Mathematics in a Jack Reacher Novel

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

Unbelievable!

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

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

Shortest No More

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

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

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

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

A Google Query

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

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

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

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

The Discovery Institute Lies Again

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

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

But what else can you expect from the Dissembling Institute?

The Noncommutative Frobenius Problem is Solved!

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

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

44 = 4*6 + 1*20,

45 = 5*9,

46 = 1*6 + 2*20,

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

48 = 8*6,

49 = 1*9 + 2*20,

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

How Stupid Do They Think We Are?

I see that the crafty and unctuous Sal Cordova is up to his old tricks again, this time truncating a quote of Darwin to make it appear that Darwin endorsed intelligent design. No doubt when called on this dishonesty, he'll call it "street theater".

David Warren: Blowhard of the Month, Again

David Warren, who I previously celebrated as Blowhard of the Month back in January 2006, is at it again.

Take a look at this recent column, which believe it or not, was actually published in the Ottawa Citizen.

From the very first line, Warren demonstrates ignorance (or dishonesty). He calls Paul Feyerabend a "scientist", when in fact, Feyerabend was a philosopher.

He then celebrates Freeman Dyson, a once-respectable mathematician and physicist who has become slightly, uh, eccentric in his dotage. (Dyson even wrote a friendly foreword to Elizabeth Lloyd Mayer's credulous Extraordinary Knowing.) Why does Warren like Dyson? I doubt Warren could coherently explain even one of Dyson's contributions. No, what Warren likes about Dyson is that Dyson is a global warming skeptic. Of course Dyson's opinion about global warming is about as valid as mine, considering that Dyson has no training in climatology and has not published any papers on the subject.

Later, Warren refers to "Darwinist cosmology". Considering that Darwin was a biologist, not a physicist or a cosmologist, I can only wonder what Warren thinks he is talking about.

Finally, in Warren's crowning moment, he completely misrepresents Michael Behe's testimony in the Dover case, claiming that "Behe demurred" when attorney Eric Rothschild said, "So you believe astrology is valid science." Of course, this is false, as a glance at the testimony will show. Rothschild never said what Warren claims. Here's the crucial exchange:


Q Under that same definition astrology is a scientific theory under your definition, correct?

A Under my definition, a scientific theory is a proposed explanation which focuses or points to physical, observable data and logical inferences. There are many things throughout the history of science which we now think to be incorrect which nonetheless would fit that -- which would fit that definition. Yes, astrology is in fact one, and so is the ether theory of the propagation of light, and many other -- many other theories as well.


Warren finishes by saying


How I wish the high priests of Darwinism could restrain themselves in similar ways. They can’t, because Darwinism is a religion, and moreover, a false religion, in fear of free inquiry.


Why is it that theists, when they want to insult science, they call it a religion?

Return of the Vanity Scam

It seems the American Biographical Institute just won't give up.

They failed to entice me by selecting me as a "Great Mind of the 21st Century", so now they've upped the ante.

Now they're nominating me as "Man of the Year".

For only $195 (or $295 if I want it laminated on "Finland Birch Wood"), I can get a decree calling me "Man of the Year 2007", "based on his outstanding accomplishments to date and the noble example he has set for his peers and entire community."



Really, I wonder how vain you would have to be to fall for this transparent scam.

Oh. About this vain. Or this vain. Or this vain...

A New Word - "Outcheap" - and McCain's Unintentional Irony

On NPR this morning there were two items of linguistic interest.

The first was this interview with Joe White, the Detroit bureau chief for the Wall Street Journal. White discussed driving a plug-in electric car, and in the discussion he used a word I've never heard before:

"The reasons why we don't have all-electric cars running around - and this goes back more than a century - is that battery technology simply hasn't evolved to the point where we can outperform and outcheap gasoline and the internal combustion engine."

The OED doesn't list "outcheap" as a word, but it's clear what it means: "to be able to be produced more cheaply than an alternative". It reminds me of a word my friend Jean-Paul once invented, as a translation for the French defenestrer: to "outwindow". He was disappointed to learn that "defenestrate" already existed in English.

