NUMBER SYSTEMS.

TAKASUGI Shinji (“surname first – Japanese way”) has, alongside a Teach Yourself Japanese site and a number of Japanese-language ones (all linked from his home page), a fascinating Number Systems of the World page that includes 60 languages, ranked in order of complexity. At the top is Nimbia (a dialect of the Nigerian Chadic language Gwandara), which uses a duodecimal system (gwom 10, kwada 11, tuni 12, tuni mbe da [12 and 1] 13, tuni mbe bi [12 and 2] 14; gume kwada ni kwada [(12 x 11) and 11, using a different word for 'twelve'] 143, wo [122] 144); at the bottom is Tongan (“Tongan has definitely the simplest number system in the world”: eleven is 1,1; ninety-nine is 9,9; &c), with many interesting languages along the way (including Polari!). (Via MzB at AskMeFi.)


[Dumb typo fixed due to vigilance of eagle-eyed correspondent: thanks, John!]

Comments

  1. I wonder sometimes about the effects that different naming systems might make people think about themselves and their relationship to ‘the world’, and would be interested to know if there’s any modern research into this, or online resources? Where family name comes before personal name as in the Japanese case, is one example; another very different one is the system of patronymics still in use in sixteenth and seventeenth century Wales – where you would get individuals with strings of names (a son/daughter of b son of c etc – recording to the great-great-great-grandfather in documents is not that rare, especially in the 16th century.) The Welsh in that period were known (and derided) for their ‘obsession’ with genealogy; the recorded naming patterns suggest that this was certainly not confined to the gentry, with their elaborate family trees.

  2. Same is true of Iceland, where people are still (if I’m correct) identified as “X son/daughter of Y.”

  3. I find it interesting that Swiss-French uses fully decimal system, unlike French French. :-) I wonder what are the cultural-historical reason behind it (influence of German?).
    (Swiss-French also uses a keyboard layout that is much closer to the American English layout than French keyboard.)

  4. Speaking of Iceland, I had a couple of Icelandic friends in college. One had a traditional patronym (his name was Sigurðer Flossison, his father was Flossi Sigurðerson, and so they went for generations); the other had a “family name” (Borg). I asked Oskar why he had a family name rather than a patronym, and he said that a great-grandfather had emigrated to France and started a business under the name Borg, which then became a family name when they returned to Iceland. Apparently, a small minority of Icelanders have family names, usually due to emigration or immigration in the past.
    He told me that Iceland maintained two phone directories: A small one for people with family names, arranged alphabetically by surname, and a main directory for traditional patronyms, alphabetically by given name, and then broken down by patronym.
    I believe that traditionally, the eldest son takes his grandfather’s name, so you get these “cyclic” names, like Siggi and his dad.
    We were drinking college-style at the time we discussed this, so consider it hearsay until independently verified. Where are the Icelandic language-hatters?

  5. The old germanic languages, before the coming of Ladin Christianity, used a hundred of six score.

    The later ones have the form of teenty (tenty) and elefty 110, before a hundred of 120 in number. See eg http://www.os2fan2.com/twelfty/twelfty.pdf . Earlier, one said, eg four and hundsixty, for the decades from 60 to 120.

    The number system wained with the coming fo the hindo digits.

  6. The old germanic languages, before the coming of Ladin Christianity, used a hundred of six score.

    Interesting! Near-innumerate though I am, I’ll have to read the article. This recalls the Babylonian sexagesimal system.

    120 is divisible by 2, 3, 4, 5, 6, 8, 10, 12, 15 and 20. Not shabby at all, especially compared to 100 and its measly 2, 4, 5, 10 and 20.

  7. des von bladet says:

    120 is divisible by 2, 3, 4, 5, 6, 8, 10, 12, 15 and 20. Not shabby at all, especially compared to 100 and its measly 2, 4, 5, 10 and 20.

    Happily, Division Technology(TM) has improved since the Babylonians.

  8. marie-lucie says:

    120 is divisible by 2, 3, 4, 5, 6, 8, 10, 12, 15 and 20

    So is 60, as the Babylonians figured out. That’s why we still use the Babylonian system for hours/minutes/seconds and degrees/angles.

