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Except for the Super Bowl logo, the only place most of us see Roman numerals these days is on clock faces, like this one atop Nashua City Hall, taken on Feb. XXVII, MMXII.
Monday, January 30, 2012

Roman numerals are interesting, not just for making a football game look pompous

David Brooks

EDITOR’S NOTE: This column originally forgot about “D”, the character for 500 - the sentence has been corrected.

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Not being what you would call a football fan, I’m not too excited about the Super Bowl – except for one thing: those awesome Roman numerals.

Admittedly, “Super Bowl XLVI” is a tad pretentious, not to mention anachronistic.

This is the computer age, so why doesn’t the NFL use binary numbers? “Super Bowl 101110” sounds pretty good.

They could even try hexadecimal, although I admit “Super Bowl 2e”, as in (2 x 16) + (1 x 14), is a little weird.

Regardless, from a mathematical point of view, Roman numerals are cool.

They represent the last, greatest gasp of humanity’s original counting method of additive tallying, with the extra benefit of incorporating the only subtractive-tallying method developed in human history. How can you not like that?

Sherley Blood, who as Latin teacher at Nashua High School South deals with Roman numerals more than most people, does like them. She also pointed out another advantage.

“I have a great set of Roman numeral birthday candles, which at a certain point get very useful. It kind of disguises it and makes it looks important,” she said.

The history of Roman numerals is a little iffy, but they most likely grew out of variations of tally-mark counting used by the Etruscans, who preceded Rome in parts of the Italian peninsula.

Tallying was humanity’s original counting method: Make one mark on a stick or bone or rock for each sheep in your flock.

Over time we needed bigger numbers, which led to separate symbols for certain accumulations of tally marks: usually 10 or 20, based on fingers and toes, but sometimes weird ones like 60, favored by the Babylonians. (Their preference lingers in our minutes-per-hour and degrees-in-a-circle measurements.)

Over time, the Romans decided on seven characters for various values: the familiar I, V and X, plus L (50), C (100). % (5o0) and M (1,000).

They still used tallying, however: 10 is X, 20 is XX, 30 is XXX.

This system is simple but makes arithmetic difficult, since a number’s length is not related to its value. Try multiplying “LXVIII times CX” on a piece of paper. I guarantee you’ll get lost, whereas multiplying “68 times 110” is a snap.

The coolest thing Romans did, however, was invent subtractive tallying.

Tallying number systems are additive. Every time you place a new character onto the number, you add that character’s value. For example, C is 100, while CX is 100 plus 10, and CXI is 100 plus 10 plus 1.

As a shorthand, however, Romans eventually decided that if you place a character to the left of a larger-valued character, you subtract its value rather than adding it.

Consider XLV, as in Super Bowl No. 45. An “I” to the right of “V” makes it today’s XLVI or 46 (additive tallying), but an “I” to the left of “V” makes it 2010’s Super Bowl XLIV or 44 (subtractive tallying).

Why do this? Perhaps because XLIV is easier to chisel onto a marble plinth than XLIIII (or XXXXIIII).

Blood, the South teacher, hypothesizes that this may have sprung out of Roman calendars, which name certain days each month by their relationship before, rather than after, festival days. For example, March 11 was called the Latin version of “five Ides” because of its position before the famous Ides of March.

That’s a really interesting idea. Whatever the reason, to my knowledge, no other civilization ever used this subtractive tallying. Romans stand alone.

The system did last for the better part of a millennium, but faded with the development of positional numbering in a fixed-base system, which we now think of as the only way numbers can exist.

Positional systems are not only easier for calculation; they let a few characters (0 through 9 for most of the world) to take on an infinite numbers of values. Try writing 1,234,567 in Roman or Babylonian or ancient Egyptian numerals: It basically can’t be done.

Combined with the ancient Hindu invention of the numeral zero as a place-holder, and its adoption by Arabs who taught it to Europeans, the system created the modern number system that underpins all of modern life.

The ancient Greeks came pretty close to inventing calculus, but their clumsy method of numerical notation got in the way. If Hindu-Arabic numbering had existed in 5th century B.C. Athens, history might be very different.

And that’s the reason Roman numerals are limited to Super Bowls, copyright dates on movie trailers and the occasional clock face. They’re cool, but not really useful for the modern age.

And I say that as somebody who recently turned LVI.

Granite Geek appears Mondays in the Telegraph, and online at www.granitegeek.org. David Brooks can be reached at V-IX-IV-VI-V-III-I or dbrooks@nashuatelegraph.com.