''Now, what I want is Facts,'' observed Mr. Gradgrind in Charles Dickens's Hard Times. ''Teach these boys and girls nothing but Facts. Facts alone are wanted in life. Plant nothing else, and root out everything else.''
We may laugh at Mr. Gradgrind today, yet it seems to me that our teachers follow him as faithfully as ever. Certainly I spent my formative years in school and college absorbing a remarkable quantity of Facts, and Facts not only relating to the material world but to matters of opinion, and even of taste. Who of us has not been taught that there is one correct way to complete a mathematical calculation, one correct interpretation of a poem by Keats, one correct reason for the Boston Tea Party, and so on?
Only as one grows older does one discover that all these facts are, after all , suspect. The angles of a triangle do indeed add up to 180 degrees if the triangle is drawn on a flat plane: draw it on a sphere, and the result is different. The distance from the Earth to the Sun is not a fixed number of miles , as we are taught in school; it continually varies because the Earth does not travel in a circular orbit. And if even these apparently inviolable facts are mutable, how much more mutable are those relating to human actions! As we investigate them more fully, we find a welter of conflicting evidence, until in the end we dare do no more than express an opinion about what we once confidently asserted was the case. As Karl Popper has pointed out, the best that we can say of a so-called fact is that it can be considered true until it is proved wrong.
The great collection of facts that we amass in our education is really no more than a set of flickering beacons which mankind has set up to guide us in our explorations of life. Like some pilot on a ship, we steer our course by them , but we must be constantly alert for changes in the geography which render some beacons inadequate, to be replaced by others. We are all in the same position as Christopher Columbus, who returned from his first voyage of exploration in 1493 to report to Queen Isabella that he had reached the East Indies and touched on an island of the Japanese archipelago when in fact, without knowing it, he had reached the West Indies and opened the way for the colonization of the New World. His mistake occurred not because he was foolish and inexpert, but because he used as the basis for his interpretation of the voyage calculations about the size of the Earth completed over a thousand years earlier by Ptolemy - calculations that later had to be considerably corrected. Like Columbus, we have to proceed with the best information available, but we must always be ready to find that as a consequence we have made a gigantic error.
Curiously enough, those most dedicated to amassing and interpreting facts, the scientists, are the people most aware of the fragility of their understanding, and the more they know about a topic the more they are aware of how little they know. For example, ask a biologist about the structure of the atom and you will probably get a fairly confident response: but ask a theoretical physicist, and you will open a Pandora's box of possible interpretations.
It is not in the nature of formal education to emphasize that our navigational beacons may be in the wrong places or, indeed, go out at any time. Teachers prefer apparent certitude and the world of Mr. Gradgrind, because without it their lecture notes look distinctly suspect. A bold attempt was made, however, to bring into the classroom a sense of questioning and uncertainty when science teaching in high schools was reshaped at the request of President John F. Kennedy. At the Massachusetts Institute of Technology, for instance, a radically new approach to the teaching of physics was worked out - one in which students were encouraged to try experiments without being told that there was one ''right'' answer which they had to achieve. This program and others like it have not, alas, been the success that was hoped for: the strain they place on teachers is too severe.
Yet without an awareness of the imperfections of our present knowledge, that same knowledge can never be improved. The route to improvement, however, can be illogical and unexpected. Albert Einstein once wrote: ''There is no logical way to the discovery of these elemental laws. There is only the way of intuition, which is helped by a feeling for the order lying behind the appearance.'' And the German chemist, August Kekule, describing how, sitting in a reverie by his fireplace, he hit upon the structure of the benzene ring through a vision of a snake seizing its own tail and whirling before him, ended his lecture by saying: ''As though from a flash of lightning I awoke; I occupied the rest of the night in working out the consequences of the hypothesis. . . . Let us learn to dream, gentlemen.''
Intuition, dreams - they seem a long way from the world of Mr. Gradgrind; yet we need them in the classroom if our educational system is to match our latent capabilities. How exciting it would be to encourage students to play with ideas, to fit facts together in new ways, to make models that may be wrong! For the willingness to make mistakes is one of the best educators of all - the willingness not to take everything on trust, but to quiz, and check, and try alternatives. By doing this we can come a great deal closer to understanding what our so-called knowledge of the world is really like. After all, by making mistakes we can discover new worlds, as Christopher Columbus learned long ago - and with very fortunate results, as it turned out