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... "and then the different branches of Arithmetic-- Ambition, Distraction, Uglification, and Derision."

(Alice in Wonderland, chapter IX: the Mock Turtle's story)

As a child I wondered for a long time what was the exact meaning of the above partition of Arithmetics quoted in the strange Mock turtle's speech. Today, I like to think it refers to that unpleasant circumstance many of us experienced sometimes: I want to get a certain difficult result (Ambition) but there is a fatal error somewhere in my argument, or computation (Distraction) and when I realize it, the construction miserably falls (Uglification) with a inner feeling of scorn (Derision). A sort of micro - Greek tragedy. Is that what Lewis Carrol really had in mind? It is possible, as he was a mathematician himself, but then did he refer to a precise incident? Did he left any comment on that passage? Has anybody quoted that passage in this meaning later?

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On the surface you have to obvious play on words with addition, subtraction, mulfiplication and division. If you want to dig deeper, probably the best resource is Martin Gardner's The Annotated Alice and More Annotated Alice for which he did quite a lot of primary literature search. For the first three questions, if you don't find an answer in those two books, then probably the answer would be "nobody knows". (Unfortunately my family's copies are on a different continent at the moment, so I can't look it up for you.) – Willie Wong Jan 26 '11 at 15:59
Actually I'm not sure if this question is suitable for MO. I found the tags "history" and "arithmetic", but I'm not asserting it 100% qualifies. – Pietro Majer Jan 26 '11 at 16:00
I assume it refers to Dodgson's opinions on abstract algebra: – Qiaochu Yuan Jan 26 '11 at 16:07
Apparently the Alice stuff is full of mathematical metaphors, e.g. the "tea party" is supposedly making fun of quaternions, with "t" for time instead of "tea", etc. There is a Notices of the AMS paper (or maybe a book review) about that somewhere, and I think Martin Gardner wrote The Annotated Alice or something similar a long time ago. There are already quite a few published analyses of all this stuff, apparently. – Zen Harper Jan 26 '11 at 16:41
@Igor: Not community wiki, I think, because the question should have a definite answer, even though it's a question about literature and not a mathematical question. – Timothy Chow Jan 26 '11 at 22:24
up vote 5 down vote accepted

Martin Gardner's Annotated Alice: The Definitive Edition says only this:

Needless to say, all the Mock Turtle's subjects are puns (reading, writing, addition, subtraction, multiplication, division, history, geography, drawing, sketching, painting in oils, Latin, Greek). In fact, this chapter and the one to follow fairly swarm with puns. Children find puns very funny, but most contemporary authorities on what children are supposed to like believe that puns lower the literary quality of juvenile books.

Gardner then goes on to say that the "Drawling-master" is a reference to the art critic John Ruskin, and gives a couple of paragraphs of biographical information about Ruskin. Given Gardner's extensive knowledge of Carrolliana, it seems likely that Carroll never published any further comments about the "different branches of Arithmetic."

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"Has anybody quoted that passage in this meaning later?" Does this qualify?

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