Recursivity

"30% Less Fat per 2 Cookies"? How much less fat per 1 cookie?

OK, I can think of a plausible reason* why it's phrased that way, but mathematically, it just sounds stupid.



* Because 2 cookies is the serving size, and maybe there's a legal requirement that any claims about "less fat" must be expressed in terms of the serving size.

It feels like something out of a Gary Larson cartoon.

The local ducks have suddenly learned to hang out on rooftops. I've lived in the same house for 18 years, and I've never seen this before, but suddenly, this year, more and more ducks and geese are perching and even sometimes nesting on rooftops.

Here are two pictures I took yesterday of a duck on the house next door, a good 20 feet above the ground. It looks like he is surveying the territory prior to swooping down and nabbing some unsuspecting child.

Be afraid. Be very afraid.

One of the things I find embarrassing about Canada is its devotion to the monarchy; it seems remarkably childish to me. As columnist Allan Fotheringham once remarked, "Grown-up nations do not need, as head of state, a woman -- however nice --who lives across a large ocean in a castle in a foreign country."

But on a recent trip to France, I saw something even more strange: a poster for the Alliance Royale. This is, believe it or not, a political movement to restore the monarchy in France. It seems largely spearheaded by someone named Yves-Marie Adeline, who actually has a blog for his royalist views. There is also an FAQ which is remarkable for its obliqueness, although it does forthrightly admit that "A law that applies uniformly to everyone leads to injustice".

Luckily, this party hasn't won any seats, as far as I can tell. Indeed, they seem to be garnering something like .03% of the vote.

Far-right crackpot Phyllis Schlafly weighs in on Expelled, repeating the usual lie that "Dr. Richard Sternberg, a biologist ... lost his position at the prestigious Smithsonian Institution after he published a peer-reviewed article that mentioned intelligent design."

Now I see that her son, Roger Schlafly, has the same affliction: about the transparent effort to relabel creationism as intelligent design in the book Of Pandas and People he writes: "Judge Jones found that the Pandas book was subsequently edited to remove references to creationism, and made inferences about the motives of the Pandas authors. I think that it is bizarre to denigrate folks for complying with a court decision."

This transparent effort to exonerate the writers of Of Pandas and People for their editing just won't fly. It is completely obvious to anyone with connected brain cells that the replacement of "creationism" with "intelligent design" was not a good-faith effort to "comply with a court decision", but a dishonest and deceptive way to make an end-run around the intent of the decision.

Roger Schlafly thinks "Evolutionists [are] preoccupied with motives". But in the law, as in everyday life, motive is often taken into account when judging the actions of people: Actus non facit reum nisi mens sit rea.

It seems that, in this case, IDiocy has a genetic component.

This is the laboratory of a Nobel-prize winning scientist, located on a street in Europe bearing the name of that scientist. Whose laboratory is it?

One of the nicest things about France is that streets are named after writers, painters, mathematicians, scientists, and other people of accomplishment. Here's a picture of a street sign in the 14th arrondissement, showing a street named after Étienne Bezout (1730-1783).

I became interested in Bezout a few years ago when I wrote an article entitled "Origins of the Analysis of the Euclidean Algorithm" for Historia Mathematica. One of Bezout's accomplishments was his textbook, Cours de Mathématiques à l'Usage des Gardes du Pavillon et de la Marine, which went through dozens of editions, first under Bezout, and later, at the hands of others. Supposedly even Napoleon I learned mathematics from Bezout's book.

Here's a picture of the science section at a bookstore in Trudeau airport in Montreal:



Among the books prominently displayed are

• Richard Dawkins, The God Delusion
  
  
• Christopher Hitchens, The Portable Atheist
  
  
• Michael Onfray, In Defense of Atheism
  
  

I don't understand why these books aren't in the religion or philosophy section.

Oh, boy, I really can't wait for this workshop, where I can pay $359 to hear Denyse O'Leary, dean of Canadian journalism, instruct me on how to construct sentences --- like this one:

Phyllis Schlafly, the nemesis of radical feminists who is just SO not invited to Hill Clinton's inagural (which may never happen anyway, the way things are going) puts in her two cents worth on the Expelled movie about the trials of being an intelligence design theorist in an ivy league of Darwin cultists:

It really takes an exceptional talent to combine this much fatuousness, name-calling, misspelling, and an inability to provide the correct name of her own movement, all in a single sentence.

One of the commenters led me to this website of Richard Bartlett, a Seattle chiropractor who thinks he can heal people using quantum mechanics.

The website consists of the most absurd woo, such as "Matrix Energetics is a complete system of healing, self-care and transformation. It is a transferable and teachable phenomenon, powered by intent, which has a physical and observable effect every time. Complete beginners as well as seasoned health care practitioners are able to perform and utilize this work to affect change-with no waiting and no running of energy. Anyone can learn this skill and practice Matrix Energetics."

Well, if it has a physical and observable effect "every time", let's see some peer-reviewed studies that prove it. Are there any? The website doesn't provide any. It does have a section called "Research", where you can read about "polycontrast interference photography", which seems to be yet another form of woo.

Bartlett seems to have a cartoon understanding of quantum mechanics, such as when he writes
"There’s something called the Heisenberg Uncertainty Principle. What that says, essentially, is you cannot observe a system without entering into that observation and therefore changing it. Scientifically, this means that if you look at something and attempt to measure its velocity, you lose track of its actual ___location. If you try and track its ___location, you lose the ability to measure its velocity. You can never actually measure both at the same time; you can observe one and change the other."

You can bet that with seminar costing as much as $545 a shot, with multiple levels, Bartlett is raking in the cash from gullible sick people.

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.

Take a look at at this article about a mystery noise that's been annoying neighbors in Pikesville, Maryland.

Residents reported explosions and flashes of light in the middle of the night. They reported the noise to the police, who seemed skeptical until they captured it on video. According to the article,

"Whatever it is there's a scientific explanation," said Johns Hopkins University Physicist Dr. Peter Armitage, who reviewed the video tape evidence and went to the neighborhood where it's happening to see if he could find any possible causes.

Armitage says more evidence is needed before he can form a scientific conclusion.

and


[Bonnie] Friedman agrees. "We even said maybe it's aliens. We're at the point where we'll listen to anyone's theory. We just need to stop it because my homeowners need to sleep."

This has apparently enraged the Discovery Institute. Spokesman John West said, "Scientific materialism--the claim that everything in the universe can be fully explained by science as the products of unintelligent matter and energy--has become the operating assumption for much of American politics and culture." He took issue with Armitage's claim that the noise and light must have a scientific explanation: "Although this line of reasoning exhibits a surface persuasiveness, it ignores the natural limits of scientific expertise... If the history of scientific materialism in politics shows anything, it is that scientific experts can be as fallible as any one else."

Biologist Jonathan Wells thinks Bonnie Friedman is not being fair by considering aliens as a valid explanation, but not God: "Probably everyone would concede that attributing design to space aliens doesn’t ultimately solve the problem; it just moves the solution further away.... Why not God?"

Sounds pretty convincing to me. I don't know why the Baltimore County police aren't considering the possibility that this sound-and-light show is supernatural. After all, the Bible tells us that God intervenes all the time in human affairs. Why not in Pikesville, Maryland?

Oops.

[All quotes from DI spokesmen are genuine, although they have been taken out of context for comic purposes.]

John Derbyshire and I disagree about many things, but one thing we can agree on is the rank dishonesty of the intelligent design movement. In this piece for National Review, he takes on "Expelled" and the Discovery Institute, and when he's done, there's not much left to say.

