Ten Reasons Not to Vote for Huckabee

The picture that has recently emerged of former governor Mike Huckabee is that of an intellectually incurious, greedy, and corrupt fundamentalist Christian.

So here are just some of the many reasons not to vote for him.

1. He thinks that scientists believe the earth is "six billion" years old. He also thinks we "just don't know" how old the earth is.

2. He covered up an incident where his son hanged a stray dog.

3. He lied about having a theology degree.

4. He claims ‘‘The Holy Bible . . . has truth, without any mixture of error, for its matter. Therefore, all Scripture is totally true and trustworthy.’’

5. In 1992, he wanted to quarantine people with AIDS, even though it was well-known then that AIDS could not be spread by casual contact.

6. He improperly claimed furniture given to the governor's office as a personal gift and then didn't list it on an inventory of office items.

7. He freed criminals who committed heinous offenses if they said they had become born-again.

8. He wants a regressive national sales tax in place of a progressive income tax.

9. In 1998, he signed a statement saying that "A wife is to submit graciously to the servant leadership of her husband".

10. He doesn't accept the theory of evolution.

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Updated: an even better list by John Hunt is available here.

Does Creationism Lead to Violence?

From Australia comes this very sad story of an argument between a creationist and two scientists that led to the death of one of the scientists after being stabbed by the creationist.

Creationists are constantly telling us how acceptance of the theory of evolution has undesirable consequences: for example, the National Association for Objectivity in Science claims that believe in evolution "can have a devastating impact on the student, leading him or her to devalue human life and possibly engage in drug abuse, sexual promiscuity, or violence, or even commit suicide."

Perhaps the opposite is true. Creationism, a form of religious dogma, can lead to violence because the creationist, having no evidence in support of his view, will become frustrated when challenged with evidence. The creationist typically believes that a supernatural being created him and that disbelief is evil. He is convinced of his moral superiority to the non-believer. Indeed, non-believers are threats, because they could spread their non-belief to others, contrary to his god's wishes.

Let's Have a Presidential Debate on Science and Technology

Politicians aren't scientists, but it's reasonable for the next President of the United States to be knowledgeable about basic issues in science and technology.

Today we're confronted by many threats and politicial choices for which a knowledge of science is useful. An understanding of the biological theory of evolution is helpful for dealing with the crisis of AIDS in Africa, the over-prescription of antibiotics, and the rise of resistance in tuberculosis and staphylococcus infections. A general understanding of biology more generally would be helpful in dealing with bioterrorism and stem-cell research. An understanding of physics would be useful in evaluating our priorities in outer space and the possibility of a dirty bomb attack. An understanding of chemistry and environmental science would assist our lawmakers in dealing with global climate change and ozone depletion. An understanding of astronomy would be helpful for evaluating the threat posed by meteoritic impacts. More generally, an understanding of how science works and the scientific method would help leaders to evaluate competing scientific claims and to distinguish science from pseudoscience.

Unfortunately, many of the presidential candidates seem more interested in establishing their religious bona fides then they are in dealing with science and technology. Some candidates seem positively anti-science: Mike Huckabee, for example, has shamelessly repeats an old canard about bumblebees being unable to fly by the laws of physics and seems to believe he is not a primate or descended from primates.

Today I join scientists and other science bloggers in calling for a national debate among presidential candidates on science and technology. Let's have a chance for the scientists and the public to ask the questions and hear the answers of those who would lead.

Paul Davies: "Too Busy" Writing Crappy Op-Eds to Justify Claims

Paul Davies, the British physicist and popularizer of science, wrote an astonishingly silly op-ed in the New York Times recently, in which he equates science and religion because both are based on "faith". It was a pleasure to see Davies' ideas completely shredded by Lawrence Krauss, Sean Carroll, and P. Z. Myers.

This isn't the first time Davies has said silly things. In The Fifth Miracle, for example, he attributes the ideas of algorithmic information theory to Gregory Chaitin, despite the fact that the Soviet probabilist Andrei Kolmogorov came up with them earlier (and despite the fact that nearly everyone calls the field "Kolmogorov complexity"). He also demonstrates his misunderstanding of Kolmogorov complexity when he says "Ordinary laws just transform input data into output data. They can shuffle information about but they can't create it." Of course, this is false. Take, for example, the transformation that maps a string x to the string xx. Then it is an elementary exercise in algorithmic information theory that the information (in the Kolmogorov sense) of xx is greater than that in x infinitely often. So, in fact, it is quite possible for "ordinary laws" to create information, in the Kolmogorov sense.

Also in the The Fifth Miracle, Davies makes the claim that quantum algorithms can make the solution of the traveling salesman problem "tractable" - a misconception so common that Scott Aaronson has resorted to debunking it in the masthead of his blog. It seems that when Davies pontificates about issues involving computational complexity and information theory, he cannot be relied upon.

Several years ago, Davies told me he would correct these mistakes (to his credit). But he's also been quoted as claiming, in Larry Witham's book By Design, that "Dembski's attempt to quantify design, or provide mathematical criteria for design, is extremely useful. I'm concerned that the suspicion of a hidden agenda is going to prevent that sort of work from receiving the recognition it deserves. Strictly speaking, you see, science should be judged purely on the science and not on the scientist." No surprise, Dembski flogs this quote whenever possible.

Two years ago, I asked Davies to justify his claims about Dembski. How, precisely, are Dembski's bogus claims "extremely useful"? Where have they been used? What about all the mathematical criticism of Dembski's work? Davies refused to justify his remarks, saying he was "too busy" to address them.

Now I see why he's "too busy". He's too busy writing silly op-eds for the New York Times.

David Klinghoffer, Meet Paul Nelson

Over at Jewcy, the repulsive David Klinghoffer offers up a defense of intelligent design, in response to Neal Pollack.

Jason Rosenhouse has taken time out from his forthcoming book on the Monty Hall problem to pen this response. As usual, it's incisive and worth reading. But there's one point that Rosenhouse didn't address.

Klinghoffer claims, "No Darwin critic that I know differs from established scientific conclusions about the age of the earth or of the universe since the moment of the Big Bang."

David Klinghoffer, meet your co-worker, Paul Nelson. Paul Nelson is a fellow at the Discovery Institute's Center for Renewal of Science and Culture. You know, the same place where Klinghoffer is Senior Fellow? Nelson is also a young-earth creationist; that is, he denies the scientific evidence for the age of the earth and the age of the universe, and instead claims the earth and universe are less than 10,000 years old. Of course, he doesn't do so because of the scientific evidence; he does so because his narrow, fundamentalist interpretation of the Bible tells him it must be so.

I suppose Klinghoffer can plead ignorance of Nelson's position. But it's hardly unknown. Nelson even contributed to a book entitled Three Views on Creation and Evolution, where he advocated the young-earth creationist point of view.

Remember when the Discovery Institute claimed "Faith healers and Holocaust deniers are not on the faculties of reputable universities. Scientists who support intelligent design are."? When that was shown to be a lie, did the Discovery Institute issue a retraction? Of course not: if they had to spend time retracting their lies, they wouldn't have the time to issue all those misleading and dishonest press releases.

There's a reason why the DI is called the Dishonesty Institute.

Narad Rampersad's Work on Combinatorics on Words

My student, Narad Rampersad, had a successful defense (or "defence", as they like to say in Canada) of his Ph. D. thesis yesterday. That's a good excuse to discuss some aspects of combinatorics on words.

In combinatorics on words, we are interested in words and their properties. By a word, I mean a finite or infinite string of symbols. The Norwegian mathematician Axel Thue initiated this field a hundred years ago in his study of infinite words avoiding squares and overlaps. A square is a word of the form xx, where x is a nonempty word. For example, the English word murmur is a square, with x = mur. Thue asked, is it possible to create an infinite word over a finite alphabet, such that it avoids squares (i.e., contains no squares)?

Over a two-letter alphabet, this can't be done: the first letter is 0, say. So, the next letter must be 1, otherwise we'd have the square 00. The third letter must be 0, for otherwise 011 would have the square 11. But then whatever you choose for the fourth letter gives a square.

Over a three-letter alphabet, however, it turns out you can construct an infinite word without squares. The construction is quite clever, and it was rediscovered by several people after Thue -- he published his work in a rather obscure Norwegian journal.

Thue also considered another kind of repetition avoidance: avoiding overlaps. An overlap is a pattern that is just slightly more than a square: it consists of two repetitions of a wordx, followed by the first letter of a third repetition. For example, the English word alfalfa is an overlap, because it consists of two copies of alf, followed by the first letter of alf.

