extent of mathematical talent in Moscow in the 1920's. And the mistreatment of Egorov, Luzin, and Florensky under Communism, and the bravery of people like Chebotaryov who stood up for them and suffered as a result, is a cautionary tale worth knowing about.

Wow, there's so many different possibilities to pick from!

How about University of Calgary prof and Stephen Harper adviser Tom Flanagan, who thinks Julian Assange should be assassinated?

Or the voters in Vaughan, Ontario, who elected that creepy authoritarian, Julian Fantino as their next MP?

Or the trustees of the Waterloo Region public school board who voted to continue to allow the Gideons to distribute their Bibles to 5th graders in public schools?

Or Gideon member Art Wagensveld who tried to pretend that his organization's Bible distribution "is in no way a religious action"?

Or Waterloo city councillor Angela Vieth, who backed removing fluoridation from the water supply and was quoted as saying "This is toxic waste, it doesn't need to be in our drinking water"?

So many bozos, so hard to choose...

William Lane Craig seems, for some reason that I've never understood, to garner disproportionate respect from theists and even some nontheists. (But then, I'm also mystified by the cult around C. S. Lewis, who seems to me to be a sloppy and childish thinker.)

Take a look at this debate entitled "Does the Universe have a purpose?" and see if Craig lives up to his reputation. Of course, in debates, where there is a limited time, we are all forced to simplify our statements, so perhaps Craig doesn't really believe exactly what he is saying. Nevertheless...

In his opening statement (jump to 13:41) , he piled false claim upon false claim. For example:

"If God does exist, then the universe does have a purpose." Really? That doesn't follow. Just because an intelligent being makes a thing X, that is insufficient to show that X has a purpose. After all, I could pick up a couple of rocks aimlessly at the seashore and put one on top of the other. What would be the purpose of that pile of rocks? Perhaps there is none at all.

"According to Biblical theism ... The purpose of life is to be found in a personal relationship with a holy and loving God. As the Westminster catechism asks, What is the chief end of man? To glorify God and enjoy him forever." Huh? This was a non sequitur. The subject of the debate was whether the universe had a purpose, not the purpose of life or man.

Craig relied upon a false dichotomy - the only two choices he presented are "Biblical theism" and "atheism". But these are clearly not the only possibilities. Why couldn't the Universe have been made by a nasty and childish god, who delights in tormenting us in new and ingenious ways? Maybe the purpose of the Universe is to amuse this god with our suffering. Or perhaps there are multiple gods, each wagering on our behavior when confronted with new diseases or painful medical procedures.

"God gives an objectively purposeful life." Not true, since we have no objective way to determine this purpose. Craig think the purpose is spelled out in his holy book. Another might say the purpose is spelled out in a different book. We have no objective way to determine which is correct... or maybe they're all wrong. Maybe a god designed our universe for the purpose of making atheism the single world belief.

"What is evil? - I maintain that evil is a departure from the way things ought to be..." Let's look at the sensibility of this definition. Perhaps I think the way things "ought to be" are that we should all have jet cars and live on Mars. Since the current state of affairs is different from the way things "ought to be", using Craig's definition I would have to say the current state of affairs is "evil". But this would not be assented to by most people who use the word "evil". Yet if I say, "Hitler was evil", this would be assented to by most people. So Craig's definition does not capture the way most people use the word "evil".

"If there is a way things ought to be, then there must be some transcendent design plan or purpose that determines how things ought to be. And so there must be some transcendent being - a Creator in fact - whose will is the basis for how things ought to be. And so evil is actually evidence that God does exist." This doesn't follow at all. Why could not a sense of "the way things ought to be" be the product of biological evolution?

And to top it all off, this was delivered with a kind of wheezy smugness out of proportion to the quality of the arguments. Bleh.

A fun article from Salon about the very worst of opinion journalism.

But how could they possibly have forgotten Charles Krauthammer, the embodiment of everything that is wrong with mainstream commentary?

Here are two perspectives on Islam of today:

A Palestinian doctor who lost his children in an Israeli attack, but continues to work for peace.

A network of Islamic schools in Britain that teaches that Jews look like "monkeys and pigs" and demonstrates the proper place to amputate hands and feet as punishment.

Which is more representative? I hope the former.

Read this Globe and Mail article about the philosophy of mind.

If philosophers think the view that "The brain is not an organ of consciousness. … The brain has no cognitive powers at all" deserves anything more than a good horselaugh, this simply shows how irrelevant philosophy has become.

Our future understanding of cognition will come from neuroscience, not from Wittgenstein.

