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.
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.
Lewis Carroll, an Oxford Don with a double first degree, 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.
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.
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?
He did actually work with permutations and cycles in voting ( https://en.wikipedia.org/wiki/Dodgson's_method ) but it's combinatorial and not very group'y. Agree with comments that this is AI generated and that the highlighted stuff isn't necessarily interesting, deep, or correct.
As for the cat's smile, analytic philosophy substance/property stuff goes back to Leibniz if not Aristotle. Dodgeson basically predates much of Russel's career, but he could have been an influence on his idea of "bundles" and he definitely influenced Quine. He wrote a few textbooks if you want to dig into his research interests but IIRC it's more along the lines of Boole and DeMorgan, even if fictional fun is arguably anticipating the next wave. I linked the haddock's eyes elsewhere in thread.. good fun but also some rich implications. Since he's preoccupied with self-reference you could argue it anticipates Godel. https://en.wikipedia.org/wiki/Use%E2%80%93mention_distinctio...
Exactly, even having a father in the 1800s reading this to their kid and instantly getting that it's a base 4 joke is such a stretch that the article lost me right there. Even after knowing what it is, it's pretty obscure to spot.
To paraphrase Tom Lehrer: Base 18 is just like base 20... if you're missing two toes!
At least that mathematical interpretation does hold up logically all the way to the punch line (even if the interpretation wasn't obviously intended by Carroll). The following section on the Tea Party is just nonsensical slop.
Regarding the Tea Party: whilst what is written is not incorrect, there are some details missing which make it unsatisfactory. The Tea Party was Dodgson's attempt to mock Quaternions, which were getting attention at the time. The 'ridiculous rotations' through space and time were his interpretation of W.R. Hamilton's theories. Note: Hamilton was bald and wore a top hat, you can see one in the statue of him at Broom Bridge in Cabra.
One of my favorite things to come out of Alice in Wonderland is the Red Queen's Race, which has been used as a metaphor in many many fields for the concept of needing to work as hard as you can just to keep up with others, not even to get ahead.
> "Well, in our country," said Alice, still panting a little, "you'd generally get to somewhere else—if you ran very fast for a long time, as we've been doing."
> "A slow sort of country!" said the Queen. "Now, here, you see, it takes all the running you can do, to keep in the same place. If you want to get somewhere else, you must run at least twice as fast as that!"
> If you multiply in base 18, the answer to 4 times 5 is 20, which is written "12" (one eighteen plus two). In base 21, the answer to 4 times 6 is 24, written "13" (one twenty-one plus three). The pattern continues. In base 24, 4 times 7 is 28, written "14." Each step up advances the multiplication base by three. The product, written in that new base, always falls one short of twenty.
The product is always 1 and some other digit but not one short of 20
And we only have two multiplications with their result, that’s hardly a pattern
21 comments
[ 2.8 ms ] story [ 57.6 ms ] threadIt 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.
Anyone interested in this ought to read Martin Gardner's book Annotated Alice https://en.wikipedia.org/wiki/The_Annotated_Alice
Let me add a few links that might be interesting:
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...
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
As for the cat's smile, analytic philosophy substance/property stuff goes back to Leibniz if not Aristotle. Dodgeson basically predates much of Russel's career, but he could have been an influence on his idea of "bundles" and he definitely influenced Quine. He wrote a few textbooks if you want to dig into his research interests but IIRC it's more along the lines of Boole and DeMorgan, even if fictional fun is arguably anticipating the next wave. I linked the haddock's eyes elsewhere in thread.. good fun but also some rich implications. Since he's preoccupied with self-reference you could argue it anticipates Godel. https://en.wikipedia.org/wiki/Use%E2%80%93mention_distinctio...
Why would anyone be expected to multiply in base 18? Why 18? Where does it come from?
At least that mathematical interpretation does hold up logically all the way to the punch line (even if the interpretation wasn't obviously intended by Carroll). The following section on the Tea Party is just nonsensical slop.
4*5 = 12 is either wrong or base 18
> "Well, in our country," said Alice, still panting a little, "you'd generally get to somewhere else—if you ran very fast for a long time, as we've been doing."
> "A slow sort of country!" said the Queen. "Now, here, you see, it takes all the running you can do, to keep in the same place. If you want to get somewhere else, you must run at least twice as fast as that!"
https://en.wikipedia.org/wiki/Red_Queen%27s_race
Also related, recently it's been used to describe involution (neijuan) in the chinese economy https://en.wikipedia.org/wiki/Neijuan
I can't remember it exactly, but in the tea-time scene, the guy gives Alice a quiz regarding the topology of a chair or something...
She tries to solve it, upon which they burst out laughing at her saying "there is no solution!"
Does anyone else remember it or am I trippin'?
The product is always 1 and some other digit but not one short of 20
And we only have two multiplications with their result, that’s hardly a pattern