The kids sometimes became pretty restless as we drove along hour after hour with the hot sun beating down on us. In August it’s mighty hot, even with all the car windows open. When children are confined to crowded quarters, they haven’t much to do except poke or tickle one another, giggle or sleep. So we used to play little games together when things became too noisy and rough in the back seat of the station wagon.
Somebody would say, “I spy with my little eye something that begins with t” (or some other letter of the alphabet). In order to guess what had been “spied,” they had to pay attention to their whole environment inside the car, out there on the road and all over the countryside, trying to discern everything whose name started with a t.
Sometimes two of us would play “Battleships.” Each player had a paper squared off by grid lines, ten squares up and down and ten crosswise, like a totally blank crossword puzzle. The vertical columns were designated alphabetically, while the rows across were numbered. Somewhere within these hundred squares each player “hid” two “battleships,” two “cruisers” and two “destroyers.” These vessels consisted of, respectively, four, three and two consecutive squares outlined heavily in pencil. Keeping their fleet’s deployment carefully concealed, the players took turns trying to locate the “enemy’s” vessels by firing a salvo of four “shots” at the other fleet, naming each target square by letter and number. After each volley the attacked admiral had to report to the assailant how many hits (if any) had been scored on what class of vessel. The game proceeded until one navy had been entirely sunk. To decide where to “fire” next, each player had to develop techniques for locating vessels and keeping track of all previous shots. Playing Battleships was a good exercise in eliminating divided spaces by logical thinking.
A third game passed a lot of time for us along dreary stretches of driving—the ever-popular “Twenty Questions.” Someone thinks of a certain item and the others search for its name, using questions answerable by a simple yes or no. Strictly speaking, the searchers are allowed to ask a maximum of twenty questions, but we usually kept on until the item was either correctly named or every player had given up.
Gradually Robin and Dawn discovered how to deploy their quota of questions in the most effective way. They first had to get some general idea of what kind of thing they were groping towards. “Is it animal, vegetable or mineral?” That’s a good opener (if your father doesn’t have you looking for the shadow of Santa Claus—Santa does have a shadow, doesn’t he?). Next they tried to locate the mystery item somewhere in space and in time. Then they turned to discovering its size, uses and behavioral characteristics. They found that the questioning procedure worked best when they asked big general questions first, and gradually narrowed the scope of successive questions down to classes that had fewer and fewer members. At last only one specific entity would remain as a possibility. Its name was of course what everyone had been looking for.
All three of these little games that we played while traveling involved a search for something. In the “I spy” game, the search is for the name of something which is quite visible nearby, but whose specific location is not yet known. In the game of Battleships, the players at least have a known set of grid lines. These, like the astronomers’ “birdcage,” give them a frame of reference for locating unseen targets.
Grids of imaginary lines must be one of the most important of all human inventions. They enable people to tell one another exactly where something of interest is situated. Thanks to ingenious astronomers, geographers, surveyors and navigators, we can locate places that we happen to be looking for on the earth or in the sky. The grid system works no matter how confusing the terrain, no matter how unmarked the ocean or how vast the dome of the sky.
The individual grid lines are logical dividers like all other logical dividers, but their crossed arrangement at right angles to each other at fixed distances establishes the two essentials of measuring: units of length and standard directions from which to take bearings, establishing angles. The grid of longitude-latitude lines divides the earth’s surface into blocks with definite dimensions, and lines them up on a north-and-south, east-and-west basis.
Descartes demonstrated that, using the grid formation of logical dividers, all geometrical forms could be translated into algebraic equations. Modern technological and scientific developments have largely been made possible by the “differential and integral calculus” which largely depends upon grids.
Playing “I spy” is quite similar to locating a geographical feature by means of the grid lines of a map, but the grid lines used in “I spy” are not so obvious or explicit. You can scan your field of visibility up and down, moving your eyes gradually from left to right, looking for an object whose name begins with the designated specific letter in the game. The edge of your first scanning pass provides a boundary along which you can run the next scan, which in turn becomes the guideline for the next scan, and so on. This system of scanning keeps you from covering the same strip of space more than once. Sooner or later you’ll encounter what you’ve been looking for. People with a less disciplined approach will make a random search of the field according to whim, with no regular procedure in mind. Wonder of wonders, these less logical searchers often stumble upon the object of their search more quickly than those who use scan lines as dividers!
