ON THE NATURE OF CONCEPTS

Let us look more closely into the new meanings suggested by Einstein’s work. A synonym for the word “meaning” is the word “concept.” Scientists prefer the latter term. The lines quoted above about the authority of the fact were written by P. W. Bridgman of Harvard. In this section we will follow the development of concepts as set forth in his Logic of Modern Physics. Wherever scientists are struggling with new forms of meaning this book is known and respected. It is perhaps the clearest statement yet produced of how a scientist today orders, or should strive to order, his intellectual equipment. “Our understanding of nature is non-existent apart from our mental processes, so that strictly speaking no aspect of psychology or epistemology is without pertinence.” Thus semantics takes a front seat at the beginning of the performance. Broadly speaking, modern science is concerned with two techniques of parallel importance: (i) instruments for conducting experiments and (2) language with which to explain the experiments. Both techniques have been refined and are constantly improved.

How do we get facts into our heads and form concepts? Einstein shattered a whole cosmology of concepts. Let us not be knocked galley-west again, says Bridgman. The attitude of the physicist must be one of pure empiricism, recognizing no a priori principles or absolutes which determine or limit new experience. Experience is determined only by experience. This means that we must give up the demand that the world outside be embraced in any one formula, either simple or complicated. It may turn out that nature can be so embraced, but thinking must be organized not to demand it as a necessity. Concepts must be so ordered that present experience does not exact hostages of the future. After Newton’s great work, the door to certain new concepts was firmly shut,

and when Einstein broke out the side of the house, the faculty nearly froze to death. Keep the door open and get used to fresh air.

Before Einstein, concepts in physics were usually defined in terms of “properties.” In Book I of Newton’s Principia we read: “Absolute, True and Mathematical Time, of itself, and from its own nature, flows equably without regard to anything external, and by another name is called Duration.” Time is something in and of itself. But, says Bridgman, if we examine the definition of “absolute time” in the light of experience, we find nothing in nature with such properties. Even a layman can check this statement. Try to think of “time” as an entity and you will be almost as baffled as in the case of “the eternal.” You can think of the face of a clock, of what occurred yesterday, or of watching Jesse Owens break the world’s record for the 220-yard dash. You can think of specific “times,” but of no universal.

Scientists observe “local times” on the earth, or “extended times” in the stellar depths. A light-year is a measurement standard in extended time, but it connotes space traversed in a year’s time. We must not talk about the age of a beam of light, says Bridgman, though the concept of age is one of the simplest derivations of local time here on earth. We must not allow ourselves to think of events taking place in Arcturus now with the connotations attached to events taking place here now. “It is difficult to inhibit this habit of thought, but we must learn to do it.”

P. Lecomte du Noiiy has recently observed: At different ages it takes different lengths of time to accomplish the same amount of work, and, as everyone realizes, the physiological significance of a day is not identical for insects and for animals that live to be sixty years old. . . . Everything occurs as if sidereal time flowed four times faster for a man of fifty than for a child of ten.

Do you remember the endless days of childhood? Our biological processes shift with age, and an hour is a different thing to a child and to an adult.

Bridgman develops various concepts for “length” in post-Einsteinian terms—where an absolute property “length” has been dropped overboard. We can talk for years about what “length” means and not arrive anywhere. To find meaning we must heave out of our armchairs, secure some meter sticks or other instruments, and with our hands perform certain operations. Follow carefully now, for we are coming to the “operational approach” so cardinal to semantic understanding. “The concept of length is fixed ivhen the operations by which length is measured are fixed.” The concept involves as much as a set of operations and no more. Applying this to “absolute time,” we find no way to measure it. No operation can be performed in respect to it. Into operations involving time, other factors enter, preventing isolation. We cannot say that “absolute time” either does or does not exist, only that no operations yet found can measure it, and so the concept, as of 1938, is meaningless.

Concepts not subject to operations are meaningless.

Speculations about an expanding universe, the curve of entropy (that is, that the universe is running down like a wound watch), are meaningless, because no experiment can yet measure the phenomena. Such speculations fall under the head of “extrapolation,” which means taking a few points on a curve and riding the line which joins them to Cloudcuckooland. It is exhilarating mental exercise and quite all right if you know that it is Cloudcuckooland. If you become serious about it, you may wake up some morning to find yourself a public laughingstock.

