Kirk Durston: Apologist for Genocide

Kirk Durston is a graduate student in biology at the University of Guelph, and the director of something called the New Scholars Society. This Society's mission statement is

"TO PROMOTE CHRISTIAN SCHOLARSHIP IN EVERY FIELD, WITH A SPECIAL INTEREST IN THOSE AREAS WHERE PHILOSOPHY, FAITH, AND SCIENCE INTERSECT, ESPECIALLY THE PROBLEMS AND ISSUES THAT ARISE OUT OF THAT INTERSECTION.

TO PROMOTE THOUGHT AND DISCUSSION WITH RESPECT TO THE SPIRITUAL ASPECT OF LIFE.

TO BE A RESOURCE TO THOSE FACULTY AND SCHOLARS WHO HAVE AN INTEREST IN DEVELOPING THE SPIRITUAL AREA OF THEIR LIVES, FROM A CHRISTIAN PERSPECTIVE."

You can find their "statement of faith" here. It's the usual fundagelical claptrap about the bible being "uniquely, verbally and fully inspired by the Holy Spirit, and that it was written without error (inerrant) in the original manuscripts."

Durston is active in fundagelical affairs. For example, look at this interview supporting intelligent design. How many misrepresentations can you find there?

Durston spoke last Wednesday, June 20, at the University of Waterloo on the topic "Is Genocide Wrong? What are moral absolutes and where do they come from?"

Durston made the usual nonsensical argument that moral absolutes exist, and that they only make sense if they come from a god. He claimed, for example, that if morals are relative, we would have not justification for claiming that the Nazi genocide of Jews was wrong. He claimed that those who follow "traditional moralilty" are happier and more successful. He insisted that Christians have a lower divorce rate than non-Christians. However, Durston's claim is at odds with a Barna survey that showed that atheists and agnostics actually have the lowest divorce rate (21%). When asked about this, Durston dismissed the evidence, invoking the classic "no true Scotsman" fallacy by claiming that many people say they are Christian when they are actually not.

Durston surveyed various ways to obtain moral guidance, but totally omitted a naturalistic approach to ethics, namely the view that ethical principles are part of our evolutionary heritage. There is a reasonable amount of evidence for this latter view, such as the work of primatologist Frans de Waal (e.g., Chimpanzee Politics, showing that chimpanzees apparently have a moral code) and the field of evolutionary psychology (e.g., Robert Wright, The Moral Animal). In general, his presentation was barely at the level of freshman philosophy paper.

But the most repulsive part of Durston's talk was when someone from the audience asked why Durston's condemnation of genocide would not apply equally well to the god of the Old Testament, who indulged in genocide himself, in particular the genocide of the Canaanites. Suddenly Durston's tune changed. Instead of condemning this genocide, Durston sought to justify it. Genocide was OK, he claimed, if his god ordained it. Indeed, he said that the only thing that prevented him from going and out murdering people for his advantage was his religious belief.

If God ordained genocide in our modern day, Durston said, he would obey. However, he said he would have to be very convinced that this call was correct. God would have to appear to all Canadians in an unmistakable way. If that happened, we would have to obey and kill those we were instructed to.

If there is any better example of how fundamentalist Christianity is morally bankrupt, I can't think of it. Any crime, no matter how vile, is OK if their god commands it. What else but religion could make a good person become an apologist for genocide?

Addendum (added October 26 2007): Kirk Durston has asked me to post this clarification regarding his views on genocide. He agrees that he would participate in genocide if God ordained it, but he says the conditions must be extremely stringent: it must be that (for example) God simultaneously appears to every Canadian, in an impressive and undeniable show, so that every single Canadian is convinced of his existence (even atheists) and also convinced that God wants us (for example) to kill Americans. Only under these very strong conditions, he says, would genocide be permitted.

In my opinion, I already summarized this view in the paragraphs above, so I don't understand the need for the "clarification", but I've added it anyway.

Kirk Durston Does Mathematics!

Kirk Durston is a local evangelical Christian who likes to construct unconvincing arguments for his faith. Every few years he trots them out at my university.

Here is one of his more recent attempts, a discussion of infinity. Not surprisingly, it is a confused mess.

Durston's argument is based, in part, on a distinction that does not really exist: between "potential infinity" and "completed infinity" or "actual infinity". This is a distinction that some philosophers love to talk about, but mathematicians generally do not.* You can open any contemporary mathematical textbook about set theory, for example, and not find these terms mentioned anywhere. Why is this? It's because mathematicians understand the subject well, but -- as usual -- many philosophers are extremely muddled thinkers when it comes to infinity.

