Ebisedian number system (I)
|From:||H. S. Teoh <hsteoh@...>|
|Date:||Wednesday, July 17, 2002, 16:04|
After countless hours of racking my brains over Ebisedian mathematical
texts and other instances of Ebisedian numbers so kindly provided by my
informant, ;-) I finally begin to understand how Ebisedian numbers work.
Because of the potentially daunting complexity of the system, I shall
first present basic numbers and counting, and in a subsequent post, I
shall describe ordinals and cardinals.
The Ebisedian number system consists of the "basic numbers", and a series
of "triads". The basic numbers are:
For numbers 2 through 9, the 3- prefix is simply the Ebisedian plural
prefix; in compounds, this 3- is dropped. (_3_ is [@\], not to be confused
with the number "3" :-).)
So far so good. Nothing unusual here. (Except perhaps for the fact that
_y'i_ is technically a nullar noun; so does it mean "zero" or the absence
of zero? Or zero is just the absence of something, anything. :-P)
Now comes the interesting part. These basic numbers are augmented by a
system of "triads", which are based on powers of 3. The triad system lets
you count above 9, and also introduces alternative words for 3, 6, and 9.
The basic idea is that the human mind isn't very accurate when it comes to
large numbers. Hence, as numbers get larger, the unit of counting should
also get larger. (Yes, this is inspired by the system from somebody else's
conlang. You are hereby acknowledged. :-P)
Each triad represents a power of 3, and is compounded with the basic
numbers to give a multiple of that power of 3.
The first triad is _kekre'kei_, or just _kekre'i_ for short. By itself,
is represents the number 3. It is, therefore, an alternative of _rei'_.
But you can compound it with _jei'_, "two", to form _kekre'jei_. This
simply means, "two units of 3", which is equal to 6. Similarly,
_kekre'rei_ is "three units of 3", that is, 9. And _kekre'dei_ is 12,
_kekre'Pei_ is 15, ... etc.
The second triad is _jekre'kei_, or just _jekre'i_ for short. It
represents the second power of 3, that is, 9. Hence, _jekre'i_ is a third
alternative for "nine". Just as with _kekre'i_, you compound this triad
with the basic numbers to obtain the series for 3^2:
jekre'kei = 3^2 * 1 = 9
jekre'jei = 3^2 * 2 = 18
jekre'rei = 3^2 * 3 = 27
jekre'dei = 3^2 * 4 = 36
The third triad is _rekre'kei_, or _rekre'i_ for short. It represents 3^3,
that is, 27. Hence, you get:
rekre'kei = 3^3 * 1 = 27 (note: same as _jekre'rei)
rekre'jei = 3^3 * 2 = 54
rekre'rei = 3^3 * 3 = 81
You can probably see a pattern now. The basic numbers can act as prefixes
as well. As we shall see in the next post, prefixed numbers act as
ordinals. Hence, _kekre'i_ literally means "the first _kre'i_", that is,
"the first triad", i.e., 3^1. _jekre'i_ means "the second triad", i.e.,
3^2. _rekre'i_ means "the third triad", i.e., 3^3.
And therefore, _dekre'i_ means "the 4th triad", which is 3^4 = 81. Hence:
dekre'kei = 3^4 * 1 = 81
dekre'jei = 3^4 * 2 = 162
dekre'rei = 3^4 * 3 = 243
And so, by using the basic numbers, we can get up to the 9th triad,
_Kee'krei_, which is 3^9 = 19683. The 9th unit of this 9th triad is
_Kee'kreKei_, 3^9 * 9 = 177147. This is the largest number in the basic
counting system. (There are ways to describe numbers even larger than
this, but I haven't worked it out yet. :-P)
Of course, one cannot forget the ultimate triad, which is the Universal
Triad, _Pe'rokrei_. Obviously, such a triad must have a value of infinity.
:-) ((Un)fortunately, the Ebisedi have not come across Set Theory and
transfinite cardinals yet, so for them, _Pe'rokrei_ is as infinite as
anyone could hope to achieve.)
That's it for the basic numbering system. Thoughts? Suggestions? Comments?
Criticisms? Flames? :-)
(ObTeaser: in the next post, we shall consider, aside from ordinals and
cardinals, the all-important question of "how does the Ebisedi answer the
question, `how many fingers do you have'?")
Airplanes stall. Computers just hang in the air...