How Lewis Carroll computed determinants

(johndcook.com)

109 points | by tzury 3 hours ago

3 comments

  • kazinator 1 hour ago
    > Dodgson’s original paper from 1867 is quite readable, surprisingly so given that math notation and terminology changes over time.

    Given that Jabberwocky is also quite readable, we shouldn't be too astonished.

  • esafak 2 hours ago
    > Arrange the given block, if necessary, so that no ciphers [zeros] occur in its interior.

    I forgot that cipher used to have a different meaning: zero, via Arabic. In some languages it means digit.

    • pinkmuffinere 1 hour ago
      lol I never made that connection — in Turkish, zero is sıfır, which does sound a lot like cipher. Also, password is şifre, which again sounds similar. Looking online, apparently the path is sifr (Arabic, meaning zero) -> cifre (French, first meaning zero, then any numeral, then coded message) -> şifre (Turkish, code/cipher)
      • celaleddin 55 minutes ago
        Nice! Imagine the second meaning going back to Arabic and now it's a full loop! It can even override the original meaning given enough time and popularity (not especially for "zero", but possibly for another full-loop word).
      • ls-a 1 hour ago
        All world languages are a deviation from Arabic
        • rmunn 39 minutes ago
          > All world languages are a deviation from Arabic

          Spouse of a linguist here. That is absolutely not true. To summarize a LOT, there are multiple languages that share common roots, which linguists classify into language "families". If you go to https://en.wikipedia.org/wiki/List_of_language_families#Spok... and sort the list by number of current speakers (which adds up to far more than the population of the world because so many people speak two or more languages), you'll find the top five language families are Indo-European (which includes most European languages, including English), Sino-Tibetan (which includes Chinese), Atlantic-Congo (which includes Bantu and many other languages spoken in Africa, most of which you probably won't have heard of unless you're a linguist or you live in Africa), Afroasiatic (which includes Arabic), and Austronesian (which includes Tagalog, which you might know by the name Filipino).

          It might be possible to claim that the Afroasiatic languages are all derived from Arabic, but the only influence that the Arabic language has had on Indo-European languages such as English is via loanwords (like algebra, for example). This does not make English a derivative of Arabic any more than Japanese (which has borrowed several English words such as カメラ, "kamera", from camera) is a derivative of English. Borrowing a word, or even a few dozen words, from another language does not make it a derivative. English, while it gleefully borrows loanwords from everywhere, is derived from French and German (or, to be more accurate, from Anglo-Norman and Proto-Germanic).

          • awesome_dude 25 minutes ago
            Can I also add that "Arabic numbers" - the numbers we use today, are actually of Indian origin, the Arabs translated the Indian logic/math texts into Arabic, and Western society used the Arabic translations (and additions like those of "Algorithm")

            https://en.wikipedia.org/wiki/Hindu%E2%80%93Arabic_numeral_s...

            • bigstrat2003 9 minutes ago
              Also as long as we are going down the terminology nerd rabbit hole: it's Arabic numerals, not numbers. Numbers refers to the abstract concept, numerals refers to the method one uses to write them down.
              • awesome_dude 7 minutes ago
                Yeah - I quoted that to show that it was normal usage rather than technical correctness - I also did the same for the name that I didn't have the correct spelling for as I wrote the comment - not sure if I should update it (with your input) or to leave it and let people work down the thread
          • ls-a 13 minutes ago
            I respect that linguists need to pay bills. I don't take my knowledge from someone who takes a wage in return
        • drivebyhooting 1 hour ago
          This doesn’t sound right. What about Chinese?
    • jacquesm 1 hour ago
      Dutch too: "Cijfer", German, "Ziffer", French: "Chifre", Spanish: "Cifra".
  • messe 2 hours ago
    HN title filter cut off the initial "How".

    You can manually edit it back in.

    • marcusestes 2 hours ago
      “Drop the ‘how.’ It’s cleaner.”
      • vharuck 1 hour ago
        It gives it a different implication. As I read it, an article titled "Lewis Carroll Computed Determinates" has three possible subjects:

        1. Literally, Carroll would do matrix math. I know, like many on HN, that he was a mathematician. So this would be a dull and therefore unlikely subject.

        2. Carroll invented determinates. This doesn't really fit the timeline of math history, so I doubt it.

        3. Carroll computed determinates, and this was surprising. Maybe because we thought he was a bad mathematician, or the method had recently been invented and we don't know how he learned of it. This is slightly plausible.

        4. (The actual subject). Carroll invented a method for computing determinates. A mathematician inventing a math technique makes sense, but the title doesn't. It'd be like saying "Newton and Leibnitz Used Calculus." Really burying the lede.

        Of course, this could've been avoided had the article not gone with a click-bait style title. A clearer one might've been "Lewis Carroll's Method for Calculating Determinates Is Probably How You First Learned to Do It." It's long, but I'm not a pithy writer. I'm sure somebody could do better.

        • miltonlost 1 hour ago
          "How Lewis Carroll Computed Determinates" is fine and not clickbait because it provides all the pertinent information and is an accurate summary of its contents. Clickbait would be "you would never guess how this author/mathematician computed determinants" since it requires a clickthrough to know who the person is. How is perfectly fine IMO to have in the title because I personally would expect the How to be long enough to warrant a necessary clickthrough due to the otherwise required title length.