Here is how Durston defines "potential infinity": "a procedure that gets closer and closer to, but never quite reaches, an infinite end". So, according to Durston, a "potential infinity" is not a set but a "procedure". Yet the very first example that Durston gives is "the sequence of numbers 1,2,3, ... gets higher and higher but it has no end". The problem should be clear: a "sequence" is not a "procedure"; a (one-sided infinite) sequence over a set S is a mapping from the non-negative integers to S. From the beginning, Durston is quite confused. His next example is "the limit of a function as x approaches infinity". But a "limit" is not a "procedure", either. Durston also doesn't seem to understand that limits involving the symbol ∞ can be restated to avoid it entirely; the ∞ in a limit is a shorthand that has little to do with infinite sets at all.

He defines "actual infinity" or "completed infinity" as "an infinity that one actually reaches", which doesn't seem to have any actual meaning that I can divine. But then he says that "actual infinity" or "completed infinity" is "just one object, a set". Fair enough. Now we know that for Durston, an "actual" or "completed" infinity is a set. But what does it mean for a set to "reach" something? And if we consider the set of natural numbers, for example, what does it mean to say that it "reaches" infinity? After all, the set of natural numbers N contains no number called "infinity", so if anything, we should say that N does not "reach" infinity.

But then he goes on to say "First, a completed countable infinity must be treated as a single ‘object’." This is evidently wrong. For Durston, a "completed infinity" is a set, but that doesn't prevent us from discussing, treating, or thinking about its members, and there are infinitely many of them.

Next, he says "it is impossible to count to a completed infinity". That is true, but not for the reason that Durston thinks. It is because the phrase "to count to a set" is not defined. We never speak about "counting to a set" in mathematics. We might speak about enumerating the elements of a set, but then the claim that if we begin at a specific time and enumerate the elements of a countably infinite set at, say, once a second, we will never finish, is completely obvious and not of any interest.

Next, Durston claims "one can count towards a potential infinity". But since he defined a "potential infinity" as a procedure, this is clearly meaningless. What could it mean to "count towards a procedure"?

He then goes on to discuss four requirements of an infinite past history. He first asserts that "the number of seconds in the past is a completed countable infinity". Once again, Durston bumps up against his own claims. The number of seconds is not a set, and hence it cannot be a "completed infinity" by Durston's own definition. Here he is confusing the cardinality of a set with the set itself.

Next, he claims that "The number of elapsed seconds in the future is a potential infinity". But earlier he claimed that a potential infinity is a "procedure". Here he is confusing a cardinality with a procedure!

Later, Durston shows that he does not understand the difference between finite and infinite quantities: he claims that "the size of past history is equal to the absolute value of the smallest negative integer value in past history". This would only be true for finite pasts. If the past is infinite, there is no smallest negative integer, so the claim becomes meaningless. So his Argument A is wrong from the start.

At this point I think we can stop. Durston's claims are evidently so confused that one cannot take them seriously. If one wants to understand infinity well, one should read a basic text on infinity and set theory by mathematicians, not agenda-driven religionists with little advanced training in mathematics.

* There are certainly some exceptions to this general rule. The "actual"/"potential" discussion started with Aristotle and hence continues to wield influence, even though mathematicians have had a really good understanding of the infinite since Cantor. Cantor met with resistance from some mathematicians like Poincaré, but today these objections are generally regarded as groundless.

Update on the Rom Houben Story

You may recall my previous discussion of the Rom Houben case. Houben is the Dutch man who has been in a coma for over 20 years, and was "discovered" to be conscious and capable of expressing his thoughts coherently through the bogus technique of "facilitated communication", or FC.

I and many other skeptics had doubts about the facilitated communication part of the story, while creationists such as Denyse O'Leary bought it unquestioningly. Creationist Kirk Durston joined the fray in the comments here, with Kirk claiming it was "doubtful that this team of scientists, headed by Laureys, is falling for fake messages typed out by a crackpot assistant" and assuring us that "We can infer from that, that what we are seeing in the video is a method that Laureys’ team has developed, or helped develop." Further, Durston accused another skeptic, the renowned bioethicist Arthur Caplan, of being "unethical" for pointing out that the bogus FC technique had been used.

Now Orac reports that O'Leary and Durston were wrong on all accounts. Further tests have shown that, indeed, Houben was not able to communicate through FC, and that Laureys and his team were, in fact, taken in by the bogus claims of an FC practitioner.

I also observe that FC has nothing to do with the other work of Laurey's team, namely developing a way to communicate with patients by asking them to associate "yes" with, e.g., thinking about playing tennis and "no" with thinking about being in his house. That's an interesting, though still controversial, idea that may be useful. It is a shame that Laureys' reputation will certainly suffer from his association with FC on Houben and his failure to use adequate controls when testing the FC claim. I also note that Laureys did not forthrightly respond to questions about his use of FC and never answered my query about it.

I feel very sorry for Rom Houben, who may be conscious but has had his voice stolen by FC crackpottery that Laureys helped publicize.

As for Denyse O'Leary and Kirk Durston, they were insufficiently skeptical and came to the wrong conclusion. Will we see them admit it? Will Durston apologize for his libel of Caplan?

A New Self-Published Creationist Book?

Oh, lookie!

Our local creationists at the University of Guelph, Kirk Durston and David Chiu, have teamed up with wacky David Abel and Donald Johnson on a book!

(Kirk Durston is the creationist who thinks that his god magically calms angry bulls, and David Chiu is the guy who stuck in an irrelevant citation to Dembski's work in a paper having nothing to do with Dembski, and told me he did it as a "courtesy".)

Judging from this excerpt, it's not likely that real scientists will take it seriously, with laughably bogus claims such as
- "Fifteen years ago, it started to be realized that `junk DNA' was a misnomer."
- "All known errors during replication result in a decrease of both Shannon and functional information"

I wondered who would publish this drivel. It's a place called "Longview Press". Never heard of it? I hadn't either. But this page suggests that it's just David Abel's private little enterprise. Wow, what a surprise.

It's in keeping with the intelligent design vanity journal, Bio-Complexity, which seems to have a hard time finding papers to publish (7 in 2 years). But hey! It has no problem publishing papers by people who are on the editorial team. And look: David Abel is there, too.

And they wonder why we call it pseudoscience.

Addendum 1: even the University of Guelph library, where Durston and Chiu are based, doesn't have the book in its collection.

Addendum 2: Thanks to Bayesian Bouffant for pointing out the self-congratulatory description of the book on Amazon. I especially love this part: "Change in the FSC of proteins as they evolve can be measured in “Fits”— Functional bits. The ability to quantify changes in biofunctionality during evolutionary transition represents one of the most important advances in biological research in recent decades. See especially, Durston, K.K.; Chiu, D.K.; Abel, D.L.; Trevors, J.T. 2007, Measuring the functional sequence complexity of proteins, Theor Biol Med Model, 4, 47".

Well, if it's "one of the most important advances in biological research in recent decades", then it's amazing how few citations there are to this groundbreaking paper. ISI Web of Science lists exactly 4 citations, 3 of which are self-citations by Abel and Trevors. Wow, that is sure important and groundbreaking.

Reply to William Lane Craig

Two readers of this blog have pointed out this post at William Lane Craig's blog. In the post, he responds to a question about my debate with Kirk Durston. Craig says I exhibit "ignorance on parade".

Well, there's a lot of ignorance to go around. My debate was with Durston, not with Craig. I was responding to Durston's claim (made at 05:37) that "Mathematics dictates that time itself would have had to have a beginning at some point in the past." In the debate that Durston took part in just a few days earlier at McMaster University, he claimed that Hilbert, in his 1925 paper, "On the Infinite" had proved mathematically that there could not be an infinite regress of causes." But this is not true. All Hilbert did in that paper was claim that then-current consensus about the physical universe was that no infinite quantities existed in it. That's a far cry from any kind of mathematical proof. William Lane Craig, like anyone else, can go read Hilbert's paper and verify that this is the case.

I pointed out that in fact, there is nothing mathematical that rules out an infinite regress of causes. For example, you could have an event at time -(n+1) causing an event at time -(n) for all positive integers n. Thus, an event at time -2 causes an event at time -1, an event at time -3 causes an event at time -2, etc. There is nothing logical or mathematical to rule this out. You can even have an infinite regress of causes if time has a beginning. If time begins at time 0, then you can have an event at time 1/(n+1) causing an event at time 1/n for all positive integers n. Thus, for example, an event at time 1/3 causes an event at time 1/2, an event at time 1/4 causes an event at time 1/3, etc. Again, nothing logical or mathematical rules this out.