We take our meter stick and measure a house lot. This is a simple operation and gives us one concept for “length.” Next we stand out in front of the house lot and measure a trolley car moving down the street. The car, unlike the house lot, is not at rest and the operations have to change. We have to allow for velocity. When the trolley car stops, measuring operations are similar to those for the house lots, but when it begins to move, length becomes a function of velocity and so “time” gets into the concept.

We now want to measure the distance between the sun and the planet Jupiter. To do so we have to throw away our meter sticks and take to telescopes. Length is no longer tactual, but optical. New operations are demanded and therefore new concepts. “To say that a star is io 5 light-years distant is actually and conceptually a different kind of thing than to say that a telegraph pole is 100 feet away.”

Turning and going down the scale from stars to molecules, we find that other instruments and operations are needed, and so the concept of length must shift again. Presently the measuring gauges are found to be atomic in structure, without clear boundaries. At very short lengths, the concept merges into the field equations of electricity. (“Long” and “short” are terms showing relations, usually relative to a man.)

Thus “length” is not something which an object possesses, as a man possesses a shirt; it is a word in our heads. Its meaning is determined by what we do, rather than by what we say, and the concept shifts with our doing. To use the same label “length” for these various concepts, says Bridgman, may be convenient, but is always dangerous, and perhaps costs too much in terms of ambiguity. Some Great Thinker is likely to turn it into stone at any moment, declaring that length is length, now and forever, and let there be no more nonsense about it.

The operational approach makes knowledge about the world outside no longer absolute, but relative. The operation is performed relative to some standard, say the gauge or the meter stick. Concepts emerge from these operations which are definite and verifiable. Another man can perform the operation and check the concept. Concepts, observes Bridgman, must be constructible out of the materials of human experience and workable within that experience. When concepts move beyond the reach of experience, they become unverifiable hypotheses.

Knowledge advances when we find how things are related and in what order. This ties in with Korzybski’s central idea of knowledge as structural.

In Chapter i we noted that the operational approach renders meaningless such Great Questions as: May space be bounded? It clears the air of scores of questions which have bemused or tortured thinkers for thousands of years. Try it yourself. Pose a Great Question, say “Is man a free agent or is his course fatalistically determined?” Look for an operation which can answer it. Keep on looking. Look under the bed, out in the garage, everywhere except into your own mind. In the end you will find that no operation is possible, and the question, to date, is meaningless. You can argue about it if it amuses you, but neither you nor your opponent can know anything about it. At least not yet. A hundred years ago the question “Is man a product of evolution?” was in a similar fix. Along came Darwin and Wallace, and by a series of operations, experiments, and deductions fixed the concept of evolution, gave the question meaning, and conclusively answered it in the affirmative. Observe that clocks and meter sticks were not much used by Darwin, but careful observations and descriptions, of a qualitative rather than a quantitative character.

Length to a physicist is no longer a property to be applied to any object, anywhere, at any time; it is a series of concepts—lengthi, house lots; length 2 , moving trolley cars; lengths, solar distances; length 4 , atoms—as many concepts as there are different operations. It may be objected that this is all very confusing. On the contrary, it was the old one-valued concept of length which furnished the confusion. When Einstein broke it open, knowledge jumped forward. The new concepts worked.

What a floodlight this throws on the notion of consistency. Consistent with what? Where? When? To use the house-lot concept of length in stellar distances, just to be consistent, brings useful knowledge to a standstill. To use “local-time” concepts in the field of “extended time,” just to be consistent, makes one an anti-Einstein-ian today, and something of an ignoramus. Similarly, to lay down the concept of free speech as practiced in America on Asiatic peoples, who have never experienced the American variety of vocal liberty, is consistent if you like, but meaningless. Consistency is a jewel if you keep it in similar contexts. If you go leaping into other times and other places, it turns to paste and colored glass. No statesman can be “consistent” if conditions change while he is in office. Ignorant of the semantic idea involved, he spends sleepless nights worrying about it, and is constantly pretending that he is a paragon of consistency. Meanwhile nothing so fires the literary talents of a newspaper editor as to catch the great man being inconsistent. The statesman should refresh his courage from Walt Whitman: “Do I contradict myself? Very well then I contradict myself.”

In addition to length, time, space, Bridgman describes modern concepts of velocity, force, mass, energy,

temperature, light, quantum theory, identity, causality, all within the framework of operations. We have not time—or, if you prefer, we have not space—to examine them in any detail here. If the reader feels his curiosity aroused, he is earnestly advised to go to the original source.

