Monday, January 19, 2009

ProfScam - Accurate or Not?

About twenty years ago, when I started teaching at Dartmouth College, a book called ProfScam appeared. Written by a journalist (and now conservative talk show host), Charles J. Sykes, and published by that fountain of evangelical foolishness, Regnery Gateway, ProfScam claimed that American university education was in a terrible state, and professors were the ones to blame.

ProfScam was passed around with astonishment at Dartmouth. Sykes described professors the likes of which we had never seen. Professors, in Sykes' view, were interested in publishing "trivial and inane research in obscure journals that nobody reads". Actually, in my field, publishing trivial results would quickly earn you a reputation for doing so, with the result that no one is likely to read what you write in the future. You won't get tenure, and you won't get promoted.

Professors, Sykes says, "communicate in impenetrable jargon, often to mask the fact that they have nothing to say". Difficult concepts in mathematics and computer science are not always easy to understand, even for experts. The "impenetrable jargon" is usually the result of striving for precision: taking an imprecise, intuitive notion of something (say "information") and trying to make it rigorous. Again, people who have nothing to say won't impress their peers.

Professors, Sykes claims, "are not only indifferent to good teaching, but actively hostile to it". Again, not in my department, where teaching is an essential component of getting tenure, and where good teaching earns you a higher annual evaluation and a commendation in department meetings.

But the main thing that I remember about ProfScam was Sykes' claim about how little time professors spend in their jobs. He claimed that the average professor works only 8-16 hours per week. Again, this didn't agree with my experience at all.

So, this past week, I decided to keep track of the number of hours I worked and what I did. Here is a summary, with times in hours and minutes.

Teaching: 6:22 (includes time walking to class from my office, setting up computer, and talking to students afterwards)

Lecture Preparation: 9:17

Preparing solutions to course assignments: 4:45

Miscellaneous course work: 2:15 (includes meeting with TA's, getting key for projector)

Office hours: 2:00

Departmental meeting: 1:00

Writing recommendation letters for students and faculty: 0:46

Answering e-mail: 6:10

Research paper preparation: 4:00

Research: 1:05

Errata for book: 0:16

Refereeing papers for journals: 2:15

Editing work for two journals: 2:33

Answering questions about the course online and in my office: 1:50

Meeting with graduate students: 2:25

Help another faculty member with grad admission: 0:20

Total time: 47:19

During a non-teaching term, I would have a very different schedule, as much of the time devoted to teaching and talking with students above would be replaced by research time.

Keep in mind that we are paid for 35 hours of work. I'm not complaining - I love my job and am happy to put in the extra hours. But I do object to being labeled as lazy by people like Sykes, who appears to have no idea what professors actually do with their time.

Saturday, January 10, 2009

Blowhard of the Month: Freeman Dyson

Most of my nominees for Blowhard of the Month are talentless, pretentious hacks. For example, David Warren of the Ottawa Citizen has won the award twice.

This month, with some reservations, I'm going to nominate a man with serious accomplishments. Unfortunately, serious accomplishments in one field don't prevent you from being a blowhard in others.

Freeman Dyson is a well-known mathematician and physicist. Number theorists know him from his earliest papers on continued fractions and Diophantine approximation, but then he got seduced by theoretical physics and most of his subsequent work was in that field.

In his later years (Dyson is now 85), though, Dyson's output has become increasingly cranky. He's commented favorably about intelligent design; yet when I questioned him via e-mail, he admitted that he had not read any of the work of Michael Behe and William Dembski, the ID movement's most prominent advocates.

Despite having no training in climatology, Dyson has sneered at the consensus of climate scientists about global warming. (The hallmark of the blowhard is to spout off in areas outside his competence.) Actual climate scientists, such as Michael Tobis, begged to disagree. Dyson used a review a review of two books on global warming, to cast doubt on the seriousness of the problem, and accused climate scientists of being contemptuous of those who disagree. Dyson's maunderings were taken apart by the actual climate scientists at RealClimate. An essay in Dyson's book, A Many-Colored Glass, also attacked the global warming consensus; his critique was dismantled by a post at Climate Progress, which didn't hesitate to call Dyson a crackpot.

Dyson even wrote a friendly foreword to Elizabeth Lloyd Mayer's credulous woo-fest, Extraordinary Knowing.

All this is in the past, so why should Dyson get a Blowhard nomination this month? It's because of an article that recently appeared in the Notices of the American Mathematical Society. Here is an excerpt:

"The mathematicians discovered the central mystery of computability, the conjecture represented by the statement P is not equal to NP. The conjecture asserts that there exist mathematical problems which can be quickly solved in individual cases but cannot be solved by a quick algorithm applicable to all cases. The most famous example of such a problem is the traveling salesman problem, which is to find the shortest route for a salesman visiting a set of cities, knowing the distance between each pair. All the experts believe that the conjecture is true, and that the traveling salesman problem is an example of a problem that is P but not NP. But nobody has even a glimmer of an idea how to prove it."

This is not even close to correct. The distinction in P versus NP has nothing to do with being a problem being "quickly solved in individual cases", but rather, that the answer can easily be verified once a small amount of extra information is provided. As stated, Dyson's example of the traveling salesman problem is not even in NP, since he states it in the form of finding the shortest tour, as opposed to checking the existence of a tour of length less than a given bound. (If I give you a traveling salesman tour, nobody currently knows how to check in polynomial time that it is the shortest one.) And finally, he blows the punchline. The decision version of traveling salesman is known to be in NP, but most people believe it is not in P. Dyson got it backwards.

