Once upon a time when I was about four years old, my father went up the road to buy a couple of piglets, and he took me along. We brought them home to our little farm in a burlap bag in the back of our pickup truck.
I guess I must have thought this was quite exciting, because my mother thought I was overstimulated. She sent me in to the living room to take a nap, even though it was only 11 a.m. So, I lay quietly on the couch and tried to get to sleep.
But after a half hour, I went in to see my mother in the kitchen. I asked her: “What comes after 999?” She explained, 1000. Okay. Since those days I have done a lot of counting.
I counted the number of three-cent stamps it would take to cover a square light-year. I counted the curves on Page Mill Road (206) and on Mt. Hamilton Road (430 up to the top) and on the back road from Weaverville through Hayfork to Cummings (2206 with an old VW bus without power steering).
I count a lot of things. Belches. Dead cars. As Lord Kelvin observed, if you don’t measure something, you don’t know scientifically what you have. The same goes for counting.
COUNTING ON THE BENCHI have seen some circuits that failed to work right because we failed to measure and count correctly the number of squares in a resistor—or a gate size. I have also seen some circuits that worked beautifully because we counted the squares wrong, but the wrong number was actually just right! And when my friends play cribbage, I comment, as they are pegging up, “You guys count funny…”
My son recently mailed me an old Calvin and Hobbes cartoon (see the figure). Well, Calvin was right! Math is like magic. But it is useful magic, and it’s simple enough for little kids to learn. And it’s not just illogical.
We discussed that 4 = 1 + 1 + 1 + 1 = 1 + 3 = 3 + 1 = 2 + 2. That’s a good definition of 4, as well as 3 and 2 and 1. It is a useful definition, and a lot of our math depends on a bunch of simple definitions like this.
Counting is, for sure, a lot easier in those Arabic numerals than in Roman numerals. I’d hate to do long division or multiplication with Roman numerals, or even subtraction!
I also count switchbacks on trails. The ascent from Yosemite’s floor to the top of the Falls takes 162 switchbacks, whereas if you go up by Mirror Lake, there’s only 106. And I counted the stone steps on the Annapurna Circuit, on the trail from Tatopaani on the great Khali Gandaki River up over the pass at Ghorapaani and down to Birethanti.
There are 8515 stone steps up and 9220 down. The stones are nicely set and are called “Gurung Staircases.” Pretty good trail! Good hard work with about 6000 feet of rise and fall.
Of course, while you’re counting, you usually need to be in good practice to keep counting and not be distracted by other things, like conversation. Don’t forget to start counting again at the right place. Also, you’ll want to have some “markers” to help you keep your place. You wouldn’t want to forget if you were at 360 or 340 or 460. I often use NSC part numbers as a marker. “The LM360 is a fast comparator.” That I can remember.
So counting is a very valuable function and we tend to take it for granted, except when a little kid asks provoking questions. Never a dull moment!
Comments invited! [email protected] —or: R.A. Pease, 682 Miramar Avenue San Francisco, CA 94112-1232