A while ago, I was teaching at the Glamorgan Summer School. Mr. Jack Jones, the trumpet player (and retired maths teacher, and ultra nice guy) in my class, told me this story of the ancestry of a male bee. Sitting comfortably? Then I’ll begin…
Females come from the fertilised eggs.
Males come from the unfertilized eggs.
So, a female bee has a mother and father. And a male bee has only a mother – a mummy’s bee, if you like.
Here’s a little diagram to show you this sequence.
At the top of the diagram is a male bee; let’s call him Alan. Below Alan [the white dot, one generation back] is his mother – call her Beatrice. Beatrice, being female, has a mother and father – Candice and Darius. Continuing the pattern, Candice has a mother and father, and Darius only has a mother. And so on. It’s an idealised generational model, by the way. I suppose they’re a bit more liberal in the hive :)
Now, if all that sounds like gibberish, check out this guy doing a much better job of explaining it all.
Anyhow, apiarists have known this for hundreds of years. Scarlett Johansson and Steve Vai know it. But it was Fibonacci who introduced the idea to the West in his Liber Abaci [not this]. The number of bees in each generation, going backwards, is therefore called – the Fibonacci sequence; i.e.,  1, 1, 2, 3, 5, 8, 13, etc. And this has many interesting properties.
Here’s one pattern: Look at the last row of 13 black and white dots on my diagram. It’s the same arrangement as a piano keyboard. More Fibonacci numbers: there are 13 notes in one octave (C to C), 8 white notes and 5 black notes. You could go on and try to find the answers to the universe or justify your belief that spiders created the world as we know it or whatever, or you could just use the patterns to mess around with and see what you can come up with.
For example, check out this video of a Tool song to which someone has kindly added an explanation as to how they used the Fibonacci sequence in the song.
Not sure I totally agree with their idea of living your life like a Fibonacci sequence. It might get a bit messy when ordering the next round, for instance. But Fibonachos, that could work…
There are some interesting reads on the Fibonacci sequence here. And check this Bobby McFerrin video out too.
So, if you know of a lovely example of this kind of thing in music or anything, please feel free to share in the comment box below.