Saturday, April 29, 2006

Preaching down

Through a glass snarkly

“I suppose you study a lot of awful learned books now.”

“They make us work good and hard, Brother Jewkins. They give us pretty deep stuff: hermeneutics, chrestomathy, pericopes, exegesis, homiletics, liturgics, isagogics, Greek and Hebrew and Aramaic, hymnology, apologetics—oh, a good deal.”

“Well! I should say so!”

Elmer Gantry, Sinclair Lewis
I caught D. James Kennedy in full Elmer Gantry mode on the radio last week. He's always a good one for pulpit pedantry. Gifted with a smooth manner and a glibness that few other preachers can match, Dr. Kennedy never fails to leave his admirers sopping wet in the deluge of his erudition. His topic was Evidence for the Miraculous, a lengthy discourse on the evils of atheism and one of several installments in his Skeptics Answered series (available on cassette or compact disc for those who could stand to sit through it more than once).

D. James Kennedy, A.B., M.Div., D.Sac.Lit., Ph.D., Litt.D., D.Sac.Theol., D. Humane Let., as he styles himself in the credits at the end of each Truths that Transform television program, is a Presbyterian minister in Fort Lauderdale whose Coral Ridge Ministries include such political lobbying groups as the Center for Reclaiming America for Christ and the Center for Christian Statesmanship. Kennedy has honored a series of politicians who match his criteria for statesmanship; in 2002 the recipient of the Distinguished Christian Statesman of the Year Award was Representative Tom DeLay, who was still a few years away from his indictment and resignation. That tells you just about all you need to know about the political bent of D. James Kennedy.

Dr. Kennedy explained in Evidence for the Miraculous that he was by no means a biblical literalist. Always the showman, he was sure that such a statement would agitate the many jot-and-tittle KJV idolators in his congregation. Kennedy hastened to reassure them: He was no biblical literalist because the Bible is replete with figurative language, which should, of course, be taken figuratively. As his listeners sighed in relief, Kennedy unleashed the flood waters of his learnèdness:
There are similes and metaphors. There are synecdoches and there are litotes and there are many other figures that might not be as familiar as that. There is metalepsis. There is hypallage. There is also allegory, apologue, paroinia. There are types and symbols. There are engimas and polyhymnia. There is ironia and intima and oxymoron, and about 790 other species of figures of speech that are found in the Bible.
I think that's enough, don't you? Kennedy actually warmed to the topic a bit further and tossed in epitrope and prolepsis, plus a couple of others he pronounced so clumsily (his glibness momentarily failing him) I couldn't transcribe them, even after listening more times than I care to confess. Kennedy followed up with some sniping at Carl Sagan's lack of faith, a favorite topic with Kennedy.

One can always rely on Truths that Transform to provide a cavalcade of every hoary argument against evolution, the Big Bang, the great age of the earth, and every other scientific discovery that runs afoul of biblical literalism. Sure, Kennedy may not be a literalist, but he's close enough for all creationist purposes. He finds no figurative language in Genesis. As you would expect, he patiently explains to his congregation that probability shows evolution to be impossible (he cites Fred Hoyle, of course). He argues that Noah's flood is responsible for the geologic strata. And on and on.

D. James Kennedy is like unto his creationist brethren in other ways, too. He and falsehood are bosom buddies.

Bearing false witness

I am agnostic on the question of whether Dr. Kennedy is a conscious liar. It's possible he has rationalized that the occasional misrepresentation is good for the souls of his congregants, but it's just as possible he has managed to deceive even himself. The Julian Huxley case, however, is difficult to consider as anything other than a blatant falsehood.
I almost fell out of my chair. A public television interviewer had just asked Sir Julian Huxley, a leading defender of evolution until his death in 1975, why he thought Darwin’s idea caught on so quickly. His answer astonished me.

“[I suppose the reason] we all jumped at the Origin [Darwin’s On the Origin of Species],” Huxley said, “was because the idea of God interfered with our sexual mores.” “Mores,” of course, is a secular term for morals.
These are the first two paragraphs of a commentary written by Dr. Kennedy for the May 2004 issue of his Impact newsletter. (By the way, a few paragraphs later he invokes Hoyle again.) Kennedy's account is personalized with details that cause the reader to assume that it is an account of a vivid personal experience. The tiny problem with this story is that no such statement by Julian Huxley has ever been documented. It seems unlikely that Kennedy was the only person in America to have seen this public television interview of Huxley. But no one else did. Nor has any such interview been uncovered in the archives of the BBC or PBS.

Kennedy did not tell the Huxley story for the first or only time in the pages of Impact, he also recounted it on Truths that Transform (as I most vividly recall). His misrepresentation of Sir Julian's views go back at least to the 1980 publication of Kennedy's Why I Believe. Edward T. Babinski called him on it and asked for documentation of the claim. As Babinski puts it, instead of Kennedy's people giving him a proper answer, “they piled lie upon lie....” See also the discussion at Evolution Blog or check out Julie's story (“They gave me four more references for this supposed Huxley quote, and they were all bogus.”) on Joe Bageant's website.

Do you remember the words of Judge Jones in the Kitzmiller decision? He wrote, “It is ironic that several of these individuals, who so staunchly and proudly touted their religious convictions in public, would time and again lie to cover their tracks and disguise the real purpose behind the ID Policy.” Some extremely religious people consider themselves exempt from the directives of their own religion when it comes to dealing with others. The remarks by D. James Kennedy concerning Julian Huxley suggest that he may be in that same category.

He said, she said, they said

Maybe The Shadow knows

The world is not waiting with bated breath for me to weigh in on the rape accusations against members of the Duke University lacrosse team. I'm not even all that sure what lacrosse is. Some kind of sport, I figure, what with there being a team involved and all. Although I am not given to following tabloid news (by which I mean the National Enquirer, the Weekly World News, Fox News, or other similar purveyors of the fanciful, fantastic, and sensational), the Duke University story has a familiar aspect I do find interesting. How is it that all these people—who were nowhere near the supposed events—know what happened? Beyond a reasonable doubt, you betcha.

I'm sure that I don't know. Defenders of the reportedly privileged white boys on the lacrosse team are quick to point out that the accuser is a prostitute. Are we to take the word of a sex worker as reliable? On the other hand, the members of the lacrosse team who hired a prostitute are johns. Should we believe the stories of guys who were hooking up with hookers? I marvel at those for whom the whole case is open and shut. No question!

Some of the blogs I frequent are generating a lot of words on this subject. For people who want a less hyperbolic treatment of the subject, I'd suggest the Duke story archives at Jeralyn Merritt's TalkLeft. While Jeralyn is pretty critical of the District Attorney who is pursuing the case, she provides all the coverage and links anyone could want to trace all aspects of the story. I also want to draw attention to Nick Barrowman's short piece at Log base 2, which is a useful example of how people can spin out completely invalid arguments (from ignorance, I charitably assume).

If I were to offer any advice (and I suppose I am about to), it would be to give it a rest. Unless you enjoy arguing from ignorance, leave the detailed commentary to people who have some knowledge about what's going on and the expertise to analyze the legal maneuvers and their meanings. All I want is for justice to be done, and right now I have almost no idea what that is. So I'll take my own advice and give it a rest.


While paging through The Essential Calvin and Hobbes this weekend, I was startled to run across a lacrosse-themed comic strip. It's just a peculiar coincidence, but what's better than a nice Calvin and Hobbes?

Wednesday, April 26, 2006

It's time for the Skeptics' Circle

Whether you believe it or not!

The 33rd edition of the Skeptics' Circle has arrived. Coturnix has sifted through the entries and posted a guide to his selections at Science and Politics. I'm pleased to report that Halfway There is represented by two articles in the category of Baloney Detection. (Have you checked your Baloney Detection Kit lately?) My first article is The Church of the Null Hypothesis (sometimes the reason you can't find good evidence is because there's nothing going on). The second is Miracles on Interstate 80, complete with eyewitness accounts (and no, they weren't really miracles after all).

Go to Science and Politics and check out all the rest!