Narad's thesis was entitled "Overlap-free words and generalizations", and he made several beautiful contributions to combinatorics on words. To describe one, I need the idea of a morphism, which is just a transformation of words defined by replacing each letter with a given word, and then joining all the results together. For example, consider the morphism μ defined as follows: replace each 0 with 01 and each 1 with 10. If I apply μ to a word like 011, I get 011010. I also need the idea of fixed point; a word is said to be a fixed point of a morphism if, when you apply the morphism, you get the same word back again. Thue discussed a special word

t = 01101001100101101001011001101001...

which is a fixed point of the morphism μ I just described. He proved the following amazing facts: first, the infinite word t contains no overlaps (we say it is "overlap-free"). Second, if an infinite binary word is overlap-free and is the fixed point of a morphism, then it either equals t or its complement, which is obtained by changing every 0 to 1 and vice-versa.

Narad generalized this last result of Thue. To explain his generalization, we need the notion of fractional power of a word. Consider a word like ingoing. We can consider this word to consist of ingo followed by the first three letters of the same word; in other words, it is a 7/4-power. More generally, a word is a k+p/q power if it consists of k repetitions of some block of length q, followed by the first p letters of that block. So the French word entente (which has been absorbed into English), is a 7/3 power.

What Narad proved is the following: the word t defined by Thue (and now called the Thue-Morse word) is the only one, other than its complement, that is 7/3-power-free and is a fixed point of a morphism. The proof is rather subtle and it appeared in International Journal of Foundations of Computer Science in 2005.

This is only one of many results contained in his thesis. I can't discuss them all, but I can't resist mentioning one other result, because it has a nice picture attached to it. Suppose we generalize our notion of infinite words to two dimensions: in other words, with every lattice point with non-negative integer coordinates, we associate some symbol. Then one can ask about avoiding squares in the plane: not just every row, column, and diagonal, but for every word defined by any line with rational slope. It turns out that one can indeed avoid squares in this case, as was shown by the Italian computer scientist Carpi in a beautiful 1988 paper; his construction used an alphabet of 16 symbols. Now instead of avoiding squares, suppose one only wants to avoid sufficiently large squares. Can we use a smaller alphabet in that case? Narad showed that if we want to avoid squares xx with the length of x greater than 2, then an alphabet of size 4 suffices. The construction can be illustrated by assigning each lattice point a square of a particular color, a different color for each symbol. Here's a portion of the result:



In January, Narad will be taking up an NSERC postdoc at the University of Winnipeg, to work with James Currie. Congratulations to Narad for a job well-done!

Debate at Waterloo

Tonight I debated Kirk Durston at the University of Waterloo on the topic, should a scientist believe in god? Eventually I'll post my slides and other information here, but for the moment, you can use this spot to post comments about the debate.

Here's my closing statement. I didn't get to read all of it because of time constraints (we were given only 5 minutes). If you read it, you will see the great debt I owe to P. Z. Myers and Carl Sagan.

Ridiculous Public Warning Signs

The Manifesto Club has a new campaign, Attention Please, to point out the absurdity of some warning signs in public places. Week 1 has a small collection of photos of silly warning signs, including one on a cactus that says "Caution: These plants are covered in sharp spikes that may puncture the skin if touched. DO NOT HANDLE".

I think they could use a much larger set of submissions, so go to it!

On Being Twice a Square

The last time my age was twice a square, I got married.

The time before that, I became of legal age.

This time around, my wife Anna decorated a finite automaton cake to celebrate. I shared it with my 4th year class on formal languages and parsing.

If Only All Theists Were This Modest

I've always been impressed with my colleague David Seljak's honesty and forthrightness. He's a professor at St. Jerome's University, a Catholic "church college" affiliated with the University of Waterloo. He sent me the following comments by e-mail and graciously allowed me to post them here:


"Christians ought to remember that normal, thinking people do not automatically see the sense in their claims. Indeed believers ought to be a minority. Even Paul says in his letter to the Corinthians. "but we preach Christ crucified: ...foolishness to Gentiles". This stuff is supposed to sound crazy to you guys. After all, we Catholics believe that if we eat the flesh and blood of a Jewish zombie who died 2000 years ago, our invisible friend in the sky will save us from death. :) Faith does not come "naturally"; that is why we call it a "gift". We should hardly be surprised when a number of people say, "no thank you, that sounds ridiculous." It seems to me that Christians should be a lot more humble about our truth claims and a whole heckuva lot more charitable to people who don't take them up."

I daresay that if all Christians were this honest and humble, the conflict between theists and atheists would dry up.

Taner Edis visits Waterloo

Taner Edis, a professor of physics at Truman State University in Missouri, and the co-editor of the anthology Why Intelligent Design Fails? visited Waterloo briefly last Friday. He gave at talk at Wilfrid Laurier University, down the street from me, on "Science and Religion in Islam". This is a topic of his recent book, An Illusion of Harmony.

I've known of his work for quite a while, but had never heard him speak in person. Edis is noteworthy in part because of his Turkish roots, which give him some insight into the Muslim world's flirtation with pseudoscience and creationism. And he is an extremely fair writer, in the model of Ed Brayton, who always tries to understand the other side's position and summarize it accurately.

He started by pointing out that different sciences have converged, through separate paths, on naturalistic explanations for the world. ( If I may quote Stephen Weinberg, "religious skepticism is not a prejudice that governed science from the beginning, but a lesson that has been learned through centures of experience in the study of nature." ) These explanations cast doubt on the reality of supernatural beings.

Scientific materialism, therefore, is a threat to modern religious belief, although technology itself is attractive. There are two kinds of responses: try to show that science supports religious belief (say, by finding passages in the Koran that supposedly presage modern scientific developments) or argue that "true science" is compatible with religion.

While there are many Christian sects that support a young-earth creationist view, in Islam, the old-earth creationist view predominates. There is a strain of Islamic creationism that originated in Turkey but has become popular world-wide. As an example, Edis passed around a truly revolting tract by Harun Yahya entitled Fascism: The Bloody Ideology of Darwinism.

Edis discussed two science-related "urban legends" that are widely repeated in Islamic communities. One was that Jacques Cousteau became a Muslim after observing that there is a salinity barrier in the Mediterranean which is supposedly mentioned in the Koran.

Edis pointed out that Muslims who advance pseudoscience are not opposed to all science and technology. As an example, he cited the Nur movement, whose followers are very pro-technology.

Edis stated that Darwinian evolution, particular human evolution, is not widely accepted in Islam because a naturalistic process with random elements is unacceptable theologically. Islam differs from Christianity in that Christianity has a large number of moderate sects that view science as a separate domain, while Muslims typically see science as subordinate to the revelations of the Koran. Liberal Muslim views are much rarer than liberal Christian views.

Edis pointed out that Muslim countries are very weak in science, although applied science does better than basic research. Those who point out that creationism is pseudoscience are labeled as "secularist".

Altogether, I found Edis' talk to be informative and well-presented. I can't say as much, regrettably, for the questions that followed. I was startled at how incoherent some of the questions were, and some questioners didn't seem to listen carefully to his replies, apparently preferring to base their remarks on caricatures.

A Muslim woman who said she was a professor of chemistry at Wilfrid Laurier (probably this professor) made two statements. First, she said that, as a chemist, she saw no conflict between science and her religion, because Islam instructs its followers to be seekers after truth. Second, she disputed the title of the talk, saying that "Science and Religion in Islam" was misleading because the talk was not about the true Islam. In other words, she employed the "No True Scotsman" fallacy.

In reply, Edis correctly observed that chemistry enjoys a slightly different position than physics or biology. Some aspects of physics and biology (e.g., cosmology, evolution) provide explanations for the world that are significantly at odds with religious claims. Chemistry, however, seems to intrude less significantly into what has traditionally been perceived as religion's domain.

Edis rebutted her second statement by pointing out that, as a non-believer, for him there was no "true Islam", but only a variety of different Islams as practiced by different religious groups. He said it would be arrogant for him to pick one of these Islams and declare it as the true Islam; that was for believers to decide. His concern was to examine Islam as it was actually practiced.

Another Muslim questioner heard Edis' response about chemistry and didn't seem to grasp the distinction Edis was making, saying that he had dismissed chemistry as less important than biology or physics (something not even remotely implied by Edis' reply). The same questioner dismissed the theory of evolution as just one explanation among many.

It was an interesting afternoon, and I only wish I had had more time to discuss with Edis after the talk.

Students Want Me to Do Their Homework

I often get e-mail messages from students in other countries. They pose a problem to me and ask for its solution, and they usually include a note to the effect that this is for their "personal research".

