The Strangest Man: The Hidden Life of Paul Dirac, Mystic of the Atom by Graham Farmelo
My rating: 5 of 5 stars

The Joys of Eccentricity

Scientific method, like human nature, is a term of approval or disapproval not a description of anything real. We use such terms as if we knew what they mean; but they are largely without any definite content. Their primary function is one of propaganda, sometimes professional, often religious, always tendentious. Taking such terms seriously - except to dismiss them - is usually bad for human beings and other living things.

This aptly-titled biography of the prominent 20th century British scientist, Paul Dirac, is an illustration of the point. Dirac was a bona fide eccentric, a nerd, a geek, probably autistic, someone who just didn’t fit wherever he found himself. He was also a genius who was the first to formulate the relativistic mathematics of quantum mechanics. How he did this was hardly methodical and can only be called scientific in retrospect.

Dirac was initially trained in what today would be termed a trade school in Bristol. There he learned, among other things, engineering drawing, and that he was hopeless with any task involving manual dexterity. He was, in a sense, the antithesis of the mythical British empiricist. He went on haphazardly to advance his studies in applied mathematics and fitfully to pursue an interest in the then nascent field of relativity physics at Cambridge.

Only by accident did he notice that the results being produced in another area of contemporary physics, quantum mechanics, by the rather more famous scientist, Werner Heisenberg, had a formal mathematical structure similar to that one of his teachers had been interested in several years before.* This lead Dirac to formulate a suggestion for the behaviour of sub-atomic particles in roughly this form:

position symbol × momentum symbol – momentum symbol × position symbol = h ×(square root of –1)/(2×π).**

This suggestion was rejected by most quantum physicists at the time as being patently unscientific, a mathematician’s fancy. Part of the reason for the disdain shown toward the idea is that the terms on the left side of his equation - the symbols for position and momentum - are entirely abstract. That is to say, they are dimensionless entities, like a mathematical point, that have no real existence outside of the mathematician’s head. By definition, they can’t be measured (or what amounts to the same thing, they could be measured in any of an infinite number of ways); so they can’t be real things. The formula, therefore, must be meaningless.

Helass for the sceptics, the eccentric formula turned out to be exactly the key required to unlock the mysteries of quantum behaviour (and in the way of science, to produce quite a few more - like the possibility of anti-matter). Either what Dirac had done was surreptitiously ‘good science’ behind its hapless façade; or what constituted good science was in need of redefinition. Subsequent results pointed clearly to the latter. Whatever Dirac had done defined proper scientific method, although no one would have admitted it beforehand.

But even Dirac didn’t know how he had arrived at his idea and therefore what his method might have been. Coincidence and history simply appeared to combine to produce a thought, which prompted him to find a certain mid-nineteenth century tome in the University Library. Hardly, therefore, a series of events to be written up in the annals of the philosophy of science. Nothing about the process could be called scientific except that it was conducted by a person who was (barely) considered a scientist.

It would seem that in surveying the history of science the vast majority of ‘breakthroughs’ both big and small occur in just this way. Whatever ‘method’ produces them only becomes visible after they are produced; and then such method typically appears to be un-replicable as a procedure or clearly inappropriate for universal application. This is, on the face of it, a highly unscientific state of affairs. If we can’t specify the process by which reliable knowledge is generated, how can we distinguish between authentic science and bogus fakery, between reason and revelation, between astronomy and astrology?

The answer is that we can’t. Not by specifying an acceptable or mandatory procedure in any case. The only way to verify the results of scientific, or any other sort of, thought is to promote widespread and unrestricted argument about it. Through such argument it might be established that there are procedural flaws in one’s thought or experiments. Equally it might be established that the existing ‘rules’ for thinking or experimenting are inadequate.

But it’s not even possible to state the criteria in advance by which the choice should be made among these alternatives. The criteria are only discovered in the argument, and then continuously re-discovered through subsequent argument. Reason itself emerges from the debate; it cannot be imposed upon the debate.

If scientific method means anything at all, it means keeping this argument going with as many participants as possible. The only way to judge the quality of that argument is how completely it ‘sweeps in’ extremes of opinion. This, I think, is the abiding political as well as personal import of Dirac’s very eccentric, and unmethodical, professional life.

*This,is the mathematics of quaternions in which multiplication of elements is non-commutative; that is, where A x B ≠ (is not equal to) B x A.

**Where h is Planck’s constant and π is the ratio of the circumference to the diameter of every circle (its value is about 3.142). This ‘matures’ by 1928 to something highly technical and irrelevant to the commentary here.

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