Can Irrational Numbers be Represented in a Computer?

I often see the following claim, or variants of it:

"In a computer (as we understand computers, at least), irrational numbers can't be fully accurately represented."

This one happens to be from Bradley Monton, Seeking God in Science: An Atheist Defends Intelligent Design, Broadview Press, 2009, p. 128, but Monton isn't alone.

This is a common misunderstanding that, I think, has two bases. First, for people without much mathematical training, a real number is inextricably linked with its base-10 (or perhaps base-2) representation. For them, the number π is 3.141592653 ..., as opposed to being defined by an integral or infinite series. Second, people without computational training often don't understand that some infinite objects -- including some base-10 or base-2 representations of irrational real numbers -- are routinely represented as finite objects in computers.

Let's take √2 as an example. Although it is irrational, symbolic algebra systems such as Maple and Mathematica routinely represent √2 "exactly" and allow manipulations with it. For example, if you type

> x := sqrt(2);
> x^2;

into Maple, it will happily return the "exact" answer 2. And, similarly, other arithmetic operations involving √2 will give the "exact" answers:

> expand((123+45*sqrt(2))^3);

3355317 + 2224665 √2;

Similarly, we can manipulate other famous irrational numbers such as e, π, etc, and often get "exact" results. The point is that many of the irrational numbers that people actually care about need not be stored in terms of their base-10 or base-2 representation.

But even if we insist that yes, they must be stored in this way, there can still be finite representations. For example, consider the base-10 number defined by having a "1" in the i'th digit if i is a perfect square (like 1,4,9,16, etc.), and 0 otherwise. Now it is easy to see that this number is irrational. But we can still store it in a finite way (for example, as a function that returns the i'th digit on input i), and do at least some simple manipulations on this representation. For numbers whose base-k representation is encoded by a finite automaton, for example, we can do addition, even if the carries come from "infinitely far" to the right. (This is not trivial.)

In fact, any algebraic number, and many others, can be stored as a finite program that on input i returns the i'th digit. In some cases we can even do this by a very simple recurrence. For example, Graham and Pollak, in a 1970 paper, gave a simple explicit recursion to compute the i'th bit of √2 .

The misguided claim I started with can be fixed. If instead we say, "The base-2 representation of most irrational real numbers is not compressible to a finite representation, so the entire base-2 representation of most irrational real numbers cannot be stored in a finite computer", we would be correct. Here "most" means "all but a set of measure zero". But this is not particularly interesting, since for actual computation we are rarely interested in "most" irrational numbers -- we are interested in the computable ones.

Review of Monton's "Seeking God in Science"

Bradley Monton is a philosophy professor at UC Boulder and a self-proclaimed atheist. He's written a little book (147 pages for the main text, not counting the preface, endnotes, index, etc.) entitled Seeking God in Science: An Atheist Defends Intelligent Design, which I finally had a chance to read. It consists of four chapters:

1. What is intelligent design, and why might an atheist believe in it?
   
2. Why it is legitimate to treat intelligent design as science
   
3. Some somewhat plausible intelligent design arguments
   
4. Should intelligent design be taught in school?
   

I'm afraid this book is not very good. Monton comes off as rather naive (displaying little understanding of the abundant and documented dishonesty in the ID movement) and ignorant of science, the history of intelligent design creationism, and its role in the creationism-evolution wars.

The first chapter of the book is devoted to one of my least favorite philosophical games: trying to create a definition for a concept that covers all possible cases, by starting with a definition and iteratively refining it. He spends 25 pages (pages 16-40) playing this game with the concept of "intelligent design" itself, in a tedious and unenlightening way (for example, he even addresses the possibility that God is biologically related to humans!) and here is what he comes up with (italics in original):

"The theory of intelligent design holds that certain global features of the universe provide evidence for the existence of an intelligent cause, or that certain biologically innate features of living things provide evidence for the doctrine that the features are the result of the intentional actions of an intelligent cause which is not biologically related to the living things, and provide evidence against the doctrine that the features are the result of an undirected process such as natural selection."

