Alice without quaternions: another look at the mad tea-party

Abstract

Ever since the publication of Lewis Carroll’s Alice’s adventures in Wonderland (1866), interpretations of its apparent nonsense have been given. In 2009, Melanie Bayley added new interpretations, for instance, that the chapter about the mad tea-party mocked the quaternions of Sir William Rowan Hamilton. In 2017, Francine Abeles argued against Bayley’s quaternion interpretation of the tea-party, and these arguments will be supported and extended by showing that Bayley’s interpretation is based on erroneous assumptions about quaternions. It can be concluded that it is indeed very unlikely that Dodgson had the quaternions in mind when writing the tea-party chapter.

Disclosure statement

No potential conflict of interest was reported by the author(s).

Notes

1 Dodgson did use negatives, but apparently had trouble with the definitions then given, as quantities ‘less than nothing’, or quantities ‘obtained by the subtraction of a greater from a lesser quantity’ (Pycior 1984, 151).

2 That Hamilton initially saw it as adding a third imaginary term to the triplets appears from a letter he wrote on the day after the discovery of the quaternions to his friend John Graves (1806–70) (Hamilton 1844, 491).

3 Apparently while investigating Graves’ new system in 1844, Hamilton found, or recognized, the what he called ‘associative’ law of arithmetic (Øhrstrøm 1985, 50).