Now, I don't want to be hard on the students. After all, maybe some of these requests are genuine. As a young student, I occasionally wrote to famous mathematicians (or people I thought were famous mathematicians) with questions, and I was often pleased to get a reply. I still treasure postcards and letters from people like D. H. Lehmer and Daniel Shanks. I would have been very hurt and insulted to get a note saying, "Don't ask me to do your homework for you", because my questions always derived from my own adolescent research.

Nevertheless, I'm often suspicious of these requests, because my guess is that most of them come from students who are too lazy to do their own homework problems, and want me to do them instead. E-mail has made it feasible for a student to receive a homework assignment, search the web for people working in that area, pose the problem to a professor, and get a result back, all in less than 24 hours -- in plenty of time to hand in for a homework assignment. That wasn't possible when communication was by postal letters. And there is definitely a different flavor between a genuine research problem (which I often receive from colleagues) and the kinds of questions these students ask.

So what to do? My solution is to respond that I am happy to answer these questions if the students ask the question again in a month. That way, if the question comes from a homework assignment, in a month the answer probably won't do the cheating student any good. If the question is genuine, and the poser really wants to know the solution, waiting a month won't hurt too much.

I throw it open to my audience: what other possible strategies are there for answering these kinds of queries?

The Discovery Institute's Latest Fellow, Mahmoud Ahmadenijad?

First, read this transcript of Iranian President Mahmoud Ahmadinejad's talk at Columbia University.

Now, ask yourself: wouldn't he be perfect as a Discovery Institute fellow?

The Discovery Institute wants to allow supernatural causation in science, "to reverse the stifling dominance of the materialist worldview, and to replace it with a science consonant with Christian and theistic convictions." (Wedge Document)

Ahmadinejad says "One of the main harms inflicted against science is to limit it to experimental and physical sciences..." and "... the material is just a shadow of supreme realities..."

The Discovery Institute wants us to "teach the controversy" about evolution. Ahmadinejad wants us to teach the controversy about the Holocaust: "...if, given that the Holocaust is a present reality of our time, a history that occurred, why is there not sufficient research that can approach the topic from different perspectives?"

I think the Discovery Institute should move quickly to hire him, before Ahmadenijad is offered a position at the Institute for Historical Review.

FaithMB = (Ignorance) + (Intellectual Dishonesty)

Marvin Bittinger is a retired professor of mathematics education and author of many textbooks. From Pharyngula I learned about his new book, The Faith Equation: One Mathematician's Journey in Christianity.

The "Faith Equation", it turns out, is this: Faith = (Mind) + (Heart) + (Will).

Now, after you've stopped laughing, here is my revision of his equation:

Faith_MB = (Ignorance) + (Intellectual Dishonesty)

Now I wouldn't be so arrogant as to claim that everyone's faith is based on the pillars of ignorance and intellectual dishonesty; I know a lot of skeptical, searching, intellectual Christians. Here the subscript "MB" on faith indicates that it only refers to the faith of one Marvin Bittinger.

Why do I say intellectual dishonesty? First, there's the matter of Biblical prophecies. Part of Bittinger's book deals with various prophecies in the Bible. He considers each one, evaluates its probability, and multiplies the probabilities together to get a very small number. He concludes the result shows that the fulfillment of these prophecies is a miracle. I'll point out that claims of Biblical prophecies that can be easily dispelled by reading TIm Callahan's book, Bible Prophecy: Failure or Fulfillment?, but that's not my main point. No, the main point is Bittinger's claim here that "the Bible contains hundreds if not thousands of prophecies which have come true, with none failing".

None failing? How about the prophecy in Matthew 24, where Jesus lists a number of coming events, such as "sign of the Son of man in heaven" and "angels with a great sound of a trumpet", etc., etc. and then says "This generation shall not pass, till all these things be fulfilled." Well, it's 2000 years later, and none of these things have happened.

The second example comes here, where Bittinger claims "Whether the earth is 10-15 billion years old (old-earth opinion) or 5-6 thousand years old (young-earth opinion) is subject to debate in scientific and theological circles". Here Bittinger shows his ignorance, because nobody claims the earth is 10-15 billion years old. The current best estimate for the age of the earth is about 4.5 billion years, and this is based on multiple lines of evidence.

The intellectual dishonesty comes in because it is not true to say that the age of the earth is "subject to debate in scientific ... circles". There is simply no debate. The evidence for the 4.5 billion year age is so strong, and the evidence against is so weak, that the question simply does not come up any more.

Another example: on page 49, Bittinger claims, "Our nation was founded on the motto 'In God We Trust'". That will certainly be news to historians, who will point out that (a) the Constitution is a secular document that doesn't mention "God" and (b) the unconstitutional motto "In God We Trust" was only approved in 1864, long after the US was founded.

The really depressing thing is that this combination of ignorance and intellectual dishonesty is the norm in Christian apologetic circles. As evangelical Mark Noll once wrote, "The scandal of the evangelical mind is that there is not much of an evangelical mind." Too bad Marvin Bittinger did not heed his warning.

By Jove, I Think He Doesn't Get It: A Night with Professor Higgins

Michael Higgins is a Catholic religious scholar, author, and local legend who is currently President of St. Thomas University in Fredericton, New Brunswick. Last night he delivered the inaugural Michael Higgins Lecture at St. Jerome's University, a church college affiliated with my own university, the University of Waterloo. The title was, "It's Tough Being God These Days", and the main theme was the new atheism.

A night with Prof. Higgins is always entertaining, as he is a witty and erudite speaker. At one point, speaking of atheists, he said, "We used to burn them", which got a good laugh. Despite his wit and erudition, I have always found Higgins' talks unsatisfying. To me, a Higgins talk is best likened to eating at an overrated Parisian restaurant. You are taken with the setting and the opulence and the view of Notre Dame. But then the food comes, and you are disappointed to discover that most of the effort has been expended on the surroundings, and little on the meal itself.

Last night was no exception. There was a bit of chest-pounding against atheism and the usual suspects of Dawkins, Hitchens, and Dennett, a rather dispirited defense of religion and an acknowledgment of some religious sins, a brief theological analysis concluding that "God is big", and a limp finish that consisted of quoting some of his favorite religious writers. I left hoping for more.

Unlike some Catholic commentators, Higgins takes the current wave of atheism seriously. He views it as a significant trend, labeling it a "virulent and subcompetent atheism" that is "seismic in its implications". However, he thinks the arguments are nothing new: "everything originated in the 18th and 19th centuries". He denigrates the "industry" of atheist writers such as Dawkins, Hitchens, and Dennett, arguing that their books are "aggressive and vituperative". Their hubris is "stunning". They ridicule "without fear that it is indecorous or unjust".

Higgins is very impressed by John Cornwell, who wrote a reply to Dawkins. He quoted Cornwell as saying that in the past, atheists were content to dispute the arguments of believers, but the current wave of atheists likes to ridicule the believers themselves. (But listen to this interview with Cornwell and Dawkins, where Cornwell is caught blatantly misrepresenting what Dawkins had to say.)

To his credit, Higgins says that religion is partly to blame. The new wave of antipathy is, he admits, "religion's own fault". He cites religion's "capacity for terror" and cites as an example "honor killings". "Religion's capacity to divide is considerable," Higgins concedes.

But it's too easy, Higgins says, to blame the excesses of religion on religion. Honor killlings do not represent religion, but terror. "No holy man" could ever claim terrorist acts as "a life-giving force". The issue, Higgins argued, is not to eliminate religion, but to eliminate the caricature of religion, to delegitimize those who speak on behalf of religion but do so inauthentically.

Atheists have the spotlight now, Higgins says, and so the media interprets religious stories in that light. The recent revelations about Mother Teresa were not interpreted according to the "theology of God's absence", but rather that she was a hypocrite or worse.

Luckily, he observed, theists outreproduce atheists, so there is little danger. The answer to the new atheism is not in "noble silence". "God is bigger than our systems" and "Once we recognize God's bigness we recognize our own fanaticism". There must be "respect between people of faith" and "Catholicism can lead".

Now, my analysis. Higgins claimed that those who attack religion are ignorant of it. He even went so far as to suggest, in answer to a question, that Hitchens was mentally unbalanced. I have a two-word answer: courtier's reply.

