Three views:
P. J. Davis and R. Hersh, "The Mathematical Experience," Houghton-Mifflin,
Boston: 1981.
"Professor Taylor [whose professional field lies at the intersection of physics, chemistry,
and materals science] was asked to comment on the contemporary view that the scientific
method can be summed up by the sequence: induction, deduction, verification, iterated as
often as necessary. He replied that he went along with it in its broad outlines. But he
wanted to elaborate:
Induction is related to my awareness of the observations of others and of existing theories. Deduction is related to the construction of a model and of physical conclusions drawn from it by means of mathematical derivations. Verification is related to predictions of phenomena not yet observed and to the hope that the experimentalist will look for new phenomena.
The experimentalist and the theoretician need one another. The experimentalist needs a model to help him lay out his experiments. Otherwise he doesn't know where to look. He would be working in the dark. The theoretician needs the experimentalist to tell him what is going on in the real world. Otherwise his theorizing would be empty. There must be adequate communication between the two and, in fact, I think there is. When asked why the profession splits into two types--experimentalists and theoreticians-- he said that apart from a general tendency to specialize, it was probably a matter of temperament. "But the gap is always bridged --usually by the theoretician."
Professor Taylar was asked how he felt about the often quoted remark of a certain theoretician that he would rather his theories be beautiful than be right. "This cuts close to the bone. It really does. But as I see it, mere aesthetics doesn't pay dividends. In my experience, I should be inclined to replace the word 'beautiful' by the word 'analyzable.' I should like my models to be beautiful, effective and predictive. But the real goal is the understanding of a situation. Therefore the models must be analyzable because understanding can come only through analyzability. If one has all of these things, then this is a great and rare achievement, but I should sat that my immediate goal is analyzability."
S. Hawking, "Black Holes and Baby Universes," Bantam Books, New York:
1993.
In theoretical physics, the search for logical self-consistency has always been
more important in making advances than experimental results. Otherwise elegant
and beautiful theories have been rejected because they don't agree with
observation, but I don't know of any major theory that has been advanced just on
the basis of experiment. They theory always came first, put forward from the
desire to have an elegant and consistent mathematical model. The theory then
makes predictions, which can then be tested by observation. If the observations
agree with the predictions, that doesn't prove the theory; but the theory survives
to make further predictions, which again are tested against observation. If the
observations don agree with the predictions, one abandons the theory.
Or rather, that is what is supposed to happen. In practice, people are very reluctant
to give up a theory in which they have invested a lot of time and effort. They
usually start by questioning the accuracy of the observations. If that fails, they try
to modify the theory in an ac hoc manner. Eventually they theory becomes a
creaking and ugly edifice. Then someone suggests a new theory, in which all the
awkward observations are explained in an elegant and natural manner....Einstein
was driven to [special relativity] not so much by the experimental results as by the
desire to make two parts of the theory fit together in a consistent whole. The two
parts were the laws that govern the electric and magnetic fields, and the laws that
govern the motion of bodies.
A. Einstein, "The evolution of Physics," Simon and Schuster, New York:
1938.
Physical concepts are free creations of the human mind and are not, however it
may seem, uniquely determined by the external world.