Sunday, 30 December 2012

Intro to Mathology: 0

One of friends, Mistah Wong (as his kids address him), teaches maths at a high school, and a while back asked me if I wanted to give a guest-lecture/class to the kids. Luckily for his class(es), this didn't wind up happening. But it did make me think a bit about what mathematics is and how I can motivate some of the crazy stuff that maths people do.

So, here's an Intro to Mathology.

I have a tendency to start lectures with either a motivating problem (usually one that you can think about if you decide to tune out to my yapping) or a quote. And here's a quote by a pretty sweet dude:

"The mathematician's patterns, like the painter's or poet's, must be beautiful. The ideas, like the colors or the words, must fit together in a harmonious way. Beauty is the first test: There is no permanent place in the world for ugly mathematics.”

-- G. H. Hardy

At the heart of it, mathematics is all about patterns. After all, one of the first pattern that each of us sees is:
$1,2,3,\ldots$
and we're taught that the next number is $$4$$ and the one after that is $$5$$ and so on. Then, (prolly) at some point after we've learned to talk, we're taught a different way to continue that pattern:
$1,2,3,5,8,13,21,34,\ldots$
called the Fibonacci sequence. Which you can extend indefinitely by adding up the last two numbers (e.g.:$$5=2+3,\; 8=3+5$$). And you're probably also told that these numbers seem to pop up quite a bit in nature.

And maybe you're like...say whaaaaat?

But whatevs - the point is that there are two different ways that we could have landed at the Fibonacci sequence:
1. pattern-finding: observe what exists in nature and notice this pattern, and
2. pattern-making: make up this weird but funky rule of adding up the previous two digits...pretty much coz you can and it's easy.

Pattern-finding is basically what we do in physicsy-types of maths, and pattern-making is often what we do in recreational types of maths and in artsy-types of maths. And that's pretty much how mathematics works.

Of course, I've just lied to you.

But that's alright, because science is about telling lies - lies that get closer and closer to the Truth.

Let's just take a looking at pattern-finding: what happens is that after you've seen a lot of these patterns happen in nature, you can start to guess where-else you might expect similar patterns: pattern-predicting. On the other hand, sometimes the patterns are pretty complicated, and you'll just have to make do with something simple that looks reasonably close to it:  pattern-matching.

But then you start noticing that certain patterns are pretty similar, and you start wondering about other similar types of patterns - maybe ones that you haven't seen (yet) in nature. And so, starting from being a practical-minded pattern-finder, you've ended up at having a go at (motivated) pattern-making.

And then you start noticing patterns in the patterns, and patterns in the patterns in the patterns...
and all hell breaks loose.

So there you go: maths=stuff to do with patterns.

Maybe I should do some actual maths next time. =P