Higgins says that the new atheism engages in a "caricature" of genuine religion. My reply: look around you. We have a local Catholic school board actually debating whether to give the HPV vaccine to girls, not because of the cost or the unproven nature of the vaccine, but because it might encourage them to engage in sexual activity. We have Muslims rioting and killing in Pakistan because of a rumor that a Christian had desecrated the Koran, all the while insisting that Islam is a peaceful religion. We have Mother Teresa working with poor and sick people, while refusing to endorse the birth control that might genuinely help them. We have Jerry Falwell blaming 9/11 on "pagans, and the abortionists, and the feminists, and the gays and the lesbians". It's not possible to caricature religion because, these days, religion caricatures itself.

I'm sure that Higgins would reply with a version of the "No True Scotsman" fallacy, because that's what he did in his talk. These kinds of actions, Higgins would say, are not genuine religion. I say, they represent genuine religion for millions of believers, and they find their justification in the holy texts themselves. Look at Kirk Durston, a local religious leader who excuses genocide in the Bible when God does it. Look at Muslims who draw their inspiration for violence from passages in the Koran such as “Believers, make war on the infidels who dwell around you. Deal harshly with them.”

I'm not saying all religious believers are of this stripe; far from it. But religion has been treated with kid gloves far too long. Higgins decried the treatment of religion in the media, calling it shallow. But when did you ever see a believer quizzed in the pages of your local newspaper about whether their beliefs are supported by evidence? Or if their beliefs are genuinely beneficial to society? In my local newspaper, faith is always treated as a positive aspect to one's personality. I see skepticism, not faith, as more worthy of respect. "There lives more faith in honest doubt, Believe me, than in half the creeds."

There was time for a few questions, and here's the one I asked. I asked why is it, when theists want to attack atheism or science, they often use religious language to do so? As examples I cited this article by a theist who suggested that evolutionary biologists answer criticism of evolution with "Darwin said it, I believe it, and that settles it," which is evidently a reference to the famous bumper sticker with "Jesus" replacing "Darwin". I pointed out that Prof. Higgins himself used this language, when he favorably cited another writer as referring to "evangelical atheists". In reply, Higgins first took exception to my use of the word "theist". (Hey, I was just trying to be inclusive; what word woud he have me use?) Then he denied that this tactic was frequently used. I find it hard to take his answer seriously, as there are many more examples. To cite just one, fellow Catholic writer Denyse O'Leary refers to the new atheism as an "anti-God crusade". Not only do theists use this religious language in attacking atheists, they use religious language that recalls the worst aspects of religion.

In the end, I don't think that Professor Higgins gets it. The new atheists have been emboldened by religion's excesses, but they don't base their arguments on that alone. Fundamentally, the new atheists are simply not convinced by religion's claims. When we hear Higgins assert that "God is bigger than our systems", we want to know, where's the evidence that what you are talking about even exists? We don't see God-talk as helpful in resolving issues; when God-talk is introduced, it moves us away, rather than towards, a solution based on rational consideration of the issues. Higgins wants to appropriate human values, such as compassion and tolerance, to religion's domain, but these values are subscribed to by theist and non-theist alike. In the end, religion doesn't have as many virtues as Higgins claims, nor does the new atheism have as many faults as he would have us believe.

Funding Ontario Religious Schools, Revisited

For comedy, there's nothing better than the protestations of the principals of local religious schools, as they try to assure us that, should they get provincial funding, they'll really be no different from other provincial schools. Previously, I pointed out that Bob Moore, principal of Guelph's John Calvin Christian School, doesn't seem to know what the word "evolution" refers to. He apparently thinks it has something to do with "origins of the universe".

Now, in the September 12 issue of the Kitchener-Waterloo Record, principal Julius de Jager of the Cambridge Christian School is the next to demonstrate significant confusion. He states that the Ontario curriculum document "does not require a teacher to teach as fact the Darwinian theory of adaptation". The poor muddled fellow can't even bring himself to use the word "evolution", it seems.

Next, de Jager adds, "Nor does it [the curriculum document] preclude a possible explanation that God created an amazing diversity in plant and animal life." Oh, right. That really sounds like science.

Guys, if you're trying to convince us that religious schools should get funded, you're doing a pretty bad job.

Objective Journalism

The current wave of interest in atheism, fueled by religion's excesses, really does represent something new. For proof, consider the photo below, sent to me by a colleague, from an independent bookstore he recently visited:



This kind of display would have been simply unimaginable at any other time in the history of North America.

And today, Representative Pete Stark (D-CA) will give his first speech after coming out as a non-theist. Again, I can't imagine any congressman having the guts to admit this in the past 50 years. (Maybe in the age of Ingersoll, but not recently.)

To any reasonable observer, these kinds of events do signal some kind of sea change in opinion.

But then, "journalist" Denyse O'Leary isn't a reasonable observer.

My parents were journalists, so I learned something about the proper practice of that craft from them. All journalists have biases, but good journalists learn to recognize them, so they don't say remarkably stupid things like, "the [atheist] crusade exudes an unmistakable air of desperation". Good journalists actually interview people who disagree with them, and summarize their views fairly.

Ahh, but fairness and objectivity mean nothing when God's on your side.

It's All About the Science, Right?

These intelligent design advocates crack me up sometimes. While the leaders furiously insist that 'it's all about the science', the grass roots behind them are constantly giving away the store.

Check out this barely literate solicitation from the elders at Trinity Baptist Church in Norman, Oklahoma, where they are trying to raise funds to bring William Dembski to speak at OU. Could the religious motivation be more clear?

"Our prayer for this entire effort is for God to open doors so the power of His gospel would be made known to groups of people who need to hear the truth."

This group is so intellectually bankrupt that they don't seem to care whether or not Dembski's claims are true -- they only want to use him as an evangelical tool. (And if they really needed $10,000 for the event, they might wind up financially bankrupt, too!)

I want people to understand and accept the theory of evolution because it's true, because it makes a nontrivial statement about the world we live in, because it's essential to understanding HIV, drug-resistant tuberculosis, and other important public issues, because it offers deep insights into why we behave the way we do, but not because it will 'lead people to atheism'. I'd much rather have scientifically-knowledgeable theist neighbors than ignorant atheist ones.

That's a Nice Rack!

Here's a moose with a great rack of antlers. Photo courtesy my graduate student Dalia Krieger, who snapped this on a recent backpacking trip in eastern Canada.

How Do You Read Recursivity?

If you'd like to receive Recursivity via a news feed, then try these links:

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and let me know how they work for you.

David Warren's Ignorance

David Warren continues to display that special blend of arrogance and ignorance that could be named after him, if Michael Egnor hadn't already been eponymized.

In this column he writes:

It is because Darwinism has embedded itself so deeply into the assumptions of our age, that it must be attacked frontally. For Darwinian assumptions cloud our view of reality. They subvert our grasp of moral issues. They make it possible for people to be dismissive, not only of art, philosophy, and religion, but of the requirements and limitations of true scientific research. They eviscerate the human spirit, by insisting that, in the last analysis, everything is random and meaningless. Conversely, they justify true fascism (“survival of the fittest”), and all the horrors of eugenics, abortions and euthanasia.

Moral relativism could not stand, except on a Darwinist base, and reason itself is rendered defenceless, by the notion that all nature was randomly contrived.


I don't know why theists like Warren continually trot this nonsense out. Darwinian evolution is a scientific theory about evolution that explains the diversity of life as we see it today. If it has implications that are depressing or repugnant to Warren, then too bad. As paleontologist George Gaylord Simpon wrote, If a sect does officially insist that its structure of belief demands that evolution be false, then no compromise is possible. An honest and competent biology teacher can only conclude that the sect's beliefs are wrong and that its religion is a false one.

Warren claims "Darwinian assumptions ... subvert our grasp of moral issues". He is foolish and mistaken in two ways. First, Darwin's theory is not an assumption, but a conclusion, based on hard research by hundreds of biologists, theist and non-theist alike. Second, Warren apparently knows nothing at all about current work on the evolutionary origins of ethics. I happen to think that Richard Alexander's book, Darwinism and Human Affairs, is one of the deepest and most profound works ever written on morals. If Warren has read it, I'll eat my hat.

Evolution says nothing like "everything is random and meaningless". Randomness plays a part in evolution, but it isn't the whole story. Randomness is represented by mutations and accidents, but selection -- a decidedly non-random process -- is also essential.

Warren confuses the descriptive nature of "survival of the fittest" with a prescription: this is how we ought to behave. But of course, he knows so little about evolution that he doesn't understand that co-operation is not ruled out by evolution, but rather is a result of it; see, for example, The Evolution of Cooperation.

Warren is the perfect blowhard. Supremely confident in his assertions, and demonstrating his supreme ignorance at the same time. Why the Ottawa Citizen continues to employ him is a mystery.