Some choice quotes:

"When talking about the creationists to people who don’t follow these controversies closely, I have found that the hardest thing to get across is the shifty, low-cunning aspect of the whole modern creationist enterprise."

"The old Biblical creationists were, in my opinion, wrong-headed, but they were mostly honest people. The “intelligent design” crowd lean more in the other direction. Hence the dishonesty and sheer nastiness, even down to plain bad manners, that you keep encountering in ID circles."

"The “intelligent design” hoax is not merely non-science, nor even merely anti-science; it is anti-civilization. It is an appeal to barbarism, to the sensibilities of those Apaches, made by people who lack the imaginative power to know the horrors of true barbarism."

My student Dalia Krieger recently defended her Ph. D. thesis successfully. She'll be leaving Waterloo soon to take up a postdoctoral position in Israel. That's a good excuse to talk about some topics in combinatorics on words.

Dalia's thesis focused on problems dealing with "critical exponents". To explain what she did, I first need to define the notion of powers in words. By a "word", I just mean a string of symbols. A square is a nonempty word of the form xx where x is a word. For example, the word murmur is a square in English (let x = mur). Similarly, we can define cubes, and more generally, n'th powers, where n is an integer ≥ 1.

We can even define fractional powers! We say that a word y is a p/q power if y is of length p, and consists of a word x of length q repeated some number of times, followed by some prefix of x. For example, alfalfa is a 7/3 power, because it can be written as (alf)²a. We say that the exponent of alfalfa is 7/3.

The critical exponent of an infinite word x is defined to be the supremum of the exponents of all subwords of x. (Here a subword is a contiguous block of letters; it is called a "factor" in Europe.) Of course, this supremum could be infinite. Given an infinite word, it is a very interesting and challenging problem to determine its critical exponent.

Now, there is a particular class of infinite words that is of particular interest: these are the word that are generated by iterating a morphism. A morphism is a map that sends every letter in some finite alphabet to a finite word. We can then apply the morphism to a word by applying it to each individual letter and concatenating the results together. Thus, a morphism is a map f that satisfies f(xy) = f(x)f(y). Provided the ___domain and range of a morphism are over the same alphabet, and the morphism is non-erasing (never maps a letter to the empty string), we can iterate a morphism, obtaining longer and longer words. If in addition f(a) = ax for some word x, then each iterate, starting with a will be a prefix of the next, so we can talk about the unique infinite word that has all the iterates as prefixes.

The simplest example of such an infinite word is the Fibonacci word, generated by iterating the map φ that sends a to ab and b to a. When we iterate this map, starting with a we get,
successively,

a, ab, aba, abaab, abaababa, abaababaabaab, abaababaabaababaababa, ...

Notice that each word is the concatenation of the previous two.

The Fibonacci word evidently contains cubes; for example, the cube (aba)^3 appears in the last word above. What is its critical exponent? In a beautiful paper in 1992, Mignosi and Pirillo showed that the critical exponent is

(5+√ 5)/2,

or about 3.618. (This is the "golden ratio" plus 2.)

On the other hand, the famous Thue-Morse word t is generated by iterating μ on 0, where μ sends 0 to 01 and 1 to 10. (Such a morphism is called "uniform" because each letter gets sent to a block of the same length.) The critical exponent of

t = 0110100110010110 ...

is 2, as was proved by Thue about a hundred years ago.

Dalia proved many results in her thesis, but here are some of the easiest to state: first, every real number > 1 can be the critical exponent of some infinite word. Second, if an infinite word is generated by a uniform morphism over the binary alphabet, then the critical exponent is always either infinite or rational. (She also gives a way to compute it.) Third, if an infinite word is generated by an arbitrary non-erasing morphism, then the critical exponent is always either infinite or algebraic. (An algebraic number is one that is the zero of a polynomial.) Furthermore, she can say which algebraic number field the critical exponent must lie in.

These are beautiful results, and the proofs are quite difficult. Before her work, computing the critical exponent of a word generated by a morphism was a kind of "black art", but now it can usually be done without too much work.

Congratulations to Dalia for a great thesis!

I rarely read Denyse O'Leary's blog because it is so unreadable: she is, without a doubt, one of the worst writers in Canada. But today I noted this post praising a recent talk by Robert Marks, the Baylor engineering professor and intelligent design advocate, on the subject of algorithmic information theory, and the work of Turing, Gödel, and Chaitin.

I wasn't at all surprised to see that O'Leary doesn't really understand what's going on. After all, she has no training in science and mathematics, and her books demonstrate her lack of understanding. In her post's most comical moment, she gives Alan Turing's first name as "Alvin", apparently confusing computer science's most famous theoretician with a chipmunk.

But Marks is not stupid, so I was surprised to see several significant misunderstandings in his powerpoint presentation.

Mistake 1: The title is wrong. He says, "Things Gödel Proves a Computer Will Never Do". But it was Turing, not Gödel, who proved that there are problems that a Turing machine cannot solve.

Mistake 2: Marks calls the idea that "There exist things that are true that cannot be derived from fundamental principles" a "new startling mathematical idea from algorithmic information theory". But it isn't. It's an old idea from Gödel, dating from 1931.

Mistake 3: Marks says "we can't write a computer program to determine anything another arbitrary computer program will do. (This is called Rice’s theorem.)". This is false (and I have just finished teaching a course about the subject). Rice's theorem is about the languages accepted by Turing machines, not the machines themselves. For example, the problem "given a computer program, does it run for more than 100 steps on empty input?" is certainly solvable, simply by simulating the program in question. Less trivially, the problem of deciding whether a given Turing machine ever makes a left move on a given input is also solvable. I sometimes give this problem as a homework problem in my course. Marks, apparently, would get it wrong.

Mistake 4: Marks says that "Gödel’s Proof (1931) showed, from any set of assumptions, there are truths that cannot be proven." Again, not true. Presburger arithmetic, for example, is complete, consistent, and decidable.

Mistake 5: This objection may be more contentious. Marks thinks the work of Gödel and Turing has important implications for physics. I don't, and the reason is that we don't prove our theories in physics the same way we prove our theorems in mathematics. Physical theories represent our current understanding of an approximation to the natural world, not diktats on how it must behave.

If anything, it at least possible that novel physical theories overturn our understanding of the importance of, say, the halting problem. As Robert Geroch recently remarked at the Perimeter Institute, the existence of Hogarth-Malament spacetime might imply that the halting problem is solvable (it provides an infinite timelike curve entirely in the history of another point, so we could set up the computation "back then" and see if it ever terminated "later").

Marks clearly derives his understanding of Gödel and Turing from reading popular works, not textbooks on the subject. I'd recommend he read Torkel Franzen's Gödel's Theorem: An Incomplete Guide to Its Use and Abuse.

As for O'Leary's claim that Gödel's and Turing's work somehow puts a "nail in the coffin of materialism", the kindest thing I can say is that she has not proved her case. Indeed, she hasn't even presented a case.

It's always fun to read the comments at William Dembski's blog, Uncommon Descent. Because that blog is carefully moderated, hardly any criticism is posted. The result is an unadulterated picture of the views of Dembski's supporters, and that picture isn't pretty. But it is funny.

Take, for example, this thread. It starts with the idiocy of Barry Arrington, who seems to think that Karl Popper wrote "scientific text[s]".

But the hilarity really starts with a post by "Gods iPod", who wrote

I PERSONALLY have witnessed a bona-fide New Testament-level miracle.