Monday, April 24, 2006

Clockwork creationism

Tick-tock for Tiktaalik

Are you a trained scientist? Most people have to say “no” to that question. Still, here is a problem in evolutionary biology that you can certainly understand. After all, I never even took high school biology and I can find the glaring flaw in an argument I heard earlier this month.

I traveled south for Easter Sunday weekend, spending several hours on the freeways of California. There are long stretches of Highway 99 where there's not much to listen to on broadcast radio. However, while surfing the AM dial, I heard a talk-show host asking a guest about Tiktaalik roseae, the recently discovered fossil that is an important transitional form between sea life and land animals.

The radio program turned out to be Kresta in the Afternoon from Ave Maria Radio. Eponymous host Al Kresta was talking to Dr. Fazale Rana, a chemist with a Ph.D. from Ohio University. Rana goes by the folksy nickname “Fuz” and is a member of the “scholar team” at Reasons to Believe, an organization whose mission is to demonstrate the compatibility of science and the Bible. As this information began to trickle out, it was pretty easy to tell where the discussion was headed.

I couldn't find an on-line archive of Kresta's program. Fortunately, I do not have to rely solely on my memory to do justice to Fuz Rana's argument concerning Tiktaalik because his points are provided in his own words in a Reasons to Believe press release. My direct quotes are all from that source. Rana's thesis is very straightforward:
If Tiktaalik is a transitional intermediate, it means that evolution from fish to land-dwelling animals must have happened in less than 10 million years. When evolutionary biologists claim that the transition from sea to land is that fast-paced, it raises very real questions about evolution as an explanation for life's history....
How did Rana come to this conclusion? As he explained to Kresta, Tiktaalik has been dated to approximately 375 million years ago. However, continued Rana, scientists believe that it could be a transitional form that was succeeded by Acanthostega and Acanthostega has been dated to 365 million years ago.

Rana's argument assumes that (a) the dates are firm and (b) ten million years is too brief a time for significant evolutionary changes. I won't argue point (b) because I don't know enough about rates of evolution to challenge it (although ten million years seems like a significant amount of time to me). I will, however, point out a problem with (a). It's very simple:

Species do not exist at single points in time. They exist in intervals of time. A species can survive for many millions of years. Fossils, however, do exist at points in time, each representing a particular animal whose lifetime was an invisible dot on the timeline of life on earth. Rana is failing to regard fossils as single representatives of their species rather than as the species themselves.

When we treat species as continua, existing over extended periods of time, we see immediately the extreme artificiality of Rana's objection. Without any assumptions concerning the rate of evolutionary change, it's clear that Rana's supposed 10-million-year period could easily have been much longer.

Although Rana works for an organization that begins with conclusions and works backward from there, he's not shy about criticizing more traditional scientists:
Evolutionary biologists have made up their minds before they even examine the data. They are so convinced that evolution is a fact they are unwilling to carefully weigh the evidence.
Perhaps, Fuz, you are the one who needs to examine the evidence more carefully. Would you like more time?

Saturday, April 22, 2006

Undercover creationists

Infiltrating the laboratory

Creationists keep trying to persuade the general public that there is a genuine scientific controversy over the fact of evolution. Their public-relations efforts are devoted to highlighting the small handful of creationists with actual scientific credentials. There are so few of them that their names are instantly recognizable, familiar from constant repetition. They are “the usual suspects”:
  • Jonathan Wells, who earned his Ph.D. in biology as part of a religious assault against evolution; Wells specializes in propaganda like his Icons of Evolution rather than in research;
  • Michael Behe, whose meager professional work is overshadowed by his role as an icon of antievolution; he was a star witness for intelligent design in the Kitzmiller case in Dover, Pennsylvania;
  • William Dembski, a genuinely qualified mathematician who uses symbology to obscure the vapidity of his creationist arguments;
  • David Berlinski, mathematician and author, whose antievolution tracts provide rich fodder for demolition by more qualified parties; Berlinski's prose is more ornate than Dembski's, but operates in the same obscurantist mode;
  • Kurt Wise, who earned his biology degree under the ardent evolutionary scientist Stephen Jay Gould but managed to hold on to his Genesis-based perspective; Wise spends less time on center stage than the other people in this short list because he strives to work as a scientist rather than as an antievolution polemicist, placing him outside the current mainstream of “scientific” creationism.

We could add a sprinkling of engineers to this roster, but we've just about run out of actual scientists. Creationists have noticed this shortage and are planning to do something about it. Just as Jonathan Wells enrolled in grad school to advance the religious agenda of his spiritual leader, Sun Myung Moon, young creationists are being encouraged to infiltrate the scientific community with the express purpose of overthrowing its secular paradigms. The Institute for Creation Research is leading the charge.

Mentoring Antiscientists

The April 2006 issue of Acts & Facts, the newsletter of the Institute for Creation Research ( in El Cajon, California, carries a short article by John Baumgardner, Ph.D. (the degree is in geophysics). Baumgardner's piece contains some of the clearest language about the creationists' plan of attack since the notorious Wedge document:

Training the Next Generation of
Professional Creation Scientists

With so many exciting young-earth research issues in genomics, modeling of sedimentary processes and tectonics, and cosmology, to name but a few, what can be done to train a new generation of gifted and motivated Christian students to become mature scientists and make fundamental contributions in these research areas? ICR's answer to this important question is to mentor, at a Ph.D. level, talented students who sense a distinct call by God to invest their lives in creation-related research.

In this new ICR initiative, the student obtains his/her professional training at an existing university with an established program in an appropriate specialty area. An ICR faculty member, working with the student's faculty advisor, serves as a mentor to help the student plan his/her academic program and to assist the student in identifying an appropriate dissertation research topic. The mentor helps advise the student in the research and coaches the student in navigating the challenges of today's academic and professional environments.

To launch this initiative, ICR, together with the Society for the Advancement of Creation Science at Mississippi State University, is sponsoring a Graduate Mentorship Workshop this summer at MSU in Starkville, Mississippi, July 16–21, 2006, for both students and Christian faculty who would like to be involved. ICR faculty, MSU faculty, plus four outside academic speakers will highlight recent research results, focus on promising new research topics, and lead an open forum to discuss how this sort of mentorship can be successful. Do you know someone who should attend this workshop? See for schedule and registration information.

The MSU website provides more information about the intent of the ICR-sponsored initiative, in case you couldn't already guess.
Our vision includes training the next-generation of Ph.D. scientists who become faculty members at secular universities throughout the world, who in turn train more students and advance the creation model yet further....

A related goal is to identify research topics, particularly in the realm of computational simulation, that are relevant and publishable within the current scientific framework but also strategic to the Biblical creationist paradigm....

We also hope to develop a new geneation [sic] of faculty at secular universities who confidently express a Biblical creationist worldview in their research and teaching.
So, do you know anyone who would like to be in Starkville this July?

Just between you and I

The biter bitten

You are never more likely to make a grammatical error than when correcting someone else's grammar. Call it “the Iron Law of Nitpicking,” if you will (or even if you won't). Its condign punishment rains down upon us know-it-alls who are always champing at the bit to help the less knowledgeable overcome their sad, sad ignorance. The Iron Law struck Dan Piraro this morning.

Bizarro grammar

In his Bizarro cartoon panel for April 22, 2006, Piraro takes a worthwhile shot at couples who inflict their self-written wedding vows on their guests. Good for him! We would owe him a debt of gratitude if his poke in the ribs incited a stampede away from self-indulgent do-it-yourself vows. What is a wedding but participation in a traditional form of public commitment, which becomes less traditional the more people insist on mucking with it? Too bad that the folks most likely to benefit from Piraro's gentle barb are the least likely to realize he's talking about them.

That said, take a look at the minister's words: “And now, having each recited the vows they have written themselves, we all realize the importance of education.” Whoa, what a burn on the feckless bride and groom! However, ... what exactly is the referent for the participial clause “having each recited the vows they have written themselves”? It's obviously supposed to be the bride and groom, but the actual subject of the sentence is “we,” the spectators and the celebrant at the wedding. Piraro has committed misplaced modification and left a participial phrase dangling. It would have been better for the minister say, “And now, the bride and groom having each recited the vows that they have written themselves, we all realize the importance of education.” All fixed!