On Design

Well, since Michael Egnor has sort of answered my questions, it's time for me to try to answer his. I'll try to be less evasive than he was.

One thing I'd like to point out is that Egnor seems to be under the misapprehension that the information theory that mathematicians and computer scientists actually study has something to do with inferring design.* This is simply not the case. Open up, for example, the book on Kolmogorov complexity by my colleague Ming Li, and you won't find a word about inferring design. (It's ID advocate Bill Dembski, of course, who is largely responsible for this confusion.) So, contrary to what Egnor thinks, as a mathematician and computer scientist I have no particular expertise on the general topic of "inferring design". It's just not something we do; maybe he should ask a SETI researcher, or a forensic investigator. But then again, Egnor has no particular expertise on the topic, either.

First, some general remarks about "design". I'll start by saying that I don't know exactly what he means by "designed". One of the favorite games of ID advocates is equivocation, so it's important to pin them down on a precise meaning. ID advocates rarely say plainly what they mean by "design". Do they mean simply that something has a pattern to it (as in "the design of a snowflake"), or do they mean something that has a "function", or must there necessarily be some teleology involved? I think it's incumbent on ID advocates to make clear what they mean. But I'll look at all three possibilities.

If ID advocates intend the first meaning ("pattern"), then the answer is clear: design need not imply a designer. The world is full of patterns that arise from the constrained nature of the physical universe. We can explain the overall pattern in a snowflake, for example, by referring to the symmetry in a water molecule in ice combined with the homogeneity of conditions as the snowflake forms. We don't normally bring in supernatural beings to explain snowflakes.

ID advocates, such as Bill Dembski, have nevertheless tried to rescue this hopeless case by bringing in probability. Dembski has argued that if an observed event fits a pattern, and the probability of this fit is extremely small, then the event must be due to design by an intelligent being. But as Wesley Elsberry and I have shown, his claim is based on incorrect mathematics combined with specious arguments. Dembski likes to say something on the order of 'witnessing specified events of low probability implicates design'. But the correct claim is merely 'specified events of low probability are never witnessed at all; if they are, that is prima facie evidence that your probability estimates are wildly off'.

Here's an example: there's a fellow with a web page who claims to have witnessed at least three independent meteorite falls. (The pictures he shows aren't meteorites, but let's ignore that for a moment.)

Now this page suggests that the probability of witnessing a meteorite land near you during your lifetime is about 1 in 2.5 million. So if the events are independent, we conclude that the probability of a particular person witnessing 3 meteorite falls in their lifetime is about 1 in 16 million million million. Even taking into account the total population of the world, this fellow's claim seems extremely unlikely. Could it have happened? Yes, but if so, we would have to consider some other possibilities: maybe the distribution of meteorite falls is extremely uneven, so that many more meteorites fall at this fellow's location than others. Maybe somebody's having him on, shooting meteorites out of a cannon towards his house. Maybe there's some other explanation entirely. In either case it's not that a specified event of low probability was witnessed; it was that our probability estimates were wrong. Dembski says design must be inferred when all other explanations are ruled out, but if my analysis is followed, inference to design no longer has the privileged place that Dembski accords it.

The second possible meaning of "design" corresponds to the inferred function of some object; this is basically the old argument of William Paley involving the watch found on the heath. While this argument may have been convincing two hundred years ago, it's convincing no longer, for the obvious reason that we know that evolutionary processes can produce function. We have good experimental evidence of this from novel mutations that, for example, allow some bacteria to digest nylon byproducts. As a computer scientist, I must also cite the artificial life experiments of Karl Sims, who showed how nontrivial and novel behaviors could evolve through mutation and selection -- something Dembski claims is impossible. Dembski has never addressed Sims' work.

The third possible meaning of "design" involves teleology; we infer a designer when we see something designed for a purpose. But either this begs the question, or it reduces to the previous paragraph about "function". So in all three cases, I don't think that seeing "design" implies a "designer".

ID advocates are always accusing others of 'wanting to eliminate the design inference from science'. Of course, this is pure nonsense. Archaeologists, for example, routinely attempt to deduce the roles that various objects played in the lives of the cultures they study. But, as Elsberry and Wilkins point out in their article from Biology and Philosophy, there is a huge difference between inferring design based on artifacts for which we have a causal story like human construction, and inferring design based on some causal story lacking any details whatsoever. They refer to this latter attempt, commonly used by ID advocates, as "rarefied design", and characterize it as "based on an inference from ignorance, both of the possible causes of regularities [that might explain the event] and of the nature of the designer."

One more point: I don't think that the question "is it designed?", in the absence of any candidate for a designer, is particularly interesting. That is, in the absence of motive, I don't think that knowing that something is designed tells you anything at all. I can do no better than to quote from Elsberry and Wilkins, who say

The problem with a simple conclusion that something is designed, is its lack of informativeness. If you tell me that skirnobs are designed but nothing else about them, then how much do I actually know about skirnobs? Of a single skirnob, what can I say? Unless I already know a fair bit about the aims and intentions of skirnob designers, nothing is added to my knowledge of skirnobs by saying that it is designed. I do not know if a skirnob is a good skirnob, fulfilling the design criteria for skirnobs, or not. I do not know how typical that skirnob is of skirnobs in general, or what any of the properties of skirnobs are. I may as well say that skirnobs are "gzorply muffnordled", for all it tells me. But if I know the nature of the designer, or of the class of things the designer is a member of, then I know something about skirnobs, and I can make some inductive generalizations to the properties of other skirnobs.

Now to Egnor's question. He wants to know why SETI is different from deducing design in biological systems. Referring to the fictional movie, Contact, where scientists received a blueprint for constructing a mechanical device, he asks, "If the scientific discovery of a ‘blueprint’ would justify the design inference, then why is it unreasonable to infer that the genetic code was designed?"

The answer is that I don't think that these situations are at all comparable. In the case of SETI, the fact that we are receiving a narrow-band signal is already suggestive, since we don't currently know any simple physical process that could produce these signals. This isn't a definite conclusion, though, because we have no idea what the probability of intelligent beings is, and we can't rule out narrow-band signals arising from some other physical process we simply don't know about.

In SETI, we are specifically looking for intelligent beings. These beings presumably live in another part of our universe, and presumably they evolved through natural processes, in much the way we did. This being the case, we hypothesize that, like us, these beings are interested in contacting other intelligent life, and would do so through radio waves. All these are assumptions based on our characterization of the "personality", if you will, of the originators of the signals. If any of these guesses are wrong, or if we are alone, we won't succeed. Our argument is based on analogy with our own thought processes, not "specified complexity" or other ID nonsense.

ID advocates, however, rule out any deductions based on the identity of the Designer. Yet, in real science, questions about intention and identity arise all the time in archaeology. To give just one example: in the 1890's, historian Arthur Evans heard of mysterious seal-stones from Crete. The identity of their creators, as well as the script used, was then unknown. Evans went on to identify the stones as the product of a civilization now called Minoan, and eventually one of the scripts, Linear B, was deciphered. The fact that ID advocates refuse to consider the really interesting scientific questions "who designed it?" and "why did they design it?" shows that they're not doing science.

To say that SETI is like the genetic code means that we have to hypothesize some designer who designed something for some reason. But where's the designer? In SETI, we can pinpoint a place in the universe where the signals are originating from. If the signals encode a machine, we can reasonably deduce that the intention is that we are to build it. But in the genetic code, who is the hypothesized designer? Where did they originate? When did they carry out their design? What is the intention of the design? All the really interesting questions are ruled as 'out of bounds' by ID advocates. Until they really come to grips with these questions, they're doing religion, not science.

As an example of something I'd find convincing, if we were to find a crashed spaceship with plans showing how to build a bacterium, and scientists carried out these plans and found that they really did construct life, then I'd find this very strong evidence that life on earth was designed.

Another point of disanalogy is that we know that DNA changes and evolves through time by processes such as mutation, gene duplication, and selection. There are even some very tentative answers to how the genetic code evolved. So the alternative hawked by ID advocates, that 'somebody made this sometime for some purpose, but we don't know where, when, or how', is not very impressive. In exactly the same way, a theory that lightning is 'caused by some intelligent being, but we don't know exactly how or why' is not very impressive, either.