I don’t expect you to believe on my say-so, but I have witnessed, not on a stage a hundred feet away, but less than 10 feet away, a woman’s leg grow about 1 1/2 inches. She was born with one leg shorter than the other. There was no song and dance, no raised voices, no spectacle, just a short request to God to heal her leg, and it did. In front of my eyes.

So yes, I believe in miracles.


Yes, that is funny. But I have to admit that I honestly feel sorry for credulous and deluded believers like "Gods iPod", who are taken in by the "leg lengthening" scam and feel that they have witnessed a miracle, when all that they have seen is a common carnie trick employed by fake faith-healers. James Randi discusses precisely this scam on pages 128-130 of his book, The Faith Healers, with pictures and an explanation of how the scam was carried out by phony faith-healer W. V. Grant.

What better evidence that we need to have courses in critical and skeptical thinking beginning in the early grades?

Growing up in the late 1960's, I was introduced to the songs of Tom Lehrer by my friend Scott Turpin. Lehrer is a mathematician who taught at MIT and Santa Cruz, but he is best known as one of the best musical satirists of all time. He produced a small number of albums in the 1950's and 1960's, but essentially stopped all performing in the late 1960's. A small number of songs written afterwards, such as the songs he wrote for the TV show "Electric Company", are available on compilations.

Now I see that a channel on YouTube has resurrected some extremely rare video performances of his songs. And here you can see a video of some of his songs about mathematics. If you, like me, never had a chance to see Lehrer perform in person, these videos will come as a welcome surprise.

It's too bad Lehrer became bored with performing and writing. I would have loved to have heard him comment on Reagan, Bush, and Bush junior.

David Berlinski is yet another of those academic nonentities that the Intelligent Design crowd has elevated to the status of expert, despite having a minuscule scientific publication record and not a single significant contribution to science or mathematics. Berlinski is fond of writing, mostly negatively, about the theory of evolution, despite understanding virtually nothing about the subject, and somehow manages to get his essays published in famous scientific venues, such as Commentary.

Berlinski is sometimes described as a mathematician, although his Ph. D. is apparently in philosophy, not mathematics. MathSciNet, the online version of Mathematical Reviews, a journal that attempts to review nearly every mathematical publication, lists exactly 8 items authored or edited by Berlinski. Two are books for a popular audience: (Newton's Gift and The Advent of the Algorithm). Of the remaining 6 items, 3 are contributions published in Synthese, a philosophical journal, for which Berlinski served as editor and wrote brief introductions and the other 3 are largely philosophical papers, published in Synthese, the Biomathematics series, and Logique et Analyse. Two of the last three didn't even merit a genuine review in Mathematical Reviews.

Berlinski also published a 1998 contribution entitled "Gödel's Question" in Mere Creation, an intelligent design book edited by William Dembski and published by that famous scientific publisher, InterVarsity Press. This piece of mathematical junk was already taken apart by Jason Rosenhouse, so I won't comment on it further other to say that it is so content-free, it could not be published in any reputable mathematical journal.

When Berlinski boasts that he "got fired from almost every job [he] ever had", one can only listen open-mouthed at the chutzpah to transform a mark of shame into a badge of iconoclasm. WIth such a miserable publication record, it's amazing he was ever hired to begin with.

Berlinski's fame, such as it is, derives from his popular books, which include A Tour of the Calculus in addition to the ones I listed above. Some reviewers, mostly those with no mathematical training, like his books for their literary value. Personally, I find them insufferable. To explain why, I can do no better than to list some excerpts from a review of A Tour of the Calculus by Jet Wimp, at that time a professor at Drexel University, and published in The Mathematical Intelligencer 19 (3) (1997), 70-72:


"Reading Berlinski's book A Tour of the Calculus, I was first angered, then revolted, then finally wearied: the three stages of grief of the hapless reviewer. Berlinski wants to maek the calculus available to everyone--anyone who wants, simply, "a little more light shed on a dark subject". This delirious tract is the result....

"Berlinski's greatest friend, but ultimately his worst enemy, is metaphor. The gongorisms that saturate this book actually confound what the author claims is its central mission: to teach the novice calculus. The Berlinski rhetoric ultimately becomes suffocating. The metaphors explode from all directions...

"This expositional overload implies a cynical disrespect for the subject...

"I was particularly annoyed by Berlinski's biographical snippets... Had Berlinski done his homework, he could have told us some interesting things about mathematicians that were really true. He might have told us, for example, that Newton's explosive temper and dark moods were most likely caused by mercury poisoning, and chemical analysis of the floorboards of his still extant alchemical laboratory have revealed heavy concentrations of that metal. But then, perhaps such an observation lacks poetry.

"I was dismayed at the author's rudimentary grasp of mathematical history. It is painful to find so little learning in a book that purports to explain an intellectual discipline...

"Of all the passages in the book, I found the following the most mortifying... I flushed with embarrassment (as would anyone who loves mathematics) when I read this rebarbative grunge quoted (disapprovingly) in a review in The New Scientist...

"Regrettably, Berlinski's readers will emerge from his verbal thickets hearing nothing."


This reviewer sees through Berlinski's obfuscations for what they are: a pretentious exercise with no relation to genuine exposition.

Now that Berlinski has appeared in "Expelled", expect to see even more of this pompous poseur in the media.

One of the few advantages to living in an area with a lot of fundamentalists is that you can obtain crackpot works of pseudoscience very cheaply at the local book sales. I'm not sure why the fundies like these things, but my guess is that credulity in one area leads to credulity in others.

I like to have these books so I can be prepared to answer their arguments, but I don't like enriching the authors. So buying used copies satisfies both desires. (I admit, however, that if the book is still in print, buying a used copy indirectly benefits the author anyway, since it decreases the supply of available copies, thus making it more likely that someone else who wants one will have to buy a new copy.)

Here's what I picked up for a total of $4 at the recent Canadian Federation of University Women booksale in Waterloo:



The work of Barry Fell is particularly interesting, because the author was, at one time, a legitimate scientist, holding an appointment in marine biology at Harvard. His archaeological ideas, however, are pure crackpottery. Fell claims that linguistic evidence, inscriptions, and architectural evidence points to substantial colonization of North America by the Iberians, Celts, Greeks, ancient Hebrews, and Egyptians, beginning about 1000 B. C. E.

Fell's arguments, such as they are, were entirely eviscerated by Kenneth Feder in his marvelous book Frauds, Myths, and Mysteries: Science and Pseudoscience in Archaeology. I recommend Feder's book to any skeptics interested in phony archaeology.

Does anyone like the movied "Expelled: No Intelligence Allowed"? Anyone?

Pretty much no, if you read the reviews at Rotten Tomatoes. So far, only 2 critics out of 22 have something nice to say, and one of them is from Mark Moring of Christianity Today. (Poor Mark doesn't seem to know the difference between "infer" and "imply".)

I love this line from the Hollywood Reporter review: "more than lives up to its subtitle". And the New York Times said, "One of the sleaziest documentaries to arrive in a very long time, “Expelled: No Intelligence Allowed” is a conspiracy-theory rant masquerading as investigative inquiry." At the end, the reviewer says, "“Expelled” is rated PG (Parental guidance suggested). It has smoking guns and drunken logic."

Welcome to Carnival of Mathematics #31 !

Step right up, folks, and behold the amazing properties of 31. Now, you all know that 31 is a prime number. But that's not all -- 31 is also a Mersenne prime, that is, a prime number of the form 2^p - 1. There are currently only 44 such primes known, and nobody knows if there are infinitely many. If I had to bet, I'd wager that the question of whether there are infinitely many will not be resolved in my lifetime.