Escape clause?

I dare say that not many people will incorrectly interpret the intent of the language in Piraro's cartoon. You'll note that I used the adverb “obviously” to describe the implied connection between the participial phrase and the bridal couple. In perusing ordinary prose, the average reader would have sailed through such a sentence with full comprehension and no frisson of confusion at the subtle ambiguity. However, nitpickers are more alert to opportunities for correction. Nothing gets our noses up in the air more quickly than the scent of a nitpicker at work. We devour our own, we do.

Having spoken my piece, I will now return to my usual post, lurking in the background, waiting for the next opportunity to pounce. I, at least, am a very lucky person. As a college professor, I enjoy an occupation that provides a significant (and even socially constructive) outlet for my tendency to correct others. Even better, I teach math, where the answers are seldom subject to debate. My occasional forays into English territory are not supported by professional qualifications. Let's say it's more of a hobby. A very risky one.

In the present instance, it behooves me to keep this post short, thereby reducing the likelihood that I will commit some egregious error therein. When you, Dear Reader, find the inevitable faux pas, please try to be gentle as you denounce my sin in the comments.

Update: Mark Liberman at Language Log took the above post as an opportunity to discuss the Bizarro cartoon in detail and my interpretation of it. He decided that Piraro probably made the grammatical error deliberately, with a nudge-nudge, wink-wink. I'm still inclined to think it was inadvertent. Go check out his article. Mark conducted a little poll among his readers and the latest results have 72% agreeing that “The cartoonist didn't understand that there is a linguistic problem in the caption.” Piraro himself, however, has not weighed in to clear the matter up.

To me, the most interesting part of the Language Log post was the history of what I called “the Iron Law of Nitpicking.” Thank goodness I was not so presumptuous as to call it “Zeno's Law,” as if I thought I had invented it. Mark runs through several previous incarnations, including a wonderful 1909 foreshadowing by Ambrose Bierce (wouldn't you know it?).

As for my making mistakes in the original post, two of my math colleagues quickly pointed out that I had misspelled a word (“themsleves,” already corrected) and used “therein” when “herein” would be more appropriate. (This second observation is echoed in the comment by attorney Neal Deesit, who notes that precision in legal documents would require the latter in preference to the former. Neal also reported the discussion on Language Log.) I caught the biggest mistake myself, one day after posting the original article: I gave the wrong month in citing the date of the Bizarro cartoon and made haste to correct it. (Mea maxima culpa.) Meanwhile, over at Language Log, Mark said that a number of his correspondents were concerned that I used the word “referent” in a casual way (as “the thing to which a reference was made”) at odds with the formal grammatical usage (”the thing that makes a reference to something else”). To that charge, I must plead guilty (as well as ignorance).

Friday, April 21, 2006

Miracles on Interstate 80

First-person eyewitness accounts!

My family is awash in Old World superstitions. My late maternal grandmother was almost certainly one of those “old wives” famous for spreading their tales. She lived in a scary world full of occult phenomena, motivated by her fears to clutch ever more tightly the rosary beads that kept evil at bay.

I'm not sure how the family penchant for superstition and religion (is there any difference?) passed me by. Somehow I ended up with a decidedly skeptical view of my childhood faith (see Axiomatic Catholicism) and a jaundiced eye for anything my grandmother espoused. She knew, for example, how to look in the eyes of an expectant mother and predict the sex of the offspring. This technique worked without fail—fifty percent of the time. Naturally, every success was tallied as a hit and every failure was dismissed as a fluke (not really a miss, mind you, because something had obviously gone wrong; those don't count).

The believer's ability to selectively filter out disconfirming evidence is a recognized trait that preserves the believer's world view. The skeptic tries to be on guard against this kind of cherry-picking of the data. However, we skeptics are vulnerable to the charge that we have difficulty being the neutral observers that we claim (or strive) to be. After all, it's not easy to see things as they are rather than as they appear to be. Believers may accuse us of resorting to facile explanations of mysterious phenomena, being reluctant as we often are to leave anything unresolved or unknown. We're spoilsports. Believers report amazing things that they insist are evidence of the supernatural, but we refuse to believe them. We dismiss their supposed miracles.

I may be an usual skeptic in that I have twice witnessed miracles. Both were stunning at the time of their occurrence. I had that shivery feeling that one gets when confronting the inexplicable. Although “inexplicable” turned out to be a misnomer (both of the stories have explanations I will soon recount), I can still recapture in my memory those long seconds of profound bewilderment and disorientation. Perhaps I brushed up against the ineffable sensation that is the believer's constant companion. My grandmother lived in a world where literally anything could happen. I wonder in retrospect why the old girl wasn't even crazier than she was. I don't think my own nerves could handle immersion in that world.

The vanishing tractor

One morning I started off for work. In those days, my usual route was along the Interstate 80 frontage road until I reached an on-ramp to the freeway. I approached the frontage road via a street that ended in a T-intersection with the road. On this particular morning, perhaps a quarter of a mile ahead of me, I saw a yellow tractor next to the chain-link fence that separated the interstate from the frontage road. Its operator was obviously engaged in some early-morning maintenance of the shoulder. I didn't watch the tractor, looking instead to the sides for other traffic. I looked forward again as I reached the stop sign at the T-intersection and the tractor had vanished.

I was nonplussed, pausing at the stop sign while I looked again in both directions. No tractor. I could see much too far for the tractor to have sped out of sight. I looked again straight ahead, where the tractor had been. The trees that lined the frontage road were right up against the chain-link fence. There was no room for the tractor to have ducked behind one of them and their foliage was too high above the ground to conceal a tractor anyway. I was completely at a loss and felt a sudden chill.

As I finally made my turn onto the frontage road and pondered the weird vanishing act I had just witnessed, I wondered whether I had actually seen the tractor in the first place. I didn't really doubt that it had been there, but it made more sense to me that I had had a momentary delusion than that a tractor had suddenly disappeared into the proverbial thin air. The best explanation seemed to be that I had hallucinated, as unlikely as that explanation might be.

I looked into the rear-view mirror. There was the tractor. It was behind one of the trees. Upon first spotting the tractor that morning, I had mistakenly thought that it was working on the shoulder of the frontage road. The tractor had actually been working the shoulder of the interstate, which was high enough to permit a tree to screen it from an observer on the frontage road. It had not been in front of the chain-link fence, it was behind it. My initial glance had been at a sufficient distance that its location was unclear. I had unthinkingly jumped to a conclusion. Since my attention was directed elsewhere, that conclusion was merely filed away in my brain and not examined. As a result, I had created a mental image of the situation that was incorrect and primed to release an explosion of confusion when it collided with reality.

Had I not caught sight of the tractor again before I got out of range to see it, I would still be wondering what happened that morning. This incident occurred about twenty years ago, so presumably by now I would have concluded that it was some aberration, still unexplained, in my brain. Had I been of a more superstitious turn of mind, I might be entertaining even weirder explanations and writing to the Fortean Society about the space singularity that had swallowed up an entire tractor before my very eyes.

The flying car

My second Interstate 80 miracle occurred one evening as I approached an off ramp I was planning to take. A dark car well ahead of me was blinking its right tail light as it took that same exit. Its other tail light was a dim red spark, difficult to see in the dark from the distance at which I was following.

The exit ramp in question leads to an overpass that crosses the interstate. You therefore have to drive up the ramp until you reach a T-intersection near the top of the overpass. As the car ahead of me began to climb the ramp, I looked away for a few seconds. I don't recall specifically what I was doing. Perhaps I checked the rear-view mirror. Perhaps I was keeping an eye on a car in an adjacent lane. Whatever drew my attention lasted only a little while. I looked back toward the off ramp I was approaching and was shocked to see that the car ahead of me had reached the top of the ramp and had continued up into the sky! There was its blinking red tail light, well above the road bed.