Now you might say that once we bring our current state of physical knowledge into the picture, the first scenario is ruled out. But even modern physicists consider the possibility of infinite time-like curves that occur in the past of some other point; for example, in their study of Malament-Hogarth spacetime. Thus, I would contend that apologists like Durston and Craig have a really naive view of spacetime, one that is essentially based on the understanding of 100 years ago, not modern physics.

When I called Durston on this at the debate, his response was really comical. Here it is as I have transcribed it, beginning at 1:06:48:

"First, regarding Hilbert. He [Shallit] pulled a mathematical trick
there. Those of you who are used to summing infinite series
will know that if the x decreases exponentially, it comes to a
finite value. So let me explain how this really works.

Let's assume... now I don't know whether he's saying that.
Has he dodged the issue here, as to whether or not the past is
infinite or not? So let's assume the past is infinite. So
let's call this debate time 0, this hour here of the debate is
time 0. The next hour after this will be time 0+1, time 2, and
so forth. And in the past, we'll go to, the last hour before
this debate will be negative 1 hour, hour negative 2, and so forth.
Now if you want to assume, and this is to illustrate why there's
a problem of traversing an actual infinite series in
reality. Let's say that each step in the series is one hour
long. Now what he seems to be arguing, or what he's insisting
here, I'm not sure, is that Hilbert, that the past can be
infinite, that is, there's an actual hour infinitely separated
from this one here. So let's call that -infinity. We'll never
get there by getting in a time machine and going back, so let's
just take a quantum leap back into the past, we're now at minus
infinity. Now some of those of you who are familiar with
infinite set theory might be a little uncomfortable at this
point because if the past is, if you're saying it actually is
infinite, what you mean is that there actually is an hour back
there that is infinitely separated from this one. So let's
count our way down now. Infinity minus 1, infinity minus 2.
It's one hour each, not an exponentially decreasing amount of
time like that little equation he put up there, but just a
steady hour each time.

Or you could go with a multi-universe, this universe is a
product of another universe, and we're working our way down
from -infinity to the present. At what point in time will you
arrive at 0? You will never traverse an infinite series in
reality if you must stop at a discrete amount of time for a
constant amount of time in between. And that pretty much lays
to rest this notion that time itself can be infinite as far as
the past goes. It can be potentially infinite. you can do
lots of mathematical things, I can hold my hands together and
say there's an infinite number of mathematical points, no
problem, those are imaginary. But the moment you have a
discrete amount, that occupies a discrete amount of time, like
a minute, or a second, or an hour, and it is not decreasing
then suddenly you have a problem, if you want to actually
traverse that infinite series in reality."


After Durston's casual slur on my character at the beginning, this is completely incoherent. My equation was not "exponential", so that criticism is nonsensical. Secondly, it is perfectly possible to have an infinite past without having any point at infinite distance from the current time; for example, we could define times -1, -2, -3, etc., without having to define an actual point called "-infinity". (In exactly the same way, the negative integers are an infinite set that does not contain an integer called "-infinity".) This is not exactly a controversial point, but it is a misconception common to undergraduates. Mr. Durston, a graduate student, should know better.

Craig doesn't seem to understand what the debate was about. He says, "What's really peculiar is Shallit's "that was then, but this is now" move—as though views of mathematical existence are tied to the times!", thereby entirely missing the point. Hilbert's claim was about the 1925 understanding of physical existence, not mathematical existence. And anyway, views of mathematical existence do change through time. Consider, for example, the views of people like Brouwer.

Craig says, "On Shallit's view the universe still came into being a finite time ago and therefore requires an external cause." No, I didn't say that at all, and I don't hold that. In my second example, I said that "you can have an event at time 1/(n+1) causing an event at time 1/(n) for all positive integers n". This doesn't say anything about time 0, and it is logically possible to have an infinite chain of causes stretching back in this way, with nothing happening at time 0 at all - an uncaused beginning.

In general, Craig seems to have an extremely naive, almost childish view of infinity. Read Craig's reply to Sobel. On page 9 he says, "Imagine an actually infinite regress of past causes terminating in the present effect. In this case, the regress of causes terminating, say, yesterday, or, for that matter, at any day in the infinite past, has exactly the same number of causes as the regress terminating in the present. This seems absurd, since the entire regress contains all the same causes as any selected partial regress plus an arbitrarily large number of additional causes as well. Or again, if we number the causes, there will be as many odd-numbered causes as there are causes, which seems absurd, since there are an equally infinite number of even-numbered causes in the series in addition to the self-same odd-numbered causes."