Finally, DNA doesn't carry any of the hallmarks of human design, the kind of design we are most familiar with. Genes, for example, are often pleiotropic; they have multiple interacting effects. Human design, on the other hand tends to separate systems so they don't interact. Human activities tend to produce texts that are quite compressible; but a typical genome is hardly compressible at all. Biological entities reproduce themselves, but few, if any, human designs have this property. When we consider an analogy, like the one Egnor proposes, to be fair, we have to consider points of disanalogy, too. (For more examples of disanalogy, see Mark Isaak's article in Reports of the NCSE, Volume 23, no. 5-6.)

Let's alter the Contact story. Suppose the signal didn't encode a machine, but rather a sequence of DNA bases S. When we create DNA corresponding to this sequence, and stick it in a cell, we get an organism that tells us all about life on some other planet. Now the analogy is even closer than before; yet I think it is clear that our inference about the origin of S is still different from any inference about our own DNA. Indeed, it is entirely reasonable and scientific to infer that S is designed by intelligent beings on another planet, but our own DNA evolved.

Finally, on an unrelated note, Egnor takes me to task for my lack of civility. This is pretty rich, considering that Egnor's buddies at the Discovery Institute routinely insult the appearance of scientists, call them dishonest, and play games such as adding fart noises to Judge Jones' Dover decision. I say, clean your own stable first. Scientists are angry at the constant misrepresentation and juvenile antics of ID advocates, and we're not going to take it any more.

* Addendum: Because ID advocates have a track record of misunderstanding even the most trivial point, I should add that of course information theory could be used to separate, for example, human-generated text from noise. As I already mentioned, natural language text is quite compressible, while noise would probably not be compressible. But here we are not detecting design per se as some abstract category; rather we are using an empirical distinction between two things we have observed: natural language text, and noise.

Towards a Canadian Republic

Good news for people who find the loyalty oath to the Queen --- a requirement for becoming a Canadian citizen --- to be an embarrassing anachronism inconsistent with Canada's devotion to "freedom of thought, opinion, and expression". Charles Roach and his group, Citizens for a Canadian Republic, are back in the game, thanks to a judge's dismissal of a shameful motion by Canada's Attorney General to prevent the suit.

Should Discovery Institute Spokesmen Be Charged with This Offense?

Excessive mooing.

José González does Dawkins

I don't watch TV, but even I know about this amazing Sony ad featuring the music of José González and 250,000 bouncing colored balls:



González is a Swedish musician, and the song in the ad is "Heartbeats", a cover of a song from a group called "The Knife".

Now he has a new album out, and guess what? It's based, at least in part, on Richard Dawkins.

I know what I want for my birthday!

More Egnorance

Well, I see Michael Egnor is at it again.

He calls my my response "odd". Apparently, where Dr. Egnor comes from, it is considered "odd" to object when someone manufactures fake quotes and attributes them to you. No apology from Dr. Egnor is forthcoming, however.

Dr. Egnor says nothing at all about the fact that both he and Tom Bethell think that SETI researchers look for prime numbers to detect intelligence, when in fact SETI's own website approvingly quotes Louis Narens explaining why this might not be a good idea. (Thanks to Eric for pointing this out.) Apparently, where Dr. Egnor comes from, it is considered bad form to retract phony claims.

Dr. Egnor says nothing at all about his friend Tom Bethell's support for crackpot views on AIDS. Apparently, where Dr. Egnor comes from, if you discourage efficacious treatment for a life-threatening disease, that's just fine. He's in good company: other prominent creationists, such as Phillip Johnson, maintain the same views. Here's an issue where a word from Egnor, a medical doctor, could really have an impact. The silence from Dr. Egnor is deafening.

No, what really gets Dr. Egnor all worked up is the fact that I didn't answer his question (although the answers in the responses at the Panda's Thumb seemed pretty good to me).

In the meantime, I sent the following question to Dr. Egnor by e-mail:


Dear Prof. Egnor:

I wonder if you see any irony in the fact that, while intelligent design proponents are complaining about the suppression of their views and the unwillingness of scientists to debate, you attack me from a weblog that does not allow comments, while the Panda's Thumb and Recursivity are open to comments from everyone ... including you.

Regards, Jeffrey Shallit

P. S. Is it your general practice to steal copyrighted photos from people's websites without asking their permission?


So I'll make you a deal, Prof. Egnor: you answer my questions, and I'll answer yours. You first.

P. S. If you're going to cite me, Prof. Egnor, please spell my name correctly. Thanks.

Aww. Michael Egnor Notices Me

Well, I see that physician and Discovery Institute shill Michael Egnor has noticed me.

Egnor, a man whose arrogance and ignorance has already led to the coining of a new word, is unhappy about my critique of Tom Bethell. So unhappy, in fact, that he has to resort to forging fake quotes from my article.

Egnor claims that I called Bethell "a liar" - he uses those two words, and puts them in quotes. Any reasonable person would come to the conclusion that they appear in my article. Only problem is, the word "liar" doesn't appear anywhere in my piece, as a text search will easily confirm. Gee, a Discovery Institute spokesman misleading the public - what is the world coming to?

What I said was, "Bethell then goes on to repeat a common lie of the intelligent design movement..." Repeating a lie doesn't necessarily make one a liar; it is possible to repeat a lie from sheer ignorance.

Next, Egnor misrepresents the thrust of my observation about SETI. Egnor says, "Professor Shallit ridicules Bethell’s observation that Search for Extraterrestrial Intelligence (S.E.T.I.) research demonstrates that, under appropriate circumstances, the scientific inference to intelligent design in nature can be a legitimate interpretation of data." Actually, I did nothing of the sort. If we were to receive a coded message from outer space reading "Welcome earthlings! We are your reptilian overlords. Submit or be absorbed!", I would gladly join the hordes defending our beloved planet from invaders.

What I actually was objecting to - and it would be clear to anyone with connected brain cells - was Bethell's false claim that the people at SETI carry out their objectives by looking for "such things as a sequence of prime numbers". They don't look for prime numbers at all, as I showed by quoting directly from the SETI web pages.

Egnor makes the false claim that Bethell was just using an example from the fictional movie Contact. Although prime numbers do appear in Contact, Bethell said nothing at all about that movie, as a simple text search of Bethell's article will show. Bethell's claim was about what SETI researchers actually do; his claim was incorrect, and Egnor still doesn't understand why.

I find it strange that Egnor, a medical doctor, would defend Bethell, a man whose command of science is so unhinged that he has problems with relativity and thinks there is no AIDS epidemic in Africa.

Addendum: there's also a delicious irony involved in Egnor's post. The DI and intelligent design proponents are always whining about how legitimate scientists want to shut down debate about ID. Egnor's post, however, is on a web log that doesn't allow comments. The Panda's Thumb and Recursivity, by contrast, permit and encourage comments. Who, really, wants debate?

Bethell the Buffoon

Check out the final exchange about intelligent design between John Derbyshire and Tom Bethell, where Bethell insists that creationism and intelligent design are as different as chalk and cheese. (Part 1 here; Part 2 here.)

In it, Bethell demonstrates once again why he is a blathering buffoon. Bethell tells us that "Structures or signals of specified complexity permit an inference to design without any necessary recourse to the supernatural" without bothering to mention that "specified complexity" is junk mathematics and doesn't permit an inference to anything at all, except that Bethell is rather gullible to accept William Dembski's assurances as gospel.

Bethell then goes on to repeat a common lie of the intelligent design movement: that the SETI Project (Search for Extraterrestrial Life) spends its time looking for "such things as a sequence of prime numbers". Sorry, Tom, that was the movie "Contact". You know, fiction?

In real life, SETI researchers look for look for narrow-band signals, because such signals don't appear to originate from simple systems, and because we believe intelligent beings, if they exist, would use a method of communication similar to ours. Repeat after me: SETI detection doesn't use prime numbers, "specified complexity", or red herrings. Bethell claims he's actually visited the SETI project, so how come he doesn't know this? Is it dishonesty, or simple stupidity?

Next, Bethell shows a profound misunderstanding of information theory when he claims, "Francis Crick, the co-discoverer of the structure of DNA was asked how the all-important coding information found its way into the DNA in the first place. It's so complex that a reliance on random events will never get us there." Bethell apparently doesn't understand that in the Kolmogorov theory of information, complexity is the same as randomness. It's easy to get complexity; all you need is a source of random events.

Here's a funny one: early on, Bethell solemnly intones that "Science is not properly based on authority, however." Later, however, in discussing the RNA world hypothesis, he says, "But I'm told that the alternative, the "RNA world," has huge complexities of its own. It's all pure guesswork." Oh. So he's been told that the RNA world hypothesis has problems, and he apparently accepts that without even looking into it. But I thought science wasn't based on authority? Mr. Bethell, meet your opponent, Mr. Bethell.