Poincare has spoken of the baleful effect of the word “heat” on physics. As it was grammatically classified among substances, physicists spent centuries looking for something in the outside world corresponding to heat— and quite neglecting the three pails of water described in Chapter 6. “Heat” is a symbol not for a thing, but for a relation. Here is a bar of steel. A thermometer shows its temperature to be 6o°. One asks, “What is the temperature of an electron in the bar?” I answer smartly, “Sixty degrees.” You answer, more wisely, “I don’t know.” We are both in error. We have not shifted our talk to the electronic level. Temperature by scientific definition depends on molecular vibration, and to have temperature at all there must be at least two molecules. An electron is below this level and so has nothing to be called temperature in its make-up.

We never experience light by itself as a thing. Our experience deals only with things lighted. Therefore light as an object traveling is very difficult to prove, and to date is more hypothesis than observed fact. Einstein assumed that light does travel by itself, but this concept may have to be modified. In the realms of quantum phenomena (behavior within the atom) the ordinary

concepts of mechanics are inapplicable. So also are relativity mechanics. Electrons do not whirl like iron wheels. This is a new kind of experience. Like the kitten, we must be still, observe, and gradually form new concepts. Indeed, the laws of mechanics may be only the statistical gross effects of quantum activity, the “aggregate action of a great many elementary quantum processes.”

I am not giving these illustrations in an attempt to teach you physics, to explain relativity, or to parade my grasp of science. I know very little about physics, but I am enormously interested in finding out how physicists handle concepts. Above other men in recent years, they have widened the boundaries of human knowledge. Forget the physics recited here, for it is negligible, but do not forget the way a modern physicist forms a concept; above all, do not forget the operational approach.

Let us now turn to the problem of how scientists communicate what they discover. “The essence of an explanation,” says Bridgman, “consists in reducing a situation to elements with which we are so familiar that we accept them as a matter of course, so that our curiosity-rests.” When you explain a thing to me and I understand it, what you have said checks with my past experience as per the filing system in my brain. “Yes, sir, that’s a Thingumbob all right, I’ve seen a carload of them.” An explanation calls up a familiar correlation, but it is by no means “absolute truth.” Its validity depends on the hearer’s experience, which may be limited. Perhaps I have never encountered a Thingumbob. Perhaps I have mis-

interpreted it. The explanation that a thunderstorm is caused by an angry god may be good enough for a Trobriand Islander. It is not good enough for a physicist. Bridgman notes three steps in reacting to new experience: i. If the experiment is not too far beyond the margin of known ground, it can be explained in concepts derived from past experience. Thus the kinetic theory of gases slid into focus without trouble.

2. If the experiment is well beyond the margin, an explanatory crisis develops. Relativity and quantum theory produced such crises. The human impulse is to force the new into the old molds and thus feel mentally relieved: “Einstein has discovered nothing new; Newton said it all long ago.” Such unwarranted explanations are pleasant for a time, but sooner or later they will be found out. “Society will not be able to demand permanently from the individual the acceptance of any conviction or creed which is not true, no matter what the gain in other ways to society.” (Reading this, I suddenly feel relieved about the fraudulent concepts—racial and national—which Hitler is trying to foist upon the people of Germany. Sooner or later their falsity will destroy them.)

3. The explanatory crisis can be faced squarely, just as the kitten faces it, with cautious investigation and an open mind. “All our knowledge is in terms of experience; we should not expect or desire to erect an explanatory structure different in character from that of

experience. . . . But only bigots, unimaginative, obtuse and obstinate, demand that all experience must conform to familiar types.” Some physicists are still afflicted with this bigotry. Why? Partly because they were brought up on Newton and the splendor of his mechanical laws, partly because they are still slaves.to bad language. “But just as the old monks struggled to subdue the flesh, so must the physicist struggle to subdue this sometimes nearly irresistible but perfectly unjustifiable desire.”

If physicists must become ascetics against the lures of absolutes, imagine the travail of a poor economist inured to little but wind for a lifetime. The great depression of 1929 was a slice of new experience as gigantic as it was tragic. Almost unanimously the economics faculty, energetically supported by President Hoover, announced that the depression was nothing new, that we had had plenty of them before—look at 1837 and 1893; that the same curve was always followed; and that it would probably all be over in ninety days. This forcing of the new into the mold of the old, this yearning for the familiar explanation, persisted throughout the catastrophe. For millions of Americans it is unshaken to this day. 1 When President Roosevelt, like a modern physicist, tried to meet new experience with new experiment, he suffered an avalanche of bitter protest. The voters with small incomes were the scientists in the premises. Most of them

1 See Robert and Helen Lynd, Middletown in Transition. The credo of the leaders of Middletown in 1936 was almost unchanged from that of 1928. kept on voting to allow him to seek new concepts for new experiences.