Now I don't particularly like this game (although it has a long history -- philosophers have enjoyed applying it to "chair", for example), because for almost any definition proposed it is easy to come up with some outlandish counterexample. Still, as a mathematician, I enjoy and admire precision, so perhaps it's not a game completely without value. But after reading his definition I could only mutter, All that work! - and he still has an imprecise and unusable mess.

Unusable, since key terms like "intelligent cause" and "undirected process" are not defined or made rigorous. Could it be, as other commentators have already observed, that when we try to define "intelligent cause" we discover that natural selection itself could be considered intelligent by our criteria? Could it be that intelligence is a continuous measure, not a discrete quality, so that speaking of an "intelligent cause" is essentially meaningless unless the amount of intelligence is quantified?

Mess, because by calling intelligent design a "theory", Monton begs the question.

Imprecise, because this definition doesn't cover much of what the intelligent design advocates themselves discuss. For example, in Dembski's book No Free Lunch, he spends a good 10 pages discussing the case of Nicholas Caputo, an election official accused of rigging elections. Dembski implies that his intelligent design methodology can help resolve the case of whether Caputo cheated. But this case has nothing to do with a "global feature" of the universe or a "biologically innate" feature of living things.

Monton seems rather naive about the intelligent design movement. For example, on page 12, he claims, "As a matter of public policy, the Discovery Institute opposes any effort to require the teaching of intelligent design by school districts or state boards of education." But this claim could only be made by someone who doesn't understand (a) that the Discovery Institute has a long history of dissembling and (b) that intelligent design, as practiced by its leading proponents (Behe, Dembski, Meyer) is largely a negative program of casting doubt on the theory of evolution, or examining its supposed deficiencies. Therefore, Discovery Institute programs like "Teach the Controversy" and "Critical Analysis of Evolution" are, in fact, just covers for getting intelligent design into the classroom. This is abundantly clear to most people who have studied the intelligent design movement in any depth.

Part of the book is devoted to analyzing the views of pro-science philosophers, such as Taner Edis, Massimo Pigliucci, and Robert Pennock. Needless to say, Monton thinks they have it wrong in many ways; they are "sloppy" and "confused". But much of his criticism seems misplaced. For example, he gives the following advice to Barbara Forrest: she "focuses too much on attacking the proponents of intelligent design for the supposed cultural beliefs they have, instead of attacking the arguments for intelligent design that the proponents of intelligent design give". But Forrest has never said that intelligent design advocates are wrong because of their cultural beliefs; rather, she has fearlessly and tirelessly explored the goals and strategies of intelligent designers, as well as the sociological and political connections between intelligent design creationism and the religious right. Monton is apparently unconcerned with these details, and that's his right. But then his criticism amounts to "I don't share your interests", and that's rather pathetic.

Monton is a fan of Laudan, citing the following passage approvingly: "If we would stand up and be counted on the side of reason, we ought to drop terms like "pseudo-science" and "unscientific" from our vocabulary; they are just hollow phrases which do only emotive work for us." I strongly disagree. As I mentioned already, almost any definition or classification is subject to exceptions, but it's still useful to be able to say something is a chair or not a chair, even if we cannot always agree about the boundaries. Science, as a social process, has a number of characteristics, and it is perfectly legitimate and useful to point out that creationism and its modern variant, intelligent design, fail to share many of these characteristics.

There are signs that although he thinks intelligent design merits a book-length treatment, Monton hasn't really grappled with the issues. For example, on page 17, he cites a beehive as an example of a feature of the universe that "indisputably exist[s] as a result of an intelligent cause" and then, in a footnote, says that "It was surprising to me that some readers objected to this line of thought, saying that ... bees ... aren't intelligent." Well, I'd guess that this surprise comes largely from the fact that Monton hasn't really thought deeply about what intelligence is. We now know a lot about algorithms and naturally-occurring tools to perform computational processes, but Monton doesn't seem to know anything about it. But then he has some real misconceptions about mathematics and computing, claiming that computers can't represent irrational numbers. (I've addressed this misconception here.)

