Sunday, February 04, 2007

Maths (part 1)

I like mathematics. Well, a bit anyway, or I wouldn't have survived these last 4 years of doing pretty much nothing but it. It's kind of interesting in places, and because I feel like it, I'm going to try and talk about why it is.

Mathematics is one of those subjects that no-one particularly understands- you get a tiny sample of it at lower levels, but for the most part you get numeracy skills and a tiny bit of applied mathematics. A lot of subjects start of rather simple and get more complex, but in a way mathematics starts off complicated then gets simple. Although you wouldn't know it to face the subject.

A lot of the time, when a mathematician starts doing stuff in mathematics, they're not sure about whether they can do it or not. For example, when Newton invented calculus (for the second time (that is, someone invented it before him. He didn't invent it twice.), the rigour behind it was created a little bit after him... this is the case for most mathematics.

At degree level we do get a bit more structured, starting with the axioms and working upwards.

The idea of mathematics, for the most part, is pattern spotting. Mathematicians take an idea, like symmetry, or shapes, or the gradient (slope) of a curve, and try and get a set of rules that describe those things. If you can find a basic set of rules that govern something, then you can find other, more odd things, that follow the same things, and know that every single result that follows from those basic rules will apply to this odd thing to.

A simple example is talking about N dimensions. You will be aware of the basic three dimensions, I should imagine (or, if you're a physicist, you can talk about your puny 10 dimensional space). Well mathematicians will talk about a space of an arbitary amount of dimensions, or sometimes even an infinite amount of dimensions. This turns out to be rather useful- in economics you will be dealing with hundreds or thousands of variables, and you can assign a dimension to each of these, and know that the rules you've shown for your arbitary space will work in economics.

With all this, it is somewhat frustrating to tell someone you do mathematics, and they ask you to multiply 79 and 81 in your head (79*81=(80-1)(80+1)=80^2-1=6399), or even worse, ask what practical use this all has. Admittedly the job applications are somewhat slim, but the applications of the most ridiculous mathematical proofs will have real life applications. Admittedly most of it will NOT, because that isn't really why we do it...

Anyway, I hope to to talk about some interesting stuff in mathematics in the next few posts, and perhaps the next time you meet a mathematician you can ask them about the Hilbert hotel, and they will either look impressed or say "what?" because they haven't studied it.....


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