The rational meaning of ‘surd’

Lewis Carroll, in his Phantasmagoria, and Other Poems (1869), constructed a poem that yielded a double acrostic, with the first and last letters of 13 words that were suggested by the 13 stanzas spelling out ‘quasi-insanity commemoration’, a reference to an Oxford commemoration ball. The first stanza, which yields the word quadratic, goes:

‘Yet what are all such gaieties to me/ Whose thoughts are full of indices and surds? x2 + 7x + 53 = 11 / 3.’

What, though, is the solution to the equation? I have seen it said that there is none, unless a minus sign is placed before the 53. But then it wouldn’t scan, and Lewis Carroll liked regular scansion: 11 / 3 is to be pronounced ‘eleven thirds’, not ‘eleven over three’.

I suspect some readers will make sense of the algebra, but I can’t. I do know that 100 years ago, the Oxford English Dictionary published its volume for words beginning SI–TH. It was so thick that it was divided into two parts. In the second part, T–TH was edited by Sir James Murray, who died in 1915, and SU–SZ was edited by C.T. Onions. Among a few articles ‘singled out as being especially conspicuous for their etymological interest’, he proudly mentioned ‘surd’.

A surd number or quantity is irrational, such as the square root of two. Its name is from the Latin surdus, ‘deaf’, and this stands for the Greek word that Euclid used, alogos, ‘irrational’. Rabelais used the term in a different context, ‘alogicque, c’est à dire déraisonnable’, which Motteux translated as ‘alogical and unreasonable’, though alogical didn’t catch on in English. The curious reason that the Latin for ‘deaf’ was used for the Greek for ‘irrational’ is the intermediate use by Arab mathematicians of the Arabic asamm, literally ‘deaf’, for surd roots. The same word had been used by Arab grammarians for a word where the second and third radicals are the same.

In that eccentric poem ‘The Loves of the Plants’, Erasmus Darwin, grandfather of Charles, used surd in another linguistic sense, to mean ‘unvoiced sound’, as when one ‘Weighs with nice ear the vowel, liquid, surd,/ And breaks in syllables the volant word.’ That’s perfectly rational.

This article was originally published in The Spectator’s November 2021 World edition.