© 2006 Ken Knowlton


A little story here, ostensibly about numbers and counting. I went to Concord No. Nine, your typical one-room, one-teacher, sixteen-kids, eight-grades country schoolhouse (white, not red). One mile away, a bit of a slog in a snowstorm. As my sister reminds me, it was also a two-indoor-privy schoolhouse. There were holes in the ground, simple plank seats (don't forget to close the lid); they were in the building proper just off the boys' "coatroom" and girls' "cloakroom" and therefore not freezing cold in the winter. But thank God for summer vacation. (I think that's why vacation came in July and August, not in the harvest season.)

I had asked Mom why did I have to go to school? She said you learn things, like how to count to 100. Good grief, I had already publicly demonstrated exactly this proficiency when a neighbor took me to visit her Catholic school in Springville. The teacher (somebody's sister) had heard that 5-year-old Kenneth could count to 100 and she said Let's hear it. So I bravely stood on a desk in front, with somebody steadying me, and I orated (the increasing-ordered list of positive integers) from one to 100 (inclusive), without one single mistake! The kids all smiled and clapped their hands. Then I said would you like to hear me count to 200? And they said yes, so I continued from 101 all the way to 200! More smiling and clapping.

I'm glad that my mother didn't see that. She had said, and implied, more times than even I could count, that she didn't want me to get a swelled head. Whenever I seemed proud of something, she made some acerbic remark, with a smirky smile. Later I learned, only by overhearing some chatter, that she really was proud of me. I don't remember her ever saying it to me. Jeez, I wished she'd told me, just once in a while. But then maybe it was idle boasting; I would not have wanted to learn that.

In spite of all the grumbling about Mom, over the years, I do give her a B-plus for child raising: I was in effect an only child; three and a half years later came Fred, then Marie a year and some after that. Having lacked playmates to speak of, I needed to meet and "play with" others my age. Mom, bless her, drove for miles around the country and collected kids for a kindergarten that she taught under our maple trees making corn husk dolls and playing games and stuff. And thus began my very own Sisyphean task of socialization.

In school, I did learn more than I had expected. Not only counting far beyond 200, I learned all about "Yulia Sus" (Ulysses) and about "Gee Argafy" (Home Life in Far Away Lands), and lots of other things our teacher knew. There were bigger kids than me, and after a while, littler ones. Older kids right there in the room showed where one might be heading a mixed bag of options and warnings.

There were embarrassments, so stunning at the moment, so trivial in recollection. Once I went to pick up a sheet of paper, which I did with a flourish, and it slipped out of my hand and landed on its edge on the floor with a surprisingly loud crack a sheet of paper! And those grownup sixth and seventh graders just stared at me. And once a metal pencil box dropped from my desk and crashed on the floor. The embarrassing noise wasn't my big problem. The thing had landed upside down and its bottom had a gorgeous design that I had never seen. Was it someone else's pencil box? What was I doing with it? I panicked. I slowly picked it up, turned it over, and it was mine after all. Why was this scared six-year-old going to remember this event for 70 years? Random snatches of memory are certainly acceptable, but why do I still cringe?

Recess could give you the feeling of a big family. We played "Andy-Aye-Over" (some call it "High-Teenie-Over" or something). One team calls out that name, and throws a tennis ball over the schoolhouse but yells "backbounce" if it doesn't go over; if it does, and if someone there catches it, they run around the building and anybody they hit with the ball goes over to their team. Even a little guy can sometimes catch the ball, or can dodge being hit, and be a hero for his or her team. Another bit of local culture, good for the little ones, was in softball you hit the ball over the fence and you're OUT!

Recess and noontime also had their perils. Once I deliberately kicked a ball into a long, dark culvert pipe hardly large enough to crawl into. Why? A silly impromptu contest. Then, terrified of getting stuck, I was made to crawl in and get it back. I did. And I never, never did that again.

