On Being a Specialist
lay M. L. CARTWRIGHT* N eminent scientist once said to me that the great British public have implicit faith in scientists when they speak on subjects outside their own field and a profound distrust of them when they speak on their own special subject, or words to that effect. On the face of it this is quite pre- posterous, but there is a grain of truth in it and perhaps one thousandth part of a grain of reason for it.
I am a mathematician, not an experimental scientist, but although mathematics is an art I hope that 1 am sufficiently near the scientists in spirit to speak as a scientist having a special subject, and mathematics is the subject par excellence of specialists. The recent advances are often only intelligible to a few experts. Before the war I used to attend Professor G. H. Hardy's seminar, or Conversation Class as it"was called, at which experts in a certain restricted range of topics in pure mathematics talked about recent work. We had tea before the lecture and at tea I often became involved in an absorbing argument about something nearly related to my own work. This had to be broken off so abruptly when the lecture began that I spent the first five or ten minutes thinking about the previous discussion and then found that the lecturer had made his preliminary explanations and definitions, the blackboard was covered with symbols which were meaningless to me and the lecture was almost a dead loss. Not quite, perhaps, for one absorbed an impression of the kind of method and the level of difficulty of the subject which may be more essential than results.
Mathematics is a subject for specialists in the sense that the specialist realises as no one else can that one broken link in a long chain of reasoning leaves the whole valueless; no pretence is possible in mathematics, the result is true or false. An immense superstructure can crumble away to practically nothinab if a mistake is found in it, and no superficial examina- tion is likely to reveal such a mistake. Many mathematicians might be taken in by the argument, but there is a feeling for the depth and quality of the reasoning which often tells the specialist that a mistake must be there although he, cannot spot it at the first reading. '
I said that I would speak as a scientist having a special subject. but, alas. I fear that it should be the past tense. I used to be fairly knowledgeable about the theory of functions of a complex variable, but then I became interested in non-linear differential equations, and so instead of keeping up with recent advances in complex variable work I acquired a curious smat- tering of highly specialised electronic valve theory, without learning the more elementary part at all, and also a lopsided knowledge of differential equations ignoring large parts of the better known linear theory. But that is what is happening in many parts of science; the growing pants are on the border lines and since it is impossible to know both sides thoroughly, a species of borderline expert arises whose speciality cuts right across the usual subject lines. It is difficult for him as it is for all scientists today to obtain the knowledge relevant to his work without prohibitive effort, and no amount of abstracting will solve the problem; for to recognise the relevancy of factors not previously considered relevant is an important achieve- ment, and here perhaps is the reason why the great British public distrusts the expert. It has a suspicion of the truth that concentration on a narrow field for a prolonged period which is essential to the evolution of a specialist is apt to produce a blinkered outlook which will fail to see important relevant factors close beside the path.
A mathematician, however, is more often asked to solve a specific problem than to give an opinion, and it is hard to see how his solution could be distrusted. But a young Cam- bridge mathematician who went into the Navy wrote: " Typical of the widespread scepticism of mathematics is the remark, frequently made after a proof has been demonstrated, even though the theorem has been completely understood: ' That's interesting, let's try it to see if it works,' and, if the theorem is one of geometry, it is drawn out with pencil and ruler. . . . Usually the layman is only convinced of the truth of a result when he has tried a few special cases ' to see if they work.' And should it so happen that the first example comes out wrong, it is the theorem which is suspected and not the work- ing out or drawing of the example." At a higher level the engineers and physicists often seem to have data up their sleeves which they would use automatically themselves, but do not think to tell the poor pure mathematician, and so they may be right in saying that the mathematician's answer is the wrong one for their problem. It is better for the mathematician to teach the engineers and physicists the techniques and ideas necessary for solving their problems.
Cambridge colleges provide unrivalled opportunities for ex- perts in different fields to meet; my left-hand neighbour may spend her days working on cheese-mites and my right-hand neighbour on crystal structures, or (for we are not all scientists) on intricacies of the Greek language. The system doesn't necessarily get the right experts together and the knowledge acquired may consist of a rather indigestible collection of curious facts such as the technique required to make toads eat steak. Even without the College system the scientist gets used to meeting experts in other fields and learns to recognise certain types; the efficient type, the inefficient type who does very well for himself by being inefficient, the type who talks interminably about his own work, the optimist who thinks he has done or is about to do something marvellous, and the pessimist who thinks what he is doing won't succeed or will raise worse problems if it does. There may be something in setting an expert to catch an expert or assess the value of his opinion.
Apart from this is there any feature common to scientific specialists which would justify the great British public in their faith in the scientist's word on topics outside his own field ? The fully fledged scientist certainly travels far and wide; our friends leave for a congress in Australia, a dinner in the United States, a committee in Rome, a conference on an island in the Mediterranean, a sabbatical leave in the United States or France. We get accustomed to accepting people of very varied nationalities as fellow scientists without bothering about their colour, creed or politics, unless of course the politics affect their science, and here it must be admitted that certain free- doms are a basic essential of scientific work, although scientists seem to differ in their interpretations and applications of the principle. As for the travelling, the scientist usually travels to meet other scientists; his committee in Rome may contain more French and American than Italian members and when I went to California the four people to whom I talked most were educated in Hungary, Switzerland, Russia and France.
Mistress of Girton college, Cambridge. I could hardly speak about typical American opinion, but then that was not what I went for. I think that the great British public should think twice about the qualifications of any scientist to speak on a topic outside his own field, but isn't that just what I have been doing in this article ?
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