> When I was a student (must have been about 1980) there was an article
> in New Scientist proposing a decimal system but with digits representing
> -4, -3, -2, -1, 0, 1, 2, 3, 4, 5 so that 16 would have been written as
> "2 (-4) ". The benefit is that multiplication tables are much fewer and
> simpler. I can't recall whether a history was given for this system.
Essentially this system was proposed by John Colson, in "A Short
Account of Negativo-affirmative Arithmetick", in the Philosophical
Transactions vol 34 (1726/7) p 161--173.
Colson's system uses the digits 0 through 9, as well as their
negatives (marked by an overbar). Colson introduces the notation,
and gives examples of translating between various representations
for some sample numbers, but then notes that one advantage of the
system is the ability to represent any number using only the
digits 0,1,2,3,4 and their negatives, thus simplifying the
multiplication process (Colson likens it to "multiplication by
inspection"). Colson ends the paper with a suggested method for
performing division in the system.
I stumbled on Colson's paper while looking for something else, and copied
it in hopes of some day having time to look for other similar material.
Sounds like the "New Scientist" is a place to start that process.
-Mark McKinzie-
mckinzie@math.wisc.edu