Re: More numbers and math

taliesin the storyteller wrote:

> * Matt McLauchlin <matt_mcl@...> [000922 09:38]:
> > I said:
> > > - can numbers be negative?
> >
> > Yes; "minus two" is "sau r'cadand" (two owed). Positive two would be "sau
> > opseiand" (two possessed).
>
> Neat!
>
> General follwup: does anyone have several number-systems for the same
> conlang? târuven's got four so far (binary, base5, base8, base24) and
> yes it's a mess!
Oh dear... and I thought Nur-ellen was original by having both decimal
(base 10) and duodecimal (base 12) numerals.  You have beaten me out of
the field.

> Numbers 0-10 (dec) in base 5:
> aìle þa ran 'venn kaìr nnta nnta-þa nnta-ran nnta-kaìr renn
>
> Conculturally, base 5 is the homey, oldfashioned, common way to count.
> Wages, prices, sizes, age, things like that. There's a system of logic
> based on 5 (true, probably true, either-or, probably false, false) but
> as I'm not a logician I can't elaborate. Base 8 is the spiffy
> simplification of base 24 and the sibling of binary. More on those some
> other time.
How different are the words in the different systems?  Does each of the
different number systems use its own morphemes for 1-digit numbers,
or the same (i.e. _ran_ is 2 in base 8 and base 24 as well)?

In Nur-ellen, the first numbers are the same in both:

1 min, 2 tad, 3 neld, 4 kand, 5 leb`n, 6 eng, 7 od, 8 tolt, 9 ned`r, 10
ker.
11 and 12 are also always called _mink_ and _ras_, the base 10 forms
**_ker min_ and **_ker tad_ are not used at all.  From then, the systems
go
as this:

Base 10:

   13 ker neld, 14 ker kand, 15 ker leb`n, ..., 20 tad`ker, 21 tad`ker
   min, 22 tad`ker tad, ..., 30 neld`ker, 40 kand`ker, 50 lebn`ker, 60
   engker, 70 od`ker, 80 tolt`ker, 90 nedr`ker, 100 harn, 200 tad harn,
   300 neld harn, 1000 keran (contration of *ker harn), 10000 ker keran,
   100000 harn keran, 1000000 million (a borrowed word as well as the
   following: 10^9 milliard, 10^12 billion, 10^18 trillion etc.).

Base 12:

   13 ras min, 14 ras tad, 15 ras neld, ..., 24 tadras, 25 tadras min,
26
   tadras tad, ..., 36 neldras, 48 kandras, 60 lebn`ras, 72 engras, 84
   odras, 96 toltras, 108 nedr`ras, 120 kerras, 132 minkras, 144 hos,
288
   tad hos, 432 neld hos, 1728 meng, 12^4 ras meng, 12^5 hos meng, 12^6
   ammeng.

In contemporary Nur-ellen, base 10 is much more popular, though _tadras_
"24", _neldras_ "36", _kandras_ "48", _kerras_ "120" and _hos_ "144"
are still in popular use.  The words _hos_ and _meng_ are also the
canonical
unspecified large numbers rather than _harn_ or _keran_.  The word _ras
min_
"13" is idiomatically used as "odd, crooked number", while the number 13
itself is usually called _ker neld_.

Zero is _uwand_ in both systems.

Huge numbers are expressed as powers of smaller numbers, usually 10 or
(less common) 12: 10^12 _rasan val e ker_ `12th power of ten';
12^7 _odan val e ker_ `7th power of twelve'.

So I have just disclosed how to build ordinals:  add the suffix _-an_.
Thus _minan_ "1st", _tadan_ "2nd" etc.

Fractions are formed by the suffix _-in_ on the denominator:
_neld kandin_ "3/4".

I haven't fixed negative numbers yet, nor mathematical operators,
complex numbers or whatever.

Jörg.