"Women Can't Write; Women Can't Paint"

How many times do you think Virginia Woolf heard that? Sexism was rampant enough in the early 20th century (luckily, we're past all that now, right?) that it was difficult for a woman to have a career as a novelist.  Add in the modernist style she used and it's a wonder that Woolf's work saw the light of day.

First, a confession.  Before picking up To the Lighthouse, I had never read any of Woolf's novels and, frankly, I was never a fan of modernist literature (Joyce, Faulkner, etc.).  I've read Dubliners, and in a fit of youthful bravado tried to read Ulysses once (I think I finished 20 pages).  About ten years ago I gave The Sound and the Fury a shot (read the first chapter, I think).  So my track record here is spotty at best and my initial impression as I waded through the first few pages of Lighthouse was one of, let's say, skepticism.  The nonlinear narrative, the near stream-of-consciousness language, the lack of action--where's the story? 

Which leads us to the question of what the point of literature is.  And by "literature" I don't mean mere fiction.  The point of, say, a Tom Clancy novel is entertainment.  It's fine to read as a way to pass time on airplanes, but we don't really learn anything about the human condition from it.  Capital-L literature, however, reveals deep truths about humanity and its place in the world.  As such, it demands more from its readers.  As I slogged through the opening scene--Mrs. Ramsay knitting socks for the lighthouse keeper's son, Lily Briscoe working on her painting, Mr. Ramsay lost in thought and grumpy as usual--I found myself drifting.  Losing my place.  Working hard to see what was even happening (answer:  not much).  Will they go to the lighthouse tomorrow?  No, says Mr. Ramsay, the weather will be no good and the sea will be rough.  James, sitting at his mother's knee disappointed, wanting to put a knife in his father's back.  Lily getting her painting critiqued by Mr. Barnes, who uses his pen knife to point at things on the canvas condescendingly.  Andrew and Minta: where are they?  Why haven't they come back?  Then, hey, here they are.  But they're late for dinner, which we get through Mrs. Ramsay's view, with idle conversation and a lot of talk about the bowl of fruit on the table.  And man, Mr. Ramsay is quite the needy sensitive academic, isn't he?

But wait.  Maybe I'm a bit like Mr. Ramsay.  Not in the needing people to tell me how important my work is, and not in the obsessed with leaving a legacy way, but in the hyper-aware of mortality, taking myself too seriously way.  And then I see that, yes, this is Capital-L literature and I am learning something about the human condition, and I've spent days just like this one, at the sea even, with my wife's family and not much happening but yet it's everything that life is; the children playing in the surf; the adults sitting on the porch reading, watching the waves, playing the guitar; and at night after dinner watching the moon rise on the horizon, drinking a cold beer; running with the dog in the sand.  No lighthouse, but maybe tomorrow we will go to the inlet to look for shells and shark teeth.

So, at some point I decided that I do like this book.  In class, feelings were mixed.  One student hated it and said so.  Others were tepid at best.  Before class I overhead a student saying that she had heard that this book is better when you're older, and I can see that.  I'm not sure how much I would have liked or understood To the Lighthouse when I was 21.  Or 25.  Or 35, even.  Which leads to another question:  do we have to read it all when we're so young?  I didn't read Moby Dick until I was past 40, and maybe that's right. 

Anyway, this is supposed to be a class about mathematics and literature, so let's get to that.  Obviously, there's a lot of nonlinearity and chaos in this book's narrative structure.  There's the uncertainty of measurement--Mrs. Ramsay is constantly checking the length of the sock she's knitting, for example.  Lily's painting will embody some of this eventually; by the end, it has gone from a fairly standard impressionist landscape to a cubist work in which Mrs. Ramsay is a blurry triangle.  There's also the trip to the lighthouse as a metaphor for the infinite, a sort of Zeno's Paradox made concrete.  But what we spent most of the math time on was the Principle of Mathematical Induction (PMI). 

Question: Can you knock down an infinite row of dominoes?  In essence, this is what the PMI is about.  There are all sorts of philosophical problems with the question, but induction is a useful proof technique when one wants to make a claim about a statement being true for all integers.  After telling the class the (probably apocryphal) story about Gauss and adding up the first hundred positive integers (answer: \( 5050 \)), I gave an induction proof for the formula for adding up the first \( n \) squares:  \[ 1^2 + 2^2 +\cdots + n^2 = \frac{n(n+1)(2n+1)}{6}.\] Induction works like this:  first prove that your proposed statement holds in some base case, usually \( n=1\) but it could be any integer; then, assuming the result is true for \( n\) prove it holds for \( n+1\).  What this amounts to, using the domino analogy, is that you can knock down the first domino, and assuming you can knock down the first \(n\) dominoes you can show that you knock down the (\( n+1\))st domino.  You may then conclude that the result is true for all positive integers; that is, you knock down all the dominoes.

Why bring up induction?  Well, Mr. Ramsay is a philosopher and there is a stretch in the narrative where he is thinking about his accomplishments. 

For if thought is like the keyboard of a piano,
divided into so many notes, or like the alphabet is ranged in twenty-six
letters all in order, then his splendid mind had no sort of difficulty
in running over those letters one by one, firmly and accurately, until
it had reached, say, the letter Q. He reached Q. Very few people in
the whole of England ever reach Q. Here, stopping for one moment
by the stone urn which held the geraniums, he saw, but now far, far
away, like children picking up shells, divinely innocent and occupied with
little trifles at their feet and somehow entirely defenceless against a
doom which he perceived, his wife and son, together, in the window. They
needed his protection; he gave it them. But after Q? What comes next?
After Q there are a number of letters the last of which is scarcely
visible to mortal eyes, but glimmers red in the distance. Z is only
reached once by one man in a generation. Still, if he could reach R it
would be something. Here at least was Q. He dug his heels in at Q. Q he
was sure of. Q he could demonstrate. If Q then is Q—R—. Here he
knocked his pipe out, with two or three resonant taps on the handle of the
urn, and proceeded. “Then R ...” He braced himself. He clenched

Qualities that would have saved a ship’s company exposed on a broiling
sea with six biscuits and a flask of water—endurance and justice,
foresight, devotion, skill, came to his help. R is then—what is R?

A shutter, like the leathern eyelid of a lizard, flickered over the
intensity of his gaze and obscured the letter R. In that flash of
darkness he heard people saying—he was a failure—that R was beyond him.
He would never reach R. On to R, once more. R—

So, he's trying to knock down dominoes, and he can't get to the \(18\)th (Hebrew numerology fact pointed out by a student in the class:  R is the eighteenth letter of the alphabet, and \(18\) means "life"; why did Woolf choose "R"? Ramsay? Reality?).  This also opened up a discussion of symbolic logic and how these systems are built.  I even drew a truth table on the board.  Good stuff.

But, we're not done.  More discussion of To the Lighthouse in the next installment.