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Just thinking about how they work here, it looks like Roman numerals are effectively a base 5 notation, with a special behavior for 5n - 1.

In base 10 math there are 18 outcomes for adding two digits, and you have to do carry operations for 9 of them. With carries there are 20 and you have special cases for 10. In Roman numerals there are 10 outcomes, you have to do carries for 5 of them, special casing for two (4 and 9), the numbers are at least one digit longer and non uniform, so it's harder to line up the columns to do an addition in the first place.

No wonder algebra was invented in Arabic.




And I'm betting that the 5n-1 behavior was probably only used by those with education, and may have even been a class distinguishing numeric feature, with the benefit of making numerals slightly impenetrable to those who didn't know the trick.


> Just thinking about how they work here, it looks like Roman numerals are effectively a base 5 notation, with a special behavior for 5n - 1.

This doesn't seem quite accurate. Roman numerals are organised around multiples of 5, whereas a base-5 system should be organised around powers of 5.




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