How do Roman Numerals Work?



In: Mathematics

It’s just a different symbolic representation of numbers. It “works” in the sense that you can scratch some symbols into the dirt or write them on paper and another person who understands the system will understand the quantity/number you’ve written.

There’s nothing special about the (0,1,2,3,4,5,6,7,8,9) base 10 system we use. We could just as easily count with fewer symbols. Computers count with only two (0,1). Roman numerals use a different paradigm of counting, is all.

I, II, III, IV, V, VI, VII, VIII, IX, X, and so-on. Arabic numerals (0-9) are thought to be easier to work with for a bunch of reasons, but again, using roman numerals is just a *different encoding scheme for the same kind of information*.

The Roman numerals were based on the tally system. At the time numbers were mostly used for counting. For example how much grain is in this storage room? How much bread do the army need every day? And so on. So they would start writing a line in the sand or on the parchment for every item they counted. However this would become quite tedious. So instead they would count using the fingers on their hands and then just write a V for every hand. But this still made it difficult to count an entire army. But they could just line their soldiers up in groups of ten and count every group, for this they would write an X. And so on they would have symbols for 50, 100, 500, 1000 and so on. Later on, after the roman period, there were a few more concepts added. Firstly the numerals had to be written in descending order. This was practiced before as well since this made it easier to write. If you had XXXII soldiers it meant that you had three groups of ten soldiers and then a group of two soldiers which is a natural way to write things. Secondly you had to use the largest numerals possible to write the number. So if three soldiers came strangling you could not just add them to the tally to get XXXIIIII but would have to erase your two last tallies and write XXXV. A third concept that were added was that you could subtract one from the count by adding the lesser numeral in front of the larger. So instead of writing VIIII you could write VIV.