Tag Archive: creativity

The blockheadedness of IQ

It seems likely that there are innate differences of intelligence. But it seems almost impossible that a matter so many-sided and complex as human inborn knowledge and intelligence (quickness of grasp, depth of understanding, crea­tivity, clarity of expression, etc.) can be measured by a one-dimensional function like the “Intelligence Quotient” (I.Q.). As Peter Medawar … writes:

“One doesn’t have to be a physicist or even a gardener to realize that the quality of an entity as diverse and complex as soil depends upon … [a] large number of variables … [Yet] it is only in recent years that the hunt for single-value characterizations of soil properties has been virtually abandoned.”

The single-valued I.Q. is still far from being abandoned, even though this kind of criticism is leading, slowly and belatedly, to attempts to investigate such things as “creativity”. However, the success of thes attempts is very doubtful: creativity is also many-sided and complex.

We must be clear that it is perfectly possible that an intellectual giant like Einstein may have a comparatively low I.Q. and that among people with an unusually high I.Q. talents of the kind that lead to creative World 3 achievements may be quite rare, just as it may happen that an otherwise highly gifted child may suffer from dyslexia. (I have myself known an I.Q. genius who was a blockhead.) [123]

Our devastating system of education

Institutions for the selection of the outstanding can hardly be devised. Institutional selection may work quite well for such purposes as Plato had in mind, namely for arresting change. But it will never work well if we demand more than that, for it will always tend to eliminate initiative and originality, and, more generally, qualities which are unusual and unexpected. This is not a criticism of political institutionalism. It only re-affirms what has been said before, that we should always prepare for the worst leaders, although we should try, of course, to get the best. But it is a criticism of the tendency to burden institutions, especially educational institutions, with the impossible task of selecting the best. This should never be made their task. This tendency transforms our educational system into a race-course, and turns a course of studies into a hurdle-race. Instead of encouraging the student to devote himself to his studies for the sake of studying, instead of encouraging in him a real love for his subject and for inquiry, he is encouraged to study for the sake of his personal career; he is led to acquire only such knowledge as is serviceable in getting him over the hurdles which he must clear for the sake of his advancement. In other words, even in the field of science, our methods of selection are based upon an appeal to personal ambition of a somewhat crude form. (It is a natural reaction to this appeal if the eager student is looked upon with suspicion by his colleagues.) The impossible demand for an institutional selection of intellectual leaders endangers the very life not only of science, but of intelligence.

It has been said, only too truly, that Plato was the inventor of both our secondary schools and our universities. I do not know a better argument for an optimistic view of mankind, no better proof of their indestructible love for truth and decency, of their originality and stubbornness and health, than the fact that this devastating system of education has not utterly ruined them. [ch. 7, 147-8]

Science and art: hidden likenesses

The discoveries of science, the works of art are explorations—more, are explosions, of a hidden likeness. The dis­coverer or the artist presents in them two aspects of nature and fuses them into one. This is the act of creation, in which an original thought is born, and it is the same act in original science and original art. But it is not therefore the monopoly of the man who wrote the poem or who made the discovery. On the contrary, I believe this view of the creative act to be right because it alone gives a meaning to the act of appreciation. The poem or the discovery exists in two moments of vision: the moment of appreciation as much as that of creation; for the appreciator must see the movement, wake to the echo which was started in the creation of the work. In the moment of appreciation we live again the moment when the creator saw and held the hidden likeness. When a simile takes us aback and persuades us together, when we find a juxtaposition in a picture both odd and intriguing, when a theory is at once fresh and convincing, we do not merely nod over someone else’s work. We re-enact the creative act, and we ourselves make the discovery again. At bottom, there is no unifying likeness there until we too have seized it, we too have made it for ourselves. [31]

How to train your chimpanzee

The main problem with school mathematics is that there are no problems. Oh, I know what passes for problems in math classes, these insipid “exercises.” “Here is a type of problem. Here is how to solve it. Yes it will be on the test. Do exer­cises 1−35 odd for homework.” What a sad way to learn mathematics: to be a trained chimpanzee.

But a problem, a genuine honest-to-goodness natural human question—that’s another thing. How long is the diagonal of a cube? Do prime numbers keep going on forever? Is infinity a number? How many ways can I symmetrically tile a surface? The history of mathematics is the history of mankind’s engagement with questions like these, not the mindless regurgitation of formulas and algorithms (together with contrived exercises designed to make use of them).

A good problem is something you don’t know how to solve. That’s what makes it a good puzzle, and a good oppor­tunity. A good problem does not just sit there in isolation, but serves as a springboard to other interesting questions. A triangle takes up half its box. What about a pyramid inside its three-dimensional box? Can we handle this problem in a similar way?

I can understand the idea of training students to master certain techniques—I do that too. But not as an end in itself. Technique in mathematics, as in any art, should be learned in context. The great problems, their history, the creative process—that is the proper setting. Give your students a good problem, let them struggle and get frustrated. See what they come up with. Wait until they are dying for an idea, then give them some technique. But not too much. [40-2]

The art of explanation

By concentrating on what, and leaving out why, mathematics is reduced to an empty shell. The art is not in the “truth” but in the explanation, the argument. It is the argument itself which gives the truth its context, and determines what is really being said and meant. Mathematics is the art of explanation. If you deny students the opportunity to engage in this activity—to pose their own problems, make their own conjectures and discoveries, to be wrong, to be creatively frustrated, to have an inspiration, and to cobble together their own explanations and proofs—you deny them mathe­matics itself. So no, I’m not complaining about the presence of facts and formulas in our mathematics classes, I’m com­plaining about the lack of mathematics in our mathematics classes. [29]

Are you looking over my shoulder?

I think that the demand for a theory of successful thinking cannot be satisfied, and that it is not the same as the demand for a theory of creative thinking. Success depends on many things—for example on luck. It may depend on meeting with a promising problem. It depends on not being anticipated. It depends on such things as a fortunate division of one’s time between trying to keep up-to-date and concentrating on working out one’s own ideas. [47]

Science: the prototypical tool of human progress

I think that science works by a careful balance of two apparently contradictory impulses. One, a synthetic, holistic, hypothesis-spinning capability, which some people believe is localized in the right hemisphere of the cerebral cortex, and an analytic, skeptical, scrutinizing capability, which some people believe is localized in the left hemisphere of the cerebral cortex. And it is only the mix of these two, the generating of creative hypotheses and the scrupulous rejection of those that do not correspond to the facts that permit science or any other human activity, I believe, to make progress. [248]