Episode 139: January 25, 2013
Real World Math
by Jason Marshall
If you take a close look at the world, you’ll find that you’re surrounded by ancient history. There are lots of great examples of this, but today we’re going to talk about one example in particular that’s near and dear to my—and hopefully your—mathematical heart: Roman numerals. These ancient numbers can still be seen all over the place—on signs, clocks, monuments, and even in movie credits! But who came up with this number system? Was it really the Romans? How exactly does it work? And why is it still used for certain things? Stay tuned because those are precisely the questions we’ll be answering today.
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Where Do Roman Numerals Come From?
The story of Roman numerals actually begins way back in the distant past alongside the story of the so-called tally-bones that we talked about in the last episode called How to Add and Subtract Like an Egyptian. As you’ll recall, the story of tally-bones begins at least 30,000 years ago when people began making notches in bones as a way of counting. The problem with this method is that it doesn’t work well for large numbers since it’s tough to tell at a glance exactly how many notches you’ve carved. So, long ago, a tally-bone carver had an ingenious idea to make every fifth notch in the shape of what many centuries later would look like the letter “V.” This clever change meant that you could now quickly count-up most of the notches on a tally-bone by counting groups of 5—something like “5, 10, 15, 20, 21, 22” instead of counting each individual notch up to 22. Much faster!
But these clever carvers didn’t stop there. For every tenth notch, they decided to make a cross-cut in the shape of what would eventually become the letter “X.” That way they could not only count by fives, they could also count by tens. For example, whereas the number 12 would look like
I I I I I I I I I I I I
in the original system, these clever new carvers would instead “write”
I I I I V I I I I X I I
The beauty of this change is that you can ignore many of the marks since the “V” and the “X” tell you at a glance how many notches come before them. If you think about it, you’ll realize that with this new system, many of these symbols don’t need to be written at all. In the case of the number 12, all of the symbols before the “X” can be completely ignored. If we do that, we’re left with the symbol
which, you may recognize, is precisely the Roman numeral for 12!
So that’s where the symbols that would eventually become Roman numerals came from…not from the Romans themselves, but from their ancestors. Or at least that’s what a lot of people think happened. In truth, there’s no way to know for sure if this is what really happened since this all took place a long, long time ago. But it certainly seems plausible to me.
How to Read and Write Roman Numerals
Now that we know where Roman numerals came from, let’s talk about how the Roman numeral system works. Fortunately, you only need to know a few things to become a Roman numeral expert. First, you need to memorize the 7 symbols commonly used today and the quantities they represent:
I = 1
V = 5
X = 10
L = 50
C = 100
D = 500
M = 1,000
Second, you need to know that just like in the Egyptian hieroglyphic system, numbers are written by combining symbols together. For example, the number 3 is written “III” (since that’s 1+1+1), the number 7 is written “VII” (since that’s 5+1+1), the number 61 is written “LXI” (since that’s 50+10+1), and so on. The last thing you need to know is that if a smaller value is written before a larger value—something like “IV” where the symbol for 1 is written before the symbol for 5—that means that the smaller value should be subtracted from the larger value. So “IV” represents 5 – 1 = 4 and “IX” represents 10 – 1 = 9.
You only need to know a few things to become a Roman numeral expert.
While those are all the rules you need to know to read Roman numerals, there are some things that can trip you up when writing them. For example, should the number 1999 be written MCMXCIX? Or can it be written much more simply as MIM instead? If you think about it, you’ll see that given the set of rules we’ve learned, these are indeed both perfectly valid ways of writing 1999. So which is right? Well, I’m not sure if one is more correct than the other, but I am sure that the first way has become the standard way of doing things.
Are Roman Numerals Still Used Today?
But why should you bother learning to read and write these archaic symbols in the first place? Hasn’t this system been abandoned in favor of our modern decimal number system? Well, yes…and no. As I mentioned at the beginning of this episode, Roman numerals still show up all over the place in the modern world. I’m not sure exactly why this is, but from the numbers on the faces of clocks to the inscriptions on monuments, buildings, and bridges; from the page numbers in book introductions to the cryptic years that roll by during movie credits; and from the names of Kings and Queens throughout history to many symbols used in math, science, music, and countless other places, we are surrounded by Roman numerals. And, as such, it makes sense to know exactly what all of those symbols mean!
Okay, that’s all the math we have time for today. Remember to become a fan of the Math Dude on Facebook where you’ll find lots of great math posted throughout the week. If you’re on Twitter, please follow me there, too. Finally, please send your math questions my way via Facebook, Twitter, or email at email@example.com.