I was working in Borders the other day and stopped for a minute (ok, twenty minutes) to flip through a copy of James Wood’s new book, How Fiction Works. The book seems friendly and wise, has good taste, and accomplishes the feat of saying things both correct and unfamiliar about novels, as here:
“…language is the ordinary medium of daily communication — unlike music or paint. Our ordinary possessions are being borrowed by even very difficult writers: the millionaires of style — difficult, lavish stylists like Sir Thomas Browne, Melville, Ruskin, Lawrence, James, Woolf — are very prosperous, but they use the same banknotes as everyone else.”
This, though, stopped me:
“We have to read musically, testing the precision and rhythm of a sentence, listening for the almost inaudible rustle of historical association clinging to the hems of modern words, attending to patterns, repetitions, echoes, deciding why one metaphor is successful and another is not, judging how the perfect placement of the right verb or adjective seals a sentence with mathematical finality.”
Followed shortly on by:
There is a way in which even complex prose is quite simple — because of that mathematical finality by which a perfect sentence cannot admit of an infinite number of variations, cannot be extended without aesthetic blight: its perfection is the solution to its own puzzle; it could not be done better.”
This could only have been written by someone who has never experienced mathematical finality! No word, no sentence is ever finished and correct the way a mathematical argument is, once all the gaps are filled and the joints sealed. You spend as long as you desire making the sentence as good as you can, and then you give up, and eventually you start to get used to the sentence in its most recent form, and after a while it seems to you that the sentence could not have been written any other way.
But an honest writer knows it’s not true.
This distinction is perhaps the most powerful reason that writing novels is a dispiriting business, and doing math a fun one.
Quomodocumque 
Hi, came across this post in tag surfer.
I think the author comes from a Chomsky linguistic tradition that treats meaning as finite, and hence having finite numbers of combination in a sentence. However, I tend to think the use of language is infinite; a word holds different meaning not only in different contexts, but also different cultures.
I think there’s a distinction between “form oriented” or “plot oriented” fiction. Writers like Flaubert, as French school children probably still hear over and over, are obsessed about every word of every sentence, and only go to from one to the next once they are convinced they have reached “perfection”. Others are losing sleep instead over the actual happenings of the story, and not worry too much whether each particular sentence.
But similar things occur in mathematics, I think. It may be that most mathematicians only think deeply of getting the right idea and proof, and then don’t care too much how to write it down (if only because, in mathematics, it is normal and expected that important ideas will be written again and again in various ways, so there is an iterative process available to improve the presentation of a given topic, through further papers and then textbooks). Still, there are many who do spend time trying to phrase things as accurately and clearly as possible, e.g., by choosing appropriate terminology and notation.
(For my part, when I was dabbling in fiction, thinking about issues with the story felt often similar to searching for the right way to solve a mathematical problem, even with sometimes the same type of apparently unexplainable flashes of insight (and the same frustration when it just doesn’t work out), and I was not that much of a stylist; conversely, I spend probably more time than average trying to polish my mathematical writings…)
The notion that words have meanings, finite, denumerable, is just a mistake. (Syntactically, of course the number of sentences is finite, or at worst denumerable.) “There is no place in semantics for meanings.” –Quine
But proofs aren’t really finished and correct either, or there wouldn’t be so many that turn out to be flawed. “Most theorems are correct, but all proofs have bugs.” –Paul Pedersen
In the end, both of them are fundamentally works of human nature.
Oh, but I want you to be dispirited again! More fiction for your fans!
(this is just selfish, I realize, but I can’t understand your math stuff.)
I’ll take a break from the dispiriting process of writing this math paper (“wait! – is this concept central to what’s going, or is it just the way I found a proof, and actually making what’s really going on harder to see?”) to say that I completely get this, and yet the phrase “mathematical finality” still makes me sort of grumpy.
Of course, say, Euclid’s proof that there are an infinite number of primes is finished and correct in a way a sentence never could be. But the average proof you’ll write (or I’ll write – Jessie isn’t the only commenter to have read your novel and none of your papers) isn’t going to be like that – it’s going to be a lot more like agonizing over making it slightly better and clearer until just deciding its good enough, and moving on. And so it bugs me that I can be told that a paper is unreadable, or nearly so – by its author, with little or no shame on display – and yet also hear a lot of unreflective self-congratulations from mathematicians about how proof makes mathematical knowledge so much more secure than other fields.
Not that you were guilty of any of that – I liked and agreed with your post (and it was nice to read about Eric Walstein! Though I never knew him well, just as an ARML coach) – but struggling with that paper I should get back to put me in the mood to quibble.
I think an attitude like Wood’s would make it really difficult to work with an editor. ;)
I agree with you on the distinction between a correct mathematical argument and a well composed sentence. I know I once wrote of a novel that I’m almost tempted to call it canonical in the mathematical sense.
but I was kind of joking, and besides, I meant the situation, not the prose down to the sentence level. ;)
(splitting this comment in two pieces was accidental… )
Wood treats the sentences in a novel the way that Yeats wanted to treat the lines in a poem– which, Yeats said, clicks shut like a box. Apparently French students are taught that Flaubert thought of the sentences in his prose the same way.
Paul Valery, on the other hand, said that a poem is never finished: it is only abandoned. In what sense could they both be right?
Art (and I emphatically do include mathematics among the arts; it sure doesn’t fit among the sciences, or as a branch of philosophy) is craft, but it’s not just craft, and the reason is that works of art are made by the total personality, not just the conscious one. On the craft side, then, we get the notion of the perfect work of craft; on the unconscious side, the realization that you stop when you can, if you can.
[…] I quote the whole thing in order to concede Wallace is in some sense disagreeing with my disagreement with James Wood. […]