Several times in the book, Monton refers to the Newtonian account of physics and argues it has been "refuted". On page 50, he uses it to argue that false scientific theories can still count as science (so if intelligent design has been refuted, it could still be considered science). On page 152, he uses it to argue that false scientific theories are routinely taught in high school science (so intelligent design, even if false, could still be caught). But this black-white classification of theories as either "false" or "not false" doesn't even come close to capturing the status of Newtonian physics. Yes, it doesn't give the right answers for particles moving at high velocity, for example. But I can't think of a single scientific theory that unfailingly predicts the outcome of every single experiment. It is more correct, I think, to view theories and equations as our models of reality and to have a good idea of their shortcomings and applicability. No one uses special relativity to solve simple problems in kinematics; they use Newton and they don't apologize for it. If we classify theories purely as "true" or "false" then we lose the nuance that some "false" theories are pretty damn good and others are worthless.

Chapter 3 summarizes some of the arguments of intelligent design advocates, such as alleged "fine-tuning", the origin of the universe, the origin of life, irreducible complexity, and the simulation argument. There is not really much analysis that is new here, but I found his discussion of the simulation argument the most interesting part of the book.

Chapter 4 addresses the question of whether intelligent design should be taught in school. By "taught in school", Monton means "taught in public high-school science classes" (although he takes two whole pages to explain this - an example of how clunky the writing is). One of the objections Monton addresses is "we wouldn't be teaching a real controversy", and he answers this by citing Michael Behe as an example of a real scientist who disagrees with the scientific consensus. Ergo, there is a real controversy. But if Monton's definition of "real controversy" is "one scientist disagrees" or even "a handful of scientists disagree", then there is a "real controversy" about relativity, heliocentrism, and the germ theory of disease. Indeed, it would be hard to come up with a scientific theory for which there is no controversy in Monton's sense. Monton's position is absurd. There are controversies, and then there are controversies; it's not a black-and-white term. The "controversy" over evolution is exactly like that over relativity: a very small number of experts in the field, and a larger number of cranks, disagree with current consensus. That doesn't mean their objections merit coverage in science class. I'm not opposed to teaching controversies, but let's teach some real ones.

Finally, I'd say that the book, and Monton himself, seems curiously disengaged from the extensive mainstream criticism of intelligent design. To give one illustration, he doesn't cite much of the literature arguing against the claims of intelligent design advocates. Nowhere will you find any mention of, for example, the fine article of Pallen and Matzke (published in 2006 in Nature Reviews Microbiology) -- although other articles of Matzke are cited -- or the article of Wilkins and Elsberry (published in 2001 in Biology and Philosophy). He lists two conferences where he's presented his work, and both of them were hosted by the "Society of Christian Philosophers". Four people are listed as endorsers on the back of his book, and three of them are non-biologist critics of evolution (Berlinski, Dembski, Groothuis). And Monton has a blog, but he doesn't allow any comments on it. I can't help but think Monton's book would have been much better if he had made more attempts to be engaged with those who disagree with him.

More Muddled Thinking about the Brain

If you can stand it, read this article by Raymond Tallis, entitled "What Neuroscience Cannot Tell Us About Ourselves".

There are a lot of confident assertions, all presented without any real evidence:

• "It is unlikely that the gap between neuroscientific stories of human behavior and the standard humanistic or common-sense narratives will be closed"
  
  
• "But there is nothing in the activity of the visual cortex, consisting of nerve impulses that are no more than material events in a material object, which could make that activity be about the things that you see."
  