I found some earlier citations using Lexis. An article in Crain's Detroit Business, April 15, 1996, quotes Farmington Hills retailing consultant Frederick Marx as saying , ''Anybody can add volume giving it away, and that's what it's becoming: a contest of who can outcheap each other.''

The second item was this interview with presidential candidate John McCain.

"One of the things that drove Harry Truman's decision to integrate our military was how shocked and angered he was by the lynchings of two African-American World War II veterans. Truman was certainly no - you know, he used racial epitats in private conversation, etc., but he believed that his oath to protect the Constitution made him responsible to protect the rights of all the American people."

Here McCain used the nonexistent word "epitat". He really meant "epithet", but was probably mixing it up in his mind with "epitaph", and so out came this mélange of both words.

Ironically, McCain also said, "Let's have some straight talk. Harry Truman was not the greatest intellect that ever inhabited the White House, but he had the right instincts, and frankly, he had the humility and inspiration to recognize that you have to suborn your personal ambitions for the greater good."

Here McCain demonstrates that he doesn't know what the relatively uncommon word "suborn" means. According to the OED, it has several meanings, but the ones that are most familiar are

• "to use illegal or underhanded means to induce someone else to do a misdeed"
  
• "to induce someone to give false testimony" (as in "to suborn perjury")
  

McCain probably meant to say "subdue" or "subjugate". I like the irony that he was calling Truman intellectually deficient while, in the same sentence, he exhibited some ignorance himself.

Talk Radio Hosts Fired for Debunking Phony Racist Memo

From the Washington Post comes this sad story about two radio talk show hosts who have been fired for debunking a rumor, long passed around in the African-American community, that the Carter administration secretly plotted to undermine domestic black leaders.

Casey Lartigue Jr. and Eliot Morgan hosted "The Casey Lartigue Show", a weekly political talk show on XM satellite radio. They discussed this phony memo which exists in various versions on the Internet. (One tip-off that it's phony? Brzezinski's last name was spelled incorrectly.) The version I've linked to is on (no surprise) the website of Louis Farrakhan.

Lartigue and Morgan were fired when they exposed the memo as a fake. In doing so, they went against the XM's lead talk show host, Joe Madison, who still believes that the memo is real.

Talk radio: where telling the truth can get you fired. I guess that's why people like Rush Limbaugh still have jobs.

Combinatorics on Words, A Puzzle, and a Silly Research Proposal

One of the areas I work in is combinatorics on words. In this field, we are interested in words (strings of symbols) and their properties.

For example, a square is a nonempty word of the form xx, where x is a word. Some examples of squares in English include tartar and murmur. If a word contains no subword that is a square, we say it is squarefree. Notice that the word squarefree is not squarefree, as it contains the square ee.

A classical question, first discussed a hundred years ago by the Norwegian mathematician Axel Thue, is whether there exist infinite squarefree words over a finite alphabet. Over a two-letter alphabet, this is not possible, as any binary word of length 4 or more contains a square. (Proof: let the first letter be a. Then if the next letter is a, we have a square. So assume the next letter is b. If the third letter is b, we have a square again. So assume the third letter is a. Now, whatever letter is chosen as the fourth letter, we get a square.)

But is it possible over a three-letter alphabet? The answer is yes, as Thue showed.

Erdős considered a variation on this problem. Instead of trying to avoid squares, let's try to avoid abelian squares. An abelian square is a nonempty string of the form x x', where x' is a permutation of x. Some nice examples of abelian squares in English include reappear (the first half of the word reappears in the second half) and mesosome. Can you find the longest word in English that is an abelian square? Hint: it represents part of the body. If you're interested in this sort of wordplay, see my page on repetitions in natural languages, where the solution to the puzzle is given.