This miracle unraveled more quickly than the incident with the vanishing tractor. In the seconds it took me to reach the exit, I calmed down as I noticed several things: (a) the blinking red light did not seem to be moving; (b) there was a car traversing the overpass, which could be the one I thought had risen into the sky; (c) a pole emerged from the darkness, showing me that the blinking red light was a suspended traffic signal.

Although I had used that same exit many times before, the perfect convergence of several factors had combined to give me an apparently miraculous experience. I was not accustomed to using the exit after dark and seeing the stop-and-go red light. I had looked away just long enough for the leading car to make its turn at the top of the ramp and momentarily vanish from my sight. The car's weak left tail light had made it easy for me to identify its brightly blinking companion with the lone traffic light. The blinking rates of the two lights were close enough to reinforce the illusion that they were the same light.

Everything made perfectly good sense—after those disorienting few seconds.

Does it mean anything?

As with the tale of the vanishing tractor, the story of the flying car is an example of the kind of observation that can either unsettle one's world view (such as mine, which is decidedly non-mystical) or, perhaps, confirm it. If you don't think the universe is organized along rational lines, then anything goes and nothing should really surprise you. There could be some entertainment value in that, but I would not welcome such a wacky world.

If I were a UFO enthusiast (by which I mean those people who think unidentified flying objects are vehicles piloted by anally-fixated extraterrestrials), I could fit the flying car incident quite neatly into my belief system. In fact, I could have ended up as a minor celebrity at various saucer conventions, oozing completely genuine sincerity as I repeat once again the story of the time when I spotted an alien piloting his disguised vehicle into the sky, no doubt to a rendezvous with the mother ship. (But why did it need a freeway ramp to achieve lift-off? Another puzzle!)

Of course, I know what really happened because the evidence dropped into my lap. Had I not taken that exit and instead driven on by, I might not have figured it out. Nevertheless, I was hardly likely to send a frantic report to MUFON (the Mutual UFO Network) about my sighting. Skepticism is something I take seriously. It would take something more compelling than a confusing incident to make me set it all aside and embrace some radical explanation. The skeptic is thoughtful and tries to regard things calmly and rationally—at least eventually, if not in the fever of the moment. A skeptic doesn't claim to know everything, but most of us like to think that the universe can be understood. And we rely on science, not on the occult. As for the bizarre events that may fall into your lives, as twice they did into mine, we have a way to approach those things, too:

All together now! “Extraordinary claims ...”—well, I'm sure you know the rest.

Thursday, April 20, 2006

Calculation without concept

Attack of the coneheads

My multivariate calculus students are not entirely happy with me. I am not entirely happy with them. The results of this week's exam on multiple integrals were—shall we say?—a trifle disappointing. Perhaps you will not be surprised to learn that I had great expectations for this exam. I had fussed over its preparation at length and I had been rather pleased with the way it progressed through the various coordinate systems (rectangular, polar, cylindrical, and spherical). I knew that some students would nevertheless insist on using suboptimal choices of coordinate system for some problems (and they did), but I keenly anticipated a generally good outcome.

That's what I get for trying to be helpful. My students swore they would have done better on the exam if I had not “tricked” them. They advanced as Exhibit A the “misleading” figure that had accompanied one of the exercises. During the hours of grading, I had marveled over what my students did to that particular problem. Let's work through their complaint and see if we can figure out what's at the bottom of it.

The exam problem in question required a given function to be integrated over a very specific three-dimensional region. Here is how I described it:
Let Q be the cone bounded by z = r and z = 2.
Okay, it's a cone with the pointy end at the origin and its axis coincides with the z axis. In the margin of the exercise, I included a generic figure of a cone in the correct orientation. It was not to scale and I left it to my students how best to label it. As shown, the figure was labeled generically: a for the radius of the circular base (is it okay to call it a base if it's on top instead of on the bottom?), h for the height, and (just for the wild ones who want to use spherical coordinates) the semi-vertex angle is labeled α.

To my surprise, most of the answers worked out by my students contained a and h in them. For some reason, they did not realize that they knew (or should know) the dimensions of the cone Q. A few had grasped that z = 2 is a horizontal plane and thus the height of the cone must be h = 2. Even these people, however, couldn't figure out the value of a despite the helpful cone formula z = r. What was going on?

This is what you taught us

A few students looked at the graph of the cone and promptly wrote down a description of the region in terms of cylindrical coordinates (good choice!):

0 ≤ θ ≤ 2π
0 ≤ zh
0 ≤ raz/h

That was, of course, fine as far as it went, but I had given them specific equations. Could we perhaps please use those? No! Never! We have a picture to look at and we will use it, damn it! Don't try to stop us!

As I questioned them, I began to understand a bit more about what had occurred. They had (several of them) memorized the cylindrical coordinate definition of a cone, but it was just memorized, not understood. I've seen this many times before, but more typically among algebra students than in the ranks of a multivariate calculus class. Perhaps the recent spring break had caused them to lose their momentum and fall back on computational gimmicks in lieu of actual understanding. But perhaps I should have seen it coming. Students had asked me several time for “formulas” for converting the limits of integration of multiple integrals from one coordinate system to another. This was a bad sign I had insufficiently appreciated. In our discussion of the exam problems, I tried to get them to go back to basic principles.

“I'm afraid that you're hoping for a step-by-step computational procedure for transforming integrals. You can do that to some degree with integrands, where it's mostly a matter of substituting for one set of variables in terms of another, but don't expect that to work for the limits of integration. It's much, much better to rework the description of the region of integration. Go back to basics when you need to. Remember similar triangles?” On the board I sketched a triangular cross-section of a typical cone.

“Remember how we got the formula for a cone in cylindrical coordinates in the first place? z tells you how high you are and r tells you how far you are from the z axis. If you know the cone's radius is a and its height is h, then r and z have to be in the same proportion.”

r/z = a/h

When we solve for z, of course, we get z = hr/a. Since I had given them z = r in the statement of the problem, it should be pretty clear that a/h = 1, so a = h. What's more, since z = 2 provides the height of the cone, as previously noted, we must have a = h = 2. The value α = π/4 falls out immediately from these results, in case anyone cared to look at the isosceles right triangle.

They were right

In a way, my students were right. I have dutifully provided them with the basic tools to describe a region like a cone in cylindrical coordinates, but I had not worked with them sufficiently to instill an understanding of the patterns behind the formulas. When they saw the unidentified a and h in the illustration for the exam problem, they instantly fixated on the formal description that I had previously helped them to master (or at least memorize). Of course, it was their responsibility to work with the tools in their hands until they became adept with them (that's why I give them assignments to do at home and quizzes to take in class), but I could have drawn their attention more strongly to the process by which we built the descriptions and emphasized the flexible ideas that drove the process rather than the formulas on which it was based.

As I said at the beginning, we're unhappy with each other. They're on notice that I expect more from them than ritual formula application. And I'm on notice that once again the ideas in my head don't magically transfer into theirs. The follow-up quiz will probably show that the exam problem was a learning experience for most of my students—at least as far as cones are concerned. If I want more trouble, I could change the region to a sector of a sphere.

But that's a different problem and a different story.

Tuesday, April 18, 2006

Climate of fear and loathing

Climate changes; Crichton doesn't

Some people go on vacation during spring break. I managed instead to spend some quality time in the basement of my parents' home. It's the house I grew up in and is therefore a treasure trove of childhood memories. On this occasion I tracked down stacks of old magazines, back issues of Fantasy and Science Fiction. I was on a quest.

My efforts were rewarded when I paged through the November 1969 issue of F&SF. There was Alexei Panshin's column on recent books (pp. 46-51). His prose was as pungent as I had recalled. In fact, my memory of the book review's acerbic tone had initially sent me on a wild-goose chase, because I had been certain that Harlan Ellison had been the columnist. No, it was Panshin, and he was reviewing a novel by Michael Crichton.