It's fun to read the comments, which are almost entirely negative.

Just when you thought he couldn't get any weirder, here is the crackpot Turkish creationist Harun Yahya (pseudonym of Adnan Oktar) blaming 9/11 on the CIA, and "deviant Arab communists, Darwinists, and materialists".

Of course, anyone who has studied the incident knows that in fact the 9/11 attackers were pious Muslims who worshipped at mosques like al Quds in Hamburg and spent much of their time talking about religion. There is simply no indication at all that they knew a damn thing about evolutionary biology or Darwin.

Yahya isn't much different from the theocrats at the Discovery Institute, who want to link Darwin to both fascism and communism.

Those creationists are just so darn cute when they try to do mathematics, you just want to pinch their cheeks.

Here's Robert Sheldon, who babbles about infinity so incoherently, the folks at Uncommon Descent thought they should reprint it for all to see. And what a mess it is.

Despite claiming that he's "gotten quite comfortable with infinity", he emphasizes that "the important thing is not to think about it too long". And that is certainly what he's done!

How many errors can you spot in this word salad? This is a good one: "For example, take the number line from 1 to ∞. It’s infinite of course. But now divide every number by the largest number on the line." Yeah, that'll work really well.

And here's another: that the cardinality of the irrational numbers is denoted ℵ₁. I guess Mr. Sheldon has never heard of the continuum hypothesis.

I think Mr. Sheldon and Marvin Bittinger should get together. What a great book they could write!

Call for papers: A special issue of Journal of the Australian Mathematical Society dedicated to Alf van der Poorten.

We solicit submissions in all areas of mathematics, and especially in the areas close to the research interests of Alf van der Poorten (e.g., recurrence sequences, continued fractions, diophantine approximation, and p-adic numbers). The submission deadline is 1 May 2011. We hope to have all submissions evaluated and make the acceptance/rejection decision by th end of October 2011 with the goal to have this issue to appear early 2012.

Please direct all submissions to Igor Shparlinski.

The Editors
Francesco Pappalardi
Igor Shparlinski
Jeffrey Shallit

Never mind that pesky 2nd law of thermodynamics! Get scammed by "free energy"!

Honestly, what kind of people fall for this crap?

I was once arguing with Eugene Volokh about the separation of church and state in the US. From his lawyer's perspective, he thought the really important issues at the church-state boundary concerned things like "parochiaid" - direct or indirect aid to religious schools - and probably most legal scholars agree with him.

But from my point of view, the really important issues concern things like "In God We Trust" on money, and "under God" in the pledge of allegiance. These seem trivial to people like Volokh, and they're often dismissed as "ceremonial deism". For example, in Lynch v. Donnelly, 465 U.S. 668, Justice Brennan (dissenting) wrote "such practices as the designation of "In God We Trust" as our national motto, or the references to God contained in the Pledge of Allegiance to the flag can best be understood, in Dean Rostow's apt phrase, as a form a "ceremonial deism," protected from Establishment Clause scrutiny chiefly because they have lost through rote repetition any significant religious content".

But now go read this article about Christian prayers broadcast over a loudspeaker at football games at Soddy Daisy, a public high school, in Tennessee. This is a pretty clear violation of separation of church and state, right? Now look at what one local parent, Jim Rogers, uses to justify the practice: "Our country was founded on the principle of religious suffrage and the freedom to express that religion. They incorporated God into our money, the oath of office, our legal system, the Pledge of Allegiance. You cannot find one aspect of our secular government that doesn’t make reference to our creator."

Mr. Rogers clearly doesn't know a damn thing about the separation of church and state, and I doubt he could explain what "ceremonial deism" is. But he does know something that Prof. Volokh doesn't: small, creeping violations of separation have a lot of symbolic value. Rogers knows damn well that having "In God We Trust" on coins is full of "significant religious content".

Lawyers love to say De minimis non curat lex. But the average person knows that when school children are coerced every day into saying "one nation, under God, indivisible", this is more than just "minimis". That's why people in favor of separation need to speak out against the smallest violation. Every crack in the wall just leads to more cracks.

Here's evangelical John Mark Reynolds on why he's proud to vote Republican.

Of all the bogus claims promulgated by evangelicals, one of the most pernicious surely has to be the implication that Republicans are morally superior.

Yes, in the 19th century the Republicans were against slavery - and at a time when many evangelicals were for it (something conveniently omitted by Reynolds -- see, for example, Daly's book, When Slavery was Called Freedom). Yet it is hardly possible to maintain that the Republican party of the 21st century is the same party. Heck, the Republicans abandoned black people only 11 years after the Civil War ended, with the Compromise of 1876. Seventy years later, we were treated to the spectacle of the Republican Eisenhower testifying against integrating the military.

The Republicans are now for "freedom of thought"? Hardly possible to maintain with a straight face - read The Republican War on Science. Republicans are, in general, far more censorious than Democrats - although the Demos have their problems, too.

Republicans are "are hesitant to make any person do good by the force of law"? Truly laughable. Republicans are at the forefront of those wanting to prevent gays from adopting and teaching in schools.

By all means, vote Republican if you think they're going to do a better job. But don't pretend moral superiority that doesn't exist. Reynolds' essay is a bad joke.

I just received the sad news that my friend and colleague, Alf van der Poorten, passed away on Saturday in Australia.

Alf (or "vdp", as he was sometimes called) specialized in number theory, and he wrote about 170 papers on the subject, specializing in continued fractions, elliptic curves, transcendence, Diophantine approximation, and recurrence sequences. He had dozens of co-authors, and he especially liked to write with his Macquarie colleague John Loxton and with Bordeaux mathematician Michel Mendès France. Alf wrote a book, Notes on Fermat's Last Theorem, which was published by the CMS in 1996, and was co-author (with Everest, Shparlinski, and Ward) of another, Recurrence Sequences, published by the AMS in 2003. We had vague plans to write a book together on continued fractions, but we never did. We did, however, write four papers together.

Among number theorists, Alf was an "original fini", as the French say. His talks were often accompanied by transparencies lettered in Alf's distinctive hand, full of quotations and puns. (A book that he co-edited in honor of the computational number theorist Hugh Williams was called High Primes and Misdemeanours.) Some of his papers contained limericks -- and not always in good taste! One of his most-cited papers was just called "Folds!". He loved the mathematical typesetting system TeX passionately, and developed a large set of his own arcane macros, which sometimes made collaboration difficult.

Alf was born during World War II to Jewish parents in Holland who gave him up to another family to protect him from the Nazis. But they all survived the Holocaust, and Alf was reunited with his parents after the war. They moved to Australia around 1950, and Alf got a Ph. D. in mathematics from the University of New South Wales in 1968. He taught at Macquarie University for many years, and, after retirement, ran his own Centre for Number Theory Research out of his home in suburban Sydney. Alf spoke English with a distinctive mix of both Dutch and Australian accents. More information about his life can be found here.

Alf and his wife Joy welcomed me during my only visit to Australia back in 1991. I spent a month living on the campus of Macquarie University and working with Alf on continued fractions. One of the papers we wrote concerned the continued fraction expansion of numbers such as 2^-1 + 2^-2 + 2^-3 + 2^-5 + 2^-8 + ..., where the exponents are the Fibonacci numbers. Working with Alf was a lot of fun. He would gesture languidly in the air with a cigarette-laden hand, moving quickly from topic to topic: Australian politics, other mathematicians he had known, an idea for our latest proof. Alf knew a lot about many different subjects and had a quip or story ready for almost anything. He had phenomenal mathematical intuition and nearly always found the right path to a solution, but he wasn't always rigorous when he wrote up his results. One of his celebrated papers, about the transcendence of automatic numbers, contained a serious flaw which he was never able to repair.

Alf travelled a lot. We worked together at Dartmouth College, and later, when I moved to the University of Waterloo, he came for one of the CMS meetings. During one of his visits, he told me about his clogged arteries. He had been walking along when suddenly he found himself unable to speak. He sat down on a bench and was taken to the hospital, where it was found that an important artery was nearly completely blocked. After surgery he made a full recovery and continued to do mathematics. More recently, he had surgery for cancer of the lip (where a cigarette had always rested in the past) and eventually developed the brain cancer that killed him. At one of the CMS meetings dozens of mathematicians signed a card for him.

Alf was active in the number theory community and served as president of the Australian Mathematical Society from 1996 to 1998 and won several awards, including the George Szekeres medal. I will miss him.

[Photo credit: Renate Schmid]

Wow. The nasty and untalented hip-hoppers Insane Clown Posse turn out to be moronic, lying Christian evangelists. Who would have guessed?

I wonder if Premise Media wants to make a documentary about them.

