» N.S. Books
June 21st, 1998.
A few years back I picked up a paperback put out by Oxford University Press, 1985. It was written by a professor who taught at the New York University, Morris Kline (1908-92). The title of the book is Mathematics and the Search for Knowledge and I quote from it:
"If physical understanding and the power to reason in physical terms about electromagnetic phenomena are lacking, what is the nature of our grasp of this reality? On what do we base our claim of mastery? Mathematical laws are the only means of probing, revealing, and mastering this large region of the physical world; of such mysterious goings-on mathematical laws are the only knowledge humans possess. Although the answer to these questions is unsatisfactory to the layperson uninitiated into these Latter-day Delphic mysteries, the scientist by now has learned to accept it. Indeed, faced with so many natural mysteries, the scientist is only too glad to bury them under a weight of mathematical symbols, bury them so thoroughly that many generations of workers fail to notice the concealment.
We are faced, then, with the amazing fact that one of the largest bodies of scientific theory is almost entirely mathematical. Certain formal deductions from this theory, such as the induction of current in wires or the reception of current hundreds of miles away from a source, can be confirmed by sense impressions, but the body of the theory itself is mathematical.
To some extent we should be prepared for this peculiar state of affairs. After studying Newton's work on gravitation we considered the question: What is gravity and how does it act? We found in that case, too, that we had no physical understanding of the action of gravitation. We have a mathematical law describing the quantitative value of this force, and, by using this law and the laws of motion, we can predict effects that can be experimentally checked. The central concept of gravitation, however, remains unknown.
We see, then, that at the heart of our best scientific theories, is mathematics or, more accurately, some formulas and their consequences. The firm, bold design of a scientific theory is mathematical. Our mental constructions have outrun our intuitive and sense perceptions. In both theories, gravitation and electromagnetism, we must confess our ignorance of the basic mechanisms and leave the task of representing what we know to mathematics. We may lose pride in making this confession, but we may gain understanding of the true state of affairs. We can appreciate now what Alfred North Whitehead meant when he said, 'The paradox is now fully established that the utmost abstractions (of mathematics) are the true weapons with which to control our thought of concrete facts.'"
Generally, I admire the mathematician, I suppose it is because, in his mathematical business, he is able to practice "the divine art of impartiality."
"And certainly to have no axe to grind is something very noble and very rare. It may be said to be the antithesis of the bestial. A series of creatures might be constructed, arranged according to their diminishing interest in the immediate environment, which would begin with the amoeba and end with mathematician. In pure mathematics the maximum of detachment appears to be reached: the mind moves in an infinitely complicated pattern, which is absolutely free from temporal considerations. Yet this very freedom - the essential condition of the mathematician's activity - perhaps gives him an unfair advantage. He can only be wrong - he cannot cheat. But the metaphysian can. The problems with which he deals are of overwhelming importance to himself and the rest of humanity; and it is his business to treat them with an exactitude as unbiased as if they were some puzzle in the theory of numbers. That is his business - his glory." (Strachey's Portraits in Miniature and Other Essays.)
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June, 1998 (2022)