|Math is discussed a lot in this "Professor Dobie Mystery" novel because both the `detective' (Dobie) and the victim (his former Ph.D. student) are mathematicians. Of course, the math doesn't have much to do with the mystery (it rarely does in the math/mysteries, I find) but it is a little more relevant here than usual.
The plot: Dobie is taking a break, working as visiting professor in
North Cyprus to get away from the troubles caused by his wife's murder
in an earlier novel (see his
first appearance in The
Catalyst), only to find that the person he is replacing
there is his former Ph.D. student Derya who has been murdered as well. Her
husband is in prison for the murder, and though it is hard to tell for
certain - since he is compelled by insanity or drug withdrawal to speak in literary metaphor only - it sounds likely that he really did it. However, by following up on a few small clues (including some data from a project she was working on), Dobie is able to discover that the murder was actually linked to a political terrorist group called "The Mask of Zeus" which had been active in the area many years earlier. The ending, I'm sure, is supposed to be a surprise so I won't give it away here.
The math: The only direct link between the math and the plot, aside from the fact that many of the characters happen to be mathematicians, is that Derya had been doing a mathematical analysis of an archaeological site at which many different cities had been built sequentially in order to determine which buildings were contemporary to each other. This is a nice idea, though it doesn't go any further than mentioning it. Still, there are a lot of nice quotes about mathematics and mathematical asides:
- P. 66: "No shortage of foxes to hunt, in mathematics. Evasive little creatures who might lead you a rare old chase through the undergrowth of Dirac equations before disappearing down a hole, by which time however they would have served their purpose and have exhausted you completely. Dobie was an old hand at the game.
- P. 106, discussing teaching style with the chair: "You might, by
way of example, readily concede A to be a matrix with characteristic
polynomial P(gk)=(-1)^n(gk-gk_1)(gk-gk_2)...(gk-gk_n) allowing J to be
a Jordan matrix similar to A. Then if the formula P(J)=Z be derived
through those successive steps with which every schoolboy is familiar,
the Hamiton-Cayley [sic] theorem can obviously be applied to obtain an
alternative method of calculating the inverse of the non-singular
matrix A. That, of course, would be clear as daylight to the meanest
intelligence. Surely then the students might not unreasonably be
requested to prove that the trace of A is self-evidently the sum of
the kth powers of the characteristic values of A and further to prove
various properties of the trace - always bearing in mind, naturally,
that trace A is demonstrably the sum of the diagonal elements of A.
"`Perhaps,' he said throughtfully, `I shouldn't assume
the students to be familiar from the outset with the canonical forms
for similarity. So I'll limit myself to the consideration of square
matrices only when discussing linear transformations and so remain
strictly within the requirements of the syllabus.'
Berry Berry said, somewhat absently, `Admirable, admirable.' One
would have said that the had other matters on his mind. That was
"`And,' Dobie said, `I'll assume the scalar field to consist
of either the real or complex numbers. It shouldn't be difficult for
them to discern which theorems can in fact be extended beyond these
restrictions and I can direct investigation in such a way as to make
heavy use of similarity.'
"`Ah. Yes. Similarity...Similarity...'"
Okay, so that is some pretty good linear algebra for fiction...but for a math professor it would not be so great. Forgetting about the fact that they use "gk" for a variable (why I can't imagine!) and that he is apparently supposed to be a bad teacher who pushes his students too hard, the reasoning is not exactly sound. (Maybe that's the point.) I mean, the Cayley-Hamilton theorem says that P(A) (and, coincidentally, P(J) too since it has the same characteristic polynomials) should be zero. (I suppose that's what the Z in the above quote represents?) And then, perhaps I'm as nutty as Dobie, but I agree that if A is non-singular (he needs to state it somewhere) then it is relatively trivial to see that you can use P(A)=0 to find a formula for the inverse of A...but the Jordan form has nothing to do with it. Furthermore, I object to the idea of using only square matrices to represent linear transformations, since this cuts out any transformations between vector spaces of different dimensions! Besides which, limiting yourself to square matrices will not help at all if the problem is that the students don't know canonical forms.
- P. 119, on vague references by the imprisoned husband to calendars and determinism: "Strangely enough these references to calendars and stars and to various obscure tamperings with the laws of temporality were the only elements in Seymour's narative that Dobie found perfectly comprehensible, recent developments in general relativity theory being after all one of his things and a field to which he'd made some respectfully regarded contributions himself."
- P. 120, some nice thoughts on mathematics: "It's funny, Dobie thought (but also sad), how many people imagine that mathematics consists of interminably applying fixed formulae to clearly defined problems and so `working them out'. Because it's not like that at all. Half the time you don't even know what you're looking for until you've found it. A great deal more than half the fime you spend looking at a blank sheet of paper and chewing the end of a pencil - the blunt end, hopefully - while you're trying to see what the bloody problem IS. You know it's there all right but no, you can't grasp it, you just can't quite percieve how to forumlate it...Mathematician's block..."
- P. 124, on considering whether the way for a writer to overcome writer's block is to imagine themselves being a famous writer: "No mathematician had ever solved a problem by imagining himself to be Henri Poincare or Dirac. Life just wasn't like that."
- P. 205, a bit of "fictional mathematics" attributed to Dobie: "For a while he watched the light sparkle on the incoming waves as they rippled gently against the rocks an broke, each one after the other, into a million shimmering facets. Dialectically speaking, the fate of each and every one of those slow-moving waves should be mechanically determinable; Dobie had better cause than most to know that it wasn't, since in 1974 he himself had formulated those variants of the Vernouli equations which were now held to demonstrate that they couldn't be, by virtue of the inherent strange attractors. Since those very calculations had two years later gained him his Chair in Mathematics at the age of thirty-four, arguably if he hadn't established those mathematical proofs he wouldn't be here in Cyprus now, watching those waves break..."
In conclusion, not my favorite book in the world, but a passable mystery with several nice references to mathematics.