5 ms·

The idea is a lot older than Al-Khwarizmi: positional base-60 fractions were already used by the Babylonians in *2000 BC*.

• ithkuil 3y ago
  Babylonians did indeed use positional notation. But they didn't use the "point" to separate integral and fractional parts of a number. Moreover they didn't even write zeros to indicate an order of magnitude! You just had to know the right scale out of context I'm going to write the numbers in base 10 just for simplicity (they used base 60 which has many more divisors and works much nicely): Numbers 20, 200, 2, 0.2 and 0.00002 would be written simply "2" The reciprocal of 2 would be 5 The reciprocal of 5 would be 2 If that doesn't seem to make sense, let's just reassert that a given "spelling" of a number actually represents infinite numbers: a base and a free "scale" parameter. Thus 5 is also 0.5 The reciprocal of 0.5 is indeed 2 and thus it works. It's like a kind of "modular" arithmetic but for scale. I know that it allowed them to consult tables with reciprocal numbers which helped them to actually perform divisions using just multiplication. I don't know what method they used to keep track of the scale. Was it some kind of out of band "context" or just using common sense to guess the magnitude of the result?