  
• "neural activity is not about anything and so can be neither correct nor mistaken"
  
  
• "A consistent materialism should not allow for the possibility of memory, of the sense of the past"
  

And Tallis seems to have no understanding of what "information" is.

But most of the article seems to be gobbledygook. If Tallis were to try to come up with a rigorous definition of words like "about", he might make some progress. By his argument, it makes no sense to count tree rings to determine a tree's age, since tree rings are not "about" the age of the tree.

As Arthur C. Clarke noted, "When a distinguished but elderly scientist states that something is possible, he is almost certainly right; when he states that something is impossible, he is probably wrong."

Psychic Fail

A photo from New Orleans.

If I were a real psychic, I wouldn't pay for "24 hr. surveillance", as the sign at the left indicates. Instead, I'd just send security guards around at the time I knew people were about to break in.

Neil Postman - Perpetually Clueless

Yesterday I attended a baseball game in Buffalo, NY: the Bisons versus the Lehigh Valley Iron Pigs. There was, as usual, a big video scoreboard in centerfield.

So this clueless quote from Neil Postman, recently posted on Doug Groothuis's blog, is appropriate:

"Media may now be serving as a surrogate for reality, and a preferred one at that. At stadiums throughout the country, huge TV screens have been installed so that spectators can experience the game through TV because TV is better than being there, even when you are there."

Postman has got to be one of the most overrated media commentators ever.

As I commented to my young son, in many ways, watching baseball at a stadium is a much better experience today than it was when I attended my first game in 1967.

It's not that "TV is better than being there" or that it is "a surrogate for reality", as Postman claims - whatever that means.

It's that a big screen offers more information than the scoreboard of 1967: you get the batter's average and other statistics; you get a reminder of what happened earlier in the game when that batter was up; and you get instant replays of interesting plays you might not have fully appreciated or understood the first time around.

Postman never really understood media; his observations are generally self-important, trite, and ignorant.

"Be it Ever So Humble" - a short story by Louise Shallit

Here's a short story entitled "Be it Ever So Humble" that appeared in Story magazine, Vol. 27, No. 115 (September-October 1945) by my mother, Louise Lee Outlaw. I think this may have been the first short story she published in a national magazine, although she had been writing for newspapers since 1938. Although it doesn't display her at the height of her powers, there are some very nice lines.

As an interesting footnote, another story in the same issue was written by Joseph Heller, who, of course, later became famous as the author of Catch-22.

The True Crocker Story

Over at Uncommon Descent, we have more playing the victim, this time about creationist Carolyn Crocker, and probably written by the World's Worst Journalist™.

For the true story about Crocker, go here.

Having Crocker as the "executive director of a think tank on integrity in science" is kind of like having Newt Gingrich as executive director of a think tank on integrity in marriage.

Religion at the Science Fair

I judged my first science fair yesterday.

There were some good projects, but most of them were a bit disappointing. The main problem was the lack of originality: most were testing hypotheses that were either obviously true or uninteresting. Good original hypotheses are hard to come by, but still...

One student from a local Christian school added evangelical Christian content to her poster and report. The project concerned determining which solvent was the best to remove stains from various materials. At the end, the student thoughtfully reminded everyone that humanity is also "stained" and that the only stain remover was Jesus.

I feel very sorry for this student, who has clearly been relentlessly indoctrinated by her teachers -- and probably instructed to add this kind of unscientific postscript to her display.

William Lane Craig Does Mathematics

In his debate with Lawrence Krauss last night (audio here), William Lane Craig says,

"But mathematicians recognize that the existence of an actually infinite number of things leads to self-contradictions. For example, what is infinity minus infinity? Mathematically, you get self-contradictory answers."

It's hard to know what Craig really means here, because it is so confused. Mathematicians routinely study "an actually infinite number of things", such as the natural numbers, the real numbers, and the complex numbers. No contradictions are involved.