    I am not familiar with “Division Technology (TM)”. How has it improved on the Babylonian system?

  9. des von bladet says:

    I don’t know what the Babylonians programmed in, but I have languages to hand with integer, rational and arbitrary precision floating point arithmetic.

  10. des von bladet says:

    I can in fact divide any integer by any other (but not-necessarily distinct) non-zero integer!

  11. m-l: The Babylonians did not know the familiar school method of dividing numbers (long division, méthode de la potence). Instead, they multiplied one number by the reciprocal of the other, and relied on tables of 1 divided by many numbers to find reciprocals (inverses). Their base-60 notation meant that 1/2, 1/3, 1/4, 1/5, 1/6, 1/8, 1/10, 1/12, 1/15, 1/20, 1/30, 1/60 were all expressible as exact values, unlike base-10 where only 1/2, 1/5, and 1/10 are so expressible.

  12. I’m planning to phase out base-sixty minutes and seconds. It will create huge demand for new watches & clocks.

  13. … in base 10 that I am already making and storing in the out house, ready for release before the changeover.

  14. Trond Engen says:

    Base 10 instead of 100? I could live with that. This would mean 36 times longer oversleep compared with base 60 and still only five minutes late.

  15. The Frick has a decimal watch by Breguet.

  16. Trond Engen says:

    14.4 times longer oversleep, of course. This is what happens with undersleep. Now to bed. May tomorrow be decimal!

  17. Trond Engen says:

    The best day since Anno Decimal.

  18. Zero is divisible by everything, and I don’t mean with remainders. That’s one reason why it’s my favorite number.

  19. Zero is divisible by everything

    A black hole is where god divided by zero.

  20. Here’s something quite interesting about the French watch trade during decimalisation. And here’s a different French decimal watch, one with two minute hands. I haven’t seen the Frick’s, but the BM has a wonderful clock & watch collection even for people like me who aren’t usually interested in clocks.

  21. Empty you use Ø (or something pretty similar) and I noticed your fb friend Peter said he uses Å as a math symbol.

  22. There’s a Sèvres sundial here in Boston. Used to be on display in the basement; now it’s locked up in storage.

  23. Zero is divisible by everything, and I don’t mean with remainders.

    Is the last part of that sentence some kind of dig at non-standard analysis ?

  24. What a shame it’s stored away! It ought to be in the sunshine.

  25. marie-lucie says:

    I have never seen a sundial that was not painted or otherwise permanently attached to a specific spot. When I was young my father (after doing all the calculations) made one on the wall of a house where we spent several summer vacations. This was in a very sunny area where each village had at least one old sundial: you don’t see them much in rainy areas. An all-purpose one such as the one featured here would have to be set up exactly in a specific place, at the right angle, taking into account the location and time of year as well as the hour of the day when setting it up. Perhaps this one is not kept outside because there is no suitable place for it and/or sunny weather is too rare to make it useful.

  26. Rodger C says:

    Reminds me of the allegory I heard long ago in a sermon: A missionary gives a remote tribe a sundial. They love it so much that etc. etc., and eventually, to protect it, they build a canopy over it.

  27. Boston’s very sunny, m-l. There are lots of sundials in England, including the big ones on walls and in lots of people’s gardens, and I remember as a seven-year-old child wondering what the point of them was.

  28. marie-lucie says:

    AJP, I have not done a survey, or even read anything about them. In my limited experience, sundials were plentiful in the South of France (and also in Italy), not so much in the North. Those English sundials In people’s gardens must be horizontal ones (or nearly so) set up on small pillars, like the ones I have seen in some French gardens (and the one in the picture must be meant as one of those). For me a typical sundial is set up high on the walls of churches and other public buildings, or of prosperous houses. It is possible that in less sunny areas the wall sundials I remember had existed in the North but might have been painted or plastered out when reliable large clocks became more widely available.

  29. AJP: I have never paid enough attention to the difference between the mathematician’s empty-set symbol and the Norse O-slash. I believe that when I first tried to adopt the former as my screen name some LH commenter waxed informative on this distinction, but it went right out the other ear.
    And I must have missed Peter’s mention of A-with-circle-on-top, but I do enjoy it when mathematicians cast a wide net for letters to stand for things.

