Q. I’ve always been curious: How in the world did Roman kids ever learn to do arithmetic with their system of letters as numbers?
— B.N., of O’Fallon
A. With even our cheapest calculators able to manipulate huge numbers in a fraction of a second, working in the Roman system at first glance does seem to border on the impossible.
As you know, instead of numbers, you have seven letters: I, V, X, L, C, D and M. But that’s just the start of your headaches. Remember, while our system sets places for tens, hundreds, thousands, etc., to make them easier to read, Roman numbers are just long strings of those letters. And, because of that, the Romans had no need to invent a “zero.”
Yet while awkward and cumbersome by our standards, doing simple math in the Roman system really was in some ways easier than our own, argues Dr. Lawrence Turner at Southwestern Adventist University in Keene, Texas. The problem may be that you’re thinking about it like a young child often begins learning a foreign language. Instead of, say, picturing a book in his mind when he reads “Buch” in German, he translates the word into English and then pictures the book.
That’s the way you’d probably approach a Roman arithmetic problem now. For example, you’d convert CXII plus LXI into 112 plus 61 to get 173, which you’d then reconvert into CLXXIII.
But, remember, the Romans couldn’t do it that way. They didn’t have our Arabic figures to fall back on. If you’re going back to old Rome, you have to do as the Romans did, as they say. So with Turner’s aid, let’s see if I can help you start to become letter-perfect in Roman numeral math:
As it turns out, addition is actually rather simple. You don’t have to memorize that 9 plus 9 is 18 and you have to carry the one. You simply write the numbers together and simplify.
Ready to try one? Let’s say you want to add CCCLXIX and DCCCXLV. First to make things easy, you’d “uncompact” the IX (9) and XL (40) into their equivalents: VIIII and XXXX. That would give you CCCLXVIIII and DCCCXXXXV.
Next, you would simply combine all the letters and group similar ones together, giving you DCCCCCCLXXXXXVVIIII. Finally, you’d simplify, turning the five C’s into a D, the two D’s into an M, the five X’s into an L, the two L’s into a C, the two V’s into an X and the IIII into the alternative IV. So, your final answer would be MCCXIV. Sure enough, if you translate the problem, you get 369 plus 845 equals 1,214.
Yes, you’d probably need to stock up on your lead pencils, but it really doesn’t seem terribly difficult once you remember to expand and later simplify the shorthand for such numbers as XL (40) and IV (4). It would be the same process for adding three or more numbers at a time — although I certainly would not want to be a checkout clerk at an ancient Roman Walmart during the Saturnalia season.
Subtraction would be addition in reverse, in which you’d cross out similar letters rather than combining them. So, let’s say you had CXXIX minus XLIII. Again, you’d expand it to LXXXXXXXVIIII minus XXXXIII. From both numbers, you’d cross off four X’s and 3 I’s to wind up with LXXXVI, proving that 129 minus 43 does indeed equal 86 in both numerical systems.
As you might imagine, multiplication and division are somewhat more complicated, but they, too, are doable. However, since I’m running short of space, I’ll let you explore Turner’s page at turner.faculty.swau.edu/mathematics/materialslibrary/roman/ for the details if you’re interested.
“Did the Romans actually calculate using these exact procedures?” Turner asks finally. “Probably not. They may have utilized shortcuts and other schemes. However, the above processes do perform the arithmetic operations by manipulating the symbols of the Roman written values directly without first converting them to our decimal representation.”
“In many respects these Roman procedures are easier than the corresponding ones for ordinary numbers since they involve only processes such as catenation, arranging the symbols in order, grouping symbols, borrowing, and crossing out.”
What was the name given to the only child born during the historic voyage of the Mayflower in 1620?
Answer to Sunday’s trivia: When Frankie Baker shot Allen Britt during a lover’s quarrel in 1899, she had no idea that her act would be immortalized in a song that remains popular to this day.
It was 2 a.m. on Oct. 15 when Britt reportedly came home to their apartment at 212 Targee St. near Union Station in St. Louis. He had been to a cakewalk, where, as the story goes, he and Nelly Bly (aka Alice Pryor) had won a prize in a slow-dance contest.
Likely furious, Baker, 22, shot her 17-year-old lover in the stomach, and he later died. At her trial, Baker claimed he had threatened her with a knife, and the jury acquitted her on grounds of self-defense.
Today such killings usually make a splash in the headlines only to fade from memory in a week or two. But this one prompted St. Louis songwriter Bill Dooley to compose “Frankie Killed Allen” soon after the killing. Perhaps because “Allen” just didn’t have the right musical ring to it, Hughie Cannon — who also wrote what eventually became “Won’t You Come Home, Bill Bailey?” — published the music to the original version of “Frankie and Johnny” in 1904, just in time for the St. Louis World’s Fair.
For the record, the song has been linked to other murders, and some say it predates the St. Louis shooting, but other historians pooh-pooh this idea. Baker died in 1952 in a Portland, Ore., mental institution when she was about 76. To see her picture, go to www.slpva.com/historic/police212targee.html.