Alice in Wonderland and Through the Looking Glass can be read as works of Mathematical Satire.
For instance:
Just as complex numbers work with two terms, quaternions belong to a number system based on four terms (see “Imaginary mathematics”). Hamilton spent years working with three terms – one for each dimension of space – but could only make them rotate in a plane. When he added the fourth, he got the three-dimensional rotation he was looking for, but he had trouble conceptualising what this extra term meant. Like most Victorians, he assumed this term had to mean something, so in the preface to his Lectures on Quaternions of 1853 he added a footnote: “It seemed (and still seems) to me natural to connect this extra-spatial unit with the conception of time.”
Where geometry allowed the exploration of space, Hamilton believed, algebra allowed the investigation of “pure time”, a rather esoteric concept he had derived from Immanuel Kant that was meant to be a kind of Platonic ideal of time, distinct from the real time we humans experience. Other mathematicians were polite but cautious about this notion, believing pure time was a step too far.
The parallels between Hamilton’s maths and the Hatter’s tea party – or perhaps it should read “t-party” – are uncanny. Alice is now at a table with three strange characters: the Hatter, the March Hare and the Dormouse. The character Time, who has fallen out with the Hatter, is absent, and out of pique he won’t let the Hatter move the clocks past six.
Reading this scene with Hamilton’s maths in mind, the members of the Hatter’s tea party represent three terms of a quaternion, in which the all-important fourth term, time, is missing. Without Time, we are told, the characters are stuck at the tea table, constantly moving round to find clean cups and saucers.
Taking both Carrol and Bayley at face value, we are left with the perception that Carrol wished to ridicule quaternions out of existence. Yet quaternions have quite a few applications today-- usually people mention 3d graphics and gimbal lock.
So, perhaps it’s premature to dismiss a philosophical concept because it is satirized in a Lewis Carrol romance. Dodgson might have thought it exceedingly odd, but the straightforward answer does not satisfy.
It boils down to the following problematics: who decides on the meaning of words? The reader (Alice), or the author (Humpty Dumpty)? And is this consistent in both oral and written language?