But maybe Craig is talking about an actual infinity of things in nature. Then he shouldn't be talking about mathematicians, but physicists. Even here, physicists do discuss an actual physical infinity - without contradictions - such as Malament-Hogarth spacetime. Examples like Hilbert's hotel, that are often proffered as insoluble paradoxes, only show that infinity needs to be treated with care and may result in scenarios that seem counter-intuitive. But so does relativity.

Infinity minus infinity is not "self-contradictory", any more than 1/0 is "self-contradictory". Lane seems not to understand that not all functions are everywhere defined. The subtraction function, for example, can be defined on most pairs of the extended reals, but not defined on (∞, ∞). What's so hard to understand about that?

Addendum As I listen to more of the debate, it seems Craig retreats a bit from his claim about mathematics. He still seems to think that an actual infinite number of objects in the universe creates "contradictions", but he doesn't say explicitly what those contradictions are.

Nobody - Even Creationists - Seems to Know How To Calculate Dembski's "CSI"

Back in 2001, when I was on sabbatical in Tucson, Arizona, I decided to spend some time trying to understand Dembski's "complex specified information" (CSI) to see if there was anything to it. The result was my long paper with Elsberry, where we concluded that CSI was a hopeless, incoherent mess that didn't have the properties Dembski claimed. A shorter version of the paper has recently appeared in Synthese.

Now, over on Uncommon Descent, there is an amusing thread which demonstrates our conclusion. Nobody, not even the creationists, can seemingly agree on the most simple assertions about CSI. That's because it's a hopeless, incoherent mess.

No Smoking Fail

This wins my award for the "No Smoking Sign Least Likely to Convince Anyone Not to Smoke". Spotted in the Surrogate's Court Building, 4th Floor, at 31 Chambers Street, NYC. At the time someone was happily smoking in one of the stalls.

Graffiti Limbo

This is just a small portion of an amazing collection of graffiti, spotted in an American city. For points, identify

the city,

the subway from which you can see it, and

the name of the location.

Conway, Diaconis, Rivest I've Heard Of - But Who's That Fourth Guy?

In this reminiscence about the late Martin Gardner, Donald Knuth points out that Gardner had correspondence with some young mathematicians who later became famous: John Conway, Persi Diaconis, Ron Rivest, and some fourth guy no one's ever heard of.

Well, it's nice to be mentioned in that famous company.

This is What a Hypocritical, Lying Weasel Looks Like

Take a good look.

Famous Astronomer with Moose

OK, it's not as good as Alan Turing with a moose, but still...

Tycho Brahe with his moose.

"Any" Considered Harmful

Edsger Dijkstra wrote a famous letter in the Communications of the ACM that appeared under the heading "Go To Statement Considered Harmful".

I'd like to make a case against the use of "any" in mathematical discourse.

The problem with "any" is that it can mean both "for all" and "there exists", and it's not always clear what is meant. "It's true for any x" probably means "for all x". But "The theorem is true for S if any element of S is a square" probably means "it's true if S contains at least one square".

I was just attending a meeting at Dagstuhl in Germany where one speaker said something like "If L is regular, then u is equivalent to v if and only if for any state q of the minimal DFA for L we have δ(q,u) = δ(q,v)". Now if you know the theorem, the meaning is clear. But if you don't, you might be left wondering, does he mean "u is equivalent to v if there exists some state q such that δ(q,u) = δ(q,v)" or "u is equivalent to v if for all states q we have δ(q,u) = δ(q,v)"?

Because of this ambiguity, I think we should avoid the use of "any" in mathematical discourse. We can replace it by "all x" or by "some x", according to what we mean.

Who's with me?

More Mary Poplin Nuttiness

I forgot to mention one more nutty claim by Mary Poplin at Waterloo: "John the Baptist recognized Jesus while he [John] was in the womb" -- and this is proof that the Jews of the 1st century had advanced medical knowledge because "only recently did scientists figure out that babies could hear and react to stimuli in the womb". She mentioned this as the way that Christianity would be useful for medical science.