The Andromeda Strain was a bestseller and led to a moderately successful movie. (Perhaps Harlan reviewed the movie. I'll have to check that out, too.) Now that Crichton is a favorite of the climate-change skeptics and, in particular, a "science advisor" to the president of the United States, it might be interesting to see Panshin's comments from three dozen years ago.
[The Andromeda Strain] has been favorably reviewed by Life, Look and the New York Times, and it has sold to the movies for an impressive sum. It is also cheap, sensationalistic, hastily written trash.... The story is either a plausible thriller—that is, you believe in the plague and in the efforts of the scientific and medical team to cope with it—or it is nothing.

Crichton bolsters his story with easy expertise and massive documentation, but the story never hangs together. The main reason is that Crichton invents his story as he goes along and is satisfied to put down the first thing that comes to mind, and one lie contradicts the next. Thus you have a bacteriologist who has won the Nobel Prize for work done in his spare time as a law student (Crichton consistently oversells)—but who doesn't know that he has a vein in his wrist.... Thus you have an Army van with a rotating antenna on top tacking back and forth across the Mojave desert taking triangulations every twenty miles on a grounded satellite—the landing site of which has already been predicted with an error of a few hundred yards. Two vans, we are told, would be suspicious. Thus you have a portentous scientific report on the probability of contact between man and other life forms with all figures to four places and a list of possibilities of encountering a life form more advanced than our own (the “7 +” level of data handling, if you please), or the possibility of encountering a life form radically different from our own, or the possibility of encountering no life at all. Crichton's documentation is fake, his expertise is false, and even his basic problem turns out to be a fraud—after a few days the plague ups and goes away.

I wonder what Panshin would have to say about Crichton's State of Fear, a dramatized cut-and-paste job of every conspiracy theory espoused by the global-warming deniers?

Wednesday, April 12, 2006

Carnival of the Liberals!

It's the 10th edition

PZ Myers of Pharyngula has chosen this blog's Reality is liberal for inclusion in the 10th installment of Carnival of the Liberals. While I hope you take time to read my contribution, make sure you check out all ten of the articles that PZ picked out. It will be worth your while.

Happy reading!

Monday, April 10, 2006

Reality is liberal

Or hadn't you noticed?

We are an empire now, and when we act, we create our own reality. —The Bush administration

The conservative moment is over. The experiment has failed, crashing down in the face of reality. The Republican Congress and the Bush White House set themselves up in opposition to the most basic truths in a display of hubris that historians will puzzle over forever. Even arithmetic is the enemy of today's shameless scions of the conservative legacy: Tax cuts and spending increases do not add up to a balanced budget. Such a surprise.

Not long ago it seemed that reality was more unpopular in the progressive community. Leftists like Alan Sokal decried the tendencies of his political allies to fall prey to extreme social constructivism: everything is relative, truth is personal, and objectivity is only a myth. Sokal famously demonstrated the willingness of the anything-goes crowd to swallow the most absurd nonsense by expressing New Age cant in the language of physics and getting it published. His lesson was that critical thinking should never go out of style. Who knew that our political opponents in the hard-headed conservative movement would turn out to be the wackiest postmodernists of all?

Nothing exemplifies this reality drift better than the GOP's behavior in Congress. The long-entrenched Democratic majority in the U.S. House of Representatives was dramatically ousted in the general election of 1994. The Republican “Contract with America” promised a series of good-government reforms, but in merely a dozen years the GOP majority has descended to a level of sleaze that exceeds anything the House Democrats managed in their forty-year reign.

Texas Democrat Jim Wright was Speaker of the House in 1989 when he was hounded from office for corruption. He was accused of bundling his old speeches in book form and selling them in bulk to circumvent limits on speaking fees. Wright was also said to be evading the limits on gifts by directing the contributions through a job his wife had. Wright's case was an example exploited by the GOP in the 1994 elections. Today we have California Republican John Doolittle, a member of the House leadership, directing campaign contributions through a company headed by his wife; she skims off a 15% commission (for no discernable work) before the contributions go into the congressman's political fund. Doolittle, however, isn't resigning in disgrace. No, he's running for re-election. Times change.

One of the planks in the Contract with America was fiscal responsibility. With the nation under the stewardship of a moderately liberal president, the House Republicans were even able to enact a balanced federal budget. However, once Bill Clinton was succeeded by George W. Bush, the doors of the candy shop were flung open and the U.S. plunged into a spending spree from which we have yet to emerge. The betrayal of conservative principles of management has been so dramatic that more authentic conservatives have felt compelled to speak out. The book Impostor by Bruce Bartlett is one notable example; in case you didn't know, George W. Bush plays the title role.

Can the conservative moment come to an end without a liberal resurgence? Some of us appear to be standing quietly by the sidelines in the hopes that the GOP implosion will continue unabated. We'll stroll in once the self-destruction is complete. That passive approach, however, could leave us holding a very empty bag. The conservative collapse is an opportunity, but mandates must be earned. To that end, liberals need to prepare themselves to take command.

The progressive on-line community is already marshaling its troops. We fell short in 2004, but that simply heightens the importance of not failing again. The nation pays a price every day that the Bush administration continues with its mendacity-based domestic and foreign policies. The truth campaign is under way, as exemplified by such manifestos as Chris Mooney's The Republican War on Science and Crashing the Gate by Jerome Armstrong and Markos Moulitsas Zúniga. Get both and get ready to be part of it.

There is work for everyone to do. What will your role be? While I am only a bit player myself, I do have a story to tell. Today I'm a math teacher who ventures in from the political sidelines occasionally to write a letter to the editor, e-mail a candidate's campaign, pony up some contributions, and participate in local rallies. (I'm tall. At one rally a campaign aide gave me the job of holding up a large sign between some banner-waving half-drunk GOP frat boys and the TV cameras. It was fun.) Before getting my faculty appointment, however, I served under the golden dome of the California state capitol as a legislative aide. I watched who pulled the levers of power and I saw some of the techniques they used. These people are accessible by citizens who take the trouble to learn some things about the system and how to work it.

Let me share that with you. First, I'll give you an example of pure serendipity, an infamous story in my academic discipline. After recounting my own initial encounter with the legislative process, I'll generalize a bit and suggest that you, too, can play the part of our humble protagonist.

A wedge of pi

Clarence Waldo did not usually spend his days at the Indiana state capitol building. A professor of mathematics at Purdue University, Waldo was checking in on the progress of an appropriation earmarked for his school. On this occasion in 1897, however, Professor Waldo unexpectedly found himself acting on his mathematical expertise and not just lobbying on behalf of his university's special interest.

House Bill No. 246 offered the state of Indiana the right to use a new and improved value of pi in its public schools—royalty free! Schools in other states would presumably have to pay a consideration and apply to Dr. Edwin J. Goodman (a physician) for permission to use his new value of pi. The debate in the Indiana State Senate was in full swing when Professor Waldo happened to look in, much to his surprise. The State House of Representatives had already passed Bill No. 246 unanimously. Waldo buttonholed some legislators, explained what they were on the verge of doing, and succeeded in getting Bill No. 246 sidetracked. On its second reading in the State Senate, the measure was “indefinitely postponed”; Bill No. 246 languished in the senate's suspense file until it died at the end of the legislative session, never more to be seen or acted upon.

Professor Waldo fell accidentally into the role of citizen lobbyist. His story illustrates how technical expertise in the right place at the right time can nudge the behavior of a legislative body. The story of Indiana's pi legislation shows us what one person can do, but in one significant aspect it fails as a cautionary tale. Bill No. 246 was ultimately trivial and it would soon have been ignored and forgotten had it been enacted into law. Today we face issues of science and technology that could powerfully shape what we learn in school, how our environment will change, and the resources we need to live. We need to find Waldo's successors, but too few of us are inclined to take up the challenge.

We live in the world that government makes for us, whether we participate in that government or not. It's time to participate—and we know where the need is.

