Counting Before and After

Dr. Burton got really excited about numeral systems in class today, and while many of us mentioned the images of the counting systems for our civilizations, no one created has a post about it (actually, it probably wasn't ever directly related to what we were talking about, but whatever). Since we all have at least a little familiarity with Roman numerals, and because numbers were important to the Romans, I figured I'd do a brief post on them.

Here's a list of the different numerals the Romans used:

1: I
5: V
10: X
50: L
100: C
500: D
1,000: M

When the Romans wrote a number, a smaller number followed by a larger number meant to subtract the first (hence they counted "before" and "after," lending my post a pun for its title); thus IIX (or 2 and then 10) is 10-2=8. When the larger number comes first, it means add; thus LI is 50+1=51. Sometimes you have to do more than one operation, such as if you had XCVI, or 10, 100, 5, 1. Thus we would start with the biggest number (100), subtract the numbers that come before, (100-10=90), and add the numbers that come after (90+5+1=96).

The Romans also had a system for fractions. For every part out of 12, they would use one dot. Once they got to 6 (1/2), they used an S and then kept adding dots for 7+. Interestingly enough, there is no subtracting here, only simple counting with a S for 1/2. Fractions were often used in Roman currency.

When the need for larger numbers came in the Middle Ages, people began putting a line above a numeral to mean "that many thousand" and lines on the top and both sides to mean "that many hundred thousands."

Numbers were important to the Romans because they did so much innovative engineering, which required numbers. They also did things like make concrete, where they would have to record what percentages of each material to add. Also, like I discussed in a previous post, they needed numbers to make maps.

Interesting Facts:
Roman numerals are still used today for recurring events such as the Superbowl.
They are also still used for monarchies (the Queen of England is Elizabeth II).
Using the standard numerals up to M, the largest number one can create without repeating a number is MDCLXVI, or 1666. A lot of Europeans thought the world was going to end in 1666, and this may have been part of the reason they thought such ("666" in Christian myth was probably a larger reason, but I thought this little tidbit interesting and hadn't actually thought of it until I wrote the numeral out).
The Roman army was organized based on their number systems. A Legionnaire would contain 1,000 soldiers, the equivalent of the letter M. Like M was the highest numeral typically used, there weren't typically ever more than 1,000 soldiers under a single man's command. A Centurion would command 100, based on the letter C. You wouldn't have random numbers like 867 (DCCCLXVII) men in a company; it was always a nice, single numeral.
Using only four numerals, the highest number that could be reached would have been MMMM, or 4,000, but we can make 9,999, which is almost 2.5 times the value.
The Romans had no symbol for zero, but they understood the concept and used a word for it.
The Romans apparently had no way to show negatives even though they showed subtraction.