Tuesday, September 02, 2003

On Numbers

As I’ve mentioned once or twice already, numbers are my game, what I’m good at. They’ve always fascinated me. When I was very young I refused to learn to read until I went to school and nothing my parents did got me to change my mind. I can be a stubborn little git when I want. :-) Numbers, though, were a completely different matter. By the time I was four I could count to any number a four-year old could conceivably come across and found basic arithmetic easy. If someone had told my parents then that fifteen years later I’d be at university studying for a degree in maths, they would not have been very surprised.

Numbers are all around us and in everything we do. The computer I used to write this post runs on numbers, for example. Try as you might, there are very few things in this world that you could explain without using some sort of number that would not be explained more simply with it. Numbers are part of nature.

We use many different numbering systems without even thinking about it, such as the bizarre system we use to split time into seconds, minutes, hours, days, weeks, months and years or those that describe height or weight. These systems seem over-complicated when compared to one of the simplest of all, the decimal system, yet we resist any efforts to change from imperial measurements to metric. Why is that? It’s certainly not because the new system is too difficult to use. Is it, then, because we think it’s too difficult to learn?

The thing that fascinates me most about numbers is that, despite them working in clear, predictable ways, they can throw up the most surprising results. Like the fact that you can never predict which numbers are prime (other than that they must be odd if they are larger than 2), or that if you pick out 23 random people the chances are better than even that at least two of them will share the same birthday. That second one goes against what most would consider logical argument but it is true.

Take the Fibonacci series, 1, 1, 2, 3, 5, 8, 13, 21, 34, 55…, where each number is the sum of the previous two. You may think that arithmetic is a creation of the human mind and that this series, made by adding its own elements together, is therefore unnatural. If that’s the case, why do they crop up again and again in nature? The number of leaf points on a fern frond and the number of petals on a flower are usually Fibonacci numbers; anything else is the exception, not the rule. How, then can the series be a man-made invention?

The Fibonacci series has other odd properties. For example, if you take any four consecutive numbers in the series, multiply the second and third together and subtract it from the product of the first and third then the answer is either 1 or –1. In fact, if you take the first four numbers the answer is 1 but if you take the fours numbers starting on the second 1 (i.e. 1, 2, 3 & 5) the answer is –1 and it keeps on alternating every time you take the next starting number. And that’s not something I’ve seen in a book, I have proven it myself.

That’s another of the things I love about numbers (and mathematics in general). These surprising results are accessible to us if we know how to get them; we don’t always have to rely on books to know that something is true. And there is a great deal of satisfaction in proving to yourself that something is or isn’t true.

I could go at even greater length about this subject (believe me, it’s been a struggle to keep it this short) but I don’t think I’ll bore you any longer. I think you’ll know by now that I’m more than a little passionate about it.

No comments: