Two styles of theorizing / Dirac:

From Eros to Gaia, 1992:

>To give to nonexperts a true impression of the Dirac style, it is best to use his own words. Here is Dirac, at the age of seventy, talking to a mixed audience at the University of Miami in Coral Gables. The title of his talk was “Basic Beliefs and Fundamental Research.”

There is one fairly obvious way of getting a new theory. Keep close to the experimental results, hear about all the latest information that the experimenters obtain, and then proceed to set up a theory to account for them. That is a more or less straightforward procedure and there are many physicists working on such lines, competing with one another, and it might develop somewhat into a rat-race. Of course it needs rather intelligent rats to take part in it. But I don’t want to speak about this method of procedure.

There is another way in which a theoretical physicist may work which is slower and more sedate and may lead to more profound results. It does not depend very closely on experimental work. This consists in having some basic beliefs and trying to incorporate them into one theory. Now why should one have basic beliefs? I don’t know that I can explain that. It’s just that one feels that nature is constructed in a certain way and one hangs onto the idea rather like one might hang onto a religious belief. One feels that things simply have to be on these lines and one must devise a mathematical theory for incorporating the basic belief.

These two styles of theorizing are well known in the history of science. Historians call the first style Baconian and the second Cartesian. Our young colleagues today, with less awareness of their place in history, are accustomed to call the two styles “bottom-up” and “top-down.” Dirac in his talk went on to explain how the very greatest theoretical physicists, in particular Newton and Einstein, worked from the top down, deducing laws of nature from fundamental beliefs rather than inducing laws from the results of experiment. Dirac himself is in modern times the supreme example of a top-down physicist. Here is what he says about himself:

"My own early work was very much influenced by Bohr orbits, and I had the basic belief that Bohr orbits would provide the clue to understanding atomic events. That was a mistaken belief.… I found out that my own basic belief was wrong and I had to go over to quite a new line of thinking. I had to have some more general basis for my work, and the only reliable basis I could think of, the only basis which was sufficiently general so as to secure me from making the same mistake again, was to set up a principle of mathematical beauty: to say that we don’t really know what the basic equations of physics are, but they have to have great mathematical beauty. We must insist on this, and that is the only feature of the equations that we can have confidence in and insist on.… How can one make beauty a fundamental test for the correctness of a physical theory? Well, it is quite clear that beauty does depend on one’s culture and upbringing for certain kinds of beauty, pictures, literature, poetry and so on.… But mathematical beauty is of rather a different kind. I should say perhaps it is of a completely different kind and transcends these personal factors. It is the same in all countries and at all periods of time.… Well, that is the essence of what I wanted to tell you. In fact one can feel so strongly about these things, that when an experimental result turns up which is not in agreement with one’s beliefs, one may perhaps make the prediction that the experimental result is wrong and that the experimenters will correct it after a while. Of course one must not be too obstinate over these matters, but still one must sometimes be bold."

Dirac was bold. His confidence in his own instinct for mathematical beauty led him in succession to three fundamental discoveries: first, the general abstract formulation of quantum mechanics; second, the correct quantum description of electromagnetic radiation processes; and third, the Dirac equation for the electron. In each case he was led not merely to a new physical law but to a new style of mathematical description of nature. And in each case the experiments proved him right, although, as he hints in the Coral Gables lecture, there were initially some contradictory experimental results which he was bold enough to ignore.

Dirac’s fundamental belief, the belief that the basic criterion for choosing a physical theory should be aesthetic, proved itself in his hands overwhelmingly successful. Nature agreed with his criterion. And this agreement between Nature’s and Dirac’s notions of beauty presents us with a new example of an old philosophical riddle. Why should Nature care about our feelings of beauty? Why should the electron prefer a beautiful equation to an ugly one? Why should the universe dance to Dirac’s tune? These are deep questions which neither scientists nor philosophers know how to answer. Dirac, by his style of discovery, has posed these questions more sharply than anyone else. More even than Newton and Einstein he used the criterion of beauty consciously and directly as a way of finding truth.<

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>In the history of science, from its beginnings to the present day, the Baconian and the Cartesian traditions have remained alive, Baconian science emphasizing empirical facts and details, Cartesian science emphasizing general ideas and principles. The healthy growth of science requires that both traditions be honored. Bacon without Descartes would reduce science to butterfly collecting; Descartes without Bacon would reduce science to pure mathematics.<

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>I have described the history of science as a dialogue between unifiers and diversifiers. Unifiers are following the tradition of Descartes, diversifiers are following the tradition of Bacon. Unifiers are trying to reduce the prodigality of nature to a few general laws and principles. Diversifiers are exploring the details of things and events in their infinite variety. Unifiers are in love with ideas and equations; diversifiers are in love with birds and butterflies. My friend and colleague, the physicist Chen Ning Yang, told me once that when he was a boy of six in China he looked up at the stars and asked what are the laws that make them move across the sky. But when I was a boy of six in England, I looked up at the stars and asked what are their names. Yang was interested in stars in general; I was interested in stars as individuals.<