Now that the years have passed and everything’s being forgotten, and now that I’ve received a terse email from Scotland with the sad news of Seldom’s death, I feel I can break my silence (which he never asked for anyway) and tell the truth about events that reached the British papers in the summer of ‘93 with macabre snf sensationalist headlines, but to which Seldom and I always referred – perhaps due to the mathematical connotation – simply as the series, or the Oxford Series. Indeed, the deaths all occurred in Oxfordshire, at the beginning of my stay in England, and I had the dubious privilege of seeing the first at close range.
I was twenty-two, an age at which almost anything can still be excused. I just graduated from the University of Buenos Aires with a thesis in algebraic topology and was traveling to Oxford on a years scholarship, intending to move over to logic….
I’ve never particularly enjoyed the mystery genre – never read any Sherlock Holmes or Agatha Christie – but I used to have a very limited list of mystery writers I devoured. My tastes ran to “series” writers whose investigator had some kind of interesting twist: Patricia Cornwell’s medical examiner, Jonathan Kellerman’s kiddie shrink, Stephen White’s adult shrink, Faye Kellerman’s tales set in a background of SoCal Orthodox Judaism.
This book came to my attention because it was presented as involving logic and mathematical philosophy, specifically, Gödel’s Incompleteness Theorems. He proved there are aspects of mathematics that, while true, cannot be proved, and a complete collection of mathematical principles can not exist. If I sound like I know what I’m talking about, that’s purely coincidental, as this is all well over my head in spite of several diligent attempts over the years to follow explanations at varying levels of complexity. So if you are beginning to break out in a mathphobic cold sweat, don’t worry, the book doesn’t require much. Everything you need is included.
The unnamed narrator is a young mathematician from Argentina who comes to Oxford to study logic. Shortly after his arrival, his landlady is murdered, and he makes the acquaintance of an éminence grise named Seldom who has reason to believe the murder is the first of a series. They join forces to understand the series, and thus predict and prevent future murders. The police, of course, are doing the same thing, but by interviewing witnesses and tracking down leads, not by considering the ramifications of Wittgenstein and Gödel.
“Think of any crime with only two possible suspects…. All too often there isn’t enough evidence to prove either one suspect’s guilt or the other suspect’s innocence. Basically, what Gödel showed in 1930 with his Incompleteness Theorem is that exactly the same occurs in mathematics. The mechanism for corroborating the truth that goes all the way back to Aristotle and Euclid, the proud machinery that starts from true statements, from irrefutable first principles, and advances in strictly logical steps towards a thesis – what we call the axiomatic method – is sometimes just as inadequate as the unreliable, approximative criteria applied by the law.”
There’s more, but that’s the basic connection. As for Wittgenstein’s Infinite Rule Paradox: “This was our paradox: no course of action could be determined by a rule, because any course of action can be made out to accord with the rule”. The upshot is, no matter how many terms of a series are discovered, we can never be absolutely certain that we know the rule that generates the series, so we can never know for sure what the next term is. So, although they are mathematicians and so enjoy playing with this stuff, they don’t really think it’s going to help predict or prevent future murders. But they’re gonna give it a try anyway.
One small thing fascinated me. The first murder victim, the landlady, was clearly patterned after Joan Clarke, one of the few female cryptographers who worked on Enigma at Bletchley during the war. However, her recruitment is fictionalized:
During the war she’d been one of a small number of women who entered a national crossword competition, in all innocence, only to find that the prize was to be recruited and confined to an isolated little village, with the mission of helping Alan Turing and his team of mathematicians decipher the codes of the Nazis’ Enigma machine.
This is exactly the same little fictionalization that’s part of The Imitation Game. It makes a great story, and it’s a terrific scene in the film, but it seems it seems it never happened: Clarke was recommended by a professor, and there’s no evidence Turing had anything to do with the crossword contest (which was, indeed, used as a recruitment tool). That such a scene shows up in two different works makes me wonder if it’s an urban myth, or if it applied to someone and the exact facts have been changed by time and secrecy.
Most of us think of mathematics and philosophy as very different fields of endeavor: philosophers are over here, studying things like ethics and truth and beauty, and mathematicians are over there playing with numbers. I’ve discovered (through moocs that often went way over my head) that it’s more complicated than that, that there is a continuum, and the point where they intersect most clearly is logic, where our narrator and Seldom dwell.
(Warning: I’m about to go above my pay grade again, so please take this with a pound and a half of salt). And here, Seldom proposes that mathematics mimics physics, where the rules change once we get down to the quantum level. His hypothesis is that what keeps us out of the mathematical “uncertainty principle” zone – where unprovable statements lie – is the mathematician’s aesthetic appreciation of simplicity and elegance in proofs, an aesthetic in existence from the time of Pythagoras. In this way he unites beauty and truth, philosophy and mathematics, aesthetics and execution, quite neatly. The point at which he departs from actual mathematical theory, I have no idea.
The book reminded me somewhat of The Davinci Code; both were published the same year (and both were made into movies, neither of which I’ve seen, but the consensus seems to be that this movie was terrible). I found Brown’s book annoying; the cliffhangers-every-five-pages and “thriller” element putting various characters in jeopardy over and over. I prefer my thrills to come from less violent sources. In typical mystery style, subtly-suspicious characters wander in all over the place, and in classic Isaac Asimov “Black Widower” style, the eventual answer comes out of left field but makes perfect sense. I have to admit my interest was not terribly high until the end, at which point I had to read it over again.
That was possible because it’s a short book and a quick read. There really isn’t much to it at all, outside of the math and the resolution, but I found that enough to make me glad I read it. Martínez – a mathematician from Argentina, by the way, like his protagonist – has written several other books; I’m interested enough to consider reading another one some day.