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Re: Do people ever make variant numerical systems for non-primitive cultures?

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  • R A Brown
    ... [snip] ... I tried this very many years ago. Certainly addition and subtraction are not exactly difficult. Multiplication was also not difficult, just
    Message 1 of 18 , Mar 5 11:55 AM
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      On 05/03/2013 14:43, Daniel Myers wrote:
      >> -------- Original Message -------- From: Leonardo
      >> Castro Date: Tue, March 05, 2013 6:52 am
      [snip]
      >>
      >> I once affirmed that to a friend and he told me "Let's
      >> check!" and started trying to make basic operations
      >> with Roman numerals. To my surprise, he succeeded! He
      >> succeeded and said: "It's not that difficult...". I
      >> watched he performing the operations while analyzing
      >> developing the methods himself and it really didn't
      >> looked very difficult.

      I tried this very many years ago. Certainly addition and
      subtraction are not exactly difficult. Multiplication was
      also not difficult, just tedious. I could find no
      convenient way, however, of doing division, except, of
      course, by repeated subtraction. It sounds as tho your
      friend probably made a better job of division that I did ;)

      >> I don't have time to repeat what he did now, but I
      >> challenge you do so.
      >
      > Agreed. Also, tools were developed to facilitate math
      > with Roman numbers - the medieval counting board in
      > particular was very successful.

      As, indeed, was the old Roman calculus.

      > Having used one I can tell you that (with a bit of
      > practice) arithmetic computation becomes almost trivial.

      Yep.

      > There's a good paper describing them and their use here:
      > http://www.amatyc.org/publications/Electronic-proceedings/2005SanDiego/Bell.pdf
      >
      > As long as a society doesn't have a need for calculus,
      > they could get along just fine without a decimal number
      > system.

      The ancient Greeks managed famously just using the letters
      of their alphabet, including a couple of obsolete ones.

      --
      Ray
      ==================================
      http://www.carolandray.plus.com
      ==================================
      "language … began with half-musical unanalysed expressions
      for individual beings and events."
      [Otto Jespersen, Progress in Language, 1895]
    • MorphemeAddict
      ... Repeated division by 2, then adding the answers that were even, should work. (I think.) Perhaps less tedious than simple repeated subtraction. Is there any
      Message 2 of 18 , Mar 5 12:12 PM
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        On Tue, Mar 5, 2013 at 2:55 PM, R A Brown <ray@...> wrote:

        > On 05/03/2013 14:43, Daniel Myers wrote:
        >
        >> -------- Original Message -------- From: Leonardo
        >>> Castro Date: Tue, March 05, 2013 6:52 am
        >>>
        >> [snip]
        >
        >
        >>> I once affirmed that to a friend and he told me "Let's
        >>> check!" and started trying to make basic operations
        >>> with Roman numerals. To my surprise, he succeeded! He
        >>> succeeded and said: "It's not that difficult...". I
        >>> watched he performing the operations while analyzing
        >>> developing the methods himself and it really didn't
        >>> looked very difficult.
        >>>
        >>
        > I tried this very many years ago. Certainly addition and
        > subtraction are not exactly difficult. Multiplication was
        > also not difficult, just tedious. I could find no
        > convenient way, however, of doing division, except, of
        > course, by repeated subtraction.


        Repeated division by 2, then adding the answers that were even, should
        work. (I think.)
        Perhaps less tedious than simple repeated subtraction.

        Is there any equivalent to the 'law of nines' with Roman numerals?

        stevo


        > It sounds as tho your
        > friend probably made a better job of division that I did ;)
        >
        >
        > I don't have time to repeat what he did now, but I
        >>> challenge you do so.
        >>>
        >>
        >> Agreed. Also, tools were developed to facilitate math
        >> with Roman numbers - the medieval counting board in
        >> particular was very successful.
        >>
        >
        > As, indeed, was the old Roman calculus.
        >
        >
        > Having used one I can tell you that (with a bit of
        >> practice) arithmetic computation becomes almost trivial.
        >>
        >
        > Yep.
        >
        > There's a good paper describing them and their use here:
        >> http://www.amatyc.org/**publications/Electronic-**
        >> proceedings/2005SanDiego/Bell.**pdf<http://www.amatyc.org/publications/Electronic-proceedings/2005SanDiego/Bell.pdf>
        >>
        >> As long as a society doesn't have a need for calculus,
        >> they could get along just fine without a decimal number
        >> system.
        >>
        >
        > The ancient Greeks managed famously just using the letters
        > of their alphabet, including a couple of obsolete ones.
        >
        >
        > --
        > Ray
        > ==============================**====
        > http://www.carolandray.plus.**com <http://www.carolandray.plus.com>
        > ==============================**====
        > "language … began with half-musical unanalysed expressions
        > for individual beings and events."
        > [Otto Jespersen, Progress in Language, 1895]
        >
      • Петр Кларк
        ... The Enamyn numbering system is based on Greek numerals (which were actually Greek letters -- see more at http://en.wikipedia.org/wiki/Greek_numerals), but
        Message 3 of 18 , Mar 5 7:50 PM
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          On Monday, 04 March 2013 20:44:20 you wrote:
          > I haven't looked at all that many systems. Do people ever make clunky,
          > irrational, and old-fashioned systems like the Roman numerals? Or are the
          > purposes of number systems so practical that most conlangers have no
          > interest in making such a complex (no, baroque) method for doing math?
          > Most other aspects of conlangs seem to be deliberately elaborated and
          > intricate, reflecting how much weirdness is out there and how the
          > complexity of a language isn't related to how materially-advanced its
          > society is. But historically, most peoples had very basic math skills.