No claim, it seems, is too deranged for Prof. Poplin - provided Christianity says it is so.

Waterloo's "Watson" Connection

Here's Waterloo's own Jesse Hoey and Robin Cohen being interviewed about "Watson".

'Watson' on Jeopardy

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 Round 2

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.

Harris v. Wolpe

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?

Rock Lobster - Performed by Old Computers & Robots

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.

The Pascal Lecture: Another Year, Another Embarrassment

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.

World's Dumbest Scammer?

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

Anti-Terrorist and Monitory Crime Division.
Federal Bureau of Investigation.
Daniel McMullen (Special Agent in Charge)

Attn: Beneficiary,

This is to officially inform you that it has come to our notice and we have thoroughly investigated with the help of our Intelligence Monitoring Network System that you are having an illegal Transaction with Impostors. We the Federal Bureau Of Investigation want you to stop further communication with any Impostors claiming to be official. During our Investigation, we noticed that the reason why you have not received your payment is because you have not fulfilled your Financial Obligation given to you in respect of your Contract/Inheritance Payment. Therefore, we have contacted the Federal Ministry of Finance Nigeria on your behalf and they have brought a solution to your problem by coordinating your payment in total $5,900,000.00(Five Million Nine Hundred Thousand Dollars).

Since the Federal Bureau of Investigation is involved in this transaction, you have to be rest assured for this is 100% risk free it is our duty to protect you. We the Federal Bureau Of Investigation want you to contact the ATM CARD CENTER via email for their requirements to proceed and procure your Approval Slip on your behalf which will cost you $150 and note that your Approval Slip which contains details of the agent who will process your transaction.

CONTACT INFORMATION
NAME: Mr. kelvin Williams
Address: 18 Koffi Crescent Apapa Lagos Nigeria
EMAIL: kelvinwilliams205@gmail.com

Do contact Mr. kelvin Williams of the ATM CARD CENTER with your details, and you full information So your files would be updated after which he will send the payment information which you'll use in making payment of $150 via Western Union Money Transfer or Money Gram Transfer for the procurement of your Approval Slip after which the delivery of your ATM CARD will be effected to your designated home address without any further delay. We order you get back to this office after you have contacted the ATM SWIFT CARD CENTER and we do await your response so we can move on with our Investigation and make sure your ATM SWIFT CARD gets to you.

Thanks and hope to read from you soon.

Daniel McMullen
Special Agent in Charge
Criminal Division
FBI Los Angeles
Suite 1700, FOB
$15000 Wilshire Boulevard
Los Angeles, California


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

Fibonacci Quarterly Goes Electronic

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...

Yet Another Christian Fake Quote

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.

So Much Stupidity, So Little Time

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.

Net Neutrality = Fairness Doctrine?

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?

Local Creationist Stupidity

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.

Strangest Moose-Related Lawsuit of the Millennium

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?

Creationists Don't Understand Consilience

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.

Vetting Insanity

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.

Everything Was Better With God

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.

David Warren Exposed

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.

Gee, It's Warmer in Buffalo Than I Thought

From The Weather Network website today:

Homeo-Apathy

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.

DADT, Ten Years Ago

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!

The National Post Responds

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.

Bob Enyart: Foolish and Smugly So

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.

Silence from the National Post

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.

Jehovah's Witness Creationist Writes Me

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.

Dear Charles Lewis: You're a Dishonest Bigot

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?

Naming Infinity

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.

Canadian Bozos of the Week

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...

Why Do William Lane Craig's Views Merit Respect?

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.

The Hack Thirty

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?

Two Perspectives on Islam

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.

Yet Another Reason to Doubt the Relevance of Philosophy

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.

Harun Yahya Blames 9/11 on "Darwinists"

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.

Creationist Mathematics

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: Special Issue in Honor of Alf van der Poorten

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