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Ebisedian number system (II)

From:H. S. Teoh <hsteoh@...>
Date:Thursday, July 18, 2002, 17:56
And now, for the second saga of Ebisedian numbers...

First of all, the $10^6 question: what would a Bisedi say if you asked how
many fingers he/she had? Well, that's a trick question. There's more than
one correct answer. If he was male, he'd probably answer:
        3Ta'gode3kekrejei.      [@\"t_hagok&?@\k&kr`&dZ&?i]

If she was female, she might answer:
        3tako'de3kekrejei.      [@\ta"kod&?@\k&kr`&dZ&?i]

(Or, if she is the sociophobic type, she might retort with _ale's `yb0_,
[?a"l&s Hy"bA] but we won't consider that possibility here.)

It'll take the rest of this saga to explain this one. ;-) (If you haven't
fainted at the X-SAMPA yet... boy, X-SAMPA sure has a way of making the
most mundane answer to an innocuous question really scary.)


OK, so from the previous post, we've all learned that whole basic numbers
and triads business. Those words aren't very useful in themselves, unless
you're a mathematician. (But not even then---mathematicians would be using
the "entity" form of those words instead. See later.) We want to be able
to describe quantities with them.  As is usual to many languages, there's
a difference between cardinals and ordinals. Cardinals describe how many
of something there are, and ordinals describe which position something is
in, in an ordered list.

Enough ado. Cardinals in Ebisedian are formed by taking the radix form of
the noun being described, and prefixing it onto the number noun. For
        3pii'z3dojei.   [@\"pi:z@\dodZ&%?i]
        "Two men."

        Formed from 3- (plural prefix), pii'z3do- (radix of pii'z3di,
        "man"), -jei', "two".

Another example:
        3mango'jekrejei.        [@\ma"NodZ&kr`&dZ&%?i]
        "Eighteen horses." (Literally, "two (groups of) nine horses".)

        Analysis: 3-, pl. pfx; mango'-, radix of _mangi'_ "horse"(*);
        -jekre'-, the 2nd triad (= 3^2 = 9); -jei', "two". Hence,
        "horses-second-triad-twice", i.e., (3^2*2) horses.

NOTE(*): _mangi'_ isn't really a horse. It's a hexapedal, slender creature
used for transportation. If this post were in Arabic, I'd translate it as
"camel" instead. ;-)


Ordinals are constructed in the opposite manner to cardinals. The number
word is prefixed, in radix form, to the noun being modified. Hence:

keopii'z3di     "the first man" (keo-, radix of "one", pii'z3di, "man")
jekreojuli'r    "the 9th house"
kekredeotaa'dri "the 12th tree" (kekre-deo- = 3*4 = 12)

Alright. We're just one more step away from deciphering the answer given
by the man/woman at the top of this message.


As some may have noticed, the system of base numbers and triads has gaps.
For example, you can't express "10", "11", "13", or "17" using that system
alone. What is needed is a way to *add* these triad multiples, in a way
similar to our decimal system (123 = 3 + 10^2*2 + 10^3*1). The triad
multiple system expresses a single "digit": 3^n*m. Now we just need to add
these things together.

In Ebisedian, additive numbers are composed from least-significant term
first, to most-significant. For example, if we wanted to express the
number 10, we could break it down as (10 = 1 + 3^2*1). We have _kei'_ for
1, and _jekre'kei_ for 3^2*1, which we can abbreviate to _jekre'i_ (3^2).
So what we do, then, is to take the stem of _kei'_, which is _ke_, add the
additive infix _3_, and then prefix it onto _jekre'i_. Thus, we obtain:
        ke3jekre'i.     [k&?@\dZ&"kr`&?i]
        "Ten" (1+9).

We can chain multiple "digits" together, too. For example, 16 decimal,
which is 121 base 3 (1 + 3*2 + 9*1), can be rendered:
        ke3kekreje3jekre'i.     [k&%?@\k&kr`&dZ&%@\dZ&"kr&?i]

Of course, you probably wouldn't hear a Bisedi say such a cumbersome word,
especially not for a small number as 16. An alternative rendering is:
        ke3kekrePei'.           [k&%?@\k&kr`&p_h&"?i]
        "16" (1 + 3^1*5).

This is possible because of the amount of overlap between the different
triad multiples. You may think of this as a base-3 system where each digit
is allowed to go up to 9, instead of being restricted to 0--2, as would be
the case in a mathematically "correct" base-3 system.

And of course, these additive numbers behave just like the other
numbers--we can make ordinals by prefixing them onto nouns, and we can
make cardinals by prefixing nouns onto them.

And thus, we can finally decipher the answers to the question given at the
top of this message:

        3Ta'gode3kekrejei.      [@\"t_hagok&?@\k&kr`&dZ&?i]
        3-      plural prefix
        Ta'go   radix of Ta'gi, masculine of _tagi'_, "finger".
        de3     additive radix of "four"
        kekre-  first triad, 3
        jei'    "two", acting here as the multiplicative factor of 3.

Hence, this word means "(4+3*2) fingers", that is, "10 fingers". Why this
odd breakdown? Mainly because the Ebisedi have two hands, and they think
it's funny to count 9 fingers and add 1. They feel it's more "natural" to
divide the fingers into 2 groups (the suffix -jei'), use the closest
triad multiple (3), and then add the leftovers (4) to the total. After
all, 2 and 4 are even numbers; 9 wouldn't be.

And on to the woman's answer:
        3tako'de3kekrejei.      [@\ta"kod&?@\k&kr`&dZ&?i]

This decomposes to:
        3-      plural prefix
        tako'   radix of _taki'_, feminine of _tagi'_, "finger"
        de3     4
        kekre   3
        jei'    2.

Why would a man and a woman give different answers? Because the Ebisedi
make a distinction between male and female body parts. The root word for
"finger", _tagi'_, is an epicene noun, which is used to refer to fingers
in general. But men have _3Ta'gi_ (male fingers), whereas women have
_3taki'_ (lady-fingers). Referring to a woman's fingers as _3Ta'gi_ could
well earn you a resounding slap, since _3Ta'gi_ are obviously not as
refined and elegant as _3takii'_. :-)


The peace of mind--from knowing that viruses which exploit Microsoft system
vulnerabilities cannot touch Linux--is priceless. -- Frustrated system


JS Bangs <jaspax@...>