Re: Numbers and math

On Thu, 21 Sep 2000, taliesin the storyteller wrote:

>A classic question is: how do you count to ten in your conlang?
Talarian is interesting in that, although it is an Aryan
(Indo-European)  language, it has no Aryan numbers [though many
gramarians argue that pamtra (5) is Aryan]. It is bas twelve and
has two types of numeric characters. The official are unwieldy
ideogrammes; the usual are derived from Indian models. I suppose
I should note that Indian mathematics are quite hot in the world
now. The numbers have been known and used in the East since about
the 12th century or so; in Persia from the 11th century; and in
the West only in the last 3 centuries or so.

1: shatla; 2: rila; 3: hohoc; 4: limtla; 5: pamtra; 6: rimtloc; 7:
matlar; 8: pretlar; 9: amtloc; 10: rapamtra; 11: hacra; 12: himtroc;
13: shatla-wa-himtroc, etc.

>Generalizing:
> - do you form ordinals from cardinals? how? if not, how?
Yes. The ordinals are quite intersting, though. Their ordinals
aren't really understood in quite the same way as ours. First of
all, there are two kinds, the "ordinary" and the "enumerative".

The ordinary so pretty much the same work as our ordinal numbers, but
they are really numeric pronouns. Thus ilimtla, fourth, can mean
"those four" or "that fourth one". For those keeping track of the
grammar, the cardinal number is prefixed with the pronominal stem i-
in order to get the ordinal. As such, ilimtla can be used in any way a
pronoun can be used: Hohe ilimtla-mat? [whose(dat.)  those_four(nom.)
- interrog_ptc.]; or Meke italimtla taahto!  [me(dat.)
those_four(acc.) give(imper.)]

The enumerative do the work of distributives and other minor types of
numbers. Thus limtlame [four(loc.)] can mean "by fours", or "fourth of
four" in combination with an ordinary: limtlame ilimtlahe [four(loc.)
i- + four(gen.)]

> - do you have a zero?
Two of em. The counting zero is tlaram, and is used like any other
cardinal number. The mathematical zero is safra, borrowed I think
from Persian, and is used in various branches of mathematics,
accounting, etc.

> - can numbers be negative?
In mathematics, yes. Though Talarians in general have little use
for maths.

> - fractions? percentiles? if it's not a decimal system, is there
>   something instead of percentiles?
There are _certain_ fractions in common use, but I don't know how
this system works yet.

Interest is paid is thousandths; and indeed higher mathematics is
done in decimal because the Indians have a base ten system.

> - how do you add, subtract, multiply and divide? (if you know how)
With a shrowampar, or ciphering board! The most common kind in use now
is an engraved bronze plate with figures embossed in it, and it has
glass or brass beads that slide up and down on wooden or (very
expensively) iron rods. This one is of Roman design, and generally has
fractional parts to the right side. The older kind is a wooden frame,
with clay or brass discs that slide on wooden rods. Some people
(usually wealthy or eccentric merchants) own a rotapraxashrowampar, a
"wheel-and-lever ciphering board"; which is a brass box with little
windows and dials that can be used to cipher mechanically.

A full counting table, as one might find in the offices of a trader or
merchant, is a good stout wooden table that has a recess for the
shrowampar near the edge where the clerk sits. Beyond that there is a
place where the money is put (usually on the left side of the table)
while on the other side are a series of long narrow boxes where jetons
are thrown, in order to keep track of the money counted.

> - what about raising to the nth power and n-roots?
Don't remember how to do that in English!

Padraic.

>t.