Friday, February 09, 2018

[bapjmsrb] Better numerals

Design some numerals for 0 through 9 so that the symbols depict the cardinality or ordinality of the number.  Best is if the value can be decoded from the visual appearance of the numeral, but next best would be if the ordering of two numerals can be easily seen visually, perhaps in complexity of the symbol.

A few possibilities:

This first one is inspired by runes.  Let 0 and 1 be special characters, represented by their current symbols, a circle and a vertical bar.  Be careful about serifs on 1.  The remaining 8 numbers, 2 through 9, are represented by a vertical bar with short horizontal lines or loops (like the letter P) hanging off of it. A horizontal line represents +1 and a loop represents +2.  The vertical bar implicitly represents a start value of 1.  There can be up to 4 loops (2 on each side of the vertical bar), signifying the digit 1+4*2=9.  This number looks like a butterfly.  The lesser digits are butterflies with fewer wings or one wing replaced by a stick.  There only needs to be at most one horizontal bar.  We should standardize the positions of the loops and the bar for each digit.

For 10 distinct digits we could do something combinatorial with 2*5.  We could also go larger and (generally) not use digits greater than 9, though they could be used for larger bases.  12=4*3, 16=2^4 look attractive.

If we special case 0, then we only need to design 9 digits, doing something combinatorial with 3*3: a stack of 2 items, each with 3 possibilities.  If we special case 0 and 1, we only need to design 8 digits, 2^3: a stack of 3 items, each with 2 possibilities.  We need to be careful that none of the combinatorial digits look like the special case digits.

We did a survey through Wikipedia of writing systems whose numerals depict the number or at least made some sense in ordering based on visual appearance:

  • Counting rods
  • Japanese and Chinese for 1 2 3 only
  • Roman
  • Aegean
  • Babylonian
  • Chuvash
  • Kaktovik Inupiaq
  • Mayan

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