into the idea. We still use a their number system today for time and geometry.
One of the things that I found amusing/odd was that even though they had a complex positional
numeric system their individual "numerals" were still little more than just tally marks which was
quite oddly base ten.
Here's what it looked like:
For at least one of my conlang/concultures I'd like to have a similar system and I wanted to create
my own version of it.
On top of that there were two other questions I'd like to have some sort of answer for:
- What if a similar system had stayed popular and developed over time much the way the
Western Hindu-Arabic numerals I grew up familiar with? - What might hand-counting look like for cultures that use this system?
remembered the binary counting system.
Demonstrated here:
I found that was a good start, 31 was an odd number though so I thought about how
to make that make sense in relation to what I know of other hand counting systems.
I reasoned that starting with the index finger made sense and would bring the count
down to an even 30, totally 60 between both hands.
To explain further here is how you count on your fingers in this numeric system I'm working on:
- Single index finger
- Index finger and thumb
- Middle finder alone (we'll assume there's no cultural stigma attached to this gesture, at least not in the counting position)
- Middle finger and thumb
- Middle and index finger
for 1 its just the index finger as you would do finger counting in the American style and
being a single finder, 2 being the index and thumb gives the same 2 gesture used in most
of Europe being two fingers, and 3 is the third finger alone. I feel these attributes make
it a bit more mnemonic and intuitive, if less consistent than the original binary system.
In my studies of numeric systems I've noticed that the first 3 numerals tend to be the most
recognizable across cultures so I apply a similar metric to these numbers.
Satisfied that I could count on my fingers up to 60 I suddenly had this suspicion that
something about the hand-counting mechanism seemed like it could provide a useful
metaphor for the numeral script.
Again I started with rally marks. Now neither I nor my conculture uses clay tablet styluses,
so we don't get the cool little pointy triangle shape, instead I started with basic tally lines
grouping them by twos - since every other number I had to put down a finger in the
counting system I figured I'd just conceptually cross it off, like this:
The up/down motion of the lateral beam came naturally as I tried to avoid munging up the
lines so they could be clearly read. An advantage of this system is that it allows you to
count by twos and fours, and 12/60 are multiples of two and four, so that's nice.
It's essentially a base 2/4 system this way, which isn't radically different than the
base 5 tally system I was taught to use as a kid.
I thought I'd take it a step further and instead of crossing every other number,
I'd cross on groups of three, like so:
This was nicer because it is easier to group larger numbers together each "character"
was either 1, 3, or 6 by nature. So we're getting closer to something usable.
Still, perhaps its because I'm mildly dyslexic, I find the readability of such characters
pretty low, so I wanted to distinguish the groups further without adding much to the
overall amount of effort and leaving it as a tally system. I thought the low/high beams
were something interesting and I wanted to enhance them a bit, make them visually
distinct and easier to identify, here's what I came up with:
The tallies work the same as before, the flourishes are just a little more elaborate to
aid visual distinction and now we can actually count by 12s! The first character is 3,
the second 6, the third 9, and the last 12.
Now I want to have standalone representations of the numbers in order to have
individual numerals for each number we need to represent. In this endeavor I
took the above symbols and simply added ticks to them to give the final number,
but grouped together inspired somewhat by Chinese characters. Here is the result:
The above image is too wide and is cropped by the forum, here's the full view if you want to see it all.
The next phase is to bring the numbers into a full fledged positional system and
grow beyond the glorified tally mark phase. However, if we are to convert this
into a true positional system, we won't really be needing the symbol for 12 so it'll
become archaic and only used for tallies. It's little more than clearly a doubled 6
anyway, so its not a huge loss.
Now we need to do some serious simplification in the same way that early letters
underwent transformation from their logographic representations into more
abstract letters. The first thing I thought to do was drop as much of the
repetitive information as possible and bring out the features of each glyph
that make them easier to disambiguate. Here's my first pass "early numeral" system:
Again too wide, here's the rest.
You can see the 3 and 4 as well as the 6 and 9 aren't terribly different. You can see
they're positionally all over the place as they're in the same locations as the
distinguishing characteristic, I'd assume this would quickly even out.
Pondering this format for a while I tried at a more mature version as seen here:
Full view here.
I'm still not thrilled with the character for 6, but overall the system is beginning to
remind me a bit of Hieratic script or maybe something else I can't put my finger on
just now, if you can think of it, let me know.
Overall I like the direction things are going with it, I might try to do without the
tall characters and fix the weirdness of the 6 and 10 glyphs but I think this is a
fairly solid basis with which to work with.
In many cultures the numeral system is distinct from the language both in form
and appearance. Even though this might look a bit like letters, be assured that
the writing systems for the associated languages and cultures would be distinctive.
Some questions for the reader:
- Any thoughts or impressions on the approach I've taken here?
- Are my images too large, should I spend the extra time to scale them down before posting?
- Say you started from the 3rd stage of "grouped tallies"
would you take a different approach than I to progress the numeral system after that? - What do you think of the practicality of the tally system?
- How do the aesthetics strike you?
(people's opinion vary a lot in this regard, I understand, but it is a sin to lack any sort of aesthetic at all) - Other ideas or comments? General observations?
- Edit: Also, let me know if this is the incorrect place or format, I've been reading the forums but not posting much and haven't quite nailed down the local conventions.
