236 ANNUAL REPORT SMITHSONIAN INSTITUTION, 195 4 



This brings us to the third question : What do we hope to achieve by 

 all this? 



THE FUNCTION OF THEORETICAL MODELS 



A theoretical model of the type we have been discussing is intended 

 to serve as a tool of research. We can think of it as a kind of adjust- 

 able template which we construct on some hypothetical principles, 

 and then hold up against the real thing in order that the discrepancies 

 between the two may yield fresh information. 



This in turn should enable us to modify the template in some respect, 

 after which a fresh comparison may yield further information, and so 

 on. The model, as it were, "subtracts out" at each stage what we think 

 we understand, so that what is not yet understood is revealed more 

 clearly. 



You will see at once that we shall judge a good model for this pur- 

 pose not so much by the success with which it imitates or predicts, but 

 rather by the clarity with which its failures enable us to infer what to 

 modify next. To be sure, our aim is to approximate more and more to 

 the real thing. But we may easily be misled into an approximation 

 process that doesn't converge. It may even pay us to discard one 

 model for another which offers us fewer numerical predictions to start 

 with, if the first model shows signs of requiring one or more additional 

 hypotheses for each phenomenon it encounters ! It is worth remem- 

 bering, in these days when predictive ability is so often confused with 

 understanding, that the epicyclic "theory" of planetary motion would 

 have been less at a loss to account predictively for the anomalous mo- 

 tion of Mercury than Kepler's theory which displaced it ! 



Our second criterion of a good research model is that it should not 

 only function normally like the brain, but also that it should go wrong 

 in the same ways. As we have seen, our model is tested most severely, 

 and is of greatest potential value, in the study of cerebral disorders 

 rather than of normal function — difficult though it is to draw the 

 line between the two areas. 



It is possible that some mathematicians may feel that no theory is 

 worthy of the name until it has produced some equations. But I want 

 (if I dare) to emphasize that what we wish to understand in such 

 multidimensional problems would be very little illuminated even if 

 we could produce a gigantic equation relating all the variables that 

 we should never measure. 



Understanding, here as always, means knowing as far as possible 

 what to expect in given circumstances, and what to infer when the 

 expected doesn't happen. The difficulty is that the data, on which 

 we want to organize our expectations by means of our theory, are 

 mostly not measurable variables but qualitative abstractions from 

 function. So it is only a small part of our aim to develop equations 