Legislators don't know science

It was the late seventies. As the first mathematician with a California legislative fellowship, I expected that my services would be eagerly sought. My experience during the placement interviews taught me otherwise. I quickly learned that the legislators and their staffs didn't know what to do with me. An aide to the chair of the reapportionment committee said, “Well, we do use a lot of numbers.” My training as a problem-solver was assumed to be limited to number-crunching. Eventually, though, I landed in the office of a senior legislator whose staff showed more savvy. One aide laughed at the notion that his counterparts in so many of the other offices thought I wanted to sit and solve math problems all day: “It just seems to me that if you apply for a job in a butcher shop, you must be looking to cut some meat!”

I then proceeded to “cut some meat” for the next couple of years. It was the real beginning of my education in the sausage factory that is our form of government. It wasn't always pretty and it wasn't always important, the bills that were debated and the laws that were enacted, but some of the measures dramatically affected the way of life of millions of California residents (both for good and for ill).

My boss was a classic liberal who thought it was the government's responsibility to protect the rights and freedoms of the individual against the disproportionate power and influence of giant special interests. He held a Ph.D. in history from Stanford and had been a college professor before his election to the legislature. He was one of the last of a vanishing breed.

The gentleman scholar in the mold of Thomas Jefferson no longer appears in the legislative or executive ranks. Although my boss would be embarrassed beyond words to be compared to Jefferson, it is entirely fair to say that he was a man of ideas who was accustomed to thinking things through. As a professor, he had put in many hours expounding on history, political science, and economics, discussing the issues with his students. Today's politician is more likely to pore over the latest poll results than read a treatise on, say, the role of regulation in a free economy. A modern politician's expertise lies in getting elected. All other expertise is relegated to staff aides and consultants.

Very few scholars are elected to public office. In particular, there are virtually no scientists serving as state or federal representatives. Successful scientists, of course, are much too busy applying for grants, doing their research, and writing their papers. Running for office would involve giving it all up. People with science training who don't pursue research careers can find more lucrative careers as consultants in the business sector than as candidates for office. A few may, of course, serve as consultants on legislative staffs, but we're still talking about a relatively small number. I knew good people in California's Senate Office of Research, but they had to keep up with the demands of forty state senators and their legislative committees and staff.

Those who know science best are largely outside the process by which science is funded, regulated, and promoted. The end result is that policies strongly affecting pure and applied research are informed more by political considerations than by standards of scientific excellence. Nowhere has this made more clear than in the wrong-headed federal approach to stem cell research, global warming, and energy resources.

These and other crucial topics in health, education, and welfare underscore the degree to which our potential problems mandate the effective use of government policy to address them. Problems of such broad scope require collective rather than individual action. Government is the instrument for joint action, which is why we cannot ignore it even if we disdain its excesses. The government is controlled by those who bother to take part in it. We cannot surrender it to the know-nothings.

A primer on the three C's

Most states have laws regulating the activities of professional lobbyists, but citizens always have a right to petition their government. If you operate without pay, you do not fall under these regulations. (Just to be safe, you can check what activities fall under your state's rules by checking into your local equivalent of California's Fair Political Practices Commission.)

Anyone who wants to be successful as a citizen lobbyist should keep three key ideas in mind:

Context: Opportunity knocks at unexpected times, so you have to be alert as circumstances change. I once took advantage of the national frenzy over our bicentennial in 1976 to promote in the California legislature the bicentennial of a famous mathematician's birth. In the wake of the fireworks and celebrations to commemorate our 200th year as a nation, it was easy to draw legislators' attention to another bicentennial and get a resolution adopted in the mathematician's honor. When the resolution was featured in a regional newspaper, one of my math professors said, “Is this how the news really happens?” Yes, it is. (And I think it later led to my fellowship at the state capitol.)

Right now northern California has been drenched by a continuous stream of rainstorms, wreaking water damage and threatening levees across the state. It's the perfect time for hydrologists and civil engineers to help their legislators understand what the priorities are, and how best to achieve them. Left to themselves, the legislators don't know. Some of them will simply believe the last lobbyist they talk to, particularly if the lobbyist represents a good source of campaign funds. We have seen especially egregious abuses in the House of Representatives, where the Republican leadership has permitted special-interest lobbyists to write the bills that regulate their own industries. (This is not exactly an innovation. Remember the scene in The Aviator where Pan Am's lawyers provide the language of a senate bill to regulate airlines?)

Content: In the example of the Indiana legislation on pi, the text of the measure was far beyond the mathematical ability of the typical legislator. (In reality it was also beyond that of Dr. Goodman, the sponsor, but that's beside the point.) If the bill's sponsor had not been willing to provide the content of the bill, it would never have been introduced. When an informal advisor to a legislator does the work of providing the language and details of a needed bill or policy, that bill or policy is much more likely to be considered for action. When I sponsored a resolution in the California legislature, the entire body of the measure was cribbed from the proposal I submitted to my state senator and state assemblyman.

Perhaps you know a technical issue in great detail and want to lend your expertise to a legislative solution, but you don't know how to frame it in language that could be incorporated in a bill. That's when you look around for allies, because there are public-interest groups in most areas of concern. If you have mastery of the technicalities, you can work in concert with someone who knows the right words and forms to use. The citizen lobbyist doesn't have to do it all alone.

Credit: The famously liberal Ronald Reagan is reputed to have said, “You can get a lot done in this town if you don't care who gets the credit.” The citizen lobbyist seldom gets any credit for his or her efforts, but that's okay. Your real concern is to get things done. The credit can go to whoever's name is on the piece of legislation that gets enacted into law or the policy that gets announced. What's more, if you're not trying to elbow your way to the front of the crowd, your work will gain credibility. Legislative halls are full of people who want to take credit for stuff. Some of them will regard you as a mark to be taken advantage of when you do most of the work and get none of the acclaim, but you're operating according to a different standard. Success is what counts.

My boss in the state legislature was famous during his tenure in the state senate for his success at shepherding legislation into law, but the truth is that many of his greatest accomplishments carried the names of his colleagues rather than his own. He was a master of the rival bill, a measure introduced to promote his approach to a state issue even when the issue was supposedly “owned” by a colleague. The colleague would keep an eye on my boss's bill, frequently cannibalizing it bit by bit, incorporating its language into his own bill until my boss would pronounce himself satisfied and quietly drop the rival measure. Many statutes in the California code books contain my boss's words but some other legislator's name.

Remember, success is what counts.

Further reading: The sad tale of Indiana House Bill No. 246 is told in Legislating Pi, a chapter of Underwood Dudley's Mathematical Cranks. Dudley points out that Dr. Goodman's definition of pi was so confused and contradictory that it is not possible to tell from the language of the bill (which Goodman undoubtedly wrote) what value he intended. Petr Beckmann gives a detailed accounting of Professor Waldo's successful lobbying in A History of Pi (see chapter 17, The Modern Circle-Squarers). Former California state senate president pro tempore James R. Mills wrote a book about the crucial Brown-Unruh years in state politics. Its title is A Disorderly House and it's out of print, but used-book sellers can easily get it for people who want to know more about California politics from an insider's perspective. Jesse M. Unruh, for whom I was privileged to work in the 1980s when he was state treasurer, presided as speaker of the assembly during the creation of the professional staff system that still supports the work of the California legislature. In an era of term limits, Unruh's staff system now has more continuity and collective expertise than the legislators who rapidly cycle in and out of the state capitol.

Friday, April 07, 2006

Pardon my president

The brief and merciful administration

January 20, 2009. The vice president walked unceremoniously into the Oval Office, Mrs. Cheney close behind him. As a White House aide gently shut the door after them, the vice president regarded the man sitting behind the large oak desk. The president's face was flushed and his forehead glistened.

“Good morning, Mr. President,” the vice president said. Cheney was punctilious in his treatment of the chief executive, always careful to provide the form if not the substance of complete deference.

“Good morning, Dick. Is everything ready to go?”

The vice president strode forward and extended his hand. The president stood up, bracing himself on the desk with his left hand and offering the right. Cheney clasped it in a brief handshake, noting that the president's palm was clammy. Given the president's appearance, he was less than surprised. At least the president's voice was fairly steady.