Mr. Bethell needs a good closer, so to finish up he reaches deep into the creationist playbook and comes up with the Colin Patterson story. It goes without saying that Bethell gets the details wrong; Patterson, for example, did not deny common descent. For the sake of argument, let's pretend for a moment that Patterson is on Bethell's side. Then the point of Bethell's misremembered anecdote is that we should rely on the authority of Colin Patterson, but not on the authority of all the other biologists who accept that evolution is the best explanation we have for the diversity of life as we see it today.

Altogether, a rather unimpressive performance for Mr. Bethell, who has been denying evolution for 30 years without learning anything about it. Funny -- he behaves just like a creationist.

Principal of Local Christian School Gives Away the Store

As I've previously discussed, there is a current push by some religious groups and the Ontario Tories to fund private religious schools. John Tory, leader of the Conservatives, awoke a firestorm of controversy when he stated that it would just fine if Christian schools decided to teach creationism.

In a September 8 letter to the editor published in our local paper, the Kitchener-Waterloo Record, Bob Moore, the principal of the John Calvin Christian School in Guelph, Ontario, calls the teaching of creationism a "bogey man". He went on to say "...evolution and creationism are non-issues." So far, par for the course.

Now, here's where Moore inadvertently gives away the store. His very next sentence is "The actual scientific study of the origins of the universe in any faith-based school would be remarkably similar to what McGuinty experienced when he was educated in a Roman Catholic faith-based school, and I suspect that he thinks he was well-educated."

Only problem is, evolution is a theory of biology that has nothing to do "the scientific study of the origins of the universe". This is exactly the kind of confusion sown by creationist tracts.

Unwittingly, Principal Moore has demonstrated a lack of understanding of evolution, and the reason why private religious schools shouldn't be funded.

Canadian Muslim Group Invites Al-Zarqawi Supporter as Speaker

Well, I see my colleague Mohamed Elmasry is at it again.

Elmasry, you may remember, is the Electrical and Computer Engineering professor who claimed that Israeli citizens were fair game:

COREN: So everyone in Israel and anyone and everyone in Israel, irrespective of gender, over the age of 18 is a valid target?

ELMASRY: Yes, I would say.

Elmasry later apologized for his remark.

Now, in his role as "Chair and National President" of the Canadian Islamic Congress, he's bringing Al-Zarqawi supporter and general froot loop Yvonne Ridley to speak in Montreal, Toronto, and Waterloo. Yes, that's certainly the way to improve relations with the Jewish community.

A convert to Islam, Ridley has urged British Muslims not to cooperate with the police and has been an apologist for both Al-Zarqawi and a Chechen terrorist involved in the Moscow theater hostage crisis.

Recently she has blustered that "However if any of those Zionist idiots continue to try and paint me as an anti-semite I must warn you ... one of my closest friends is one of Britain's best defamation lawyers." Let's see, the last British journalist that blustered about libel in the same way was David Irving... and that didn't work out so well for him, did it?

In response to accusations of anti-Semitism, Ridley writes "Well a semite is a person who can be an Arab or a Jew ... hmm, so these dingbats are accusing me of hating the entire Jewish and Arab world?" Except that, as Robert Wistrich points out in Antisemitism: The Longest Hatred, "`Antisemitism' is a problematic term, first invented in the 1870s by the German journalist Wilhelm Marr to describe the `non-confessional' hatred of Jews and Judaism which he and others like him advocated... `Antisemitism' -- a term which came into general use as part of this politically motivated anti-Jewish campaign of the 1880s -- was never directed against `Semites' as such.... ...As a result, for the last hundred years, the illogical term `antisemitism', which never really meant hatred of `Semites' (for example, Arabs) at all, but rather hatred of Jews, has come to be accepted in general usage as denoting all forms of hostility towards Jews and Judaism throughout history."

I don't like the fact that B'nai Brith "would have supported" a ban of Ridley from Canada. By all means, let the attention-seeking froot loop speak. Her own words demonstrate her intellectual bankruptcy and the dangers of mixing religion with politics.

Mathematics in a Jack Reacher Novel

Lee Child is the author of a series of 11 novels involving Jack Reacher, an ex-Army MP who travels around the US, shooting up bad guys, saving the good guys (and gals), all while having no fixed address and no possessions. Think of The Saint, but more laconic, and on steroids.

In the latest Jack Reacher novel, Bad Luck and Trouble, we are suddenly informed that Reacher has "some kind of a junior-idiot-savant facility with arithmetic." (This characteristic never appeared before in any other Reacher novel.) Reacher uses the number 8197 as his ATM card PIN "because [97] was the largest two-digit prime number, and he loved 81 because it was absolutely the only number out of all the literally infinite possibilities whose square root was also the sum of its digits. Square root of eighty-one was nine, and eight and one made nine. No other nontrivial number in the cosmos had that kind of sweet symmetry. Perfect."

Of course, 0 and 1 also have the property that their square root equals the sum of their digits, but Reacher apparently dismisses these as "trivial".

This kind of property -- that a number's square root equals the sum of its digits -- is exactly the kind that most mathematicians would dismiss as uninteresting. There are at least two reasons. First is the privileged position given to base-10 numeration. In base 10, the square root of 81 equals the sum of its digits, but that's not the case in base 2, where 81₁₀ = 1010001₂, so the sum of the base-2 digits is 3. Why should we single out base 10, rather than some other base?

Second, the reason why 0, 1, and 81 are the only numbers with the Reacher property is essentially trivial: the sum of a number's digits grows, at most, something like 9 log₁₀ n which, as n goes to infinity, is much less than sqrt(n). So we already know, with essentially no calculation, that there can only be a finite number of Reacher numbers in any base; the fact that there are three of them is not particularly interesting.

[Exercise: 81 also has the property that its fourth root equals the sum of its digits, when expressed in base 2. Find another number besides 0 and 1 with this property. Extra credit: explain why nobody cares.]

Elsewhere in the novel, Reacher explains how he would choose a 6-digit password:

"Six characters? I'd probably write out my birthday, month, day, year and find the nearest prime number." Then he thought for second and said, "Actually, that would be a problem, because there would be two equally close, one exactly seven less and one exactly seven more. So I guess I'd use the square root instead, rounded to three decimal places. Ignore the decimal point, that would give me six numbers, all different."

So what's Reacher's birthday? Keep in mind that, according to the novels, he seems to be between 35 and 55 years old. I'll give the answer in another post - if anybody cares.

Update: (April 3 2015). Here's a genuine mathematical question. Fix a base b, such as 2 or 10. Are there infinitely many numbers n such that n is a power of the sum of the base-b digits of n? Reacher's number 81 works in base 2 and base 10, for example. For base 2, the first few examples are 0,1, 81, 625, 7776, 16807, 46656, 59049, 1679616, 1475789056, 6975757441, 137858491849, 576650390625 and form sequence A256590 at the On-Line Encyclopedia of Integer Sequences.

Stupid Tory Tricks: Religious Schools In Ontario Could Teach Creationism, Get Public Funds

The aptly named Progressive Conservative leader John Tory, in his push to fund religious schools in Ontario, says it would be just fine with him if Christian schools teach creationism as a legitimate alternative to evolution.

For those outside Ontario: here, public funds are used for the public schools and for the "separate schools" -- those that are run by Catholic religious groups. These Catholic schools are a parallel system, with their own elections for school boards, and are an unfortunate result of the compromise that led to Confederation 140 years ago. As a result of the London Conference of 1866, separate schools were guaranteed in in Québec and Ontario, but not some other provinces. Section 93 (3) of the Constitution Act (formerly called the British North America Act) reads

(3.) Where in any Province a System of Separate or Dissentient Schools exists by Law at the Union or is thereafter established by the Legislature of the Province, an Appeal shall lie to the Governor General in Council from any Act or Decision of any Provincial Authority affecting any Right or Privilege of the Protestant or Roman Catholic Minority of the Queen's Subjects in relation to Education:

Not surprisingly, other religious groups, including Protestant and Jewish groups, have objected to the special treatment received by Catholics in Ontario. But instead of attempting to end public funding for all religious schools, the Progressive Conservatives have made funding of all accredited religious schools part of their party platform in the upcoming provincial elections. Polls show, however, that the majority of the public is opposed to this change. Rick Johnson, head of the Ontario School Boards Association, resigned his position to run for one of the opposition parties, the Liberals.

According to an interview with Tory I heard on the CBC this afternoon, “They teach evolution in the Ontario curriculum, but they also could teach the facts to the children that there are other theories that people have out there that are part of some Christian beliefs."

