n o i s e i s a r t

So I went to the buddhist temple last night for the first time in probably two years. After the meditation, this little old lady was walking out to her car. She asked me if I was Josh’s friend. When I said yes, she asked if I was a musician. I told her no. “Not even a bass player?”

Wow. Woken up this morning by a phone call asking for a counterexample to the claim ‘Knowledge is Justified belief’.

Seriously – when you’re an undergraduate philosophy major, they never really tell you that you may actually need to know this stuff.

I think I mentioned Gettier, but didn’t really explain what he did, since my friend was talking about I guess a prior stage of epistemology. Instead I think I had some weird ramble about unjustified true beliefs – thinking all black people are robots, and all robots are good cooks, then inadvertently pointing to a chef and saying ‘that guy’s a good cook’. (I did just wake up, remember).

But then I remembered what seemed like the perfect counterexample. The Titus-Bode Law was an astronomical law in the 1700s that governed the placement of the planets in orbit around the sun.

It correctly predicted the existence of the asteroid belt, and of Uranus. But then it turned out to have just been a coincidence, as the remaining planets aren’t even close to their predicted positions.

So the example works for the asteroid belt & for uranus (I know there is a planet orbiting the sun at whatever AUs distance – Hey, look! A new planet. I knew it!) – since the new planets were correctly predicted via an incorrect assumption.

And now I have this strange drive to read about Twin Earth, H2X, and ‘Twater’…

When I was a Junior in high school at Millbrook, a girl named Lissa Harris was in the class ahead of me. At her graduation, she read a poem that totally amazed me. I remember being so jealous (and I think I still am) – it was a ‘found poem’ from science texts, and I remember a metaphor involving atoms, eyelashes, and apple stems that I can’t quite seem to recreate.

Point being, it was an amazing poem that I still remember, and the stanza about Van der Waals is something I wrote, more then ten years later, trying to rip Lissa off.

3.

twelve-six potential, van der waals

attraction is the root of repulsion means

at a distance, particles are pulled

in proximity repulsed.

A few parameters approximate equilibrium

and things look simple and harmonic

where the energy is lowest

we find a comfortable orbit

but heat them up and they escape

evaporating into infinity and disappearing.

we spend more time in attraction

because repulsion is stronger.

Molecules can attract each other at moderate distances and repel each other at close range. … Van der Waals forces are… feeble; but without them, life as we know it would be impossible. Water would not condense from vapor into solid or liquid forms if its molecules didn’t attract each other. Intermolecular forces are responsible for many properties of molecular compounds, including crystal structures (e. g. the shapes of snowflakes), melting points, boiling points, heats of fusion and vaporization, surface tension, and densities. Intermolecular forces pin gigantic molecules like enzymes, proteins, and DNA into the shapes required for biological activity."(*,*)

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.

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