          The Enamyn numbering system is based on Greek numerals
          (which were actually Greek letters -- see more at
          http://en.wikipedia.org/wiki/Greek_numerals), but since the Enamyn numbering
          system is octal (1-8, no zero), some Greek numerals were not used:

          α = 1 ι = o 11 (d 9) ρ = o 111 (d 73)
          β = 2 κ = o 21 (d 17) σ = o 211 (d 137)
          γ = 3 λ = o 31 (d 25) τ = o 311 (d 201)
          δ = 4 μ = o 41 (d 33) υ = o 411 (d 265)
          ε = 5 ν = o 51 (d 41) φ = o 511 (d 329)
          ϛ = 6 ξ = o 61 (d 49) χ = o 611 (d 393)
          ζ = 7 ο = o 71 (d 57) ψ = o 711 (d 457)
          η = 8 π = o 81 (d 65) ω = o 811 (d 521)

          Obviously, the values after η differ from their Greek counterparts, which is
          likely why the numbering system switched to Enamyn letters in the late fifth
          century AD, when the written language switched from Greek letters to a newly
          formulated native script which was a significant improvement over the Greek
          alphabet.
          Side note: I'm aware that this is a really *odd* way of counting, and I'm
          wondering if it's just a little too weird. I know that there are some cultures
          that count with base-8, but this way of counting seems pretty unique.
          Comments?
          Oh, and if you're interested, here's the Python code that will convert
          from decimal to octal, Enamyn-style:

          def ash(n):
          n = int(n) - 1
          if n >= 0:
          return str(ash(n / 8)) + str((n % 8) + 1)
          else: return ""

          In case you're wondering, "ash" means "eight".
          :Peter
        • MorphemeAddict
          What is the largest number you can write in this system, and how do you write numerals greater than that? stevo
          Message 4 of 18 , Mar 5 7:56 PM
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            What is the largest number you can write in this system, and how do you
            write numerals greater than that?

            stevo

            On Tue, Mar 5, 2013 at 10:50 PM, Петр Кларк <pyotr.klark@...> wrote:

            > On Monday, 04 March 2013 20:44:20 you wrote:
            > > I haven't looked at all that many systems. Do people ever make clunky,
            > > irrational, and old-fashioned systems like the Roman numerals? Or are
            > the
            > > purposes of number systems so practical that most conlangers have no
            > > interest in making such a complex (no, baroque) method for doing math?
            > > Most other aspects of conlangs seem to be deliberately elaborated and
            > > intricate, reflecting how much weirdness is out there and how the
            > > complexity of a language isn't related to how materially-advanced its
            > > society is. But historically, most peoples had very basic math skills.
            >
            > The Enamyn numbering system is based on Greek numerals
            > (which were actually Greek letters -- see more at
            > http://en.wikipedia.org/wiki/Greek_numerals), but since the Enamyn
            > numbering
            > system is octal (1-8, no zero), some Greek numerals were not used:
            >
            > α = 1 ι = o 11 (d 9) ρ = o 111 (d 73)
            > β = 2 κ = o 21 (d 17) σ = o 211 (d 137)
            > γ = 3 λ = o 31 (d 25) τ = o 311 (d 201)
            > δ = 4 μ = o 41 (d 33) υ = o 411 (d 265)
            > ε = 5 ν = o 51 (d 41) φ = o 511 (d 329)
            > ϛ = 6 ξ = o 61 (d 49) χ = o 611 (d 393)
            > ζ = 7 ο = o 71 (d 57) ψ = o 711 (d 457)
            > η = 8 π = o 81 (d 65) ω = o 811 (d 521)
            >
            > Obviously, the values after η differ from their Greek counterparts, which
            > is
            > likely why the numbering system switched to Enamyn letters in the late
            > fifth
            > century AD, when the written language switched from Greek letters to a
            > newly
            > formulated native script which was a significant improvement over the Greek
            > alphabet.
            > Side note: I'm aware that this is a really *odd* way of counting,
            > and I'm
            > wondering if it's just a little too weird. I know that there are some
            > cultures
            > that count with base-8, but this way of counting seems pretty unique.
            > Comments?
            > Oh, and if you're interested, here's the Python code that will
            > convert
            > from decimal to octal, Enamyn-style:
            >
            > def ash(n):
            > n = int(n) - 1
            > if n >= 0:
            > return str(ash(n / 8)) + str((n % 8) + 1)
            > else: return ""
            >
            > In case you're wondering, "ash" means "eight".
            > :Peter
            >
          • Alex Fink
            ... I think a more germane question is this: how do you write numbers using this system if they don t end in a bunch of ones? The actual Greek system gets to
            Message 5 of 18 , Mar 5 8:11 PM
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              On Tue, 5 Mar 2013 22:50:22 -0500, Петр Кларк <pyotr.klark@...> wrote:

              >On Monday, 04 March 2013 20:44:20 you wrote:
              >> I haven't looked at all that many systems. Do people ever make clunky,
              >> irrational, and old-fashioned systems like the Roman numerals? Or are the
              >> purposes of number systems so practical that most conlangers have no
              >> interest in making such a complex (no, baroque) method for doing math?
              >> Most other aspects of conlangs seem to be deliberately elaborated and
              >> intricate, reflecting how much weirdness is out there and how the
              >> complexity of a language isn't related to how materially-advanced its
              >> society is. But historically, most peoples had very basic math skills.
              >
              > The Enamyn numbering system is based on Greek numerals
              >(which were actually Greek letters -- see more at
              >http://en.wikipedia.org/wiki/Greek_numerals), but since the Enamyn numbering
              >system is octal (1-8, no zero), some Greek numerals were not used:
              >
              >α = 1 ι = o 11 (d 9) ρ = o 111 (d 73)
              >β = 2 κ = o 21 (d 17) σ = o 211 (d 137)
              >γ = 3 λ = o 31 (d 25) τ = o 311 (d 201)
              >δ = 4 μ = o 41 (d 33) υ = o 411 (d 265)
              >ε = 5 ν = o 51 (d 41) φ = o 511 (d 329)
              >ϛ = 6 ξ = o 61 (d 49) χ = o 611 (d 393)
              >ζ = 7 ο = o 71 (d 57) ψ = o 711 (d 457)
              >η = 8 π = o 81 (d 65) ω = o 811 (d 521)

              I think a more germane question is this: how do you write numbers using this system if they don't end in a bunch of ones?

              The actual Greek system gets to make straightforward use of addition: if you wish to write 438, well, υ 400 and λ 30 and η 8 appear in the table, and you catenate them to add and get υλη 438.

              But in your system, say I want to write the octal number 438 (= decimal 288). Do I still write υλη, even though there's no arthmetic sense in which υ means 411 and λ means 31 here? Do I decompose it as 411 + 21 + 6 and write υκϛ, even though that's not parallel to your expression 438 for it in Arabic digits?

              Alex
            • Logan Kearsley
              ... Sadly, I cannot provide examples of conlangs with entirely non-place-value systems. However, Klingon uses a place-value system that s rather different from
              Message 6 of 18 , Mar 7 10:32 AM
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                On 4 March 2013 18:44, Matthew George <matt.msg@...> wrote:
                > I was thinking about Roman numerals, and how terrible for performing
                > mathematics that whole system is. Then it occurred to me that I've never
                > encountered a conlang with a system anything like it. Toki Pona's is
                > somewhat similar, but much simpler, and is obviously related to that lang's
                > design intent. Pretty much all of the other variation I've heard about
                > involves numerical bases. But the place-value system, complete with zero,
                > is always what people seem to choose.
                >
                > I haven't looked at all that many systems. Do people ever make clunky,
                > irrational, and old-fashioned systems like the Roman numerals? Or are the
                > purposes of number systems so practical that most conlangers have no
                > interest in making such a complex (no, baroque) method for doing math?
                > Most other aspects of conlangs seem to be deliberately elaborated and
                > intricate, reflecting how much weirdness is out there and how the
                > complexity of a language isn't related to how materially-advanced its
                > society is. But historically, most peoples had very basic math skills.
                >
                > I'd love to see counter-examples to the modern place-value system. Can you
                > recommend any?

                Sadly, I cannot provide examples of conlangs with entirely
                non-place-value systems. However, Klingon uses a place-value system
                that's rather different from what most people are familiar with; it's
                got three numerals, but the digits run 1 to 3, not 0 to 2.
                Counting goes as follows:
                1 - 1
                2 - 2
                3 - 3 (three ones)
                11 - 4 (one three and one ones)
                12 - 5 (one three and two ones)
                13 - 6 (one three and 3 ones; this is the kind of weird part)
                21 - 7 (two threes and one one)
                etc.

                Most representations are the same as in a regular place value system
                with zero, except for powers of the radix, which have one less digit,
                eliminating the zero. A mechanical transformation can be done on any
                regular place-value system to turn it into a zero-less system like
                this.

                I came up with a mixed system (intending to use it for Mev Pailom, but
                that hasn't worked out very well as of yet) with basic numerals for 1,
                2, and 5. Counting goes

                1
                2
                1 and 2
                2 2s
                5
                5 and 1
                5 and 2
                5 with 2 and 1
                5 with 2 2s
                2 5s
                ...
                2 and 1 of 5 = 15
                ...
                2 2's of 5 = 20

                I don't have any sort of extra-linguistic numeral-only notation for it
                yet. And it gets very clumsy when trying to describe numbers much
                larger than 80 (2 2s of 2 2s of 5). So it needs a bit work still.

                -l.
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