I was really keen to share with Numberphile viewers a discovery that I made which I was really surprised by. Everyone is familiar with the Fibonacci numbers: 1, 1, 2, 3, 5, 8, 13, which appear all over nature, such as in the five-pointed star of an apple or the petals of a flower. Fibonacci made them famous by writing about their occurrence in nature, but it turns out he wasn’t the first to discover these numbers. In fact, they were first discovered by musicians and poets in India.
These musicians and poets were interested in making complex rhythms, and as they started to count the number of different rhythms as the rhythm got longer, they discovered that it was the Fibonacci numbers that counted them. For example, with a rhythm of length five, there are eight different rhythms one can make with long and short beats. This is why adding the two previous numbers in the sequence together gives you the next one - because one can generate the rhythms of length five by taking the rhythms of length four and adding a short beat, or the rhythms of length three and adding a long beat.
These numbers were already being talked about in India several hundred years before Fibonacci came across them. The Indian poet Hemachandra wrote about these numbers, so they should really be called the Hemachandra numbers, not the Fibonacci numbers. Fibonacci could have been exposed to these numbers during his time in Northern Africa, where he learned about a lot of the ideas of India and the Arabs, which he then brought to Europe with his book Liber Abaci. I have another interesting way to think about long and short beats. You can try it at home by counting the number of ways to climb a set of stairs, taking either one or two steps at a time. This same challenge is related to the Fibonacci numbers, which have had a resurgence in poetry as a poetic form. This form, called a fib, has each line of the poem following the Fibonacci numbers in terms of syllables. Gregory Pincus was the first to come up with this idea.
I offered my Twitter followers a challenge to write their own fib, and the best one was by @benbush: “Tweet, Tweet, Marcus, here’s my fib, an unwise ad-lib, wait fib on Twitter I’m confused, how many of my 140 have I used.”
I’d love to see the fibs that YouTube commenters will come up with for this video. Marcus’s artistry is being able to write a piece of music and apply a bit of mathematics to it, creating something harmonious and complex.