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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
by Chinjut 5mo ago
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.
- yread 5mo agoYou'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
- Chinjut 5mo agoI'm a mathematician, and my reaction here is somewhat different.
- wzdd 5mo agoPeople said the same thing about a joke Douglas Adams made in his Hitch Hikers series -- that the (corrupted) Ultimate Question to which the answer was 42 ("what do you get if you multiply six by nine?") was a maths joke because 6x9=42 in base 13. Douglas Adams said this was nonsense.
- Xirdus 5mo agoReminds me of one of my favorite joke programs. #include <stdio.h> #define SIX 1+5 #define NINE 8+1 int main() { printf("%d\n", SIX * NINE); }
- srean 5mo agoDidn't Linus #define THREE as something else in Linux source code. Was that the 2-3-4 tree? Can't seem to find it now.
- Xirdus 5mo agoIt was from some filesystem code. https://news.ycombinator.com/item?id=7296497 https://news.ycombinator.com/item?id=7296497 unsigned three = 1; unsigned five = 5; unsigned seven = 7; These actually get changed through pointers to consecutive powers of 3, 5 and 7 respectively. `three` is initialized to the 0th power of 3, but because only a single 1 is needed by the algorithm, `five` and `seven` are initialized to the 1st powers instead.
- srean 5mo agoAh right. Thank you so much. At least I wasn't hallucinating.
- BoardsOfCanada 5mo agoAnd by accident, 42 happens to be the first base after her multiplication gives the answer 19 here (when 20 would be expected), although it would produce an answer of "tenteen", not twenty.
- yread 5mo agoSo what's a good math joke? I like this one: Young mathematician goes to first grade and the teacher asks who knows what is 1+2. She stands up and says "I don't know what is it, but I do know that it's the same as 2+1 as addition is commutative in the monoid of natural numbers"
- standardly 5mo ago[dead]
- Chinjut 5mo agoWhy 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.
- raldi 5mo agoI agree. She’ll never get to 20 because kids only do the times table up to 12.
- Xirdus 5mo agoUp to 12? Is that a British/Anglosphere/Victorian thing? In Poland they teach up to 10, which is suffinient for arbitrarily large numbers because they also teach long division and how to combine it with times table. Technically up to 9 would be sufficient but 10 is such a nice round number.
- AnotherGoodName 5mo agoIt is yes. The anglosphere has historically been somewhat base 12 in currency, time and units of measurement. Currency is now metric but there’s still a few base 12 things in common usage (feet and inches) in the us at least. Nobody’s gone to metric time yet and base 12 transfers smoothly to base 60 too.
- j16sdiz 5mo agoThe leading theory is they are quaternions. https://www.tandfonline.com/doi/full/10.1080/26375451.2022.2085446#d1e104 https://www.tandfonline.com/doi/full/10.1080/26375451.2022.2... https://www.newscientist.com/article/mg20427391-600-alices-adventures-in-algebra-wonderland-solved/ https://www.newscientist.com/article/mg20427391-600-alices-a...
- Chinjut 5mo agoThese links' mentions of quaternions are about a different part of the book (the tea party). Furthermore, even regarding that different part, your first link explicitly debunks the second link and disavows the quaternion connection the latter alleges. Your first link's whole point is to conclude "it is indeed very unlikely that Dodgson had the quaternions in mind when writing the tea-party chapter."