The Super Bowl approaches. And with it come three symbols seen everywhere: LII.
Most dramatically sculpted in ice on Nicollet Mall, LII is of course 52 written in Roman numerals. Although these numerals were once the way a vast civilization wrote all of its numbers, in the modern world most people only encounter them at Super Bowl time.
We should all be grateful for the reason why: Roman numerals were replaced by the far superior number system we use today, without which computers and much of modern technology would not be possible.
While writing Roman numerals can be unwieldy — think of MCMLXXXVIII for 1988 — what really makes them pale in comparison to our present number system is their lack of place values. In the number 1988, for example, the 1 stands for one thousand because it is in the fourth position (counting from the right), while in 156 the 1 stands for one hundred because it is in the third position.
By contrast, the two Xs in XI and XVI both represent 10, even though they occupy different positions.
This difference makes addition and multiplication dramatically more difficult with Roman numerals. We can add 45 and 32 with two simple computations: add 4 and 3 and put the result in the second position, then add 5 and 2 and put the result in the first position. We get 45 + 32 = 77.
Now try doing the same computation in Roman numerals: XLV + XXXII. It’s a mess.
What does this mean for practical applications? Computers rely on being able to represent every piece of data as a number, and every number as a string of 0s and 1s. Additionally, this must be done in a compact way that allows for easy storage. That would have been quite challenging for the Romans, both because they often required lots of symbols to represent relatively small numbers (such as 1988), and perhaps more fundamentally, because they didn’t have a numeral for zero.
Computer software also takes advantage of quick addition and multiplication operations offered by number systems with place values (as in the case of 45 + 32 = 77).
In short, even if they’d had the right technology, the Romans couldn’t have built a functioning computer because of their number system.
While we’re busy appreciating the hidden genius of our number system, we should take a moment to be thankful to some of those who gave it to us. First come the Babylonians, who more than 4,000 years ago used a number system with place values. However, rather than 10 possibilities for each digit, they had 60! They too had no symbol for zero, but simply left a space in their numbers when required.
Next, we should pay homage to the civilization in India in the first few centuries AD; they gave symbolic form to the concept of zero, and shortened their list of allowable digits to 10.
Then let us thank the House of Wisdom in Baghdad, an intellectual center where the great Persian mathematician al-Khwarizmi (from whose name is derived from the word “algorithm”) wrote a text around 800 AD that spread the Indian system throughout the Middle East and North Africa.
Finally, let us be grateful that a medieval Italian diplomat was assigned to a post in what is now the Algerian port of Bejaia. His son, known today as Fibonacci, grew up curious about mathematics and the ideas that surrounded him on the south shore of the Mediterranean. Fibonacci returned to Italy and in 1202 wrote a hugely influential book containing a description of the number system he learned of in Bejaia.
The number system we use today had arrived in Europe, and with it the foundations of modern computing and technology.
So as the Super Bowl buzz builds this week, be grateful that no one thinks of the game as being held on Feb. IV, or of each quarter as being XV minutes long.
Rafe Jones, of Eagan, is associate professor of mathematics at Carleton College.