[jacobolus]

Roman numerals are profoundly misunderstood by most people today, whose main knowledge about them is that various authority figures use them as an example of an awkward and cumbersome precursor to Hindu–Arabic numerals, backed up by a slight bit of personal experience learning to encode/decode Roman numerals, which is difficult because nobody today has any substantial amount of practice at it.

Roman numerals are a recording tool, not a calculating tool. Romans did calculations using pebbles or other counters on a counting board. Roman numerals are just a way of recording the state of a counting board before/after performing some algorithm. The goal of them is to be as direct and faithful a record of the counting board state as possible.

[WalterBright]

> Romans did calculations using pebbles or other counters on a counting board.

I think you just made my point :-)

Have fun doing long division that way.

[jacobolus]

You can do long division just fine on a counting board, though it is unclear if people had developed something like the modern elementary school division algorithm 2000+ years ago.

We don’t really know much about people’s calculation algorithms, because they were an oral tradition not written down, and only a very small number of counting boards (e.g. made of marble) survived; others were presumably made of leather, wood, cloth, lines scratched in the dirt, ....

Japanese soroban experts handily beat westerners at doing division, in both speed and accuracy. There is no reason to believe that calculation experts of the ancient world would not have been comparably competent.

[WalterBright]

> You can do long division just fine on a counting board

I searched around a bit, and didn't find much of anything you could do with a counting board beyond division.

[mlyle]

Counting boards / the abacus are about as good as you get for calculating methods until mechanical calculators and logarithmic slide rules. So it's not really fair to say the Romans had a disadvantage here when no one had anything better. (Granted, the wire abacus was faster than counting boards / jetons).

[ghayes]

Wouldn’t a slide-rule be a similar modern day approach?

[jacobolus]

An (analog) slide rule is a whole lot faster than doing digital arithmetic. But it’s approximate, yielding about 3 digits of precision, or maybe 4 digits on a large slide rule.

With an abacus or with written numbers, you can get 10 digits of precision (or 50) if you are willing to put the work in.

[mlyle]

You can iterate slide rule calculations to get more precision, too... You're not restricted to the width of your abacus nor the number of sigfigs you can get in a single slide rule calc..

[yjftsjthsd-h]

That's genuinely interesting, but doesn't really change that it's a terrible system for abstract calculations.

[edanm]

This is not the first time I've seen you writing about this on HN.

Do you have a good source to read more about this? Both about the distinction you're making (recording vs. calculation) and in general about historical capabilities around them? I'm very interested in learning more!

[DonaldFisk]

The Romans also used the abacus for numeric calculations: https://en.wikipedia.org/wiki/Roman_abacus

[Koshkin]

Yes, and in fact it was a seminal discovery that one can calculate (‘calculus’ means ‘pebble’) by manipulating symbols.