For many years it was not known whether one could construct an infinite word over a 4-letter alphabet that contains no abelian squares. But in 1992, Veikko Keränen showed that one could. His construction involves constructing a map that sends each letter in {a,b,c,d} to a string of length 85. Starting with a, one then simply iterates this map. For more information, visit Keränen's page.

Now we've covered combinatorics on words, and the puzzle. It's time for the third item in the title. Go visit this silly research proposal by a professor of civil engineering and engineering mechanics at Columbia University. The proposal is so poorly written that I can't really tell what he has in mind, but he seems to suggest representing strategies for development in third-world countries by strings of symbols that specify a temporal sequence of events. I really hope this is a joke, but if it is not a joke, I hope it doesn't get funded.

New Study Shows "Cell Phone Tower Allergy" All in the Mind

I have two relatives who believe that electromagnetic fields are having a deleterious effect on their health.

Although I doubt this new study will convince them, it's still relevant. Elaine Fox, of the University of Essex, studied 44 people who claimed they were sensitive to cell phone towers and 114 normal people. They then exposed them to signals from the mast, sometimes telling them when the tower was on or off, and sometimes not telling them.

When the subject did not know whether the tower was on, they were not able to decide any better than chance whether the tower was on or not. When they knew, the sensitive people exhibited significantly more symptoms than the ordinary people.

This establishes with reasonable certainty that "cell phone tower allergy" is all in the mind. Their symptoms may be real, but they're due to fear and hysteria, not the signals.

Good and Bad Reporting

Contrast this article from yesterday's National Post about the rise of atheism with this series by local religion "reporter" Denyse O'Leary.

The National Post article points out that the non-religious in America have grown from 8% to 14.3% of the population between 1990 and 2001, and that a 2006 study shows 20% of young adults are non-religious, up from 11%. The article discusses the recent atheist books by Sam Harris, Richard Dawkins, and Christopher Hitchens, and quotes prominent atheists such as Dan Barker and Annie Laurie Gaylor of the Freedom From Religion Foundation, and Herb Silverman, an atheist mathematician who successfully challenged a South Carolina law that established a religious test for public office, in conflict with the US constitution.

Now, any sensible person would conclude from the statistics in the National Post article and the wave of best-selling atheist books that interest in atheism is increasing, and the Post reporter has a brief analysis why: former UW professor Michael Higgins is quoted as saying "There is a profoundly anti-religious sentiment that exists in the culture-at-large as a result of 9/11" and "There is a souring against religion. There is a general perception that most political and social problems have been generated by religion [and] this comes from the danger people fear as a consequence of 9/11."

Now look at O'Leary's "reporting". She calls the rise of atheism an "anti-God crusade". (Isn't it strange that when theists want to insult atheism, they resort to using explicitly religious language that recalls the bad aspects of religion?) And she suggests that the rise in the interest in atheism is really due to the failure of materialism. She even denies that atheism is on the rise, claiming "atheism ... is stagnant or withering away". Of course, no actual statistics are provided to support this claim. I wonder what it would be like to live in O'Leary's topsy-turvy world.

In her series, O'Leary doesn't do any actual reporting. You will look in vain to find O'Leary actually interviewing anyone, particularly an atheist, to find out what they believe. No, O'Leary resorts to quoting the work of real journalists, journalists who have actually bothered to do the legwork required for an article. Instead, the series consists mostly of sneers and insults directed at atheists and amateur psychologizing:

"...Materialist science is in trouble. And the trouble does not stem from traditional religions, though materialists are - as one might expect - quick to blame their troubles on traditional religions and to reassure themselves that - despite all the evidence - traditional religions are doomed. But, materialists are also smug and thus cannot imagine or respond to any source of trouble arising from their interpretation of the evidence.

They have apparently decided instead to target the Christian religion as the source of their problems. One outcome is that, as we shall see, many materialists want to start a new religion to compete with the traditional ones, including a Darwin Day (Christmas, Eid al-Fitr, and Chinese New Year all rolled into one?)..."