So 31 = 2⁵ - 1. And 2³¹ - 1 = 2147483647 is a pretty interesting number, too. It's another Mersenne prime, and it's also the largest integer representable in 32-bit signed arithmetic. Because of that, when programs die because of integer overflow, you might end up with 2147483647 in some unexpected places, such as this video game, where a Toyota GT achieves the faster-than-light speed of 2147483647 mph.

So if 2⁵ - 1 is prime, and 2 ^{25 - 1} - 1 is prime, is 2^{2 25 - 1 - 1}-1 also prime? Regrettably no. We currently know 4 different prime divisors of 2^2147483647 - 1, and they can be found here, on the line labeled M ( M (31) ).

Oops, I got sidetracked there. Let's go back to 31. One more property of 31 (which I got from the very cool book by François Le Lionnais, Les Nombres Remarquables) is that it is the only prime number known that can be written in two different ways in the form (p^r - 1)/ (p^d - 1), where p is a prime and r, d are integers with r ≥ 3 and d ≥ 1. One such representation for 31 is (2⁵ - 1)/(2-1). Can you find the other?

OK, enough about 31 ... back to the carnival!

Step right up, and learn how to factor monic quadratic integer polynomials at Life Jelly. Too easy for you, my friend? Then you can go directly to factoring arbitrary quadratics.

Polynomials not your game? Then how about figurate numbers? The simplest example of a figurate number is the total number of balls in an equilateral triangle, like a rack of pool balls. A rack of pool balls has 5 rows of balls with 1,2,3,4, and 5 balls, for a total of 15, so 15 is the 5th triangular number. Denise, at Let's Play Math, has a gentle introduction to these numbers. Question: what's the smallest number ≥ 1 that is both triangular and square? Can you prove there are infinitely many? (See Beiler, Recreations in the Theory of Numbers, Chapter 18, for more about these numbers.)

I'm allergic to cats, but don't let that stop you from visiting Calculus for Cats and the Prime Number Theorem over at catsynth.com.

What's that you say? Not hard enough? Then drop on over to Charles Daney at Science and Reason for an introduction to the factorization of prime ideals in extension fields. You might want to scan his previous entries if you're entirely lost.

Now, wait, I understand, you've had enough algebra. It's time for geometry. Visit 360, the informal blog of the Nazareth College Mathematics Department, for some real life nonagons. Were the Beatles really closet Bahais?

It took me a while to figure out why David Eppstein's blog is called 11011110; maybe there was a hex on me. I guess he's lucky his parents didn't name him George. But his blog always contains deep and beautiful results explained in simple ways, and this contribution about biclique covers is no exception. Step right up!

Our last geometric contribution comes from Praveen Puri at Math and Logic Play, who offers a puzzle based on the square. Free admission!

Next up, we have a bevy of logical beauties. While we're waiting for Jason Rosenhouse to finish his book on the Monty Hall problem, you can think about this variation from Magpie Tangent. Almost Philosophy gives us an introduction to propositional logic. Quan Quach at blinkdagger gives us a macintosh mystery with a prize for the winner. And Presh Talwalkar at Mind Your Decisions recounts a classic, the hat problem.

After all that logic, it's time for some illogic. Visit my own blog to see how a mathematics educator abuses mathematics for Jesus .

That's all there is folks, there isn't any more. Until Carnival of Mathematics #32, that is.

I've previously commented about Marvin Bittinger's book, The Faith Equation: One Mathematician's Journey in Christianity. I called it a "combination of ignorance and intellectual dishonesty". Now that I've had a chance to read it more carefully, I find I was too kind. It is pure and utter dreck. Actually, "dreck" is far too kind. I find it hard to convey the self-satisfied stupidity that is found on nearly every page.

Instead of giving a detailed critique, in the spirit of the Carnival of Mathematics, I'll focus on some of the questionable mathematics that Bittinger uses.

Christian apologists have long been fascinated by the power of mathematics. My colleague Wesley Elsberry has taken apart an argument from 1925 here, where the author claims that the current rate of growth in human populations implies a young earth. The writer of that bogus argument claimed that "Figures will not lie, and mathematics will not lie even at the demand of liars." Unfortunately, the reverse is true: it's easy to lie for Jesus, mathematically. And probability theory is one of the easiest tools to abuse.

In The Faith Equation, tiny probabilities are assigned, often with little or no justification, and probabilities are multiplied together with no evidence of independence. These tactics are particularly evident in Chapter 4, "The Probability of Prophecy". In this chapter, Bittinger concludes that prophecies in the Bible constitute an event of probability 10^-76, which is a miracle that proves the accuracy of the Bible and the existence of God.

As I've already pointed out, Bittinger ignores significant criticism about his claimed prophecies. Tim Callahan's Bible Prophecy: Failure or Fulfillment?, Farrell Till's Prophecies: Imaginary and Unfilfilled and Jim Lippard's Fabulous Prophecies of the Messiah all take issue with many of the prophecies claimed by Christians. I see no sign that Bittinger has read these critiques; he certainly hasn't cited them in his reference list.

I'm not going to get into the accuracy of individual prophecies here; instead, I want to comment on one tool that Bittinger uses to justify his small probabilities. On page 93, we read:

"There is a concept from probability that we use often in these arguments. Suppose an assertion, such as God promising never again to flood the earth after the time of Noah's Ark, occurred t years ago, and to date the prophecy either has not been fulfilled or was just fulfilled. Statisticians would then estimate the probability of the event to be approximately one over twice the number of years: 1/(2t). We refer to this as the time principle and use it extensively."


There are two problems here: first, the "time principle" is completely nonsensical and second, it is not used by "statisticians" as Bittinger claims.

The "time principle" is nonsensical for several reasons. First, it is based on years, an entirely arbitrary way to measure time. We can get any probability we like from the formula 1/(2t) simply by changing the unit of measurement. If we measure time in centuries instead of years, the probability increases by a factor of 100. If we measure time in seconds, the probability decreases by a factor of about 31,000,000. Second, a well-established principle of probability is that if a space is partitioned into events, the sum of all the probabilities must be 1. But the sum of 1/(2t) for t from 1 to n can never be 1, since it is .91666... for n = 3, and 1.041666... for n = 4. Third, it doesn't take into account the character of the assertion. If I asserted in 1975 that "people will write the year 2000 on their checks", this would clearly not be fulfilled until 25 years later. Yet it would occur with probability 1 (or at least close to 1), not 1/50 as the "time principle" suggests.

Is the "time principle" used by statisticians, as Bittinger claims? I used MathSciNet, the online version of Mathematical Reviews, a review journal that attempts to review every noteworthy mathematical publication. I found no references to this principle anywhere in the literature. I then consulted a statistician down the hall at my university, who had never heard of this principle and agreed it was nonsensical.

So Bittinger's "time principle" is pseudomathematics, and is not used by genuine mathematicians. I asked Bittinger where he got it from, and he replied, "Your point is well-taken and I must admit that in some ways the time principle is a stretch. I did "develop" it on my own, and had it corroborated by a top-notch statistician in my department - mathematicians do that you know. I should have said something to this effect, and not "from probability."" I am glad that Bittinger admits that his "time principle" is bogus, and I hope to see a forthright admission to this effect on the website for his book.