    Stu: No, you are overthinking as usual.

  30. John Cowan says:

    That was you yourself, Empty, quoting Wikipedia here.

    Å is of course not only the Nordic letter, but the symbol for ångstroms (1 Å = 10⁻¹⁰ m). It’s capitalized because unit abbreviations named after people are, though the unit itself is not: thus the abbreviation for watts is W whereas the abbreviation for meters is m.

  31. That was you yourself, Empty, quoting Wikipedia here.

    In the same comment thread one finds empty charging himself with overthinking:

    In demonstrating that someone was beneath my notice, the trick would be to do it without appearing to take any notice of them. But what if they didn’t notice that I was taking no notice? An option worth exploring might be to piss on them while appearing not to notice that they are there. But by the time I got that far with my overthinking of the problem I would have lost the I-don’t-care contest anyway.

    But his charge is untenable. The same kind of problem, with regard to “sincerity” instead of deprecation, was known in the 17C to European writers on morality. Luhmann on this subject: “How to communicate one’s own sincerity without communicating it ? And what happens when the interlocutor recognizes that this is what one is doing ?”

    empty, you reached the same kind of conclusion on this aspect of “morality” that is now generally accepted by philosophers. I suspect that you dismissed the argument that led to it as “overthinking” because the conclusion seems paradoxical. But you have other choices.

    One is to provisionally accept the conclusion and continue to think about its implications. If something seems wrong, it may be due neither to overthinking nor underthinking, but to a decision to stop thinking when the thinking gets tough.

  32. Those English sundials In people’s gardens must be horizontal ones (or nearly so) set up on small pillars, like the ones I have seen in some French gardens (and the one in the picture must be meant as one of those). For me a typical sundial is set up high on the walls of churches and other public buildings

    No, no, you’re wrong about British sundials, m-l. They’re all over the place, both horizontal and vertical, and some are very famous, like the big wall-mounted one at All Soul’s designed by Sir Christopher Wren (it was moved from the tower to the courtyard in the 19C). Actually there are tons of them in Oxford. Here’s another famous one, at Corpus Christi College, where the time is read off the shaft of the column.

    And of course many people who live out of the city have the horizontal pedestal-mounted kind in the garden.

    I’m really missing that preview button.

  33. Å is of course not only the Nordic letter, but the symbol for ångstroms

    No, it had nothing to do with units: “I had a similar issue several years ago when I wanted to denote the interior of a subset A of a topological space by an A with a little circle on top of it, and was told that such a thing was quite impossible. But I’m certain that 50 years ago that was the way everybody wrote an interior.” Not being mathematicians his real intention here, asking Does anyone know the right way to get the disjoint union of two sets X and Y in TeX? , is above both of our heads, I suspect.

  34. marie-lucie says:

    AKP, I had no idea that sundials of both kinds were so popular in England. Of course I have not spent much time there. I stand corrected!

  35. marie-lucie says:

    I meant AJP, of course.

  36. AKP is his younger brother.

  37. John Cowan says:

    Until I looked, my guess was that Frei Otto was the German version of Free Willy.

  38. AJP, Peter was not so much thinking of the Norse A with circle on top as he was wishing he could place a circle of an letter. If X denotes a set of points then X with circle on top may denote the interior of X. If Omega denotes a set of points then Omega with circle on top may denote the interior of Omega.

    Stu, it seems that I sometimes fling this word “overthinking” around without much thought. I’m sorry I flung it at you. All I meant about dividing 0 by x without remainders is that 0/x is always a whole number. I was not saying anything about dividing *by* 0, so that neither Paul Ogden’s reply about black holes nor your reply about (I think) infinitesimals was strictly relevant — except that I did seem to be asserting that 0 can be divided by 0, didn’t I? Certainly 0 is the most interesting number to divide 0 by.

    I don’t want to read any more of that old thread.

  39. I sometimes fling this word “overthinking” around without much thought.

    Tee-hee !

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