Along the way, O'Leary manages to plug her books. (No article by O'Leary is complete without self-promotion.) She resorts to the hoariest clichés, calling atheists "militant" and "dogmatic".

There is an interesting parallel here between O'Leary's parasitic use of other reporters' work to construct her series, and the behavior of creationists. Like creationists, O'Leary didn't do any actual research of her own. Like creationists, O'Leary isn't interested in exploring her subject, the evidence, or why people believe they way they do. Like creationists, O'Leary spends most of her time denigrating a view she doesn't accept.

My parents were journalists. Some journalists are friends of mine. Ms. O'Leary, you're no journalist.

Turku's Fibonacci Smokestack

From my student, Dalia Krieger, here's a picture of a smokestack in Turku, Finland, that displays, in neon, the first 10 Fibonacci numbers. Why is it there? I have no idea. But why should Finland have all the fun? Let's put the Thue-Morse sequence on some smokestacks.

Why Do They Always Lie?

Take a committed theist, ask him or her to say something about atheism, and just wait. The lies will come pouring out of their mouth like water from a fountain.

This article by Peter Berkowitz, who teaches law at George Mason, and is a "senior fellow at Stanford's Hoover Institution", is no exception. How many lies can you find?

It starts in the smarmiest possible way, taking a cliché from Ecclesiastes to argue that the new wave of atheism books (which Berkowitz calls, unimaginatively, the "new new atheism") is confirmed by "biblical wisdom". This is the equivalent of the traditional response of the theist when an atheist makes a good point: ignore it, and say "God loves you anyway".

Next, Berkowitz sneers at Dawkins, Hitchens, Harris, and other atheist writers by describing atheism as a "profitable business" --- as if writing books that people want to read is somehow morally objectionable, and as if religious organizations haven't been raking in the tax-exempt cash for years.

We have to wait until the fourth paragraph before we get the first outright lie. Berkowitz claims "... the new new atheism proclaims its hatred of God and organized religion loudly and proudly from the rooftops". The only problem is, atheists don't hate the Christian God or any other god, any more than we hate the tooth fairy or the Easter bunny or Emma Bovary. You can't hate something that doesn't exist, and fictional characters don't inspire hatred the way real dictators do. Atheists might hate how a misguided belief in a deity or deities causes people to misbehave, and we might hate the division that religion causes, and we might hate some institutions of organized religion (and have a good reason to do so), but we don't hate Berkowitz's god.

The fifth paragraph has another lie. Berkowitz claims "[The new new atheists] contend ... we can now know, with finality and certainty, that God does not exist..." Really? Is that really what they say?

Nope. Take Richard Dawkins, for example. In The God Delusion, he makes the point that you can't know with certainty that there is no god. On page 51, for example, Dawkins defines a strong, or category 7, atheist as someone who says "I know there is no God, with the same conviction as Jung `knows' there is one." He then says "I'd be surprised to meet many people in category 7" and that he does not count himself in this category. He says he is "in category 6, but leaning towards 7 - I am agnostic only to the extent that I am agnostic about fairies at the bottom of the garden." A category 6 atheist says, according to Dawkins, "I cannot know for certain but I think God is very improbable, and I live my life on the assumption that he is not there."

There is much more to dispute in Berkowitz's piece, but I confess I grow weary at the weak excuses he uses to prop up religion, the straw men he erects to attack Hitchens, and the transparently sneering rhetoric. Hitchens, Berkowitz says, "shows no awareness that his atheism, far from resulting from skeptical inquiry, is the rigidly dogmatic premise from which his inquiries proceed, and that it colors all his observations and determines his conclusions." But modern atheism isn't a dogmatism, since it offers no creed to rigidly adhere to, only a disbelief in the creeds of others. To call this dogmatism is to insist that the barefoot man really does have a secret cobbler he visits on the side.