Chapter 6 of The Faith Equation discusses the power of prayer. He begins by discussing a controversial study by Randolph C. Byrd that appeared in Southern Medical Journal 81 (7) (July 1988), 826-829, which claimed to show that heart patients showed a statistically signficant benefit from intercessory prayer. Bittinger does not acknowledge any criticism of the Byrd study; indeed, he says, "To a statistician, Byrd's study proved intercessory prayer was effective." But Tessman and Tessman (Skeptical Inquirer (March/April 2000), 31-33 pointed that Byrd's study is bogus for three reasons: the analysis of the results was conducted in a non-blinded fashion by Byrd, the criteria used for evaluating the outcomes were created after the data had been collected, and the study's co-ordinator was non-blinded. Bittinger does not cite the work of Tessman and Tessman, nor other critiques by Sloan, Bagiella, and Powell (Lancet 353 (1999), 664-667) and Posner (Scientific Review of Alternative Medicine 4 (1) (Spring/Summer 2000). By refusing to acknowledge informed criticism of these prayer studies, Bittinger abdicates his responsibility as a professor and an academic.

These two examples should suffice to show how the case in The Faith Equation is so transparently weak that even non-mathematicians should be able to spot the flaws.

Seen the silly movie Expelled? Go read the debunking first. (I have a small part in the debunking; the NCSE has cited my review of Pamela Winnick's book in support of their case.)

Well, it looks like the proposed April 18 presidential science debate in Philadelphia is not going to happen. Obama, to his discredit, has refused to participate, and McCain didn't even respond; Clinton was non-committal.

But the good folks at Science Debate 2008 aren't giving up. The latest proposal is a nationally-televised debate on NOVA, the PBS science show, on either May 2, 9, or 16, with host David Brancaccio.

If you have any contact with the campaign staff of the 3 major candidates, contact them to let them know you want this debate to happen.

Update: Clinton and Obama refused to participate in the science debate, but they have time for this debate at Messiah College on "faith, values, and other current issues".

I'll be speaking at the University of Guelph, at the invitation of the Guelph Skeptics, on Wednesday, March 26, at 7 PM in Thornborough 1200. The title of my talk is "Misinformation Theory: How Creationists Abuse Mathematics". There's a little more info here. If you read Recursivity, stop by and say hello.

No, it is not appropriate to use the comments section of my blog to arrange "meetups" for your loony conspiracy theories.

(Yes, believe it or not, somebody tried to do this. For friggin' St. Louis.)

After the introduction by Richard B. Lee, the presentation by A. K. Dewdney, and the presentation by Graeme MacQueen, there was a brief intermission, followed by a question-and-answer period.

After the deniers spoke for about two hours, the organizers allowed only about 30 minutes for questions. The question period was moderated by Michael Keefer, a professor in the School of English and Theatre Studies at the University of Guelph. Keefer is the author of this criticism of Alexander Cockburn for not buying the theories of 9/11 deniers, and as such, is placed firmly in the "9/11 Truth" camp. (For Cockburn's columns, go here and here; for more "9/11" material by Keefer, go here.)

The first question was, "What evidence would be required to disprove the theories presented here tonight?" The responses ranged from "We are not at a position to say" (paraphrased) to Graeme MacQueen's claim that he read 9/11 firefighters' testimonies looking for evidence for and against his hypothesis of an explosion.

The next question was, "Popular Mechanics says cell phone calls can be made from planes. If they cannot, does this mean that the US government's analysis is flawed, or was their a conspiracy?" (paraphrased). In response, Dewdney says it's up to people who claim the calls can be made to explain them, not up to him.

The third question asked, "Do you think the initial 9/11 Commission report was a deliberate attempt to mislead people, or was it just mistaken conclusions due to time pressure?" Graeme MacQueen thinks it was deliberate, and as evidence, said that Philip Zelikow (executive director of the 9/11 commission) was a friend of Condoleezza Rice, so the 9/11 Commission wasn't independent.

The fourth question asked, "Who benefits?" The response was that the US benefits by seizing Iraqi oil supplies. The Iraqi people will never regain control of their own oil. The reasons for the invasion of Afghanistan are similar, and the goal is complete hegemony by the US empire.

The fifth question asked, "Was there any attempt by NIST to model the airplane crashes?" Answer: no, there was not. The University of Waterloo should model these events. Dewdney agreed.

Finally, I had a chance to ask a question. Earlier in the evening, I had argued with the moderator Michael Keefer, and he was doing his best to avoid seeing my raised hand. In the classiest event of the evening, A. K. Dewdney intervened and said, "Can we have a question from my friend?" I think he deserves a lot of credit for this gesture, particularly because he knows I am a fierce critic of his position. I listed 3 falsehoods in Dewdney's presentation (Keefer tried to cut me off after 2) and asked for their reply: the wrong number of Airfone calls from UAL 93, the use of the word "pull" does not mean controlled demolition, and the debris in Shanksville. Dewdney acknowledged that there was debris, but again used the opportunity to cast doubt on the crash by saying that inflight magazines were found 15 miles away, suggesting that UAL 93 was shot down.

Afterwards, I had the opportunity to chat briefly with some of the attendees. One person thanked me for offering the only rational voice of the night, but others thought I was misguided. I made the analogy of 9/11 denial to creationism, to which one attendee responded, "I don't believe in evolution -- I'm a Christian".

Conclusion: the speakers presented a case for conspiracy that was superficially persuasive, but only if one has not read any rebuttals to their bogus claims. In general, the speakers did not have the professional qualifications to comment on the events, and as academics, behaved irresponsibly in so doing. They also failed to acknowledge that experts who do have the relevant qualifications take issue with their theories. The U of W Debate Club should be ashamed of its role in the event, allowing the deniers to speak so long and unopposed, and allowing a "moderator" and question-taker that were not neutral.

At the beginning, "moderator" Richard B. Lee asked, "Why have the floodgates not opened? Why is the media not filled with page after page of penetrating investigative journalism?" The answer is clear: because the claims of the "9/11 Truth" movement are sheer crackpottery, no matter how many scholars subscribe to them.

If the organizers of this event think they will make political hay out of it, I think they are sorely mistaken. As Chip Berlet has pointed out, no successful political movement in North America has ever been based on allegations of conspiracy. By focussing on bogus claims of controlled demolition, we lose focus on what really matters: how the US was led to war by a dishonest administration, and how the US can now repair the damage it has wrought and its reputation in the world. And how the civilized world can best counter the genuine threat posed by fundamentalist religions of all stripes, including the violent and radical Islam that caused 19 young men to take the lives of thousands of others on September 11, 2001.

According to this article in the New York Times, the US Air Force Academy in Colorado Springs recently paid $13,000 to 3 self-proclaimed "ex-terrorist" speakers who are now evangelical Christians. Walid Shoebat, Kamal Saleem, and Zachariah Anani are accused of being frauds. (For more about Anani, see this article in the Windsor Star.)

This is yet more disturbing news about how the US military academies are functioning as evanglical indoctrination enters.

For other parts of this series, go here, here, here, here, and here.

The last speaker of the evening was Graeme MacQueen, who was introduced as a retired professor of Religious Studies at McMaster University in Hamilton, Ontario. His specialties include Buddhist studies. Like the other speakers, MacQueen has no professional background to discuss the physics and engineering aspects of the World Trade towers' collapse, but that didn't stop him from pontificating on the subject.

He started by thanking Adnan Zuberi and Adam Parrott for organizing the evening. (As an aside, I note that when I asked a member of the UW Debate Club who Adam Parrott was, he had no idea. I find it strange that an organizer of the evening's events would be unknown to members of the club that sponsored the presentation. Both Parrott and Zuberi are listed on this page as "grassroots organizers" for the misnamed "9/11 Truth" movement.)

