The power of distinction

There are lots of jokes that start out, "There are two kinds of people in the world." My favorite goes, "There are two kinds of people in the world: those who think there are two kinds of people in the world, and those who don't. I'm one of those who don't."

Making simple distinctions is a powerful tool for thinking. A favorite is the distinction between concepts that are necessary and those that are arbitrary.

I think this should be taught in kindergarden. In many domains there can be differences of opinion that could cause troubles. But mathematics is a good example, and one where there shouldn't be a lot of room for opinion.

Consider the concept of number. We teach our children to distinguish between groups that contain two items and groups that contain three items, and four, and so on. That distinction, in and of itself, and depending on your point of view might be either necessary or arbitrary. For example, some might think it more important what color the objects are (or what shape, etc.), rather than their number.

However, once we introduce the concept of number, things get interesting. It is necessary and not arbitrary that if you combine two groups that each contain two elements, that the new, larger group contains four elements. On the other hand, it is arbitrary and not necessary that we use the numeral "2" to label groups with two items and the numeral "4" to label the new combined group.

This use of the graphics "2" and "4" is a social convention and nothing more. We might just as well have used "2" and "9". The fact that we agree on the former, and that everyone uses it, is, of course, helpful for communication. But which symbols we use is arbitrary. In the other system, it would still be true that "2" combined with "2" yields a new group of "9".  That is necessarily so.

Sorry that I don't have the reference, but I have seen an educational study in which a boy who could not "get" the symbols we use was helped by a researcher. The researcher got several matchboxes and put different numbers of pebbles in each box. Then the researcher invited the boy to look in each box and draw something on each box to help him know how many pebbles were in each one. This technique helped the boy past his difficulty with arithmetic, and once he realized the numerals were arbitrary, he could accept and learn the conventional ones.

Another distinction that I have been thinking about is that between things that work whether you believe in them or not, and things that only work if you believe.

Every time that I fly in an airplane, I find myself disbelieving that something so large and heavy can actually get off the ground. Despite my disbelief, every one--so far at least--has actually taken off.

As a lad, I watched Peter Pan with my sisters and they were dismayed when I didn't join in the clapping to save poor Tinkerbell's life. The fact is that the film had already been made and there was nothing that could change the outcome.

I don't have anything profound to offer about this last distinction, except to urge my audience to graciously accept the things that happen in spite of their disbelief, and to believe for all they are worth in situations where that can make a difference.

Effects of a great man

This is dedicated to my dear friend and cousin, Harold Conrad.

We grew up together, being neighbors, sharing the same school and church and grandparents. Besides that, some of the more memorable events of my life occurred in your company.

Wonder. You lived in the town of Taber, and I lived on a farm 7 ¼ miles north of town. One summer night, I slept over at your house. The next morning, I awoke in an attic bedroom with an inexplicable feeling of excitement and certainty that it was going to be an extraordinary day. We rode out to our grandfather's farm, west of town, in the back of a truck. You took along your bicycle, and that day, with your encouragement, I learned how to ride a bike. Wow, what a day!

Novelty. Soon after our rural party line was finished, you phoned me from town, and I enjoyed my first telephone call. Our phone number was 949-23 and we could tell the call was for us by hearing two rings close together, immediately followed by three rings close together. After a longer pause, this would repeat until we answered or the caller gave up. We were in the modern world.

Surprise. One summer day, we were playing marbles, and you won with a spectacular shot, ruining my own strategy. I was suddenly seized by a strange and irresistible feeling, and threw my marbles towards the north as hard as I could. An early experience with anger closely followed by shame at my behavior, and amazement at the loss of control. The start of a life-long challenge.

Neighbors. When your father's house on the farm was finished, your family moved from town into the farm house, and we became neighbors. We rode to and from school together on the bus. Sometimes, I would sleep in and miss the bus and have to walk a quarter mile or more to the next corner to catch it. Lots of the time we spent together was on this bus, because we were one grade apart in school. Neighbors and friends.

Gratitude. You saved my life once. We were swimming in your father's pond, and I tired and panicked. You immediately grabbed me in a headlock, as we had been taught as boy scouts, and towed me to shore. To this day, I am in awe of your presence of mind, and thankful for your quick thinking. Everyone that I have ever touched for good in my life after that owes you a debt of gratitude.

Learning. Together with a few students, including our mutual cousin and friend, Burton Conrad, we formed the Apogee Scientific Organization in high school, and practiced model rocketry. At least to the extent permitted by the Canadian Department of Transport. This became a life-long hobby of yours, and one that I enjoyed for many years during our youth. Fun in school.

Phlegmatism. During one rocket launching session, I was ranging (upwind and several hundred yards from the launch pad, in position to observe the highest altitude (apogee) attained by a rocket of my making). I had spent hours gluing, painting, and polishing, and I dissolved into tears when it blew up upon launching. You came over and offered the comfort of the phlegmatic point of view. I have learned much from this incident, though I still struggle to put this into practice, being more melancholic in nature. Learning of a different kind.

Camaraderie. Our paths parted when I graduated from high school. When I came home, proud in my knowledge of computers, you showed me what you had been doing on your own personal computer (an IMSAI 8080, if I remember correctly). The things you accomplished on your own amazed me. I enjoyed trying my hand at your lunar landing simulator (and decided not to become an astronaut). How wonderful to meet again with yet another common interest.

Embarrassment. During your older brother's wedding reception, some of your cousins sang a song, which included this challenge to you, "be a man and be wed." I empathized with you, imagining that you might find this embarrassing. But, as I looked over at you, I saw that you took it in stride and good humor. And a short while later, you married your Rosa, and have raised a wonderful family. No need to worry, you have things under control.

Nostalgia. You and Rosa bought my father's farm when he had to retire after his stroke. We visited your new farm house, and enjoyed visiting with you and your new daughter. And playing with your updated lunar landing simulator. And what a surprise to see all the hot peppers that you had grown--I hadn't imagined that could be done in Canada.

Again, our paths have parted, and we have not spent as much time together as I would have liked. I want you to know how important you have been to me, and what an impact for good you have been. Thank you for your enduring kindness and example. The effect you have had on my life is invaluable.