The Pseudoscience Constellation

Did you ever notice that buying into one form of pseudoscience often begets other kinds of foolishness? Phillip Johnson, the lawyer who had a religious experience after a messy divorce, is not only one of the founders of the modern intelligent design movement; he's also an AIDS denier.

Russell Humphreys, the young-earth creationist, also denies that global warming is a problem.

Recently I learned about another example, possibly one of the most impressive yet. R. Webster Kehr is a Mormon and ex-Marine who

- thinks "evolution is the most absurd scientific theory in the history of science!!"

- denies Einstein's theory of relativity and the photon theory

- thinks that the naturals and the reals are the same size, even though he admits there is no bijection between them. He also describes himself as the author of many mathematical papers, although oddly enough, MathSciNet doesn't list a single one.

- subscribes to cancer quackery

You have to work pretty hard to be so deluded in so many fields simultaneously.

Mathematics Journal gets Sokaled

Over at That's Mathematics, the author reports that his paper of gibberish mathematics was actually accepted by the journal Advances in Pure Mathematics. This gives you some idea of the quality of that journal.

The paper contains such deathless phrases as "By a little-known result of Fibonacci..." and "It is not yet known whether every real, surjective, pairwise regular functor is ultra-standard". The author pairings in the bibliography include Atiyah and Leibniz, and Atiyah and Eudoxus. Very nice work.

Creationist Mathematics

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

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

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

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

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

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

The Ol' Information Bait-and-Switch

It seems that my criticism of aging philosopher Thomas Nagel has got the folks at Uncommon Descent running scared. That's because they know their bogus claims about information are being exposed.

I gave an example that trivially refutes Stephen Meyer's claim that "information always comes from a mind": weather prediction. Meteorologists record information such as wind speed, wind direction, and temperature to make their predictions. Under both the informal definition of information used in everyday life, and the formal technical definitions of "information" universally accepted by mathematicians and computer scientists, these quantities indeed represent "information". What is the response?

Of course, it's the old information bait-and-switch trick: Dembski is now claiming that my example was "unspecified information", whereas Meyer was talking about "specified information".

Dembski is an old hand at the information bait-and-switch game, as Elsberry and I showed in detail in our peer-reviewed article. He moves from one definition to another seamlessly, as it suits him, for whatever argument is at hand. This is most apparent in his estimation of probabilities, where he switches back and forth between the uniform probability interpretation and the causal-history interpretation, depending on which one gives the answer he requires. We discuss this at length in our article.

Furthermore, the notion of "specification" comes from Dembski himself, and as Elsberry and I showed, it is completely incoherent. Nobody can say whether a given string is "specified" or not, and "specification" fails to have the properties Dembski claims it has. No mathematician or computer scientist, other than Dembski and his intelligent design friends, uses Dembski's measure or does any calculations with it. To pretend that it is meaningful is not honest.

Just to give one example, here is Dembski and his deep technical and mathematical "proof" that "the [sic] bacterial flagellum" is specified:

"At any rate, no biologist I know questions whether the functional systems that arise in biology are specified." (No Free Lunch)

So, a challenge: which, if any of the following strings constitute "specified information"? Be sure, in your answer, to give all the things that Dembski says are required before one can be sure: the space of events, the rejection function, the rejection region, the "independently-given" specification, the relevant background knowledge, the independence calculation, and so forth.

1. VUIAPIDESFFGWNHCOIDTGLTJCITMTRITIEIISPOFKAAMORSFEOSDSCDNNRHTEHETCOSOUNETNGQBJINB
2. INFORMATIONCSFVICJUWOEFNLMICPTHOPIISDSTNFJABGEODTQIITUNDHGASTRDNEIKTGSBTOHEERCSE
3. UOTDCTTADWDHINEEFVJETIIICIRPAQDCFLNTNOGROFSGOEFRNSSKTIOPTJMBNMSSUNIHOCEGTAEHISIB

Meanwhile, Dembski needs to inform his acolyte "Joe G", who thinks that the proper definition of "information" is "the attribute inherent in and communicated by one of two or more alternative sequences or arrangements of something (as nucleotides in DNA or binary digits in a computer program) that produce specific effects". Well, by that definition, my example of the information used in weather prediction is indeed information -- there are many alternatives in wind speed, direction, and temperature, and no one can doubt that different arrangements of these quantities produce different effects -- namely, different weather.