When you are looking for a word, however, a specific word out of all possible words, your search is almost futile if you don’t have clues. In the game of Twenty Questions the answers to your queries give you clues which help you to narrow down your field of search by the familiar process of “Divide and Eliminate.”
If the word happens to be the name of an object, event or person that once actually existed or still exists, it’s fairly simple to locate it by familiar ways of dividing space and time. Is it on earth? Yes. Is it in the Western hemisphere? Yes. Is it in North America? Yes. In Canada? Yes. Is it east of Vancouver? No. The technique is to divide a space into two portions and ask if the item you’re after is located in one of them. If it is, you divide that portion into two smaller regions and ask again. If the object of your search isn’t in the part you ask about, you eliminate that part and go on to divide the other. By dividing and eliminating, the area you have left to search becomes so small after several divisions that you can hardly miss what you’re looking for. Time can also be divided into BC and AD, before or after some well-known event, a certain century, year, day, hour or whatever.
If you have to know what kind of thing you are looking for, you will need some way of dividing the world according to qualities, properties and characteristics. Fortunately our society’s ideas about the kinds of things have been laid out for us in various classification schemes. Named classes of things are arranged in an orderly progression from the most general classes with the most members through classes with fewer and fewer members, down to the names of specific individuals. In Twenty Questions, when you know the principles by which the names of classes were arranged in a particular classification scheme, you can always locate the kind of thing you are looking for by asking your questions so as to divide and eliminate certain portions of the big scheme. It’s like finding a certain twig on a tree by eliminating main branches, then subbranches, then other twigs.
Every kind of thing you learned about in school has its place in a conventional classification scheme. That’s how they divided your education into the various “subjects” which you studied. In each subject you are taught the layout of a set of slots or pigeonholes within which each kind of thing you study in that subject has its place. These conceptual “slots” or containers are commonly called classes.
A class is a name for an imaginary collection of all those things that have one or more characteristic in common. It should be noted, however, that classification is not merely a device for keeping similar things together. It is also a way of excluding all those kinds of things that are considered to be significantly different from those that are understood to be inside the class.
The class of organisms includes all living things, but excludes the class of all inorganic things that have never lived. Animals and plants are somewhat alike in that both are living. Both are therefore included in the class of organisms. But animals are also (usually) quite different from plants in certain ways, so the more general class of organisms is subdivided into the subclass of animals and the subclass of plants. Less inclusive subdivisions of the more general, more inclusive classes are usually considered to have a lower rank as “subclasses.”
In a similar way, the subclass of animals may be further subdivided according to the group characteristics of the various kinds of animals. Thus arise the classes of mammals, birds, reptiles, fishes, insects, mollusks, etc., all of which are subclasses of the more general class of animals. Each of these subclasses—mammals, for example—may be further subdivided according to the ways the animals’ young arrive in the world, or by the ways they eat, or by the characteristics of their feet, or by any other distinctive differences.
Thus in our society all kinds of living things have been given a place in a great classification scheme which ranks them from classes that are more inclusive through those that are less inclusive, down to particular individuals. Biologists have special technical names for these ranking levels of generality. The principal ones are: phylum, class, order, family, genus, species, section and group. But for our purposes all of them may be called classes which have subclasses. A dictionary’s definition of a word first names a general class, then mentions the characteristic differences of this particular subclass which distinguish it from other subclasses of the same rank. For example, a freeway is a road for high-speed traffic, divided into at least two broad one-way double-lane strips to which access is restricted and on which the speed limit is set very high.
Each society divides the world it experiences into kinds or classes somewhat differently. One society may distinguish more colors in the rainbow, or fewer, than another. In the Eskimo languages there are many more words for snow than there are in English. Specific snow conditions helped or hindered traditional Eskimo activities. In Arabic, fine distinctions are drawn between various kinds of camels, distinctions that would never occur to most North Americans. Experts in every vocation notice differences that untrained people are almost certain to miss. Talk to surfers about winds and waves. Each society has its own classification scheme for everything. Its teachers help their students to fill up any empty slots in their individual versions of the great classification scheme. They introduce them to things they don’t already know. The more definitions they can understand, the “better educated” they are.
