scanman’s posterous

What's the next number in this sequence: 1, 1, 2, 3, 5, 8, 13, 21...? Anyone who has read Dan Brown's The Da Vinci Code will know that the answer is 34. The sequence is one of the first codes that readers are challenged with in the thriller. Even if you haven't read Dan Brown, spotting the underlying pattern is not too difficult. You get the next number in the sequence by adding together the two previous numbers. So 5+8 gives you 13, for example.

These are some of Nature's favourite numbers. They can be found all over the natural world. Take a pineapple and count the number of cells climbing up the side of the fruit, then count down one of the other spirals and you'll find two numbers in the sequence. Count the number of petals on a flower and it is nearly always either one of these numbers or twice one of these numbers (some flowers are built as if they are two flowers, one on top of each other).

The sequence is named after the great 13th-century Italian mathematician Fibonacci, who spotted the importance of the sequence when he was investigating how the number of rabbits evolves from one generation to the next. But he wasn't the first to reveal the importance of these numbers - a 6th-century Indian poet called Virahanka was perhaps the first to single them out as significant. Virahanka discovered that these numbers count rhythm patterns.

Virahanka was interested in rhythms that you can make out of long and short notes. A short note lasts one beat, while a long note lasts two beats. For example, how many rhythms can you make that are four beats long by making different combinations of short and long beats? You could do short, short, short, short, or long, long, or short, short, long, or short, long, short, or, finally, long, short, short. That's five different rhythms.

If you now analyse the number of rhythms with five beats, you'll get eight different rhythm structures, the next number in the Fibonacci sequence.

The connection with the Fibonacci sequence becomes clear when you realise that, if you want the number of rhythms with N beats, then there are two ways to get them: take the rhythms with N-2 beats and add a long note; or take the rhythms with N-1 beats and add a short note. The total number of rhythms therefore consists of simply adding the two previous numbers in the sequence together.

this, incidentally, is my 100th post on posterous. i thought it fitting that i post about numbers :)

surprising that i've persisted so long with what started out as one of my usual experimental forays into social media.

after 38 months of blogging, i'm a little short of 500 posts on my original blog. i think it's testimony to the ease of use of posterous as a microblogging tool that i've reached 100 in just 3 months.

many thanks to the friends and visitors who have visited and commented on my posts here, on twitter & facebook.

In 2003, an independent scholar from New Jersey began submitting limericks for a competition in mini-AIR, the monthly online supplement to my magazine, Annals of Improbable Research. The contest challenges readers to read an off-putting scholarly citation, and explain it in limerick form. Martin Eiger so consistently won that we eventually banned him as an unfair competitor, gave him the title Limerick laureate, and now publish him every month. He handles a huge range of subject matter.

An early Eiger limerick summarised a Japanese study called Pharmacological Aspects of Ipecac Syrup (TJN-119) - Induced Emesis in Ferrets:

If you're hoping to hash out a thesis,
And stuck for a topic: emesis,
As triggered in ferrets
Undoubtedly merits
Much more than a mere exegesis.

Warwick University mathematician Jonathan Warren's 1999 treatise On the Joining of Sticky Brownian Motion includes a three-page proof of the Non-cosiness of Sticky Brownian Motion. Eiger explained that:

Though only three pages - a quickie
- the Warren proof really is tricky.
It puts forth the notion
That Brownian motion
Is cosy, except when it's sticky.

A team from the University of Manchester and Germany's Albert-Ludwigs-Universität Freiburg produced a study in 2000 called The Functional Morphology of the Petioles of the Banana, Musa textiles. Eiger produced this summary:

The petiole's structure is vexing.
It bends, but it's strong. How
perplexing!
The veins through its length
Account for its strength.
Its U shape accounts for its flexing.

In 2004, the journal Brain and Cognition published a paper called Feigned Depression and Feigned Sleepiness: A Voice Acoustical Analysis by four researchers at the University of Connecticut. Eigerised, it became:

When people pretend they're
depressed,
Or when they pretend they need rest,
Their speech rates will change,
But never the range
Of pitches they use. Who'd've
guessed?

pure genius!

eiger's title "limerick laureate" is very apt!!