My old friend The Man Who Knew Arithmetic was not, of course, a mathematician. All the mathematicians we ever met were terrible at arithmetic -- and most of them were, in a sheepish kind of way, proud that they were terrible. The further we went in school, the farther into abstruse math we got, the more likely we were to have a teacher who would ask the class, two or three times a year, "Wait. In this number system, is 3 plus 2 5 or 6? I can never remember."
The Man Who Knew Arithmetic was terible at math because, as all his math teachers used to point out, he was not interested in ideas. He did not care about ordered sets. He cared about multiplying 79864 by 83201 in his head -- and getting the answer faster than any calculator could. Read off five numbers of six digits to him and he would add them together and give you the answer in a second or so.
The Man Who Knew Arithmetic always got along fine with mathematicians -- each felt so superior to the other. Some teachers used to make mistakes in class purposely, I think, so he could correct them and they could deliver a little abashed and happy lecture on the difference between mathematics and addition. But The Man Who Knew Arithmetic had trouble with ordinary people. He used to tell them they were a year older than they thought.
"You see," he would say on the morning of someone's 29th birthday, "in our system of birthdays you only become one year old after you've already finished your first year. So you're in your second year all the time people say you are one year old. Right now you think you're 29 but you've already lived 29 years and you'll never see 29 again. Actually you're already over 30."
Telling that to anyone, male of female, liberated or unliberated, when they've been worried for weeks about being 29 is not a good way to spread cheer. But time itself -- time and numbers -- got revenge on The Man Who Knew Arithmetic, He turned 29 himself, and all his friends gave him a 30t birthday party. Then those new little LED calculators came into his office -- the big old mechanical machines were put back in the supply closet standing in neat rows like the dinosaur skeletons in the natural history museum -- and the new little calculators were faster than he was. The Man Who Knew Arithmetic grew quieter -- like an uncle who knows magic tricks in a family where all the kids finally are old enough to figure out how all his tricks are done.
I thought he had forgotten arithmetic, and might move on to something else, like diagramming sentences or naming the different kinds of quarks. But 1979 gave him a whole new topic and a whole new crusade.
"I've just been invited to an end-of-te-decade party," he shouted gleefully over the telephone.
"So have I," I said.
"Then let's go together," he said, chuckling. "I'll pick you up about nine o'clock, December 31 -- 1980."
"You mean 1979," I said.
"You don't understand arithmetic," he said quietly, and I realized he'd been going through this same explanation over and over again for all our friends. "You have to start back with the first year of the calendar. Obviously, there was no 0 A.D. Rught?" he said.
"Is this the birthdays again?" I said. "Because I never really understood that to begin with."
"So the first year of the calendar was 1 A.D., and it was over on January 1, 2 A.D. The second year ended on January 1, 3 A.D., and the year 10, ending the first decade, ended on January , 11 A.D. All decades are ten years long, and all have begun the same way, with the year ending in 1, and ended with the year ending in 0."
I have counted this out on my fingers - the only way I can do arithmetic, though I was never much good at math, either. And The Man Who Knew Arithmetic is absolutely right. I got him to admit that the "70s would be over on January 31, 1978, but he made me admit that in that case, the '70s were not a decade -- just a nonade, nine years, plus one year out of the decade of the 1960s.He explains it to everyone, actually changing his personality by effort of will from The Man Who Knew Arithmetic to The Man Who Knows Arithmetic.
It is even possible that he has new worlds to conquer. I walked through the accounting department at the office last week and noticed that the little calculators had been replaced. They were very fast, but they didn't put out a tape, so no one could go over a column of figures to check it for errors. The new machines may add and multiply faster -- but they certainly print slower even thatn the old mechanical dinosaurs. The Man Who Knows Arithmetic will once again be able to outdo them.
And 1980, the last year of the seventh decade of the 20th century, is going to be a happy one for Anybody Who Knows Arithmetic.