It seems that what bothers Craig is perfectly understandable to any mathematician: namely, that the set of positive integers has the same cardinality as the set of integers greater than n (for any positive n), and the same cardinality as the set of even positive integers. All this was well understood 125 years ago, but it seems the Christian apologists haven't caught up.

Altogether, I would say these arguments by Durston and Craig are embarrassingly naive.

Casey Luskin: Information Theory Expert

Well, it looks like the Discovery Institute was so unnerved by my pointing out the misunderstandings and misrepresentations in Stephen Meyer's book, Signature in the Cell, that they devoted two whole chapters to attacking me in their new book. The always-repulsive David Klinghoffer called me a "pygmy" and made fun of the name of my university (page 6). Paul Nelson called my critique a "fluffy confection" and alleged I was guilty of "sophistry". Casey Luskin said I indulged in "gratuitous invective".

The DI's responses to my arguments about Signature are about at the level of what you'd expect from them. I already replied to Paul Nelson months ago here, but of course they didn't see fit to reference that.

In their new book, they trot out lawyer Casey Luskin as their new expert on information theory. Luskin's main points are

(1) Shannon and Kolmogorov complexity are not "useful metrics of functional biological information" and
(2) eminent scientists have adopted Dembski and Meyer's notion of "functional information".

Here's my response:

(1) No measure of information is perfect. Both Shannon and Kolmogorov have proved useful in biological contexts; to claim, as Luskin does that they are "outmoded tools" is ridiculous. An exercise for Luskin, or anyone else: do a search of the scientific literature for "Shannon information" in biology, and count how many hits you get. Now do the same thing for "functional information". See the difference?

Indeed, it is the apparent incompressibility of the genome that suggests, through Kolmogorov complexity, that random mutations played a very significant role in its creation.

(2) Luskin cites a 1973 book by Orgel, where Orgel used the term "specified complexity", as evidence that creationist information is used by real scientists. However, Orgel did not give a rigorous definition of the term, and no one has since then. The term was only used in a popular book, and Orgel never published a definition in the peer-reviewed scientific literature. Dembski later claimed that Orgel's term was the same as his, and Luskin now repeats this falsehood. A lie can travel around the world, while the truth is just lacing up its sneakers.

Luskin points out that very recently, Szostak has introduced a notion of "functional information". However, Szostak's "functional information" is not a general-purpose measure of information. It certainly does not obey the axioms of information as studied by information theorists, and it does not obey Dembski's "law of conservation of information". Furthermore, it is only defined relative to a set of functions that one specifies. Change the functions, and you might get a completely different measure. So it is clear that Szostak's measure is not the same as Dembski's.

Might Szostak's idea prove useful one day? Perhaps, although the jury is still out. It has yet to receive many citations in the scientific literature; one of the papers cited by Luskin is by creationist Kirk Durston. The last time I looked, Durston's paper had essentially no impact at all, to judge by citation counts.

In any event, my claim was "Information scientists do not speak about ‘specified information’ or ‘functional information.’” Luskin offers Szostak as a counterexample. But Szostak is not an information scientist; he's a biologist. No discussion of "functional information" has yet appeared in the peer-reviewed information theory literature, which was my point. Luskin's trotting out of Szostak's paper does not refute that.

My Debate Video is Finally Available

Back in October 2007, I debated intelligent design advocate Kirk Durston at the University of Waterloo. The debate organizers promised that video would be made available, but it never appeared on the debate website.

Now an e-mail message informs me that the debate video is available here, while the Q&A that followed the debate is available here.

My impression after the debate was that I did pretty well, demonstrating that Durston's claims were not substantiated (and in at least one case, that he blatantly misrepresented his sources). The local campus paper, the Imprint, seemed to agree.

However, the gentle and happy theists at Atheism Sucks! didn't appreciate my performance. They said I "sucked". I think that fairly represents the level of their critique.

More Silliness about Infinity

Once again we have someone claiming that infinity does not exist in the real world, and giving Hilbert as proof. The last time it was William Lane Craig and Kirk Durston. Now it's Uthman Badar, Australian Muslim advocate:

Start watching at 1:08:12. He says,

"I agree there's no problem with infinity in mathematics or in physics or in other studies. That's not the point. There's a difference between infinity, the potential infinity as an idea and actual infinity in the real world. Don't take my word for it, here's what the mathematicians say. David Hilbert ... is a renowned mathematician of the, or was, of the 20th century after whom Hilbert spaces and Hilbert operators that are prevalent in quantum mechanics is used, he said, "The infinite is nowhere to be found in reality. It neither exists in nature nor provides a legitimate basis for rational thought. The role that remains for the infinite to play is solely that of an idea."

