Sunday, March 29, 2009

Fibonacci's sequence

I find a pleasure in certain numbers and number patterns. For example, I like to think certain stores gained their name because 7 and 11 are prime numbers, although I’ve been told the name has to do with the hours these stores were originally scheduled to be opened.

Whatever. Reality is overrated.

And, while I find prime numbers interesting as singularities and the ratio pi a curiosity with it’s odd tendency to somehow not repeat itself, I really like the Fibonacci sequence.

First, consider the word Fibonacci. Nice. Rounded. Fills your mouth with just the right amount of foreignness. Of course, it’s the guy’s name. Mr. Fibonacci. Interesting fellow, but not my concern just now.

Nope, it’s the numbers themselves: 0, 1, 1, 2, 3, 5, 8, 13, ... continuing, I suppose, to infinity. I can’t help thinking there’s a mystery in this sequence. First, it delineates the spiral forms of nature. Think sea shell…. Or spiral nebula, if that works for you. That’s a pretty nifty thing.

But for me the real mystery is the sequence itself, or more properly, the first two numbers of the sequence, the zero and the one. You see, the rule for creating the Fibonacci sequence goes like this: you take the first two numbers, add them together and you get the third number -- which explains why the third number is 1. After all, 0 + 1 = 1…. And then you continue to take the last two numbers and add them together to get a next number in an ever expanding arc.

Fair enough…. But from where do the first two numbers come?

The zero and the one -- nothing/ nada and something -- In order for this process to begin you can’t have just the one thing, you have to have the ‘nothing.’ Both something and nothing have to exist at the same time. Except, of course, ‘nothing’ doesn’t exist -- it’s, well, nothing….

Now, OK, I know that we just have to set up a mathematical rule that you have a zero and a one and there ya go…. But, imagine you’re back at the beginning of everything; time, matter, whatever -- everything. Well, no, not at the beginning of everything, but just before the beginning of everything. Not a micro second before, since no time exists, but just before. There’s nothing/ nada… and then, poof, there’s a something. And since there’s a something, well, there’s no longer any ‘nothing.’

My point here is that you can't really have something and nothing at the same time.

But in the Fibonacci sequence, that’s exactly what you have to have in order for the thing to work -- or at least for the whole thing to begin. And I suppose if something never begins it doesn’t exist…. But of course it does exist.

Now what a pleasant paradox that is. Makes my brain itch. In a good way, I mean….

Now, I’ll confess that I don’t think mathematicians have a problem with this. As I said earlier, they postulate a zero and a one and Bob’s your uncle.

But still….

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