Well, my 53rd birthday is coming up in a couple of weeks, so here's what I'd like:

Please make a donation to any or all of these fine organizations:

- the National Center for Science Education - the main US organization fighting the nonsense of creationism and intelligent design

- the American Civil Liberties Union - one of the few organizations devoted to preserving our rights and fighting the creeping totalitarianism of government

- the Canadian Civil Liberties Association - the Canadian version of the ACLU

- the James Randi Educational Foundation - devoted to improving critical thinking and exposing the charlatans of pseudoscience and quack medicine

- the Southern Utah Wilderness Alliance - a small grassroots organization devoted to preserving wild areas in my favorite part of the world

- Planned Parenthood of Waterloo Region - here in the Bible belt of Ontario we need Planned Parenthood to get out the information that anti-abortion groups want to suppress

- Ecojustice Canada - formerly the Sierra Legal Defence Fund, one of Canada's leading environmental organizations

That's what I would like.

Why is it whenever an organization starts talking about "truth", it's a good bet they're going to be spouting the most incredible lies?

To give just a few examples:

- the 9/11 "truth" movement

- Creation Truth Ministries

- the Discovery Institute's "truth about the Dover trial"

So it was no surprise for me to get e-mail from Turkish creationist Harun Yahya called "An invitation to the truth". It would be funny if it weren't so pathetic.

This message was filled with statements such as "The Chinese people and other nations will also rejoice under the protection of the Turkish-Islamic Union" that seem to be taken directly from some old Stalinist literature.

Or this one: "They should write down little notes that explain the invalidity of evolution". Maybe they should write down little notes explaining that Harun Yahya is a raving imbecile.

Just imagine what an appalling, grotesque, and totalitarian world it will be if morons like this get more power.

How long ago do you think your common ancestor with the moose lived?

Take a guess, and then check your answer here.

Here is a neat trick that lets you avoid initializing large arrays. I learned about it long ago from Aho, Hopcroft, and Ullman, The Design and Analysis of Computer Algorithms, an old but still great book — but I think it is probably an old hacker's idea.

To illustrate the idea, suppose we are trying to solve the element distinctness problem on a restricted universe. In this problem we are given a list of integers and we want to determine if there are any repeated elements. The input is an array A[1..n] of integers, where each integer is between (say) 1 and M, where M is not so large compared to n — maybe M is about 10n or something like that.

The usual way to do this is to create an array B[1..M] such that B[j] = 1 if j is an element of A, and 0 otherwise. We start by initializing all the entries of B to 0. Then we loop through the elements of A. For each i, 1 ≤ i ≤ n, we first check B[A[i]]. If it equals 1, then the value A[i] already occurred in A. Otherwise, we set B[A[i]] := 1, to signify that we've seen A[i].

If M = O(n), this gives a linear-time algorithm for element distinctness. It even lets us list the repeated elements, if there are any.

Now here's the deal. Suppose we are solving element distinctness many times in a program, as a subroutine. Then it is conceivable that initializing all the entries of B to 0 could actually be a significant time drain. Although we have to allocate the memory for B once at the start, could there be a way to avoid the time-consuming Θ(M) initialization for B each time we call the subroutine again? We have to handle the problem that the entries of B could be arbitrary junk that we have no control over.

The answer is yes, using the following trick: instead of containing 1 or 0, we will set it up so that B[j] contains the position p in A where j is found. The key point is that we always actually verify this by looking at A[p], so we can never go wrong, even if B[j] is junk. More precisely, we want to ensure that if B[j] = p, then A[p] = j.

Now for each i we are going to check to see if A[i] = d has already been seen. To do this, we look in B[d]; say it equals c. If c is not between 1 and i-1, then we know that c represents uninitialized junk, so we can confidently ignore it and set B[d] = i.

If c is between 1 and i-1, then it either represents a true pointer back to the place in A where d was found earlier, or it just happens to be junk that is in the right range. In either case, we look at A[c]. Either it equals d, in which case we have found d earlier in the array at the entry A[c], or it equals something else. In the latter case we also set B[d] = i. This works whether B[d] is a true pointer or not!

Here's the code:

for i := 1 to n do
     d := A[i]
     c := B[d]
     if (c < 1) or (c ≥ i) then
              B[d] := i
     else if A[c] = d then 
               print(d, " occurred at positions ", c," and ", i) 
     else B[d] := i;

And that's it! This code fragment prints out the duplications. Of course, if you'd rather terminate as soon as a repeated element is found, you can do that instead. Or if you'd rather save the repeated elements in a linked list, you can do that, too. And of course, this trick can be used in other settings, such as large sparse matrices, where you want to avoid initialization costs.

