Friday, February 3, 2012


When I was in graduate school I developed a method for solving particularly difficult mathematical problems of the kind that sometimes took days. The strategy was to keep the problem “lightly” in mind all the time. By lightly I mean, focusing continually on the problem and the pertinent details and related deductions while avoiding obsessing about any particular strategy for solving it. The longer I’d go, the more difficult it would become to preserve the state of willed obsession and yet the solution would finally come, often emerging spontaneously, proving that sometimes the deepest reasoning the mind does is subconscious.

January felt like that. I’ve been thinking about how to restructure my fencing training and competition in order to become a better fencer. As part of another project I’ve been reading some archaeological research, in particular Stein et al’s “Revisiting Downtown Chaco” and George Pepper’s 1905 paper “Ceremonial Objects and Ornaments from Pueblo Bonito.” As an adolescent I imagined that science and knowledge developed linearly. Later, I learned that even in something as rigorous as mathematics, the development of knowledge is much more like the development of a theme in musical composition. Important knowledge is reasoned, or discovered, then lost and rediscovered sometimes simultaneously. In the light of Lekson’s revolutionary history of the ancient southwest it might be a good time to review Pepper’s work chronicling the finds of the Hyde/Putnam excavations. If Lynn were reading this over my shoulder she’d no doubt bring up “The Glass Bead Game,” and rightly, too.

In January I also had a bout with the flu as has she. The flu sucks. In “Seven Pillars of Wisdom,” T.E. Lawrence describes how he developed his famous strategy for the Arab insurgency while suffering a severe illness. Unfortunately, I have to report that my own recent illness led to no such astonishing insights, at least that I’d recognize as such.

There was a compensation, however. We’ve just seen the BBC production “Sherlock Series 2,” the second installment of the modern day re-imagining of Sherlock Holmes by Steven Moffat and Mark Gatiss. The first series of three feature length films was a perfect delight. And yet, the second series surpasses it. It was by far the best drama I’ve seen in the last year and notably puts to shame every American film we’ve seen since “Michael Clayton.” They are literate, witty and filled with original dramatic riffs built from modern technological culture.

They are also allusive. Dr. Watson’s blog happens to latch at 1895, which was also was the original Holmes’ annus mirabulis, the year of some of his greatest mysteries. I’m inclined to think that 2011, was Moffat and Gatiss’s 1895.


Mark said...

I hadn't seen this post. Was reminded of the story of Poincare's discovery of the theta-Fuchsian functions...

"It is time to penetrate further and to see what goes on in the very soul of the mathematician. For this, I believe, I can do best by recalling memories of my own. But I shall limit myself to telling how I wrote my first memoir on Fuchsian functions. I beg the reader's pardon; I am about to use some technical expressions, but they need not frighten him, for he is not obliged to understand them. I shall say, for example, that I have found the demonstration of such a theorem under such circumstances. This theorem will have a barbarous name, unfamiliar to many, but that is unimportant; what is of interest for the psychologist is not the theorem but the circumstances.

"For fifteen days I strove to prove that there could not be any functions like those I have since called Fuchsian functions. I was then very ignorant; every day I seated myself at my work table, stayed an hour or two, tried a great number of combinations and reached no results. One evening, contrary to my custom, I drank black coffee and could not sleep. Ideas rose in crowds; I felt them collide until pairs interlocked, so to speak., making a stable combination. By the next morning I had established the existence of a class of Fuchsian functions, those which came from the hypergeometric series; I had only to write out the results, which took but a few hours.

"Then I wanted to represent these functions by the quotient of two series; this idea was perfectly conscious and deliberate, the analogy with elliptic functions guided me. I asked myself what properties these series must have if they existed, and I succeeded without difficulty in forming the series I have called theta-Fuchsian.

Thomas William Jensen said...

Sorry, Mark. With a lot going on, (rambles in desert canyons with old friends among them) I've been remiss about my blog so I just saw your comment. Poincare's reminiscence was new to me and I liked it a lot. I don't know that it enables one to see why goes on in the soul of a mathematician as much as it says that at a certain level it's opaque. In any case, I loved it. Thanks.