He started by saying, "I have two modest aims: why a reasonable person might have serious doubts about the official explanation about why the two World Trade Centre towers came down the way they did... why a reasonable person might want to explore another theory: controlled demolition." This indeed, sounds very modest. But soon the veneer of reasonableness was stripped away, as he described the generally-accepted model of the Towers' collapse and then said, "A rather obvious fraud, in my view." This kind of behavior is typical of the "9/11 Truth" movement. Their claims are outlandish and unsupported; yet if you do not agree, you are in league with fraud. By using the word "fraud", MacQueen denigrates the dozens of structural engineers, fire engineers, and civil engineers who have looked into the buildings' collapse and have paintstakingly devised the generally-accepted theory. There is no legitimate reason to believe that all these researchers have engaged in fraudulent activity, and it is a gross calumny to say so.

Much of MacQueen's argument was devoted to the principle that since, if you looked at the video of the World Trade towers' collapse, you would describe what happened as an "explosion", therefore there must have been an explosion that caused the collapse. He consistently denigrated the idea that to understand exactly what happened, you would need to understand anything substantial about physics, civil engineering, or building construction: "You don't need a Ph. D. to look at these photographs".

He plotted the position of the top of one tower through time, and was astonished to discover that the resulting graph formed a parabola similar to free fall. (I imagine professors of religious studies don't have much time to study equations based on gravity.) This "grade-school physics" exercise, he claims, is enough to rebut the thousands of hours of study by civil engineers on the World Trade Center collapse, and the report by the National Institute of Standards and Technology.

The only alternative to the NIST theory, according to MacQueen, is controlled demolition, brought about by explosives, incendiaries, or both, through a covert operation.

"Controlled demolition" of the WTC, of course, is one of the favorite assertions of 9/11 deniers. But they offer no plausible rationale why anyone would want to carry out both a plane attack and a controlled demolition. Why not just the demolition? Wouldn't it be much more sensible to plant bombs in the WTC and then blame those on terrorists? After all, terrorists already bombed the WTC back in 1993. 9/11 deniers consistently fail to address this.

Further, if the government carried out the plane attack, why would they bother with setting bombs, too? The destruction wrought by the planes alone seriously damaged the buildings, and repairs would have cost hundreds of millions, if not more. Why wouldn't that be enough as a pretext for war, if that were the government's plan? 9/11 deniers have no answer.

Furthermore, seismic data offer no support at all for the contention that there was an explosion before the collapse of the buildings. How do 9/11 deniers explain this? Silence.

During his presentation, MacQueen referred several times to the Journal of 9/11 Studies for support for his claims. The editors of this "journal" are Kevin Ryan, Frank Legge, and Steven Jones -- three men heavily involved in the "9/11 Truth" movement. No one taking issue with "9/11 Truth" claims is involved. This is not a scholarly journal in any sense of the word; it is a propaganda outfit for deniers.

The latter part of MacQueen's presentation was devoted to his analysis of the testimony of firefighters. He said, "I decided to read it and look for evidence of explosions". Sounds to me like looking for evidence to support one's preconceptions (although later he backtracked and said he also looked for evidence against the idea of explosions). MacQueen seems to think that one can get at the truth of whether or not there were bombs planted in the building by analyzing the testimony of people who were there.

The problem is that the WTC collapse involved fire, structural damage, and probably small explosions as pockets of fire encountered volatile chemicals. Furthermore, we lack the vocabulary to describe what happens when a building collapses from the top down; it is not a phenomenon we encounter very often. Lacking such a vocabulary, anyone might have called what happened an "explosion" without meaning that a bomb was involved.

To illustrate this, consider the 1945 crash of a military plane into the Empire State Building. Witnesses described the sounds of gunshots (but were in fact the sound of elevator cables snapping). By the MacQueen principle of witness reliability, if witnesses heard gunshots, then there must have been gunshots inside the Empire State Building.

In summary, I heard a discussion of building collapse by a man not professionally qualified to do so, a foolish reliance on the use of the word "explosion" to imply the existence of a bomb, and a lack of any explanation why both a plane crash and a bomb would be used by the government to bring down the World Trade towers.

For part 1, go here. For the intro to this series, go here.


After discussing the cell phone calls, Dewdney moved on to another area far from his expertise: the collapse of the World Trade towers.

He showed a picture of one of the towers with an arrow pointing to part of it, with a caption reading "Molton [sic] steel pours from side of WTC 1". The resolution of the picture didn't allow me to conclude that anything molten at all was pouring out, certainly not molten steel. If anything was pouring out, why couldn't it have been molten aluminum? Aluminum melts at 660° C, while steel melts at 1370-1550° C.

Dewdney went on to discuss the collapse of WTC 7. He repeated the long-debunked falsehood that Larry Silverstein, who leased WTC 7 from the Port Authority, admitted that WTC 7 was brought down by controlled demolition. Silverstein used the word "pull" and Dewdney repeated the falsehood that "pull" is demolition slang for "bring down a building by controlled demolition". As Debunking 9/11 Myths explains in detail, this is not the case. The word "pull" was referring to the decision to remove firefighters from the building. Dewdney claimed that Silverstein "changed his story", when in fact Silverstein simply clarified what he meant.

If the expressions "pull" and "pull it" (not, I emphasize, "pull it down") are slang for controlled demolition, then the 9/11 deniers should have no problem providing a citation to a book, newspaper, or magazine article where this expression is used as the 9/11 deniers claim. I have searched myself, using the New York Times index, and Lexis/Nexis, but so far have failed to produce a single citation supporting the deniers' claim. On the other hand, "pull" can and has been used in the context of removing firefighters from a building. See here, for example, where accounts from 9/11 firefighters both use this word.

As an academic, Dewdney had a professional responsibility to provide his audience with the alternative (and widely-accepted) explanation for Silverstein's remarks, and not to repeat falsehoods about the meaning of "pull" without supporting evidence. (I'll also point out that Graeme MacQueen, a self-described expert on the analysis of texts, spoke after Dewdney and did not see fit to mention that there was any controversy about the textual analysis of "pull".)

Dewdney went on to discuss the Shanksville and Pentagon crash sites. He claimed that every other plane crash has produced large amounts of debris, but these crashes did not produce any. This is a falsehood in two ways. First, there have been plane crashes without large amounts of easily-visible debris, namely, this 1997 crash in Indonesia. (See the comments for a picture of some of the debris.) Secondly, the Shanksville crash certainly did produce debris, and some of it can be seen here.

Dewdney thinks that Flight 93 did not crash, but was shot down by an A-3 Thunderbolt. As evidence, he points to a "mysterious white twin engine jet aircraft" seen around the crash site. But this "mysterious" plane has already been identified, as Dewdney should know: it was a "Dassault Falcon 20 business jet owned by the VF Corporation" and it had been contacted by the FAA to examine the UAL 93 crash site and mark its position.

To conclude: Dewdney's performance was extremely disappointing to me. His presentation was filled with falsehoods, and his alternative scenarios ludicrous. Apparently I am not the only one to think so; even some 9/11 skeptics have effectively disowned Dewdney's claims. When people on your own side think you've gone too far, it's time for some serious self-analysis.

Yet Dewdney's presentation was praised by the other presenters, including Richard B. Lee and Graeme MacQueen. Why do they think this farrago of falsehoods deserves praise?

"A lie can travel halfway around the world while the truth is still putting on its shoes." (often attributed to Mark Twain, but may really be due to Charles Haddon Spurgeon).

