NATURAL HISTORY, STATISTICS, AND APPLIED MATHEMATICS

ONE FEBRUARY AFTERNOON about twenty years ago, I was conducting a field trip in Natural History for a class of intelligent amateurs varying widely in age, social status, and scientific sophistication. One had his master's degree in botany and was then a manufacturer dealing with polymerized molecules. Another, a wholesale grocer of much native intelligence, had had no formal education since the time he left high school to help support his widowed mother. There were two high school biology teachers, a bored investment banker, and the gracious, gray-haired president of the city's most exclusive garden club. Conducting such a class through the winter woods is a real challenge. Problems must be put on such a fundamental level that the most advanced students will be bored, yet in such simple terms that the beginners are not overwhelmed. Finally, I hit upon an exercise so effective that I used it year after year, first with these night school classes and then with college students. Eventually I exposed graduate students to it with such uniformly excellent results that now I use it in discussions with fellow scholars; biologists, mathematicians, social scientists. On that February afternoon I selected a big white oak tree and, leaning against it, addressed the class somewhat as follows: "It is just over a hundred years since this hillside was first taken title to by pioneers from Virginia. In that time many things have happened on this site. There are certainly hundreds of ways you can find you way to analyzing the main factors in what has taken place here. There is one very easy way, that I know of for certain. It is probably not the only easy one but most of the other methods are difficult and indirect and time-consuming. Now your assignment for the next hour is to find what were the main steps in vegetational change on this site in the last century. You can all solve the problem with no more technical equipment and no more botanical training than you now have. We'll take this tree as the center of a hundred foot circle. What has happened here in a century? Don't neglect any kind of evidence, just because it seems trivial. The world is full of easy keys to important problems; only once in a while does a genius come along and label these trivial keys as significant evidence. I warn you there is such a key here and most of you will ignore itthough it is in plain sight and requires no book learning to interpret correctly. Any one of you could solve this pro.blem given a day or two; several of you I know will work it out laboriously this afternoon; is there anybody here who can find the easy way in the first five minutes?" There wasn't. In twenty years I have had just two students who had the wit to notice that all the time I was talking to them my left hand was playing idly with a scrap of barbed wire which sticks out an inch or so from a scar on the big oak. Off to the left about thirty feet is another tree with a similar scar, though without any barbed wire, and way off to the right in more or less of the same straight line, is another oak with two such horizontal scars, one about a foot above the other. There had, you see, been a wire fence strung through the woods, using the trees as posts. When the land on both sides of it was acquired for an arboretum, the barbed wire was mostly removed but it had stayed in place so long that some of the trees had buried it in their bark. This was more than just a fence row; it was a section line, the boundary between two farms which had been differently managed. One had been cut-over and fairly heavily grazed; the other family had only taken out a tree here and there. If one figures out where the fence once ran and then comes and stands on the fence line and faces first towards one farm and then turns round about and faces away from it, he sees two different landscapes. On one side there are few large trees, no big oak, and a good number of vigorous young trees in groups of two or three, showing where an old stump had sprouted. There are plants which indicate a former pasture, a few surviving grasses and one prairie rose not too happy in the shaded woodland, There are a number of dead red cedars, red cedars being planted everywhere thereabouts by the birds but able to survive only in the sunlight. In the other direction there are big oaks, little underbrush, no stump sprouts, no cedars, and scattered dogwoods. Facing west one looks into a typical first-growth white-oak-sugar-maple woodland; facing east into vigorous second-growth woods. If he looks up and down the old fenceline he can see how, for some decades, the woodland trees sent husky branches out sidewise towards the sunlight of a brushy pasture, branches which are just now beginning to die in the heavier shade of the maturing second growth. The greatest delight I ever had as a teacher was when at last one alert student glanced at the barbed wire I had been handling, looked back and forth along the line of old trees for further scars, stood on the former fenceline looking first due east and then straight west, then gave me a wink and went and lay under the big oak until his fellow students solved the problem by their own slower witted techniques. He is today a highly successful pro. fessional rose-breeder but as I follow the careers of my other students I note that they all profit by the