Joe G, get with the program! Just say my example is "unspecified", and be done with it! No need to trouble yourself with actual thinking.

Failed Olympic Medal Predictions

Leading up to the Olympics, there was a lot of hype about the work of Colorado College economist Daniel K. N. Johnson and his predictions about the Olympic medal count. For example, he was interviewed on NPR and featured in the Wall Street Journal. Prof. Johnson's method was based on five factors only: GDP per capita, total population, political structure, climate, and home-nation bias, and was touted as "remarkably accurate".

Now the results are in. Here are Johnson's predictions of the top ten medal winners, compared to the actual total these countries won:

Country	Johnson's prediction	Actual result
USA	103	110
Russia	95	72
China	89	100
Germany	66	41
Japan	37	25
Hungary	31	10
Italy	29	28
Great Britain	28	47
France	27	40
Australia	26	46

Rating a prediction p as good if .75r ≤ p ≤ 1.25r, where r is the actual result, I'd say Johnson made 3 good predictions out of his top 10: China, USA, and Italy. And he made some really bad ones, including Hungary, Great Britain, and Australia. Altogether, Johnson's predictions don't deserve a place at the podium.

The Davis-Weller Study on HIV Transmission Misrepresented Again

In 1999, Davis and Weller published a paper in Family Planning Perspectives entitled "The Effectiveness of Condoms in Reducing Heterosexual Transmission of HIV". Their meta-study combined results from other studies about couples where one partner was HIV-positive and the other not, with respect to how often a condom was used. Unfortunately, their conclusions (and the conclusions of an earlier study by Weller alone) have been systematically misrepresented by conservative Christian activists.

I've written about this misrepresentation before. In 1993, Harold Albrecht, a local MP, misrepresented the earlier study by claiming that "An analysis by researchers at the University of Texas estimates that when condoms are used, the risk of acquiring HIV from an infected partner is 31 per cent over a year's time."

Now the work of Davis and Weller has been misrepresented again. Our local paper, the Kitchener-Waterloo Record, has a "Community Editorial Board", where local residents are tapped to write a series of opinion pieces. (I was on the Board in 2000, and you can see my columns here.) Yesterday the Record carried this column by Harriette Mostert, who is described as a "part-time teacher and a longtime community volunteer".

Mostert claimed that this NIH report says that "HIV/AIDS carries a 15 per cent risk of transmission even with a condom". However, the NIH report was referring to the Davis-Weller study, and it is being misrepresented again.

The Davis-Weller study found that using a condom reduces the risk of HIV transmission by 85%. Now, you might think that Mostert's 15% figure is just 100%-85%, and so she's correct. But you would be wrong.

Davis and Weller were studying the reduction in risk obtained when using a condom; Mostert incorrectly labels this the "risk of transmission". They're not the same at all. I think most people would interpret "risk of transmission" as meaning "the chances that you will get the disease in a single encounter", and indeed, that's the interpretation I got when I asked several people what they thought it means. Or maybe it means "the chances that you will get the disease in a year"? The lack of units should raise warning bells in the mind of any educated person.

The answer is that Davis and Weller found that in one year, 6.7 infections per 100 person-years occurred when a condom is not used, and 0.9 infections per 100 person-years occurred when a condom is always used. The reduction in risk is therefore (6.7-0.9)/6.7, or approximately 85%. Contrary to Mostert, the "risk of transmission" when using a condom is less than 1 infection in 100 person years. There's no way this can be characterized as "15%".

Mostert uses this bogus figure to argue for "chastity or monogamy", and smugly concludes "Interestingly, this is also consistent with the ideals set out in many faith communities." She fails to note that the very study she cites concludes "These data provide strong evidence for the effectiveness of condoms for reducing sexually transmitted HIV."

David Berlinski, King Of Poseurs

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.

Lying for Jesus, Mathematically

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.