Martin Gardner’s The Annotated Alice explains the subtleties, mathematical and otherwise, of both Alice books in engaging detail. It explained things I never understood, and showed me things I missed (and then explained them). Besides the mathematics there are references to politicians and events of the era, and jokes that would be known only to people at Oxford.
Lewis Carroll was such an interesting person, right from his study [0] of geometry, algebra [1], to his incessant word play and pioneering forays in the then new field of photography.
One of your favourite “real characters”? Do you just mean… people? Or does this mean something else I’m missing?
I meant people. Let me correct it. He was quite a character too, although with sad undertones. I doubt he ever felt understood.
This article has no references to back up its claims, some of which seem like a stretch without further evidence (e.g., "The Cheshire Cat is a property without a carrier" being a critique of group theory). Are there references that back these claims up?
I like the idea of explaining the math in his writing. I very much dislike changing people's writing to "adjust" the reading level. That's no longer their writing. Just use a different example or explain what was actually written rather than dilute famous prose.
graded readers has always been a resource for language learning.
Re: "The multiplication that does not work", nothing in the quoted text seems to indicate that each multiplication should be interpreted in a different base, or anything like this. Certainly not that "four times [n]" should always have its result read in base 3n + 3 specifically.
It seems more likely to just be an absurd joke where Alice finds herself with an altered version of multiplication where 4n is interpreted as n + 7, causing multiplication to grow more slowly than normal, causing her to exclaim "I shall never get to twenty at that rate!" (a common exaggerated but non-literal use of "never", similar to "This is taking forever!" meaning "This is taking a long time!", not "This will literally never end").
The idea that we're instead supposed to think Alice thinks "four times 13 (decimal)" is to have its output read in base 42 (decimal), thus as "1A", considered distinct from "20", the latter being what would be "twenty", and thus she will literally never get to "twenty"... This just doesn't seem well-supported by anything in the text.
Why would you need to presuppose some inexplicably shifting number base to get the result of "four times [n]" always equaling n + 7? What does that get you over just more simply observing "For Alice, four times [n] has come to be n + 7"? Shifting number bases are a pointless supposition here. They don't explain anything better than what is already happening without them.
You're absolutely correct, the base is not specified. That's the joke. 1-1=0 would not be a joke. Perhaps it's better not to think of it as a joke. When mathematician reads what seems like nonsense, questions like "hmm is there a base where this would be true?" and "which bases is this true in?" pop up
Martin Gardner’s The Annotated Alice explains the subtleties, mathematical and otherwise, of both Alice books in engaging detail. It explained things I never understood, and showed me things I missed (and then explained them). Besides the mathematics there are references to politicians and events of the era, and jokes that would be known only to people at Oxford.
Lewis Carroll was such an interesting person, right from his study [0] of geometry, algebra [1], to his incessant word play and pioneering forays in the then new field of photography.
Anyone interested in this ought to read Martin Gardner's book Annotated Alice https://en.wikipedia.org/wiki/The_Annotated_Alice
Real Life Adventures of an Oxford Don https://www.csmonitor.com/1995/1120/20122.html
In the Shadow of the Dreamchild https://en.wikipedia.org/wiki/In_the_Shadow_of_the_Dreamchil...
Let me add a few links that might be interesting:
How Lewis Carroll computed determinants https://www.johndcook.com/blog/2023/07/10/lewis-carroll-dete...
Condensation of Determinants, Being a New and Brief Method for Computing their Arithmetical Values https://www.gutenberg.org/files/37354/37354-pdf.pdf (cited by John D Cook in his article)
[0] Lewis Carroll's Mathematical works https://en.wikipedia.org/wiki/Lewis_Carroll#Mathematical_wor...
[1] Dodgson condensation https://en.wikipedia.org/wiki/Dodgson_condensation
One of your favourite “real characters”? Do you just mean… people? Or does this mean something else I’m missing?
I meant people. Let me correct it. He was quite a character too, although with sad undertones. I doubt he ever felt understood.
This article has no references to back up its claims, some of which seem like a stretch without further evidence (e.g., "The Cheshire Cat is a property without a carrier" being a critique of group theory). Are there references that back these claims up?
I like the idea of explaining the math in his writing. I very much dislike changing people's writing to "adjust" the reading level. That's no longer their writing. Just use a different example or explain what was actually written rather than dilute famous prose.
graded readers has always been a resource for language learning.
Re: "The multiplication that does not work", nothing in the quoted text seems to indicate that each multiplication should be interpreted in a different base, or anything like this. Certainly not that "four times [n]" should always have its result read in base 3n + 3 specifically.
It seems more likely to just be an absurd joke where Alice finds herself with an altered version of multiplication where 4n is interpreted as n + 7, causing multiplication to grow more slowly than normal, causing her to exclaim "I shall never get to twenty at that rate!" (a common exaggerated but non-literal use of "never", similar to "This is taking forever!" meaning "This is taking a long time!", not "This will literally never end").
The idea that we're instead supposed to think Alice thinks "four times 13 (decimal)" is to have its output read in base 42 (decimal), thus as "1A", considered distinct from "20", the latter being what would be "twenty", and thus she will literally never get to "twenty"... This just doesn't seem well-supported by anything in the text.
Why would you need to presuppose some inexplicably shifting number base to get the result of "four times [n]" always equaling n + 7? What does that get you over just more simply observing "For Alice, four times [n] has come to be n + 7"? Shifting number bases are a pointless supposition here. They don't explain anything better than what is already happening without them.
You're absolutely correct, the base is not specified. That's the joke. 1-1=0 would not be a joke. Perhaps it's better not to think of it as a joke. When mathematician reads what seems like nonsense, questions like "hmm is there a base where this would be true?" and "which bases is this true in?" pop up