Re: base-20 (was Re: Numbers from 1 to 12 in Ayeri)

On Fri, Aug 20, 2004 at 02:01:58PM -0400, Trebor Jung wrote:
> Hmm... I wanted something exotic so I made Kosi base-20, but I don't really
> know how such a system works. I know that there are separate lexemes for the
> numbers one through twenty in base-20 languages (Kosi üs, ket, kom, ner, öt,
> sab, het, kaes, kic, den, len, töl, tin, von, sihn, sen, ein, naem, tuan),
> but not much else... Could someone please enlighten me?
The term "base 20" can mean different things in different contexts.  I
don't know how it is used linguistically; it may in fact refer to no
more than the existence of separate lexemes for first twenty natural
numbers.  However, mathematically it requires a positional notation
system in which each position has a value twenty times the
next-lower-valued position.

That is, the way we write numbers, we know that the sequence of digits
"2004" refers to the number "two thousand four" because the 2 occupies a
place that is worth 10 times as much as the place occupied by the first
0, which is worth 10 times as much as the place occupied by the second
0, which is worth 10 times as much as the place occupied by the 4, which
since there's nothing after it must be the units place.  So we know that
the represented number is equal to 4 x 1 + 0 x 10 + 0 x 100 + 2 x 1000 =
4 + 0 + 0 + 2000 = 2004.

In a mathematical base-20 notational system, then, you would first of
all need to devise single digits to represent the numbers ten
through nineteen.  It is common to use letters of the alphabet for
this purpose, so the digits could be 0-9 and A-J; however, to avoid
confusion with 1, you would probably want to skip I and use J and K
instead.

So counting would go like this:

         0, 1, 2, 3, 4, 5, 6, 7, 8, 9, A, B, C, D, E, F, G, H, J, K,
        10,11,12,13,14,15,16,17,18,19,1A,1B,1C,1D,1E,1F,1G,1H,1J,1K,
        ...
        90,91,92,93,94,95,96,97,98,99,9A,9B,9C,9D,9E,9F,9G,9H,9J,9K,
        A0,A1,A2,A3,A4,A5,A6,A7,A8,AA,AA,AB,AC,AD,AE,AF,AG,AH,AJ,AK,
        ...
        K0,K1,K2,K3,K4,K5,K6,K7,K8,KK,KK,KB,KC,KD,KE,KF,KG,KH,KJ,KK,
       100

Where "100" represents 20 x 20, or the number we call "four hundred" in
English.   My age, 36 decimal, would be represented as "1G" (1 x 20 +
16).

Some non-decimal notational systems found in real languages work a
little differently: instead of having digits for 0 through (base)-1,
with 0 as a placeholder, they have digits for 1 through (base).  It's
easy to demonstrate how this works using a decimal system: instead of
digits 0 through 9, use 1 through X, where X represents 10 (like it does
in Roman numerals).  You would then count like this:

         1, 2, 3, 4, 5, 6, 7, 8, 9, X,
        11,12,13,14,15,16,17,18,19,1X,
        21,22,23,24,25,26,27,28,29,2X,

etc.  X = 10, 1X = 20, 2X = 30, 9X = 100, X1 through
XX are 101 through 110 (followed by 111 in its usual place), etc.

Whichever way the notation works, you would generally expect a language
that counts in base N to have words for 1 through N (with or without a
word for zero) as well as for powers of N: N times N, N times N times N,
etc.   Thus in English we have independent words for "hundred" and
"thousand".  Now, English doesn't have a separate lexeme for "ten thousand",
instead counting the number of "thousand"s as if "thousand" it were a
unit of measurement, but other languages do have such lexemes.

-Marcos