If you're reading this blog, the name A. K. Dewdney (Alexander K. Dewdney, "Kee" Dewdney to his friends) is probably well-known to you. Dewdney was for many years the editor of the mathematical recreations column in Scientific American, taking over from Martin Gardner and Douglas Hofstadter. He is also the author of various books on mathematics and computing, including The Planiverse, The Tinkertoy Computer, and others in my personal library. I always regarded his columns and books with affection, because he is a good writer and his interests closely intersected with mine, and I was pleased when he briefly became a member of my own Department of Computer Science at the University of Waterloo.

Unfortunately, I can no longer read his work with the same unalloyed pleasure, because Dewdney has turned into a 9/11 denier.

His views on 9/11 are, to put it politely, outlandish and completely divorced from reality. This is particularly ironic, since in 1998 he published Yes, We Have No Neutrons: An Eye-Opening Tour through the Twists and Turns of Bad Science, in which he took on Freud, the Biosphere project, cold fusion, and other episodes of bad science. If only Dewdney applied that same kind of skepticism to his own views on 9/11.

Dewdney presented at the 9/11 Denier Event held at the University of Waterloo on March 19. His presentation, I regret to say, was laced with falsehoods.

Dewdney started by discussing the cell phone calls made from the hijacked jetliners. His thesis is the following: it is impossible, or nearly so, to have made cell phone calls from the doomed planes. Therefore the "official account" of 9/11 is false, and a more plausible explanation is that the cell phone calls were faked by the government, who had access to the passenger lists before take-off. With wiretaps, the government could have listened to the passengers ahead of time and made tapes of their speech. Then, using a voice modulator, the government could imitate their speech with "trained operators". With this technology, the government would manage to fool all of the relatives and friends that were called on 9/11.

No, I am not kidding. This is really his thesis, and he finds it more plausible than the generally-accepted account.

In the past, Dewdney has provided accounts that are even more outlandish. Here you can read the original "Ghost Riders in the Sky" scenario, where Dewdney suggests that the hijacked planes were actually taken over remotely from the ground and flown into the targets (presumably by the government). He also suggests that Israel was involved in the attacks. A later version of "Ghost Riders" was published in The Revisionist, an online journal that proclaims itself "The World's largest website for Historical Revisionism!" and features on its front page "The Holocaust Controversy: A Case for open Debate". (The vast majority of the content of this "journal" is devoted to Holocaust denial and other anti-Semitic content, with articles by known Holocaust deniers such as Ingrid Rimland, Germar Rudolf, and Bradley Smith. I have asked Prof. Dewdney how his work came to published in such an unsavory place, and he has not given any satisfactory response.) (Update: in private e-mail to me, Dewdney states that he was unaware that his article was published in this journal.) In this later version, Dewdney describes his experiments attempting to complete cell phone calls at various altitudes, and concluded that "cell phone calls from passenger aircraft are physically impossible above 8000 feet above ground and statistically unlikely below it." He also suggests that the pilots and passengers of the hijacked planes were actually all killed with Sarin nerve gas, as the planes were taken over remotely from the ground. Another proposed scenario is that the hijackers were fooled into becoming trained pilots for another reason, and that, again, Mossad was involved. I have asked Dewdney if he still stands by the scenarios in the various versions of Ghost Riders, but he has not answered this query.

This gives some background to Dewdney's presentation on March 19. He started by stating that his expertise is in cell phone calls, and that he has learned a lot about them since he began his investigations. (Dewdney, it appears, has no formal training in cellular communication. The theme of people speaking beyond their trained expertise is one that would repeat itself during the evening.) He claimed that there were 10 cell phone calls from UAL 93, 2 from AA 175, and 1 from UAL 77, as well as 2 Airfone calls from UAL 93.

This was the first falsehood of his presentation. According to the 9/11 Commission report, at least 22 Airfone calls were made from UAL 93 (not 2, as Dewdney claimed). His other numbers are also out of line with the 9/11 Commission Report.

As far as I can tell, no one disputes the technical feasibility of completing Airfone calls from the hijacked planes. In fact, it is from the Airfone calls that we have the most detailed picture of what took place on UAL 93. The existence of these Airfone calls casts very strong doubt on the relevance of the claimed inability to make cell phone calls from the planes. Indeed, what would be the purpose of faking cell phone calls, when Airfone was accessible? Dewdney conjures up a picture of a vast government conspiracy competent enough to fool relatives into thinking their loved ones were on the other end of the line, yet not competent enough to realize that cell phone calls were not feasible from the air. The kind of mental contortions one has to go through to find Dewdney's scenario plausible boggles the mind.

Dewdney claimed that his experiments show that a cell phone has only a 9% chance of successfully completing a call at 8000 feet; a 30% chance at 6000 feet; a 44% chance at 4000 feet, and an 89% chance at 2000 feet. But in the case of UAL 93, the two cell phone calls were made when the plane was approximately 2500 feet above the ground. (The plane was flying at about 5000 feet of altitude, but the terrain below was mountainous and hence the 2500-foot figure.) According to Dewdney's own figures, there would have been an excellent chance to complete such calls.

Dewdney sneered at the account of Mark Bingham's phone call to his mother, because Bingham reportedly said, "Mom, this is Mark Bingham." Again, the implication is that the government is smart enough to fake a call that could fool Bingham's mother, but not smart enough to realize that a son would be unlikely to tell his mother his last name. (The largely sympathetic audience chuckled.) What Dewdney and the ghouls in the audience fail to realize is that, under pressure, people do silly things. When distracted, I have picked up the phone at home and said, "Shallit", something I usually only do at work. I have also signed a Christmas card to my mother with my full name, by mistake. Anyone who has read reports of the 9/11 phone calls realizes they depict passengers under great stress, and it is foolish to read anything sinister into Bingham's faux pas. But then, this is standard fare for deniers, to examine transcripts with a magnifying glass for anything that could remotely be said to support their claims, while ignoring the big picture. Update: as a commenter has pointed out, Mark Bingham's mother says that this was an inside joke. See here for more details.

Arthur C. Clarke, who died this week, once made the following trenchant observation: "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 very probably wrong." Keep this in mind when considering Dewdney's claims about the impossibility of cell phone calls from airplanes.

More later.

Richard Borshay Lee is an anthropologist of some renown who is currently Professor Emeritus at the University of Toronto. He is sympathetic with the misnamed "9/11 Truth" movement, having authored a paper entitled "The Elephant in the Living Room: What really happened on 9-11?" (scroll down on that link). Last night, he was the "moderator" (as described on flyers for the event) for the debate-that-was-not-a-debate hosted at the University of Waterloo.

The role of a moderator is not to take sides. Lee didn't observe this rule, however, as he launched an attack against the "official version" of 9/11 in his introduction.

Lee claimed that "Serious scholarship will be presented to you tonight". In fact, what we heard were the standard falsehoods of the 9/11 Truth movement, and discussion of the fine points of building collapse by a man not even remotely qualified to discuss the issue. Lee claimed that he would present "a forum in an atmosphere of open-minded scholarly challenge". But there was no challenge, since no one from the opposing side was permitted to speak. The question period was extremely limited.

Here is my open letter to Prof. Lee. If he responds, and agrees to let me post his response, I will post it below.


Dear Prof. Lee:

Last night, I witnessed your performance as "moderator" of the event "A Forensic Analysis of September 11, 2001: Questioning the Official Theory" that took place at the University of Waterloo.

The role of a "moderator" is not to take sides, and yet you did. In your opening, you repeated several falsehoods of the misnamed "9/11 Truth" movement. You sneered at the idea that the 9/11 hijackers could "expertly" pilot the planes and crash them into their targets.

