The n-Category Café

Some participants in the Secret Blogging Seminar debate, such as Terence Tao, were keen to provide a continuum between mathematics and physics. An important point to note in this respect is that physics is guided by other than empirical considerations. Earlier in the book, pp. 9-15, Polanyi discusses how Einstein came to relativity theory more by way of what we have heard him call above validation than by verification. He continues:

When the laws of physics thus appear as particular instances of geometric theorems, we may infer that the confidence placed in physical theory owes much to its possessing the same kind of excellence from which pure geometry and pure mathematics in general derive their interest, and for the sake of which they are cultivated.(p. 15)

Again we are returned to the passionate, personal engagement of the scientist with their field. I’ll leave you with his diagnosis of the mistake which encourages us to discount this engagement:

We cannot truly account for our acceptance of such theories without endorsing our acknowledgement of a beauty that exhilarates and a profundity that entrances us. Yet the prevailing conception of science, based on the disjunction of subjectivity from objectivity, seeks–and must seek at all costs–to eliminate from science such passionate, personal, human appraisals of theories, or at least to minimize their function to that of a negligible by-play. For modern man has set up as the ideal of knowledge the conception of natural science as a set of statements which is ‘objective’ in the sense that its substance is entirely determined by observation, even while its presentation may be shaped by convention. This conception, stemming from a craving rooted in the very depths of our culture, would be shattered if the intuition of rationality in nature had to be acknowledged as a justifiable and indeed essential part of scientific theory. That is why scientific theory is represented as a mere economical description of facts; or as embodying a conventional policy for drawing empirical inferences; or as a working hypothesis, suited to man’s practical convenience–interpretations that all deliberately overlook the rational core of science.

That is why, also, if the existence of this rational core yet reasserts itself, its offensiveness is covered up by a set of euphemisms, a kind of decent understatement like that used in Victorian times when legs were called limbs–a bowdlerization which we may observe, for example, in the attempts to replace ‘rationality’ by ‘simplicity’. It is legitimate, of course, to regard simplicity as a mark of rationality, and to pay tribute to any theory as a triumph of simplicity. But great theories are rarely simple in the ordinary sense of the term. Both quantum mechanics and relativity are very difficult to understand; it takes only a few minutes to memorize the facts accounted for by relativity, but years of study may not suffice to master the theory and see these facts in its context. Hermann Weyl lets the cat out of the bag by saying: ‘the required simplicity is not necessarily the obvious one but we must let nature train us to recognize the true inner simplicity.’ In other words, simplicity in science can be made equivalent to rationality only if ‘simplicity’ is used in a special sense known solely by scientists. We understand the meaning of the term ‘simple’ only by recalling the meaning of the term ‘rational’ or ‘reasonable’ or ‘such that we ought to assent to it’, which the term ‘simple’ was supposed to replace. The term ‘simplicity’ functions then merely as a disguise for another meaning than its own. It is used for smuggling an essential quality into our appreciation of a scientific theory, which a mistaken conception of objectivity forbids us openly to acknowledge.

What has just been said of ‘simplicity’ applies equally to ‘symmetry’ and ‘economy’. They are contributing elements in the excellence of a theory, but can account for its merit only if the meanings of these terms are stretched far beyond their usual scope, so as to include the much deeper qualities which make the scientists rejoice in a vision like that of relativity. They must stand for those peculiar intellectual harmonies which reveal, more profoundly and permanently than any sense-experience, the presence of objective truth.

I shall call this practice a pseudo-substitution. It is used to play down man’s real and indispensable intellectual powers for the sake of maintaining an ‘objectivist’ framework which in fact cannot account for them. It works by defining scientific merit in terms of its relatively trivial features, and making these function then in the same way as the true terms which they are supposed to replace.

Other areas of science will illustrate even more effectively these indispensable intellectual powers, and their passionate participation in the act of knowing. It is to these powers and to this participation that I am referring in the title of this book as ‘Personal Knowledge’. We shall find Personal Knowledge manifested in the appreciation of probability and of order in the exact sciences, and see it at work even more extensively in the way the descriptive sciences rely on skills and connoisseurship. At all these points the act of knowing includes an appraisal; and this personal coefficient, which shapes all factual knowledge, bridges in doing so the disjunction between subjectivity and objectivity. It implies the claim that man can transcend his own subjectivity by striving passionately to fulfil his personal obligations to universal standards.