Berkowitz can't resist implying that his religion would never, ever result in the nasty kind of violence we see emanating from Islam: "today's bestselling atheists suppress crucial distinctions between the forms of faith embraced by the vast majority of American citizens and the militant Islam that at this very moment is pledged to America's destruction." What he fails to see is that that American majoritarian faith also results in reprehensible violence. To name just three examples from the last year:

• Charles Carl Roberts, home-schooled by religious parents, killed 5 and wounded 5 more Amish schoolgirls in October 2006 because he was angry at God.
  
  
• Brian K. White, a religious musician, beat to death a 75-year-old former Soviet political prisoner in New Jersey because the man refused to buy his religious CD's.
  
  
• Joshua Royce Mauldin, who claimed he was called by God to be a minister, seriously burned his 2-month-old daughter's face by jamming her in a microwave.
  

Berkowitz concludes by claiming, "Of all the Bible's sublime and sustaining teachings, none is more so than the teaching that explains that humanity is set apart because all human beings--woman as well as man the Bible emphasizes--are created in the image of God". Berkowitz may feel this is "sublime" and "sustaining", but I just regard it with sorrow. What could be more responsible for our ecological crisis than this silly, deluded view that man is somehow elevated above everything else in nature?

If this mess of lies and foolishness is the best the theists can offer, then the atheists have already won.

Innumeracy In "Zits"

The July 12 2007 panel for the "Zits" comic strip has the main character, Jeremy, computing how much he's getting paid.


Panel 1: "I can't believe I'm getting paid ten bucks an hour for this!"

Panel 2: "That's like, five bucks every half hour!"

Panel 3: "Or 16.6¢ per minute ... or, uh... only .0027¢ per second."

Panel 4: "Time flies when you're having fun, but it totally drags when you're getting paid by the hour."


Which one of the authors of this strip, Jerry Scott or Jim Borgman, can't divide?

Added July 23 2007: I received the following reply from Jim Borgman:
"You're right. Jeffrey. Sorry for the error. Maybe we should have you
look over our syndication contract?"

Literal Answers to Rhetorical Questions

As mentioned on Weekend Edition, here is a funny page giving literal answers to rhetorical questions, many inspired by popular songs.

But the number of examples is not very large. We need some other examples. Here are a few:

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Where have you gone, Joe DiMaggio?

Joltin' Joe is buried in Holy Cross Cemetery in Colma, California.

What's new, pussycat?

Nu is the frequency of a wave in physics, an Egyptian god, a Chinese ethnic group, and a former Burmese prime minister.

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Can you come up with some more questions and answers that deserve to be on that page?

Intelligent Design: The Scientific Theory That Improves Your Bottom Line

I see that William Dembski, fresh from raking in thousands of dollars for not testifying in the Dover trial, has now branched out into explaining his business savvy to the masses. Look at this announcement for a conference at Southwestern Baptist Theological Seminary for a conference entitled "Intelligent Design in Business Practice: How design assumptions impact management, leadership & organization".

This page has more details. Since ill-conceived ideas like this have a history of vanishing without a trace, I'll repeat the description below:

Successful business leaders are intelligent designers, guiding organizations along innovative paths to achieve ends otherwise unattainable. Intelligent designers are not micromanagers, who short-circuit the freedom and creativity that organizations need to thrive. At the same time, intelligent designers do not encourage unbridled autonomy, which sets organizations adrift, causing them to lose focus and discipline. By striking a proper balance between guidance and autonomy, intelligent designers promote a synergy between organization and leadership that can actualize undreamt possibilities. Intelligent design for now is best known as a scientific alternative to Darwinian and self-organizational approaches to biological origins. This conference brings together scholars and business leaders to discuss the implications of intelligent design for business practice. In particular, this conference will explore how design principles shape the beliefs of leaders about the people they lead, the nexus of innovation, the incentives to entrepreneurship, and the methods for managing organizational change. The overarching theme of this conference is "the business leader as intelligent designer."

Wow. A conference not to miss! Probably they can have breakout sessions entitled "Destroying Darwinism for fun and profit", "God wants you to be rich", and "Street theater: fruitful career choice?"