Conversation consists largely of people describing to each other what they think is, was or will be the case in a certain unclear situation, and what it all means. If those conversing are using the same definitions, tentative opinions may be confirmed, information conveyed and mutual understanding enhanced. If they aren’t using the same definitions and classification scheme, the conversation will break down very quickly. Members of social classes and people with different occupational know-how sort themselves out into social groupings by the things they can successfully talk over with each other.
Just as we locate objects in space by using a grid of imaginary lines for dividers, and locate events in time by using known events for dividers, we locate classes of things by using the organized structure of a classification scheme, with its divisions between classes in the same rank and between those in higher and lower ranks. “Vertical” separations between classes and “horizontal” separations between ranks function as a kind of conceptual grid. Anyone who can frame definitions using a common classification scheme can easily enter into conversations and play Twenty Questions, not to mention other games requiring a knowledge of classification, such as logic.
Suppose you are settling down to watch the World Series on TV. You’d like to kick off your shoes and put on comfortable slippers. But you don’t want to miss the game by going off to the bedroom to get your slippers. Your young nephew, Sherlock, has come to visit you and he’s not particularly interested in watching the baseball game. He’s over there in the corner, poring over the ninth volume of your encyclopedia. You therefore ask him to fetch you your slippers.
Sherlock arrived by bus just this afternoon on his first visit to your place. He doesn’t know much about the layout of your house or where you keep your slippers. Nevertheless after a brief pause he nods, gets up and leaves the family room. The lad is thinking. What is going on in Sherlock’s logical mind? Let’s see. Hm-m-m-m.
“Tidy people usually keep slippers in bedrooms (unless a dog has carried them off).
These are tidy people (and they don’t have a dog).
I must find uncle’s bedroom.
This is the guest room—my room.
This is a boy’s room—David’s, not uncle’s and auntie’s.
This is a girl’s room—Trudy’s, not uncle’s and auntie’s.
This is a bathroom, not a bedroom.
This large bedroom must be uncle’s and auntie’s.
Those slippers will be in here either on the floor or on a closet shelf.
They are nowhere on the floor.
Therefore the slippers must be in a closet.
There is the closet.
No slippers on the floor.
There they are on the shelf.
. . . Here you go. Here are your slippers.”
Thank you! Good thinking, Sherlock!
A boy who was not used to working through classification schemes by definitions, dividing and eliminating all the way, might have searched through every room in the house, randomly and perhaps fruitlessly.
If he had interrupted your program to ask you where the slippers were, you could have given him various alternative sets of directions. Directions are clues designed to shorten the long process of dividing and eliminating defined classes in order to arrive at a correct conclusion.
You might have told Sherlock to look forty feet away. This information would narrow a random search, so that he would look only at places near the end of a forty-foot imaginary string, the radius of a circular dividing slash.
Or you could have described in detail the pathway he should follow. “Go down the hall to the first wall and turn right. Go straight ahead and through the first door ahead. Turn left immediately. Go to the next wall and turn left. Open the door there and look up.”
Alternatively you could have described for him the whole layout of the house, naming the various room spaces and their order along the hallway. By counting doors and making his way past the sequence of spaces, he would arrive at your closet.
If you had happened to have the housebuilder’s original blueprint handy, the boy could have used that set of imaginary lines like a map.
Sherlock might have elected to extract from you the location of your slippers by something like a game of Twenty Questions. Each question would divide the house space in two. By eliminating the “no-slipper” portion after each division, the slipper-containing region would eventually become so small that the boy couldn’t miss finding the footwear.
The definitions of words in the dictionary express in many ways the accepted classification schemes which provide logical guidelines for rational thinking. These are the first cousins of geographical grid lines, international boundaries and property lines. When logical Sherlock grows up, he’ll get along just fine with land surveyors and baseball umpires. A society’s top authorities and judges are specifically appointed to make decisions according to socially accepted lines of distinction.
