Re: Numeral systems was:Re: Getting into the intro game

Raymond Brown writes:
 > Must be read in monotype font!
 >
 > At 7:36 am -0700 15/5/02, Clint Jackson Baker wrote:
 > >Siyo!
 > >Just off-hand, I know that in Ainu they use base 20
 > >and only have names for numbers up to 800 (base 10).
 > >
 > >Clint
 > >
 > >--- Jake X <alwaysawake247@...> wrote:
 > [snip]
 > >> >orthographies and non-base-10 counting, and also a
 > >> lack of skill in both
 > >> >subjects :(( .
 > >> >
 > >> Me too!!!! (ever done anything with the Akkadian
 > >> base 60?)
 >
 > In this digital age of cyberspace, shouldn't we thinking of base 64?
 >     :)
 >
 > As Father Joachim Bouvet (17th cent. missionary to China), Gottfried
 > Leibniz & Umberto Eco have noticed, I Ching hexagrams provide us with the
 > symbols:
 > - -    ---    - -    ---    - -    ---    - -    ---
 > - -    - -    ---    ---    - -    - -    ---    ---
 > - -    - -    - -    - -    ---    ---    ---    ---
 > - -    - -    - -    - -    - -    - -    - -    - -
 > - -    - -    - -    - -    - -    - -    - -    - -
 > - -    - -    - -    - -    - -    - -    - -    - -
 >
 >
 > - -    ---    - -    ---    - -    ---    - -    ---
 > - -    - -    ---    ---    - -    - -    ---    ---
 > - -    - -    - -    - -    ---    ---    ---    ---
 > ---    ---    ---    ---    ---    ---    ---    ---
 > - -    - -    - -    - -    - -    - -    - -    - -
 > - -    - -    - -    - -    - -    - -    - -    - -
 >
 >
 > - -    ---    - -    ---    - -    ---    - -    ---
 > - -    - -    ---    ---    - -    - -    ---    ---
 > - -    - -    - -    - -    ---    ---    ---    ---
 > - -    - -    - -    - -    - -    - -    - -    - -
 > ---    ---    ---    ---    ---    ---    ---    ---
 > - -    - -    - -    - -    - -    - -    - -    - -
 >
 >
 > - -    ---    - -    ---    - -    ---    - -    ---
 > - -    - -    ---    ---    - -    - -    ---    ---
 > - -    - -    - -    - -    ---    ---    ---    ---
 > ---    ---    ---    ---    ---    ---    ---    ---
 > ---    ---    ---    ---    ---    ---    ---    ---
 > - -    - -    - -    - -    - -    - -    - -    - -
 >
 >
 > - -    ---    - -    ---    - -    ---    - -    ---
 > - -    - -    ---    ---    - -    - -    ---    ---
 > - -    - -    - -    - -    ---    ---    ---    ---
 > - -    - -    - -    - -    - -    - -    - -    - -
 > - -    - -    - -    - -    - -    - -    - -    - -
 > ---    ---    ---    ---    ---    ---    ---    ---
 >
 >
 > - -    ---    - -    ---    - -    ---    - -    ---
 > - -    - -    ---    ---    - -    - -    ---    ---
 > - -    - -    - -    - -    ---    ---    ---    ---
 > ---    ---    ---    ---    ---    ---    ---    ---
 > - -    - -    - -    - -    - -    - -    - -    - -
 > ---    ---    ---    ---    ---    ---    ---    ---
 >
 >
 > - -    ---    - -    ---    - -    ---    - -    ---
 > - -    - -    ---    ---    - -    - -    ---    ---
 > - -    - -    - -    - -    ---    ---    ---    ---
 > - -    - -    - -    - -    - -    - -    - -    - -
 > ---    ---    ---    ---    ---    ---    ---    ---
 > ---    ---    ---    ---    ---    ---    ---    ---
 >
 >
 > - -    ---    - -    ---    - -    ---    - -    ---
 > - -    - -    ---    ---    - -    - -    ---    ---
 > - -    - -    - -    - -    ---    ---    ---    ---
 > ---    ---    ---    ---    ---    ---    ---    ---
 > ---    ---    ---    ---    ---    ---    ---    ---
 > ---    ---    ---    ---    ---    ---    ---    ---
 >
 > (The damn ASCIIization makes the hexagrams look tall and thin!)
 >
 > The above is the Fuxi order which is the one sent to Leibniz by Fr Bouvet,
 > and not the Wengwang order given in books which use the hexagrams for
 > oracular purposes.
 >
 > Ray.

Now this is interesting, because it resembles my own base-16 lechib
numerals in that a numeral is actually a number in binary in a
"notational subsystem".  Monospace fonts are even more important for
this than for the hexagrams:

    0       1       2       3

+-----+ +--+--+ +-----+ +--+--+
|     | |  |  | |     | |  |  |
|     | |  +  | |  +--+ |  +--+
|     | |     | |     | |     |
+-----+ +-----+ +-----+ +-----+
      |       |       |       |

   4       5       6       7

+-----+ +--+--+ +-----+ +--+--+
|     | |  |  | |     | |  |  |
|  +  | |  +  | |  +--+ |  +--+
|  |  | |  |  | |  |  | |  |  |
+--+--+ +--+--+ +--+--+ +--+--+
      |       |       |       |

   8       9       10      A

+-----+ +--+--+ +-----+ +--+--+
|     | |  |  | |     | |  |  |
+--+  | +--+  | +--+--+ +--+--+
|     | |     | |     | |     |
+-----+ +-----+ +-----+ +-----+
      |       |       |       |

   B       C       D       E

+-----+ +--+--+ +-----+ +--+--+
|     | |  |  | |     | |  |  |
+--+  | +--+  | +--+--+ +--+--+
|  |  | |  |  | |  |  | |  |  |
+--+--+ +--+--+ +--+--+ +--+--+
      |       |       |       |


Hexagrams (or "quadragrams" to give an equivalent base-16 system)
would probably be easier to draw, but these do have some advantages -
they're oriented by the "tail" at the lower right, for one thing, and
you can write them in a vertical sequence without worrying about them
running into one another.  Also, both systems here are very easy to
tamper with (if handwritten) - you can easily add a bar or complete a
broken line.  I do have a more complex, "secure" variant, which might
be more appropriate if you're writing a cheque, but it's too
complicated for me to reproduce in ASCII.  I have a PNG I'll put up
sometime.

Even the simple form above is a little hard to write fast, though.
I'm working on a handwritten variant, but I haven't had much luck
yet.