Physicists are continually hunting for the fundamental bricks of the universe. It was recently thought that such a brick had been found in electrical charges. There is no justification for this tidy view, no experimental proof. The necessary operations have not been performed. The theory of relativity holds reasonably well for large dimensions in the outside world. The quantum theory holds reasonably well for small dimensions. 1 At the borderland, the two theories clash. So the dogmatist leaps to the conclusion that both must be wrong, and that modern physics cannot be taken seriously. But just why must the universe be explained by one consistent universal law? Suppose it does not act that way in fact? Suppose that large-scale and small-scale events do follow different patterns? Suppose that we do live in several kinds of space at the same time? The fact that our minds want simple laws is no reason for supposing that nature must be simple. Will the concept work? Can another man repeat the operation? Here lies the determining factor for knowledge.

Attempts to simplify nature and reduce it to general laws have had a gloomy history. Newton’s mechanics,

1 A good working definition of quanta is “counts made by human counters.” When we count i, 2, 3, we are defining quanta, which consist of undivided intervals between the counting steps. In sub-microscopic regions the behavior of some things may be described in terms of the relations between whole numbers, 1, 2, 3, with po confusing fractions.

gravitation, thermodynamics, the principle of similitude, the theory of ultimate rational units, are useful in certain contexts, but they do not unveil the whole world outside. “The task of finding concepts which shall adequately describe nature and at the same time be easily handled by us, is the most important and difficult of physics, and we never achieve more than approximate and temporary success.” Fortunate it is that nature does happen to disclose some simple, approximate rules over certain classes of phenomena that are good enough to allow us to build Boulder Dams and X-ray tubes. I wish we had some simple rules at least half as accurate to guide us in economics and politics.

What is the ultimate nature of matter? The question we know by now is meaningless. It would make layman as well as physicist feel better to answer it—even as the idea of God makes some people feel better. How does the outside world work in a given context, approximately? That seems to be the sum and quest of human knowledge. It will give us as much power over the environment as we are competent to handle.

I have taught you very little physics, but I trust I have told you enough to make it clear that Einstein has not shunted science into ghostly realms where “Everything is electricity—electricity is unknown—therefore everything is unknown;” where “Science has banished materialism and spiritualism has returned to the hearts of men.” Gibberish of this nature has been prevalent when nonscientific people have discussed modern physics. It is

a mixture of ignorance, wishful thinking, and bad language. By getting rid of absolutes, the scientific method stands on the firmest ground in its history. It is sad that some of the older scientists cannot give up their fixed ideas and accept the gain which has been made.

Einstein brought us closer to the world outside, thrusting aside the barriers of the observer’s senses. We have a like task in the social studies, the outside world of behaving human beings. Our problem is to see Germany, see Spain, see big business, see money and credit, see poverty and unemployment, see modern technology, not as entities walking, but as their referents really order themselves. Our task is to thrust aside dogma, one-valued judgments, untenable identifications, and so come closer to what is actually going on beyond our skins. We cannot, alas! bring these matters into the laboratory as the scientist can bring cosmic rays, but we can learn to use our minds like scientists. We can adopt the operational approach; we can appreciate the flexibility of concepts; we can avoid fraudulent explanations of the new in terms of the old; above all, we can strive for the great discipline of agreement.

By long and painful experience I have learned that a tennis ball goes harder and straighter to its destination when one has a rocking balance, swaying from foot to foot like a dancer, with muscles flexible and relaxed. When a rigid position is taken, muscles tense, weight firmly planted on both feet, the fearful wallop one gives the ball usually sends it over the backstop or lamely

into the net. We need flexible concepts as well as flexible bodies to meet the outside world.

Modern physics has rung down the curtain on absolutes. Scientists now devote themselves more to cutting into the margin of the unknown than to framing eternal laws. The semantic discipline has a kindred aim. It is not an absolute, but only a useful method for cutting into the margin of opaque language, making communication clearer. It cannot clear up all talk. There are blind spots in Korzybski, in Ogden, in Bridgman. The book you are reading has many of them. Presently, on these foundations, somebody will come along and give the study another forward push—progressively narrowing the margin of the unknown.

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