Over at the creationist "Leadership University" site, Doug Groothuis has a piece called "Six Enemies of Apologetic Engagement", where he lists some ways that evangelical Christians fail to carry out their mission effectively.

It's a real hoot. "Ignorance" is one of the enemies, but Groothuis also makes the bogus claim that "macro-evolution is false, and good arguments have been raised against it from both nature and Scripture". He actually cites the vastly-ignorant Phillip Johnson -- a lawyer with no training in biology -- as someone who has made good arguments with "intellectual integrity" against evolution. (Groothuis also misspells Johnson's first name.)

I remember the time that Phillip Johnson arrived at the Usenet newsgroup talk.origins, back in 1993. He arrogantly rode in on his evangelical high horse to do battle with the godless evolutionists, confident that his rhetorical skills would hide his lack of biological knowledge. The result was not pretty at all. Johnson had to leave in a cowardly huff because he couldn't handle the criticism from people who actually knew something about the subject.

"Cowardice" and "arrogance", however, are two of Groothuis's problems with evangelicals. He says that evangelicals should "cultivate real dialogue with unbelievers". Is that the very same Doug Groothuis who routinely bans commenters at his blog who disagree with his claims? Why, I believe it is.

Doug -- you're a first-class hypocrite.

Here's a poem by Hooper Reynolds Goodwin that was published in the journal Scripta Mathematica in 1953. I liked it very much when I was a teenager, and I still think the last two lines are excellent.

PARABOLA

This curve I'm plotting? A parabola.
This point is called the focus; it's the point—
Oh, no, not an ellipse. Ellipses have two foci:
Here, I'll show you one I've drawn.
You see the difference. These two lines of the parabola,
They stretch out wide and wider,
"World without end," as preachers say.
(I don't know what they mean; perhaps they don't);
But you see how it goes.

There was a man—Sir Isaac Newton, I believe it was—
Who had the notion a parabola was an ellipse,
Its other focus at infinity.
You may not understand just what he meant;
You have to sort of take the thing on faith.
The keenest scholar can't quite picture it, you know.

I've often thought,
It might be called a symbol of man's life;
A curve of ever-widening sweep.
And here in this world
Is the focus we may call, say, temporal interests,
Food and drink and clothes . . .
But yet it cannot be that this is all;
For out beyond the reach of sight must be
Another point, a heavenly focus, see?
'Round which the sweeping curves of human life
Complete the ellipse.
Fantastic? Well, perhaps,
But yet the more I think of it...

And here—
Another thing I've often thought about:
Suppose we draw here two parabolas
With axes parallel, and let the arms cross—
"Intersect" the word is—at this point.
Now if there be a focus
Somewhere out beyond the bounds of space,
And these are two ellipses,
As Sir Isaac thought they were,
Why, don't you see, they'll intersect again
Somewhere out there.
Just as two lives that once have crossed,
Then gone their separate ways,
And one has disappeared long since into the void of death
May—but who knows? It's just a thought...

Well, come again; I don't get callers often.
They don't see much in old folks nowadays,
And when a man's not only old, but got his head
Stuck always in a book of "AnaIyt!"
Young people think I'm queer; they can't see why
A man that doesn't have to study graphs
Should plague his head; don't understand that such
Dry, dull things as a parabolic curve
May bring up mem'ries of a face that's gone.

---

The author, Hooper Reynolds Goodwin (December 5 1891-October 13 1964), was born in Marblehead, Massachusetts. Raised by Unitarians, he attended Boston University and was ordained as a Methodist minister. Later he became an Episcopalian minister. He served in churches in Bethel and Randolph, Vermont.

I am very grateful to his granddaughter, Sue Maltais, for providing a photo and information about his life.

It seems every week I get an announcement for a new journal. This week it's Journal for Algebra and Number Theory Academia, which gets my nomination for the Clunkiest New Journal Title of 2010.

My sabbatical is over and it's back to a teaching term. Classes start next week.

Here's what I'm doing today (with updates throughout the day):

5:30 AM Woke up, had breakfast, and started answering e-mail. Hey, the Phillies are in first place in their division! I worked on processing mail for the journal I edit, the Journal of Integer Sequences.

7:40 AM The kids are off to school - both of them are now in high school! (urk)

8:30 AM Arrived at work. I'll be teaching a multi-section course on algorithms. I'm teaching two sections, with 60 students each, and another instructor is teaching the third -- so there's a lot of coordination to do. I sent e-mail to the other instructor with some suggestions about the first two assignments. I found my book of notes and overhead slides from the last time I taught the course. Some things I can reuse, but other things I will revise.

