Reductio, Murder, Math

So, I’m up late after dancing and can’t sleep and I’m thinking about this great article I read today about the Humanities, and how we as a society are slowly eroding their importance by forcing them to justify themselves in economic terms.

It was really good, but there was this one epigram about how nobody was ever killed for getting Hubble’s constant wrong. Which may be true, but math and science have their own martyrs – not just Galileo’s ‘eppur si muova’ or Giordano Bruno before him. They were killed for heresy, by people who believed them to be not just wrong, but so gravely wrong their ideas were too dangerous to allow.

My favorite math martyr is Hippasus (… of Metapontum, says Wikipedia). He was killed by the Pythagoreans because he was telling people that the square root of two is irrational. The thing is, the Pythagoreans knew he was right. They knew that he was right, and that the foundation of their religion (and thus their temporal power) was flawed.

Galileo and Bruno could be accused of being misled, or incorrect. Hippasus couldn’t – the proof’s so elegant that it’s impossible to argue with.

Suppose the square root of two were rational.

Then there would be a ratio of p and q, where p and q don’t have any factors in common (i.e., they’re mutually prime)
and p over q squared is two.

so p squared over q squared is two
so p squared is two q squared.
so p squared is even.
so there’s a number r, equal to q squared, where two r equals p.
therefore four r squared is equal to two q squared.
therefore two r squared is equal to q squared.
so q squared is even.
Therefore p squared and q squared have a factor in common
And so p and q must also have a factor in common
But we defined them as mutually prime.

Driving home the other night I was trying to think of how to express the mathematical idea of elegance. I think most peopl edon’t understand how mathematicians view math, or understand how much art there is to it. This idea of elegance – where somehow the means by which you arrive at a conclusion transparently illustrates that very conclusion – it’s so appealing and not really found anywhere else.

Which is to say, that proof’s one of the most elegant ones I know.

A Rabbit As King Of The Ghosts

The difficulty to think at the end of day,
When the shapeless shadow covers the sun
And nothing is left except light on your fur—

There was the cat slopping its milk all day,
Fat cat, red tongue, green mind, white milk
And August the most peaceful month.

To be, in the grass, in the peacefullest time,
Without that monument of cat,
The cat forgotten on the moon;

And to feel that the light is a rabbit-light
In which everything is meant for you
And nothing need be explained;

Then there is nothing to think of. It comes of it-
self;
And east rushes west and west rushes down,
No matter. The grass is full

And full of yourself. The trees around are for you,
The whole of the wideness of night is for you,
A self that touches all edges,

You become a self that fills the four corners of
night.
The red cat hides away in the fur-light
And there you are humped high, humped up,

You are humped higher and higher, black as
stone—
You sit with your head like a carving in space
And the little green cat is a bug in the grass.

-Wallace Stevens