Wednesday, 30 May 2012

Numbers

I was just spinning round in circles thinking "What could I write a blog about?". I sit before a soroban. I'm sure I've mentioned it somewhere in the dusty realms of the rambly detritus that makes up most of my blogs - it's a cute Japanese abacus that I originally bought with the intention of facilitating addition in a fun and new way, but never got round to learning how to use it. I am going to try though.

A lot of this rambly detritus comes out of my mouth and is directed towards my poor mother, who I've always been one to plague with questions to which she has not an answer. Some of it is maths related, because I often find maths fascinating - certain parts of it - and she remarked that the way the number system works is just remarkable, that "Noone could ever just devise a system like that." Totally agreed on that one.

As often the case, this is a rumination about something which I don't know a great deal. Have fun <3.

The number system is such a curious thing. It fits together perfectly, and you have to ask: how much of it is natural of the system of numbers to which we've given a name, and how much of it is purely of our own construction, that fits together just the same? An even bigger question: is there such thing as a natural number system? It's easy to think "Yes, of course, numbers are as natural as volcanoes and trees," but I honestly can't say if that's accurate or not.

Imagine apples. A tree full of apples. You take a group of apples and divide them like the primitive caveman you may or may not be (just kidding, I know y'all aren't cavemen. I think.) You identify a single apple, and by some linguistic means or another, you give a designation for the singularity of that apple. In other words, you say there is "one" apple. You understand that it means one single apple, and not many of them. You then add another apple to the party. You clearly understand the distinctness of the separate apples - you feel them, see that they're independent of each other, realise that affecting one apple doesn't affect the other apple. You conclude that they're separate and come up with a word for there being one apple, and a second apple. You call this "two". So it goes on. Unless you're a culture that only has words for "one," "two" and "many", of which there are some.

Those are named numbers. We use them all the time. But what about when you move away from names and you deal with the abstract, the constructions of algebra, for instance? Geometry and the rules that hold it in harmony? Are they as grounded as the difference in the number of apples? I guess that they must be, because algebra generates rules that you could just as well use for apples and get the same result - geometry, too. Perhaps for every mathematic rule, there is some way you can use objects to demonstrate them. But is that any better than writing down "the area of a circle is pi*r^2"?

And also, are basic numbers even grounded in natural principles? If we put together ten apples, we can count them and say "One, two, three, four, five, six, seven, eight, nine, ten," and point to each one in a determined position along the line of apples. A French person would count them similarly, "Un, deux, trois, quatre, cinq, six, sept, huit, neuf, dix." But what about someone who uses a different base of counting? We use base-10 - it's convenient because we have ten fingers, and this convenience is echoed in the ongoing battle between metric and imperial measurements. You see conflicts between base-12 and base-10 all the time: measurements are done in both inches (12 inches in a foot,) and centimetres (100 centimetres in a metre;) the clock, zodiac chart and western year are split into twelve; a dozen is twelve and a gross is 144, or twelve twelves, the origin of the word "grocer". They're just two different ways of counting, and both equally valid, but both bases will get you a different English word when counting apples, even though you mean the same thing. If you have 64 apples (which is 12 to the power of 1.673657673906779, God knows why you'd ever want to know that,) that would be 54 in base-12.

But whatever base or language we express it in, numbers are always going to be the same, expressible in one form or another. Perhaps in that sense, they're really objective. Hard to say.

The world of maths is full of constructions and numbers, and who really knows what there is that makes numbers work. They're just awesome like that.

I've only got one apple left :(.

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