Philosophers, theologians and scientists try to clarify and defend the definitions which occur in those sections of the classification schemes which deal with classes of the greatest generality. They discourse about being, space, time, quality, quantity, human nature, spirit, divinity, mass, energy, causes, the natural, the supernatural, and so on. By establishing basic conceptions in these most general subjects, thinkers fashion a frame of reference that provides a place, a value and a set of relationships for everything and everyone. The dominant conception of the way things go becomes the general structure of a society’s view of the world.
Human beings are both inquisitive and inventive. Someone is always making a new discovery in science, originating a novel idea or inventing some extraordinary machine. In the past, such innovations as the notion of a sun-centered solar system, the great corporation, the steam engine, the automobile, electronics, television, nuclear fission, or the computer, badly upset our social definitions. They redirected our activities and forced upon us major adjustments to our attitudes and understanding of the world around us.
Until after the Middle Ages, the realm of astronomical objects was called “the heavens.” Heavenly bodies belonged to a higher order of things. They were exalted above the earth, not only in terms of altitude but also in status. In the heavens, divine and unblemished perfection reigned. The sun and moon were affixed to perfect crystalline spheres which circled daily about the static earth. If the planets seemed to wander back and forth in the heavens, that was because they were mounted on other smaller epispheres that rotated on the framework of the larger sphere that carried them around the earth. The spheres were kept in motion by angels appointed to their task by God, who dwelt in a heaven beyond the sphere of the fixed stars. In those days the realm above was smallish, permeated by the divine perfection of light, mathematics and the “music of the spheres.” Everything moved around the earth, the abode of humankind, which was the center of God’s attention. The earth was chiefly important because it was the scene of a dramatic rescue operation designed to deliver humanity from the taint of earthly imperfection, sin, misery and death.
The invention of the telescope changed all that. Accurate measurements by astronomers showed that the orbits of the planets were ellipses, not perfect circles. There were mountains on the moon with jagged profiles much like earth’s mountains. The moon was not a perfect sphere, and it was made of earth-like stuff. Blotchy spots could be seen to move across the face of the sun—unthinkable celestial pock marks! So the evidence indicated that the earth itself was only another planet and that it, like all the others, moved around the sun. The earth turned out not to be the center of things after all. The human race had been sadly demoted. The fixed stars were found to be unimaginably far away. The heavenly bodies were subject to the very same laws of physics which scientists had found to be operating on the earth. Reluctantly, people began to think of themselves as traveling through the vast, silent, emptiness of space on a smallish whirling ball without anything under it, destination unknown. The world had begun to feel like a lonely place, altogether mechanical and meaningless.
Heaven was still “up there” somehow, somewhere, but in no particular direction. Scientifically knowledgeable people couldn’t locate God anymore. As the prestige of scientists and engineers rose higher and higher, the status of religious authorities sank lower and lower. The world was simply not the way they had always said it was. A new worldview had to be formed and accepted before a revised classification scheme could be framed. Philosophers, theologians and scientists profoundly disagreed even among themselves about the way things ought to be redefined.
After hundreds of years their work is still not complete. Astronomers have been observing enigmatic objects out there in space such as quasars, pulsars and black holes. Nuclear physicists are hot on the trail of quarks, gravitons and gluons. What next will they discover or invent—or imagine?
In the meantime, where are we human beings? Who are we? What should we do? Where are we going?
Locating things and being located is important to everybody. We have to know where to look for what we want to find. We have to know where we ourselves are with respect to that location, and how we can get there from here. Once we have decided on the direction in which we will head out, we have to know how to keep on the right course until we arrive at our destination. That’s why the layout of a society’s imaginary dividing slashes, definitions and classification schemes is so important. These things help everybody to know what they most need to know to get along in the world.
Because we share so many classified definitions, my children and I can play Twenty Questions. One of my jobs as a parent is to search out the surest knowledge I can find about things divine, human and earthly, and to share this knowledge with my children. They, like all of us, desperately need a reliable classification scheme that will enable them to set goals for themselves and follow a way that will bring them at last to the end of the right road.