Why is 8 in Roman numerals VIII, when IIX is shorter?

by tombojuggles
Jooseman

Those standard Roman Numerals, with the subtraction rule (such as IV and IX, where the smaller value letter to the left of a larger value one is subtracted) is a much more recent invention than you may think. It was created as a way to standardise (It's not an official thing, but it's the most common modern usage) Roman Numerals, and has a few rules for it.

  1. The subtractive numeral to the left must be I, X, or C. The 'five' numerals V, L, and D cannot be used. M cannot be used because it is the biggest numeral anyway.
  2. The subtracted number must be no less than a tenth of the value of the number it is subtracted from. So an X can be placed to the left of a C or an L but not to the left of an M or a D. The correct way of looking at this rule is that each power of ten is dealt with separately. So 49 is XL IX (without the spaces), not IL.
  3. Only one smaller number can be placed to the left. So 19 can be depicted XIX but 17 cannot be written XIIIX or IIIXX

So the reason that it's not IIX is to keep it standard, and much less complicated. That's one of the reasons why they had to standardise it with the subtraction rule, to keep writing dates in it much more simple (as well as to prevent confusion, as many dates of the same year have been written differently)

Usage in Ancient Rome however, was nowhere near this standardised. While this Subtraction rule was used in Ancient Rome, it was much more of an alternative practise, so for example, they would mostly write IIII, or VIIII instead of IV and IX. You can even see this carry over in certain clocks today, using Roman Numerals, where IIII is used for 4.

The Romans however, did definitely seem to have a preference for not using the subtraction rule, preferring IIII and VIIII, however they would use both, sometimes even within the same document (now you see why they wanted a more standard modern way.) An example of this is on the numbered entrances to the Colosseum. The numbers do not use the contraction IV or IX. This means that arch 29 is XXVIIII and arch 54 is LIIII, however, the contraction for 40 which is XL, is used.

Occasionally they even use double subtractions (like you said in your question) in Ancient Rome, for example IIXX instead of XVIII, and sometimes even V and X isn't used, so 6 would be IIIIII.

So to sum up your question, it's VIII to keep with standard rules in place, however they didn't follow these in Ancient Rome consistently.

Sources

http://www.web40571.clarahost.co.uk/roman/howtheywork.htm (With more examples of what I've been saying)

http://dmaher.org/Publications/romanarithmetic.pdf (If you wish to know more about Roman Arithmetic)

A Guide to Ogam (More about the Ogam language/Alphabet, however there is a comparison with Roman Numerals.)

http://www.storyofmathematics.com/roman.html

xaliber

You might want to try in /r/linguistics, perhaps