8:50 AM Time for coffee! While I was gone, we got an espresso machine. I don't like the taste, though -- the coffee machine at Oberwolfach was much better. The one here at Waterloo makes coffee that's way too bitter for me.

9:00 AM Damn, the radio feed from WBUR is acting up, so listening to the news is painful. I switch to the BBC radio program "Newshour".

9:10 AM There's a really interesting article by Lionel Levine and Jim Propp in the latest issue of the Notices of the AMS, on sandpiles. I'll have to think about this stuff more when I get a chance.

9:16 AM Answered e-mail about upcoming information session on graduate study in CS.

9:28 AM Noga Alon is visiting Waterloo, so I sent him an e-mail message asking if he would have a few minutes today or tomorrow to discuss a problem.

9:30 AM Working on the first assignment for my algorithms course. It's not easy to create good, interesting problems about big-O notation. And I want problems whose solution isn't on the web! I had a good one last year but I don't want to reuse it.

10:15 AM Got a couple of problems written, but still looking for a really hard one. Time to go check my (physical) mailbox on the second floor. Most mail comes electronically these days, but still...

10:35 AM OK, I have a draft of the first problem set done. Not completely happy with it. Sent it off to the other instructor for his comments. Noga Alon says he'll be in soon. Now - time to answer some e-mail.

11:20 AM E-mail! It's the bane of my existence. I get lots of messages a day, and don't know what to do with all of them. Best is a message that requires little thought and demands an immediate response. Worst is somebody asking a question that I'm not quite sure how to answer. I don't answer and it gets buried, perhaps never to emerge again. My mailbox always has hundreds of messages and is slow to load. Wish I could get it better organized.

Eating lunch while working. I always get hungry around 11 AM and it's hard to resist eating lunch early.

11:50 AM A colleague from another country was denied a visa to visit Canada and present a paper at a conference. This is really outrageous. I've got an appointment with my MP next week to discuss this case. I'm printing out the documentation that the colleague sent me.

12:00 Noon There's a new version of the APL I use on my mac, APL X. Paid $160 Canadian for the update through paypal.

12:30 PM Spent the last half hour trying to submit a paper to Information Processing Letters. Gone are the days when you could submit a paper by e-mailing some files to the editor. Now you have to go through a web-based form where you attach files, etc. These nearly always are terrible, offering way too many options for some things and not enough for others. I've spent 30 minutes on it so far and am still not done.

12:45 PM Whew! Submission finally done.

12:50 PM Got passcode for new version of APL, and installed it. Seems to work OK.

1:00 PM A colleague once suggested trying to find examples of k-tuples of integers S where g₀ (S) > g₁ (S) > g₂ (S), where g_i (S) is the largest integer having exactly i representations as an N-linear combination of the elements of S. Ran my little APL program and found the example S = (40,46,59,61,92), where g₀ = 373, g₁ = 354, and g₂ = 340. It would be interesting to show there are arbitrarily long descending chains like that. Do you need larger and larger k-tuples to get them?

1:20 PM Went down to the visitor's office to try to find Noga Alon, but didn't find him.

1:25 PM Worked on the algorithms course web page.

1:35 PM Off to the grad course info session to present information about my Winter 2011 course on formal languages.

1:55 PM Back from the course presentation.

2:00 PM Noga Alon kindly came by and we talked about the separating words problem. At the same time our local computer people came by and tried to figure out why Thunderbird has lots of problems with my mail. Chaos!

3:30 PM Department meeting - free cookies. We learned about a new draft policy on privacy at the university, which as currently drafted would have the unfortunate effect of preventing professors from archiving things like student project for more than one year. This would make writing recommendation letters difficult in many cases. I certainly hope this draft policy will be rewritten.

5:15 PM Department meeting's over, and we're done for the day.

Now you know what a typical non-teaching day is like.

Wow, Doug Groothuis has banned me from his blog for writing the following, which he refused to publish:

I think this excerpt shows why, for non-Christians, C. S. Lewis's philosophy is regarded as deficient.

Lewis didn't know anything about evolution. He didn't understand that what he called "morality" is a fact about human evolution; that we are programmed by evolution and culture to regard certain behaviors of others as acceptable and other behaviors as less so. Once this is understood, Lewis's confusion simply vanishes.


He calls this "pugilistic, pugnacious, and pernicious propositions."

Students of Groothuis should be aware: he does not tolerate any kind of dissent. If I were you, I'd look for another teacher, one that respects the give-and-take necessary to acquire knowledge.