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I think it's a fair point that the reason dividing MCMLXVI by XXXIX seems daunting is mostly due to lack of familiarity with the notation. Roman numerals jump u

I think it's a fair point that the reason dividing MCMLXVI by XXXIX seems daunting is mostly due to lack of familiarity with the notation. Roman numerals jump up in value by factors of 5 then 2, which is 10, so translation to/from base-10 Arabic numerals can be done inline... assuming you ignore the god-awful reverse-order-means-subtraction rule, and the fact that you don't have any letters for fractional numbers or huge numbers. The post seems to imply you can't do the doubling algorithm with Arabic numerals, but of course that's wrong. It also associates roman numerals with abacus computations, which is probably historically sensible, but to me the columns of the pictured abacus are literally base-10 positional notation and so more akin to Arabic numerals. For the abacus to "really" be like roman numerals, you'd have to remove one bead from each section of the pictured abacus. Representing four (or one, for the top sections) would be done by moving a bead to the next grove in sequence. You'd be able to tell it was a bead from the previous section because every section would be required by law to use a different kind of bead.

jacobolus 10y ago
It’s not clear how much the “hand abacus” pictured, with its sliding counters in grooves, was used in practice. Most calculations in Roman times were probably done with a free-form counting board with some kind of tokens (for instance “calculi”, i.e. pebbles). We don’t have a lot of surviving evidence though, since a wood/cloth/drawing-on-the-ground counting board with pebbles for counters isn’t exactly the most permanent artifact. The way such counting boards worked in Europe in the Middle Ages was to put pebbles on horizontal lines representing powers of ten, or in the spaces between the lines representing five times some power of ten. The Roman ones probably weren’t too different.

jacobolus 10y ago

It’s not clear how much the “hand abacus” pictured, with its sliding counters in grooves, was used in practice. Most calculations in Roman times were probably done with a free-form counting board with some kind of tokens (for instance “calculi”, i.e. pebbles). We don’t have a lot of surviving evidence though, since a wood/cloth/drawing-on-the-ground counting board with pebbles for counters isn’t exactly the most permanent artifact. The way such counting boards worked in Europe in the Middle Ages was to put pebbles on horizontal lines representing powers of ten, or in the spaces between the lines representing five times some power of ten. The Roman ones probably weren’t too different.