The mark of the blowhard is not simply to comment on areas outside his competence, but to do so publicly, with the weight of his reputation behind him, while not doing the appropriate background reading and refusing to seek the opinions of actual experts in the field before publishing. In doing so, the blowhard frequently makes mistakes that would be embarrassing even for those equipped with an undergraduate's knowledge of the area. Freeman Dyson is the Blowhard of the Month.

Added January 13 2009: Prof. Dyson has very kindly responded to my e-mail, and concedes his description was wrong and that he was speaking outside his area of expertise.

How Come This Never Happens to Me?

According to this article in the Spokesman-Review, Tony Mantese got an unexpected visitor to his house in Spokane, Washington yesterday.

It was a baby moose that crashed through his basement window.

Despite the fact that we have "Moose Welcome" signs all over our house, we never get this lucky.

Sunday, January 04, 2009

How Not to Communicate Mathematics

My colleague David Goss, who is the Editor-in-Chief of one of my favorite journals, the Journal of Number Theory, has started a new and unusual feature: video abstracts for accepted papers.

In a recent message to the NMBRTHRY mailing list, he suggests the following video as a "terrific example of what is possible with this technology". The video is of the renowned number theorist, Alain Connes, discussing his paper, Fun With F1.

Although I think the use of video abstracts is a clever idea that could be quite useful, I'm afraid I have to differ with David about this particular video. I think the video exhibits many of the problems inherent in trying to communicate advanced mathematics:

1. Assuming too much. What percentage of viewers will even know what A1, A2, B2, and G2 are? My guess is that, even among number theorists, only a small percentage will know what is being referred to here.

2. Not explaining enough. In the video, Prof. Connes talks about his paper, but never says explicitly what F1 actually is. (He says it is the field with characteristic 1, but of course there is no such field; we are meant to understand that it is not an actual field, but some sort of degenerate analogue of finite fields.)

3. Not giving any examples. It's often hard to grasp abstract mathematics without a simple example that one can manipulate.

Finally, it doesn't help that Prof. Connes has a very strong French accent that makes much of the video difficult to understand. (He also breaks into French in several sentences, seemingly without noticing.)

Alain Connes, a Fields medallist, is a much better mathematician than I am, but I don't think this video will be at all useful for the vast majority of mathematicians who view it.

A New Blog for Skeptics and Humanists

I am glad to see that the Center for Inquiry has started a new blog, Free Thinking. With contributors such as Derek Araujo, D. J. Grothe, and Joe Nickell, it should prove to be a lively addition to the blogosphere.

Saturday, January 03, 2009

Test Your Knowledge of Information Theory

Creationists think information theory poses a serious challenge to modern evolutionary biology -- but that only goes to show that creationists are as ignorant of information theory as they are of biology.

Whenever a creationist brings up this argument, insist that they answer the following five questions. All five questions are based on the Kolmogorov interpretation of information theory. I like this version of information theory because (a) it does not depend on any hypothesized probability distribution (a frequent refuge of scoundrels) (b) the answers about how information can change when a string is changed are unambiguous and agreed upon by all mathematicians, allowing less wiggle room to weasel out of the inevitable conclusions, and (c) it applies to discrete strings of symbols and hence corresponds well with DNA.

All five questions are completely elementary, and I ask these questions in an introduction to the theory of Kolmogorov information for undergraduates at Waterloo. My undergraduates can nearly always answer these questions correctly, but creationists usually cannot.

Q1: Can information be created by gene duplication or polyploidy? More specifically, if x is a string of symbols, is it possible for xx to contain more information than x?

Q2: Can information be created by point mutations? More specifically, if xay is a string of symbols, is it possible that xby contains significantly more information? Here a, b are distinct symbols, and x, y are strings.

Q3: Can information be created by deletion? More specifically, if xyz is a string of symbols, is it possible that xz contains signficantly more information?

Q4: Can information be created by random rearrangement? More specifically, if x is a string of symbols, is it possible that some permutation of x contains significantly more information?

Q5. Can information be created by recombination? More specifically, let x and y be strings of the same length, and let s(x, y) be any single string obtained by "shuffling" x and y together. Here I do not mean what is sometimes called "perfect shuffle", but rather a possibly imperfect shuffle where x and y both appear left-to-right in s(x, y) , but not necessarily contiguously. For example, a perfect shuffle of 0000 and 1111 gives 01010101, and one possible non-perfect shuffle of 0000 and 1111 is 01101100. Can an imperfect shuffle of two strings have more information than the sum of the information in each string?

The answer to each question is "yes". In fact, for questions Q2-Q5, I can even prove that the given transformation can arbitrarily increase the amount of information in the string, in the sense that there exist strings for which the given transformation increases the complexity by an arbitrarily large multiplicative factor. I won't give the proofs here, because that's part of the challenge: ask your creationist to provide a proof for each of Q1-Q5.

Now I asserted that creationists usually cannot answer these questions correctly, and here is some proof.

Q1. In his book No Free Lunch, William Dembski claimed (p. 129) that "there is no more information in two copies of Shakespeare's Hamlet than in a single copy. This is of course patently obvious, and any formal account of information had better agree." Too bad for him that Kolmogorov complexity is a formal account of information theory, and it does not agree.

Q2. Lee Spetner and the odious Ken Ham are fond of claiming that mutations cannot increase information. And this creationist web page flatly claims that "No mutation has yet been found that increased the genetic information." All of them are wrong in the Kolmogorov model of information.

Q4. R. L. Wysong, in his book The Creation-Evolution Controversy, claimed (p. 109) that "random rearrangements in DNA would result in loss of DNA information". Wrong in the Kolmogorov model.

So, the next time you hear these bogus claims, point them to my challenge, and let the weaselling begin!