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# Harpelan number system

From: Nokta Kanto Friday, March 7, 2003, 15:24
```*delurks*

The number system postings have prompted me to post my own. Harpelan writers
count in a unique way. They count up until they're halfway there, and then
they turn around and count down until they arrive. They use a base 12
system, but their way of counting only needs symbols to represent the
numbers zero through six. There are 13 digits in total. (There is also a
special character for number 7.)

BTW, there are meanings and connotations associated with the first 8
numbers. Why amn't I ever this creative before midnight?

1: The Source
2: The Pair
3: The Fulcrum, The Thumb
4: The Edifice (Permanence and Sturdiness)
5: The Door
6: The Flower (Order and Symmetry)
7: Chaos
8: The Whole, The Universe (8=1+7)

I will write the digits as 0, 1-, 1+, 2- ...etc.., 5-, 5+, 6-, 6+

Counting from 12 to 24 goes like this:
1+ 0
1+ 1+
1+ 2+
1+ 3+
1+ 4+
1+ 5+
1+ 6+
2- 5+
2- 4+
2- 3+
2- 2+
2- 1+
2+ 0

The 1+ digit indicates that progress is relative to 10 (base 12). When it
gets to 2-, counting switches to track progress relative to 20 (base 12). A
writer of Harpelan would find it just a little bit odd using our system when
transitioning from 199 to 200: it would feel like a huge leap, because
anything starting with one-hundred would feel closer to one-hundred than
two-hundred.

Once you reach seventy-three, counting goes by subtracting from 144 (base 10):

69:    6- 3+
70:    6- 2+
71:    6- 1+
72:    6+ 0
73: 1- 6- 1+ (That's 144 - (72 - 1) = 73)
74: 1- 6- 2+
75: 1- 6- 3+

The number system also distinguishes between cardinals and ordinals:
Cardinals always use augmented (+) digits for the final digit, while
ordinals use diminished (-) digits. (Ordinals for computers are written with
an augmented digit, though; this acknowledges the off-by-one problem. Array
element 5 is 5+, although it is actually the sixth (6-) element.) I'm still
trying to work out how to do arithmetic in this number system.

So, is anyone willing to write 2003 in this system?

----
"Everyone's different, except me." --Noktakanto
```