Kasner and Newman, contemporary renowned mathematicians: "The infinite certainly does not exist in the same sense that we say there are fish in the sea. Existence in the mathematical sense is wholly different from existence of objects in the physical world."

...
There's no way in the real world, within our sensorially perceivable naturally world within space time that infinity can exist. If it does, you end up with a whole host of contradictions. If we had an infinite number of people in the room and five have left, how much do we have? An infinite number of people! But five have left! So, there's a distinction between the idea of infinity and the ontological reality of infinity in the real world."

Krauss's response is good. First, Hilbert was not a physicist, but a mathematician; his opinion about physical reality was not definitive back in 1926, when his article was written, and it is certainly not definitive now. Hilbert provided no empirical evidence that the infinite cannot exist in nature, and these days, physicists routinely consider the possibility of various aspects of infinity in nature. Does it or doesn't it? We don't know for sure, but we can't rule it out by Hilbert-style thought experiments alone.

Second, Uthman starts with a premise like `you can fit an infinite number of people in a finite room' (not an exact quote), which nobody is asserting. Then he asserts a contradiction where none exists. Yes, it's true that if you remove a finite number of items from an infinite set, the resulting set is still infinite. Why is this a contradiction? The answer is, it's not. Infinite quantities don't behave like finite ones, so they may not match the average person's intuition, but that's not the same as a "contradiction".

Test if You Know What You Don't Know

One of my favorite quotes is due to the American humorist Josh Billings (Henry Wheeler Shaw):

"I honestly beleave it iz better tew know nothing than two know what ain't so."

Sometimes this is reported as:

"It's not what you don't know that scares me; it's what you know for sure that just ain't so."

Now here's a little test that claims to identify your "risk intelligence quotient": not what you know, but how accurate your estimates are of what you do know.

I'd love to see the blustering creationists Denyse O'Leary and Kirk Durston take this test. My guess is, they wouldn't score very high.

So take it, and leave your score in the comments.

Why Can't Creationists Do Mathematics?

I suppose it's not so remarkable that creationists can't do mathematics. After all, almost by definition, they don't understand evolution, so that alone should suggest some sort of cognitive deficit. What surprises me is that even creationists with math or related degrees often have problems with basic mathematics.

I wrote before about Marvin Bittinger, a mathematician who made up an entirely bogus "time principle" to estimate probabilities of events. And about Kirk Durston, who speaks confidently about infinity, but gets nearly everything wrong.

And here's yet another example: creationist Jonathan Bartlett, who is director of something called the Blyth Institute (which, mysteriously, lists no actual people associated with it, and seems to consist entirely of Jonathan Bartlett himself), has recently published a post about mathematics, in which he makes a number of very dubious assertions. I'll just mention two.

First, Bartlett calls polynomials the "standard algebraic functions". This is definitely nonstandard terminology, and not anything a mathematician would say. For mathematicians, an "algebraic function" is one that satisfies the analogue of an algebraic equation. For example, consider the function f(x) defined by f^2 + f + x = 0. The function (-1 + sqrt(1-4x))/2 satisfies this equation, and hence it would be called algebraic.

Second, Bartlett claims that "every calculus student learns a method for writing sine and cosine" in terms of polynomials, even though he also states this is "impossible". How can one resolve this contradiction? Easy! He explains that "If, however, we allow ourselves an infinite number of polynomial terms, we can indeed write sine and cosine in terms of polynomial functions".

This reminds me of the old joke about Lincoln: "In discussing the question, he used to liken the case to that of the boy who, when asked how many legs his calf would have if he called its tail a leg, replied, "Five," to which the prompt response was made that calling the tail a leg would not make it a leg."

If one allows "an infinite number of polynomial terms", then the result is not a polynomial! How hard can this be to understand? Such a thing is called a "power series"; it is not the same as a polynomial at all. Mathematicians even use a different notation to distinguish between these. Polynomials over a field F in one variable are written using the symbol F[x]; power series are written as F[[x]].

Moral of the story: don't learn mathematics from creationists.

P.S. Another example of Bartlett getting basic things wrong is here.

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.

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.