On Mother Nature

pi

“God, after all, can effortlessly spit out the infinitely long decimals of Pi. On a whim. While he’s sippin’ a brew and munchin’ some cheetos.

Because that’s how the Almighty rolls.”

Imagine a circle.

That’s right. Take that wonderful goody-two-shoes shape of two dimensional Euclidean geometry. It’s neat, it’s tidy, not as obtuse as a triangle (or god forbid, a square), compact, space efficient, and yes, undeniably sexy.

If Kylie Minogue was a Euclidean shape, she’d be a circle.

Now as we all know, the circle (and its three-dimensional brother, the sphere) is nature’s favourite shape. It occurs in everything, from the shape of soap bubbles in the bath to the wave expansion of sound disturbance at a concert. Everything from teensy atoms to humongous stars and planets are connected with the circle.

You know, in the Medieval Ages, they believed that the compass, with its magical ability to produce the most perfect of shapes — must have been one of God’s divine instruments.

Then again, would God really need a compass if he was God?

Never mind.

The point is, the circle is beautiful. It’s divine. It’s perfect.

On Mathematicians

Now we turn to the mathematicians.

It was known as early as the Egyptians that the ratio of a circle’s circumference to its diameter is constant. After that, more and more accurate approximations to this mysterious number proliferated through the years — 6 decimal places by Archimedes’ time and up to 100 decimal places by Newton’s time.

In 1706, William Jones — probably due to a lack of stationary and ink — began using the symbol Pi to represent the tedious number. Then in 1761, the German mathematician, Johannes Lambert proved Pi is irrational, and in 1882, Ferdinand von Lindemann (also German) proved Pi is transcendental.

Let’s talk about what these two facts imply.

Being irrational, Pi can never be written down as a terminating number, nor does it ever repeat. If you possessed an infinite amount of boredom, time, space, and pencil lead, and wrote out Pi all the way to infinity — you’d never see a pattern.

Being transcendental, Pi can never be constructed with a straight edge ruler and a compass — meaning, given theoretically perfect tools, you would never be able to measure out Pi or in particular, you would never be able to construct a square with the same area as a circle.

You put these two mathematical facts together and there is only one thing to conclude:

Pi is an awful, atrociously foul number.

On the Fundamental Question

And so we come to a fundamental, philosophical divide.

Nature has the ability to make perfect circles every time. God, after all, can effortlessly spit out the infinitely long decimals of Pi. On a whim. Just like that.

Because that’s how He rolls.

To the Almighty, Pi is indeed wonderful, beautiful, and simple.

But for us mere mortals with comparatively little brain space, we usually have to truncate Pi. So when we use calculators or a computers, programmed with only a finite number of decimal places, we’re not using Pi as nature intended it, but the imperfect, imprecise version we’ve constructed for our own evil schemes.

For the most part, this is okay.

Nobody (except for the clinically unhinged) loses sleep over the fact that we’re only using 16 decimal places. The resulting error between mathematical prediction and true phenomenon is so inconsequential, nobody cares.

But you see, all this buildup — it was just a metaphor.

An attempt to explain to you the difference between man, mathematics, and nature.

An attempt to explain that yes, nature is indeed wonderful and perfect, but sometimes, we aren’t always able to capture this magnificence completely. Especially when we impose our own mathematical rules to describe it.

So here’s a question: At what point does the difference between mathematical representation, pragmatic implementation, and true reality have severe consequences.

When it comes to maths, I don’t really consider myself a noob.

Of course, there’s a lot I don’t know. In fact, it’s a common belief that the last mathematician to know ‘everything’ (that is, to at least be familiar with everything) was David Hilbert — and that only really applies to the early 20th century.

Today, there is simply no way for you to be an expert in every field or even, in a substantial number of fields. There’s simply too much to know. You’d be spending the whole span of your life, playing catch-up with what’s been done and what’s being done.

But yeah. I’m not a noob, y’know?

For example, I think it’s safe to say I know my way around integration. Single, double, or triple integration — no problem. Laplace integrals, Fourier integrals, Elliptic integrals — piece of cake. Even more deviant and exotic creatures like Error functions, Fresnel integrals, Airy integrals, and so on and so forth I’ve encountered.

Today, however, I met a new beast. At first glance, I treated with disdain.

After longer, more protracted glance, I’m happy to report I’m still…uh…pretty repulsed by the whole thing.

The formula in question was derived by the Australian mathematician, John Henry Mitchell in 1898. The formula, which can be used to calculate the wave resistance for ships of different forms, was intended to revolutionize the Naval Engineering community.

It didn’t.

The popular theory is that the engineers took one look at the formula, went “Eeewww”, and promptly burnt the article.

People then go on to theorize that Mitchell’s short career (10 years?) in research mathematics was due to his disgust at the reception of this work.

But looking at the formula, can you really blame the community?

Yuck.

Things I Don’t Care to See #138: A quintuplet integration.

P.S. If you’re feeling particularly bad about the poor Aussie, don’t be. His work in the 1898 paper is now seen as one of the most important and revolutionary contributions to hydrodynamic ship resistance.

If only I can be so lucky.

I think it speaks volumes about my character when I walk into the office of the senior Research Director at one of the premiere mathematics departments in the world and go,

Moreover, the fact that by now, he’s used to my shenanigans and actually understands what I mean, says as much about him as it does about me.

It’s always puzzled me why some graduates are so afraid of saying the wrong things around their supervisors. My advice: Go ahead and say what you want. If the person can’t take it, you never wanted to work with them in the first place.

Get out before it’s too late.

No time to write, tonight.

I know, I know. Don’t look at me like that.

I’ll see if I can fit ya in, real soon, m’kay?

1. It’s 2008. Four years ago, I was a geeky, awkward, angst-ridden high school teenager. My, things haven’t changed at all.

2. Research is lagging. Must re-focus.

3. Man, Zooey Deschanel. She’s so fine. She’s so fine she blows my mind.

4. I miss having a cat. Is “loneliness” a likely cause of early death? I hope so.

5. Time to get my life in order. No more excuses. It’s 2008.