“I'm glad you could join us, Lynn. I'm sorry Laura couldn't be here.”

The Cheneys knew that the first lady had been furious when her husband broke the news of the morning's plans and had refused to participate. Instead she was in the private quarters of the White House, waiting out their final hours before the noon inauguration ceremony. She would, however, join the president and the Cheneys for the limousine ride to the Capitol.

A muffled rap on the door signaled that another expected guest was about to be admitted and the secretary of state walked briskly past the White House aide who held the door for her.

“Good morning, Mr. President. Good morning, Mr. Vice President. Mrs. Cheney.”

The president had hoped that someone would say something uplifting on the occasion of his last day in office, but his guests were all business. It would have been difficult in any case to offer the customary platitudes about missions accomplished or goals achieved. The nation was eager to see him gone and his approval numbers had long languished in the low twenties, rivaling Nixon's just before his resignation. The disastrous 2006 elections had saddled him with a Democratic House of Representatives and nonstop congressional hearings on executive branch corruption had taken a toll. Articles of impeachment had not been voted, but scores of Bush administration officials had scrambled to secure immunity in return for their testimony. The American people seemed simultaneously disgusted and fascinated by the spectacle. The president had been disappointed in his hopes that they would soon be sated and lose interest. Instead the voters had decided that the 2006 results were a half-measure. They had used the 2008 election to increase Speaker Pelosi's margin in the House and broken the tie in the Senate, making Harry Reid the majority leader. Both the Democratic and Republican nominees for president had campaigned against the incumbent, the latter only slightly less overtly than the former.

The secretary of state was carrying a slender portfolio. She slipped a single sheet of paper out of it, stiff bond paper carrying the White House letterhead, and placed it on the desk before the president. He took up a pen and quickly signed it. “Here you go, Dick.”

“Thank you, Mr. President.” The vice president accepted the proffered sheet of paper, folded it carefully, and slipped it into the inside pocket of his coat. The secretary of state pulled another sheet of paper from her portfolio and placed it before the president. George Bush stared at it for several seconds, then wielded his pen again.

“Thank you, Mr. President,” said the secretary of state, suddenly keenly aware that it was now just a courtesy title. She carefully placed the resignation letter back into her portfolio. Mrs. Cheney began to rummage in her large handbag and pulled out a Bible. With impeccable timing, a muffled rap on the door accompanied the entrance of Mr. Alito, the junior associate justice of the Supreme Court. The Court was precariously split down the middle and the president had been unable to fill the Stevens vacancy because the emboldened Democrats in the U.S. Senate had blocked his nominee. The Democratic president-elect would begin his term of office with a crucial Supreme Court appointment.

President No. 44

Justice Alito was wearing a business suit rather than judicial robes. He greeted the occupants of the Oval Office and they quickly arranged themselves, Cheney with his right hand lifted, his left hand on the Bible in his wife's hands, and Bush and Rice to one side. “Please repeat after me. I, Richard Cheney, do solemnly swear that I will faithfully execute the office of President of the United States, and will to the best of my ability, preserve, protect, and defend the Constitution of the United States.” The former vice president echoed the justice's words, ending his recitation with an emphatic, “So help me God!” The words were a traditional coda to the presidential oath of office, but they were not actually in the U.S. Constitution.

“Congratulations, Mr. President,” said Justice Alito, shaking Cheney's hand. The new president exchanged a quick kiss with the new first lady and then shook hands with his immediate predecessor and the secretary of state. “Okay,” he said. “Let's finish this.”

Secretary Rice dipped into her portfolio again. In addition to the presidential resignation letter, it contained her own previously signed presidential pardon and one other sheet of White House stationery. She placed it on the desk and President Cheney signed it. He handed the document to Bush, who stared at it until Rice suggested she take care of it for him. He gratefully handed his own presidential pardon to the secretary of state.

“Of course, it's not like we are really going to need that,” he said, trying to make light of it.

“It doesn't hurt to be safe, George,” said President Cheney. The former president's eyes widened at the use of his first name and he flinched as if struck. Bush opened his mouth as if to speak, then closed it again. Finally, he said, “Well, I'd better go find Laura and get ready for the inauguration ceremony. I'll see you there, Mr. President.” He uttered the final salutation very precisely, with an exaggerated tone, but was disappointed that Cheney showed no reaction. The 43rd president of the United States left his former office, trailed by the secretary of state and the associate justice. The Cheneys were alone in the Oval Office.

Mrs. Cheney looked at the president's desk. “You may as well try it out, Dick.”

The 44th president of the United States moved around the desk and sat down. “I do believe I still have a bit of work to do,” he said. The president began pulling open the drawers. Most of them were nearly empty, but that had been true throughout the eight years of the Bush administration. The Oval Office had been less of a work room than a meet-and-greet facility. The room's decor and appointments still reflected the tastes of its recent occupant, but that would soon change. An army of White House staffers was poised to sweep into the offices and living quarters as soon as the Bushes left for the inauguration ceremony; they would rapidly box up and remove all of the items specific to the Bush administration and put in place items chosen by the incoming president. The departing president did not have to suffer the indignity of spending his final days among packing crates and such. His office was his until the moment he left it.

“Here it is,” said President Cheney. He picked up a half-empty bottle from the drawer he had just opened and handed it to his wife. She tucked it into her handbag. White House aides were famously discreet, as a rule, but Cheney saw no reason to provide any additional rumor fodder during the transition.

“We don't know when he last had a drink,” observed the first lady.

Cheney gave a sharp laugh as he stood up. “You saw him. Face all red and sweaty. Laura's been hovering over him to make sure he takes his Antabuse, but it's been too much for him. For months now. I knew he'd need a quick drink this morning before facing the end.”

“But at least he was right about the pardons, wasn't he? I mean, we aren't really going to need them, are we?”

“Don't worry about it. Like I told George, it's insurance. Doesn't hurt to be safe, especially with the whack jobs who'll be in charge after the inauguration. It's kind of funny, you know. Al Gore still thinks he was the legitimate 43rd president and today he thinks he's going to be sworn in as the 44th. He'll probably never really know he's the 45th, not unless he sics Attorney General Spitzer on all of us and we have to wave those pieces of paper in their faces.”

The news media were already referring to the scheduled swearing-in ceremony as the “Restoration Inauguration.” One liberal commenter using the name “Winston Smith” on the Daily Kos blog had proposed that the United States adopt the Prestimion option and expunge all trace of the Bush administration from the federal records. Right-wing blogs had exploded in paroxysms of outrage, denouncing Winston Smith for his Stalinist approach to history. The screams finally died away to a disgruntled muttering when the fearless keyboard brigades were introduced to the literary significance of the name Winston Smith and realized they had been pranked. There followed several long complaints that the joke had not been funny, clever, or even very credible.

The president of the United States arose from the desk that had been so briefly his. “Let's get out of here,” he said. “I'm going to need some cups of coffee in me if I'm going to stay awake through the tree-hugger's speech.”

The first lady was still fretting.

“Do you think we did all we could do, Dick? I mean, what about Karl and some of the others?”

Karl Rove had been convicted for blowing the cover of a CIA operative. He had filed his appeal the week before the November election. No one in the White House had appreciated his timing.

“What about Karl? What about the others who went running to Fitzgerald or Conyers? They can go fuck themselves.”

Exeunt omnes

Wednesday, April 05, 2006

Waking up with dKos

It's not a slumber party

It's only one line in a long profile of Daily Kos's Markos Moulitsas in the San Francisco Chronicle, but it's not an accidental one:
And eventually, he says, the online ranters have to get out of their jammies.
Markos clearly managed to get Chronicle reporter Joe Garofoli to pick up a sideways slam at the ill-fated Pajamas Media. Remember Pajamas Media? Don't worry. Hardly anyone does. It was supposed to be the big new idea in on-line reporting, although it never became more than one additional bit of iconic sidebar jazz to add to its participants' usual Internet offerings.

Nicely done.

Saturday, April 01, 2006

So much smarter than you

Ogawd, not more Berlinski!