However, your objections are not based on any rational evidence. The hardest part of flying a plane is taking off and landing, and the hijackers didn't have to do either one. In each plane, one hijacker received significant flight training; all 4 were certified pilots. Hanjour, for example, had extensive simulator training on small commercial jets. The others "had all logged a minimum of 250 cumulative flight hours" (Dunbar and Reagan, 2006). Hanjour and Jarrah had "training flights down the Hudson Corridor, a busy low-altitude path along the Hudson River that passes by the World Trade Center" (Dunbar and Reagan). Furthermore, there is good evidence that the hijackers didn't "expertly" pilot their planes. "The planes made sharp turns of up to 330 degrees and at times dropped precipitously. Passengers and flight attendants on all four planes reported erratic flying." (Dunbar and Reagan)

You also claimed that "No steel frame building in history ever collapsed before." This is not true. I would advise you to look into the 1967 collapse of the McCormick Center in Chicago, a steel-frame building that was left in rubble after a fire. The New York Times article of January 17, 1967 said "Heat from the blaze twisted and curled massive steel girders."

I see that you have had a distinguished career as an anthropologist at the University of Toronto. When you repeat falsehoods that are so easily refuted, you sully your own reputation, and you bring ridicule to your institution. You should be ashamed.

Should you choose to reply, please let me know if I can post your reply on my blog, recursed.blogspot.com.

Citation: Debunking 9/11 Myths: Why Conspiracy Theories Can't Stand Up to the Facts, Dunbar and Reagan, eds., Hearst Books, 2006.

Here is the text of the questionnaire passed out at last night's 9/11 denier event. You were supposed to check either "agree", "disagree", or "no opinion" at the beginning of the presentation, and then again at the end.

Exercise for the reader: in what ways, exactly, are the statements slanted to get the desired answers?

1) The U. S. government's official theory of 9/11 is complete and correct.

2) The Canadian government should launch a federal inquiry into 9/11.

3) The media is covering 9/11 in a fair manner.

4) The truth about 9/11 is important to the public interest.

Last night I attended a presentation hosted by the University of Waterloo Debate Society entitled "A Forensic Analysis of September 11, 2001: Questioning the Official Theory". It was a truly shameful event, and there was plenty of shame to go around.

Let's allocate the shame:

A large portion of the shame goes to the Debate Society, which plastered the campus with misleading flyers that suggested to many that a genuine debate would take place. I met students in the hall who expected to hear both sides presented, and were surprised when I told them that the presentation would be completely one-sided. The student organizer of the debate, Adnan Zuberi, refused to answer my e-mail questions about why there would not be a speaker presenting the other side; when I asked him again at the debate, he claimed he never received my e-mail (although I sent it multiple times to two different addresses, including the one on the event flyer). I asked Mr. Zuberi if he was part of a "9/11 Truth Group", and he refused to answer. (I was told by other members of the Debate Society that Mr. Zuberi is, indeed, a member of a "9/11 Truth" group.) Casting even more shame on the Debate Society, everybody involved in the public presentation, including Richard B. Lee, the "moderator", and Michael Keefer, the man who selected questioners at the end, was part of the "9/11 Truth" movement.

Why didn't the Debate Society present someone on the other side? I was told they tried, but couldn't find anyone. But they are a "debate society", not a "one-sided presentation" society, and they had an obligation to find someone to respond to the falsehoods that were presented.

Next, there's an ample portion of shame to be allocated to the four academics who participated in this event. As academics, they should have ensured that contentious issues are treated fairly and that valid opposing views are noted. As academics, they had an obligation not to speak outside their areas of expertise (at least, not while relying on their credentials as professors, which were prominently featured on the flyers and in the introductions). Instead, what did we get?

At the opening, we got an admonition by Richard B. Lee (a retired professor of anthropology at the University of Toronto) about how his views deserve respect, an admonition that included long-debunked false claims about the piloting abilities of the 9/11 hijackers.

We got a presentation by Alexander Dewdney, my former colleague in the Computer Science department at Waterloo, filled with distortions, non sequiturs, and falsehoods (more later).

We got another presentation by Graeme MacQueen, a retired professor of Religious Studies at McMaster, that prominently featured an analysis of the physics of 9/11 building collapse (although MacQueen has no formal training in the subject).

And we got questions chosen by Michael Keefer, who was a professor of English and Theatre at the University of Guelph.

To my knowledge, none of the four men had any formal training in civil engineering, telephone networks, or building contruction; yet these subjects featured prominently in the presentation.

I'll have more to say about the arguments presented and the psychology of denialism in future posts.

And here are some of them:

Dewdney, Part 1

Dewdney, Part 2

Graeme Macqueen

Questions and answers

From my perspective, it seems that there is an increasing number of cases of innumeracy in books and newspaper articles. Many of these articles are written by educated people -- people you would think should have no problem calculating a percentage or dividing one number by another. But you'd be wrong.

Here are two cases I recently noticed.

In Jeffrey Toobin's recent examination of the current Supreme Court, The Nine, he writes

On Wednesday, November 8, the first complete election figures in Florida showed Bush ahead of Gore by 2,909,135 to 2,907,351, or a margin of 1,784 votes.... The new results, announced on Thursday, November 9, cut Bush's margin to 327 votes --- or .00000056 percent.

Actually, 327 votes divided by 5.8 million is about .000056, or .0056 percent. Toobin evidently divided by 100 instead of multiplying, and hence obtained a result off by a factor of 10,000.

Here's another case: in a recent article in the Peterborough Examiner about my friend Mark Stanley, the reporter writes

"...an online mineral store called the Mineralogical Research Co. sells fulgerite for $6 a gram. That means an 18-kilogram fulgurite would be worth about $3,000."

Here the author apparently divided 18,000 grams by $6 to get the figure of $3,000. The correct amount, of course, is 18,000 grams multiplied by $6/gram, for a total of $108,000. She was only off by a factor of 36, better than Toobin. (I won't comment about her misspelling of "fulgurite".)

Update: Jeffrey Toobin sent me a nice note, acknowledging the error.

The downtown core of the small city where I live (Kitchener, Ontario) has seen many businesses fold in recent years. The city has attempted to revitalize the core in various ways, with mixed success.

Now Waterloo regional police have fined two mainstays of the core, Casablanca Books and the K-W Book Store, both on King Street. These are excellent used bookstores just 5 minutes away from where I live. And their "crime"? Opening for business on Monday, February 18, the new provincial holiday called "Family Day". Luckily, the police later dropped the charges, because the law has an exception for small bookstores.

If store owners want to open on a holiday, that's their business, and the government shouldn't meddle with it. This kind of nonsense is going to further drive businesses out of the core.

My son pointed out the following image to me.



Doesn't that perfectly describe your experience arguing with creationists, intelligent design proponents, crystal healers, holocaust deniers, global warming deniers, and 9/11-truthers?

According to an article in the National Post, a York University student officer cancelled a debate on abortion to be held in the student centre, between Jose Ruba of the Canadian Centre for Bioethical Reform in Calgary and Michael Payton, a member of the York University student group, Freethinkers, Skeptics and Atheists.

The debate was cancelled by Kelly Holloway, president of the York University Graduate Students Association, because "This debate, over whether or not women should be able to have an abortion, is not acceptable in the student centre" and "People in this country have had the debate over abortion. The Supreme Court made a decision, and that's good enough for me…. I think we should accept that the debate is over."

But simply because the Supreme Court has decided one way doesn't end the debate. Courts sometimes overturn their own decisions, and people have the right to debate whether they should. The university, above all places in our society, should be a place where controversial subjects can be examined. Although I'm definitely pro-choice, this was a bad decision by Holloway and York.