It’s a tool; a ratio, providing us simple rules for doing circular estimates. Admired regularly – and we all remember that today’s pi! Hooray! Let’s eat pie.

You may have noticed that the first paragraph of this article was immensely poorly written, and didn’t sound like good writing at all. And you’d be right – except writing it wasn’t easy as you’d think. I’ve written it under a constraint – that is, I’ve picked an arbitrary rule to follow, and have had to choose my words carefully in order to do so.

Now, you might think “Isn’t this supposed to be a maths website? This is surely more about English than Maths!” – and you’d again be right, except for two things. One is that the constraint I’ve chosen above, one which others have used before, is very mathematical, as I will shortly explain. And secondly, isn’t choosing arbitrary constraints to work under, making things much more difficult for yourself, and then seeing what happens, part of mathematics we all know and love?

The first paragraph was written in what’s come to be known as Pilish – a particular type of constrained writing in which the length of each word in letters corresponds to a digit in our much-hallowed circle constant, π. So, the first word has three letters, then one, then four, then one and so on. You can probably see now why it sounded like I’d temporarily forgotten how to write. (Equally, you may be thinking the same about these following paragraphs, but that would just be mean. And, excepting some spectacular statistical coincidence, they don’t have word lengths corresponding to the subsequent digits of π).

In fact, if anyone was paying attention, one of our celebratory Piπ Day guest posts this week, by Alex Bellos, was written entirely in Pilish. Did you notice?

You might be familiar with some other examples of Pilish, or pi-length words – common mnemonics for remembering the first few digits of π include such classics as ‘How I wish I could calculate Pi’, ‘May I have a large container of coffee’ (attributed to Martin Gardner), and the boozer’s favourite ‘How I need a drink, alcoholic in nature after the heavy lectures involving quantum mechanics’. This kind of aide-memoire comes under the umbrella of ‘piphilology’, and is sometimes referred to as a ‘piem’ (a pi poem). In fact, our own Peter Rowlett wrote briefly about it after a talk at the BSHM in 2010.

In fact, people have gone much further than this – a version of Edgar Allan Poe’s ‘The Raven’, called “Poe, E: Near A Raven” has been ‘translated’ into Pilish, and encodes 740 digits of pi. The same author, mathematician and wordplay fan Mike Keith, has published a whole book, ‘Not A Wake‘, which includes 10,000 words, each encoding one of the first 10,000 digits of pi. The book contains poetry, short stories, haiku, two crosswords and an entire film screenplay, among other writing styles.

This type of ‘constrained writing’ is something fans of words and the mucking about with thereof are often engaged in.

As well as constraining words using digits, word fans think up many kinds of writing involving various constraints – such as lipograms: books which go wholly without using a particular glyph (much as this paragraph has).

Author Georges Perec famously wrote an entire French novel, ‘La Disparition‘, without using the letter *e* – especially a challenge since it’s the most common letter in French. It’s also the most common letter in English, which is why it’s especially impressive that the whole work was translated into English by Gilbert Adair, again without using the letter *e*, and published as ‘A Void’^{1} It’s since also been translated into at least nine other languages, again without using the letter most common in that language.^{2}

Perec was a member of Oulipo – a collection of French writers and mathematicians who play with constrained writing – founded in 1960, and with many well-known authors as members, they use constraints to inspire more interesting stories. They deal in lipograms, palindromes, restrictions on word length, vowel sounds and many other types of constraint – including some based on mathematical puzzles, like knight’s tours or particular number sequences.

Given π’s popular symbol status, it’s no surprise that it’s been used for constraining text – but what about other mathematical constants? Wouldn’t the ultimate constraint be a book written using word lengths matching the digits of $e$, without using the letter *e*, written while under the influence of e? I’d read that.

- Perec also later wrote another novella, ‘Les Revenentes’, using only the vowel e – which has been translated into English by Ian Monk as ‘The Exeter Text: Jewels, Secrets, Sex’. [↩]
- The story, brilliantly, is a mystery novel in which the letter e has gone missing and nobody knows where it’s gone. [↩]