If I could vote in Ontario (I can't, since I'm only a permanent resident, not a citizen), I certainly wouldn't give my vote to someone who doesn't know the difference between a fact and a theory, and who thinks that creationism is a scientific theory that is suitable for teaching in Ontario's science classes.

Unbelievable!

Go read this column from an editor of the Galesville Republican, a small paper in Wisconsin. The writer, a certain Rose Eddy, compares the Freedom from Religion Foundation (an excellent organization devoted to the separation of church and state - I'm a member) to the Ku Klux Klan, the Nazis, and Al Qaeda.

There's been a lot of whining in my local paper about how "people of faith" are misrepresented in the mainstream media. The funny thing is, the kind of misrepresentation Christians get in the media is nothing compared to the abuse regularly heaped on atheists.

Shortest No More

Well, as I anticipated, my shortest google query that returns no results no longer qualifies. So I'll have to try another. This time, though, I'll cleverly disguise it so that google won't find it.

The first three letters of my query are "zk0".

And the last two letters are "q" followed by 1+6.

Can anyone find a query of 4 letters and numbers that returns no results?

A Google Query

What's the shortest string of lower-case letters and numbers (no spaces or other characters) you can type into google and not get any hits?

The shortest I've found so far, by non-systematic experimenting, is of length 5. I'd tell you what it is, but then it would be indexed by google and hence no longer work.

Oh, what the heck. I'll tell you anyway: zk4qj .

There. I've said it. And now. like Frankenstein, my lovely creation will soon be destroyed.

The Discovery Institute Lies Again

In this latest posting, the Discovery Institute shows once again why it has a well-deserved reputation for dishonesty.

The DI is touting William Dembski's No Free Lunch as "essential reading". But there is no mention that the book has received uniformly negative reviews from biologists and mathematicians, nor that the centerpiece calculation of the book, an estimate of a probability associated with the bacterial flagellum, is off by about 65 orders of magnitude. There is no mention that the definition of "complex specified information" is nonsensical and does not have the properties claimed for it. There is no mention that David Wolpert, co-discoverer of the "No Free Lunch" theorems mentioned in Dembski's book, criticized Dembski's argument as hopelessly imprecise.

But what else can you expect from the Dissembling Institute?

The Noncommutative Frobenius Problem is Solved!

I rarely get the opportunity to talk about research problems on this blog, but this is an exception.

Consider the famous "Chicken McNuggets problem": if Chicken McNuggets are sold at McDonald's only in boxes of 6, 9, or 20 McNuggets, what's the largest number of McNuggets you can't buy at McDonald's? The answer happens to be my favorite number, 43. (Why it is my favorite is a story that will have to wait for another day.) Notice that you can buy any number of McNuggets greater than 43. For example,

44 = 4*6 + 1*20,

45 = 5*9,

46 = 1*6 + 2*20,

47 = 3*6 + 1*9 + 1*20,

48 = 8*6,

49 = 1*9 + 2*20,

and any number greater than 49 can be obtained by adding an appropriate multiple of 6 to these.

In general, you're given a set S of integers, and you want to know the largest number that cannot be expressed as a non-negative integer linear combination of the elements of S. This is called the Frobenius number because Frobenius is supposed to have mentioned it often during his lectures.

Of course, such an integer may not exist. For example, if S = {4, 6}, then you can only get multiples of 2 by forming an integer linear combination of 4 and 6. So you need to impose an important condition: the greatest common divisor of the elements of S must be 1. If this is the case, then you can express every sufficiently large integer as a non-negative integer linear combination of the elements of S.

Now, solving the classical Frobenius problem is easy in some cases. For example, here's a well-known formula for the case when S has only two elements, x and y, and here it is: xy - x - y. So, for example, the Frobenius number of 5 and 7 is 23. Every number larger than 23 can be expressed as a non-negative integer linear combination of 5 and 7. 24, for example, would be 2*5 + 2*7, and so forth -- but 23 itself cannot.

Greenberg wrote a paper in 1988, and Davison wrote another paper in 1994, in which they gave an efficient algorithm for three numbers.

Unfortunately, the general problem was proved NP-hard (under Turing reductions) by Ramirez Alfonsin in 1996. Roughly speaking, this means the problem is at least as hard as many classical problems for which we still have no efficient solution, such as the traveling salesman problem.

About 6 years ago, I suggested generalizing this problem from numbers to strings of symbols (sometimes called "words"). This kind of generalization is a typical activity in mathematics and theoretical computer science. You take a well-studied problem over one kind of domain, and see how the problem translates in another. The classical Frobenius problem dealt with positive integers, so we'll replace them with strings. Now S will be a set of strings.

Now we have to find the analogue of a non-negative integer linear combination. This is no problem: strings like to join up with other strings, in a process called concatenation, so our non-negative integer linear combinations will be replaced by all possible ways to concatenate the strings of S, using any of them any number of times (including 0 times). This process is sometimes called Kleene closure after the American logician Stephen Kleene, and we write it as S^*. For example, if S = {0, 01}, then S^* = { ε, 0, 00, 01, 000, 001, 010, ... }. That funny ε at the beginning is the usual mathematical representation for the empty string: the string with no letters at all in it. Notice that order matters in concatenation (houseboat isn't the same as boathouse), so we've gone from a commutative setting to a noncommutative one.

So S^* is an infinite set of strings. (By the way, in this particular example, where S = {0, 01}, the set S^* happens to have a nice description: it's the set of all strings that don't begin with a 1, and don't have two consecutive 1's appearing anywhere.)

OK, now we've generalized the "non-negative integer linear combination" part. How about the condition that the greatest common divisor (gcd) of the elements of S must be 1? Well, the point of that condition was just to ensure that every sufficiently large integer had a representation, so rather than worrying about how to define the greatest common divisor of two strings, let's replace the gcd condition with: every sufficiently long string must be in S^*. There's another way to say this: the complement of a set T is the set of all strings occurring in the universal set that don't occur in T. Here the universal set is just the set of all strings. So our condition is that the complement of S^* should be finite. In the arcane lingo of mathematicians, we can abbreviate this as: S^* is co-finite.

Now, are there any examples where S^* is co-finite? Yes. One example is S = {1, 00, 01,10, 000, 01010}. It shouldn't be too hard to convince yourself that every string except 0 and 010 can be written as concatenation of strings in this set. So in this case S^* is co-finite.

Finally, we need an analogue of the largest integer not representable. That's not hard --- it's just the length of the longest string not in S^*. In the previous example, where S = {1, 00, 01,10, 000, 01010}, the answer would be 3, since 010 is the longest string omitted from S^*. Let's call this the Frobenius number of the set of strings S.

Now it's not too hard to show that if the longest string in S is of length n, and S^* is co-finite, then the Frobenius number is bounded by a function which is exponential in n. For example, over an alphabet of two letters, you can show that the Frobenius number is < (2/3)*(4ⁿ - 1). (In case the exponent doesn't show up well in your browser, that's 4 to the n power, minus 1, times two-thirds.)

I figured out this generalization a while ago, and the upper bound a year or so ago. But I could not find any example where the Frobenius number was anywhere near as big as that upper bound. Indeed, for a long time, the worst-case example I knew was when you took S to be the set of all strings of length n, together with all the strings of length n+1. In this case, the Frobenius number is easily shown to be n² - n - 1.

I gave the problem to my Ph. D. student Zhi Xu, who only started a few months ago. We tried many different possibilities, but eventually we figured out that you should try sets S that contain almost all strings of some lengths, omitting only a few. And recently he made a big breakthrough: he was able to construct examples where the Frobenius number is exponentially large in n, the length of the longest string. Here's one of his examples: take S to be over a binary alphabet, that is, over {0,1}, and let it contain all the strings of length 3, all the strings of length 5, except that you remove the strings {00001, 01010, 10011}. Then S^* is co-finite, and the length of the longest string not in S^* is 25. For example, 0000101001100000001010011 can't be gotten by concatenating the strings of S.

So our understanding of Frobenius problem for strings is now greatly improved, in the sense that there is an exponential upper bound and a class of examples that provides an exponential lower bound. The bounds are not exactly tight, but they are much tighter than ever before. Zhi Xu has many other results on this problem, and you can see our paper on the subject here. We wrote it together with Jui-Yi Kao, another student of mine who also made some very nice contributions. I expect this paper will form the basis of Zhi Xu's Ph. D. thesis. Of course, there is much more to be done in this area.

I hope you enjoyed this tour of my recent research, and congratulations to Zhi Xu for a job well done!