On 2 November 2016 at 20:47, Benjamin Atkinson <benjamin.atkinson@gmail.com> wrote:
We understand the Klingon number system was originally ternary, but was decimalized to facilitate communication with other civilizations. Might we report units of 'uj' as 0.1 uj, 0.2 uj, etc?
Note that while the original Klingon counting system is ternary, it's *not* a base-3 positional system (which you seem to have assumed) but a 3-adic one. To quote The Klingon Dictionary, "Counting proceeded as follows: 1, 2, 3; 3+1, 3+2, 3+3; 2×3+1, 2×3+2, 2×3+3; 3×3+1, 3×3+2, 3×3+3". Note that 6 (decimal) is *not* "20" (i.e., 2×3, which is what it would be under a base-3 positional notation), but rather "13" (i.e., 1×3+3, which is what it would be in 3-adic notation). Similarly, 9 (decimal) is not "100" (1×3×3), but "23" (2×3+3). Under such a system, the fractional units would *not* be written as 0.1, 0.2, etc. I believe they would be 2'3.1, 2'3.2 in the quote notation (https://en.wikipedia.org/wiki/Quote_notation), though you should check my math. -- De'vID