And one big event: sliding down a foottrack-pitted snowbank, I flipped, and hurt my leg, real bad. They carried me to the schoolhouse. There I lay on the bench waiting for my folks to come for me, and the teacher said I was so brave. Brave, my eye. What else could I do but lie there in pain? Not much help from my Mom in the next couple of days she thought that if I just used the leg it would get better (as with polio 16 years later). She was like that, like what do they call them, crusty unscientists? Finally she detected a tiny bump in the shin. Then came a visit to the doctor, diagnosis of hairline crack, time in a cast, and one morning that Ma and Pa crawled out of bed early to find me crutching my way around the table, proudly counting my circuits by plunking an X's on the typewriter. They smiled.

Soon, back to school. We had all-classes movies about animals and other nature stuff. And Halloween, and Christmas, and other parties with all the kids and their folks. At one of them my cute before-school-age sister, who couldn't read yet, sat in front to recite "The Night Before Christmas," cued page after page by the pictures as she flipped through the book. I sat beside her, to prompt her, but she did the entire thing perfectly, all by herself. Big brother was becoming superfluous.

More perils. On the way home from school, two other wayward kids and I stopped at the small pond, a familiar playland during the summer. But this was winter and our self-imposed task was to break up the ice on the pond. With a good section turned to big icecubes, I decided to cross from one side to the other. I realized, of course, that the ice chunks wouldn't hold me up very well, so I ran and stepped on them ever so lightly. Well, they didn't hold me up at all, and I sank up to my waist in ice water, almost a mile from home. It was a cold, cold walk home. Shivering and dripping, I crawled into the house, hid my clothes and left my shoes in the bathtub. My dad later asked me How did your shoes get wet? I said I don't know (like it wasn't an interesting question) and he let it drop. He could have asked Were your feet in them at the time? or Are those the socks you put on this morning? Or You didn't fall into a pond on the way home by stepping on chunks of ice too small to support a flea, did you? Maybe he could read on my face that a discipline-worthy something had happened, and he didn't want to deal with it. I sure didn't.

More trouble. Or, perhaps, an opportunity for self-betterment. Shirley, bigger than me and two years older, had suddenly attacked me at noontime, and beat me up, with our teacher present and not interfering! I got back at her on the way home running by her I gave her a good backhand whack in the chest and ran on ahead, met my mother in the garden and told her about the unprovoked attack. Shirley soon arrived, complaining that I hit her in the breast (what "breast"?). No serious punishment for me, but a stern warning from my mom: you must never hit a girl or a woman in the breast, never, never, do you understand? Which started my life-long quest for an answer to the more general, philosophical, ethical and good-citizenship question that everyone must surely face more than once: Exactly When is it OK for Who to Hit Whom How Hard in the What?

(Apropos of which, there's a memorable quip from the archives of Kenneth's News, that bona fide and trusted record of happenings around farm and greater neighborhood. Young Freddie asked "Will the little baby cry if we hit her just once?" In truth, this is really heartening, for it suggests that civilization fosters a growth out from inborn barbarism, rather than a descent into it, as many features of modern society might mislead one to believe.)

Another good thing about all grades in one room: it's easy to ooze (sneak?) over from one grade into the next, first in spelling, later in arithmetic, and so forth, and finally to be completely in the next grade, all in one year! Thus I oozed, ever so smoothly, from first into second. Even so, Mom thought I was slow in arithmetic. Maybe she was onto something: throughout my technical career, only one of my patents, the one shared with Ron Graham, was based on mathematical combinatorics. (I had conjectured that you could perform a particular task for all positive integers except 2, 5 and 9; it was Ron, a proper mathematician, who proved it.)

But there was a downside to grade-sneaking. Ever after that first year, I was one year younger than my classmates, a slowly simmering social disaster. Let's skip over that right now, stay tuned.

As they say, it takes a village to raise a child. My school and the farms for a mile around were quite some village. Indeed, a kid there could learn one heck of a lot more than counting to a hundred, or even to ten thousand. Lots of things, entirely other kinds of things. As Einstein put it so neatly: Not everything that can be counted counts, and not everything that counts can be counted.

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