Recursivity

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.