Day 15: Mad as a hatter

I bought the New Scientist a couple of weeks ago and keep bringing it out when on the bus. It's brilliant, I've learned all about The Peter Principle - which I may come back to in a later blog - high frequency, low-arousal religious rituals and their opposite counterparts. I also learned about the theory that Professor Charles Dodgson aka Lewis Caroll wrote Alice in Wonderland partly as a satire on the 'semi-colloquial', 'semi-logical', new fangled contemporary maths professors he had to endure, with all their new fangled reinterpretations on classical mathematical theory, at Oxford.

Take the Mad Hatters tea party where the Hatter, the March Hare and the Dormouse are stuck at the tea table, because they have fallen out with Time, who now won't let them move the clocks past 6 o'clock. They are stuck at the tea table, constantly moving round to find clean cups and saucers. This is an exploration, apparently, of William Rowan Hamilton's work on 'quaternions'. Where, after years working with three terms but could only make them rotate in a plane, when he added a fourth term (which he called Time) he got the three-dimensional rotation he was looking for. (I'm afraid my brain is not able to put it any better than Melanie Bayley, who did the research so I'm just paraphrasing her).

However, I like the bit where the Mad Hatter apparently pokes fun at an aspect of quaternions which says that x=y is not the same as y=x. When the Hare tells Alice to 'say what she means' Alice says that 'at least I mean what I say, which is the same thing'.

"Not the same thing a bit! Why, you might just as well say that 'I see what I eat' is the same as 'I eat what I see!'"

This seems entirely sensible logic to me. Am I missing something?

Anyway, I'm not sure what mathematic concept is being satirised by padlocking the Mad Hatter to a bus stop, so any thoughts greatly appreciated.