Just this once more, okay? Then I promise to stop. I'm sure I can. It's just that—well, how should I say it?—this is so damned weird! I'm scratching my head and need to get this off my chest. (Nice mixed metaphor there, if you'll excuse my patting myself on my own back. Ow!) I promise you will find this amazing.

Let's begin with a little math lesson. That's always a good way to gather a crowd. Come a little closer, kids, and Dr. Z will astonish you with his great wisdom! I take for my text a reading from the book of Tom the Apostol, Chapter 3, Section 2:
The equation limxp f(x) = A is read: “The limit of f(x) as x approaches p is equal to A,” or “f(x) approaches A as x approaches p.” It is also written without the limit symbol, as follows:

f(x) → A as xp.

This symbolism is intended to convey the idea that we can make f(x) as close to A as we please, provided we choose x sufficiently close to p.
That was a perfectly straightforward description of the notion of a mathematical limit. Here's a concrete example to show you that you understand the basic idea:

Let f(x) = x2, which is often called the squaring function (the reason for this is left as an exercise for the student). Evaluating function notation is no big deal in a simple case like this. If you're told that x = 3, you just plug in 3 wherever you see x (the number you plug in is called the argument of the function), like so:

f(3) = 32 = 9.

Okay? If we revisit the limit idea with the squaring function in mind, replacing p with 3 and A with 9, we find ourselves looking at the statement that

x2 → 9 as x → 3.

Does that seem reasonable? As x gets closer and closer to 3, x2 gets closer and closer to 9. If you look at the accompanying graph of y = x2, you may be able to persuade yourself that this is true. You would be correct to think there are subtleties which we have avoided here, but feel free nevertheless to congratulate yourself on having grasped a key fact about the squaring function: when two numbers are close together, their squares are also close together. The closer the numbers, the closer their squares. It's not exactly rocket science at this point.

Once upon a time in Prague

I finally got around this year to reading David Berlinski's A Tour of the Calculus, the 1995 book that tried to popularize calculus and helped him make his mark as an author. Since I usually assign some outside reading to my calculus students in order to keep them from thinking that everything is in the pages of their textbook, I welcomed the appearance of the Berlinski book and its nontechnical approach. Before I found the time to read it on my own, however, some of my colleagues shared their disdain of Berlinski's prolix prose and metaphor mania. My ardor cooled and the book got shoved to the back of my stack of reading material, where it's languished the past decade.

In the intervening years, Berlinski has been busily pimping for the Discovery Institute, where he is a senior fellow with DI's Center for Science and Culture. Despite his yeoman service on behalf of the exponents of intelligent design, Berlinski claims a general agnosticism about the topic and does not profess to be a creationist. He prefers merely to lob his mathematically laden bombs at the theory of evolution. Such nonsense made me even less inclined to dig out his book on calculus, because he struck me more and more as a player of perverse intellectual games, pretending a kind of neutrality while focusing all of his attacks on the scientific side of the evolution/creation argument.

Berlinski has not escaped unscathed. I wrote about his wrongheadedness myself in David Berlinski vs. Goliath, but for a real nuts-and-bolts evisceration of his arguments, see what Mark Chu-Carroll has to say about Berlinski's Bad Math at Good Math, Bad Math:
In my never-ending quest for bad math to mock, I was taking a look at the Discovery Institute's website, where I found an essay, On the Origin of Life, by David Berlinksi. Bad math? Oh, yeah. Bad, sloppy, crappy math.
This surfeit of criticisms of Berlinski, although I fully agreed with them, finally tweaked my conscience and reminded me of the unread calculus book. Perhaps Berlinski's seduction by the dark side of creationism had drawn him away from more constructive efforts. I had read enough of his prose and seen him on enough video to remain wary of his tendency to talk down to people, but A Tour of the Calculus was supposed to be an attempt to speak to the general public. I needed to read it to see for myself.

It didn't take too many pages for me to see that all of Berlinski's pomposity is at full play in A Tour of the Calculus. He lards the text with digressions and obscure allusions (perhaps I am not educated enough to appreciate him). The mathematical concepts are recast in odd ways that confuse rather than shed light. The writing is self-indulgent. These are disappointments rather than surprises. Nevertheless, I promised you a surprise, and it's time for me to deliver. I began with a short math lesson on the squaring function because it is at the center of a bizarre tale recounted by Berlinski in Chapter 15, A Prague Interlude.

Berlinski goes to Prague University to lecture on Tychnoff's theorem, a sophisticated result from topology. One of his hosts is Professor Swoboda, a mathematician. “Swoboda is extraordinarily intelligent,” Berlinski tells us. Please remember these things. Berlinski is giving a math talk attended by an extraordinarily intelligent mathematician. Here is an extended quote from the middle of his narration:
I am supposed to talk about Tychonoff's theorem, but to my surprise I find myself explaining the elementary calculus to a roomful of mathematicians, re-creating in my own mind the steps that Bolzano took in order to define continuity. For some reason I feel it absolutely crucial to explain how the concept of a limit is applied to functions. No one seems to mind or even notice.

“A function indicates a relationship in progress, arguments going to values. Given any real number, the function f(x) = x2 returns its square, tak? ... In go arguments 1, 2, 3, out come the values, 1, 4, 9.... As the arguments of f get larger and larger, its values get larger and larger in turn.* ... Now imagine,” I say, “arguments coming closer and closer to the number 3, tak?”

I walk back to the blackboard and show the men in my audience what I mean, writing, 2, 2.1, 2.2, 2.3, 2.4, 2.5, 2.6, ..., before the function.

“What then happens to the function? How does it behave?” I ask, realizing with a sense of wonder somewhat at odds with the hard-boiled pose I usually affect, that a function is among the things in this world that behaves—it has a life of its own and so in its own way participates in the drama of things that are animate.

“I mean,” I say, “what happens to the values of f as its arguments approach 3?”

I look out toward my audience. Swoboda and Schweik are looking at me intently, their faces serene, without irony. It is plain to me that they do not know the answer yet.

“They approach, those values, the number 9, so that the function is now seen as running up against a limit, a boundary beyond which it does not go.”

Swoboda leans back and sighs audibly, as if for the first time he had grasped a difficult principle. The room, with its wooden pews and narrow blackboard, is getting close.

I say, “The concept of a limit, as it is applied to functions, is forged in the fire of these remarks.”
There's more. Much more. But enough. Can you explain this passage to me? Berlinski begins by admitting he is talking about elementary calculus, but then has his roomful of mathematicians rapt in awe as he reveals that values of the squaring function approach 9 as its arguments approach 3. College students would not be surprised by this result, let along a roomful of mathematicians.

I presume Berlinski intends this as an extended metaphor, because otherwise he is cruelly mocking his Hungarian Czech colleagues. The point of the metaphor, however, is completely and entirely lost on me. His absurdist account continues with yet another elementary limit. A moderately competent Calculus I student would dispatch it promptly and math teachers could do it in their heads, but Berlinski presents it to his audience with drama and mystery. The mathematicians leave the seminar at its conclusion and trudge down the street, exhausted. “Their tread is heavy and tired.”

I know how they feel.

Update: David Berlinski has complained of his rough treatment at the hands of the proprietor of Good Math, Bad Math. While trying to defend his mathematical arguments against Mark Chu-Carroll's criticisms, Berlinski mentions my comment about his visit to Prague University and objects:
If you check the index to my A TOUR OF THE CALCULUS under 'limits' you will find page references to a complete and precise definition. The section in Prague was, of course, intended to be dream-like. It is not the mathematicians who are diminishing in sophistication, but the narrator.
Was that supposed to clear things up? If you have the stomach for more, Berlinski has returned to Good Math, Bad Math for Round 2. If, like me, you're ready for a rest cure, here's an opportunity to avert your gaze. (But don't forget to bookmark Good Math, Bad Math for future reference. Good stuff is added every week.)

*Berlinski is assuming that the x values are positive. If negative values are permitted, then larger x values do not always result in larger squares. For example, −1 is greater than −2, but (−1)2 is smaller than (−2)2.