On the Nature of the Function Expressive of the Law of Human Mortality

OF THE DISCUSSION Mr R. G. Barley, in opening the discussion, referred to the statement at the beginning of paragraph 3 of the paper: When the graduation of mortality statistics is being discussed it is frequently said that: the mathematical formula used is of no importance, that any formula will do if it fits. Such an attitude denies any reality to the process of graduation. Those words seemed to him to imply a sharp division between the scientific sheep, concerned with the reality which might be attributed to the process of graduation, and the unscientific or practical goats, concerned only to secure, for example, a workable table of premiums. That was a distinction which he did not believe existed in fact, and he thought that it was that statement which was at the bottom of some of the difficulties which he had found in reading the paper. When a graduation was being made for a specific practical purpose there were always considerations which removed the result to some degree from that which might otherwise be regarded as ideal. It was essential to take into account whether it would be safer for such a practical purpose to over-estimate or to under-estimate mortality, and whether the trouble and expense of refined methods were justified by either the size of the experience or the use to which the results were to be put. He would assume for the purposes of the discussion that considerations of that kind might be entirely disregarded. There were still left, however, at least two possible attitudes towards the graduation of mortality data. The hypothesis that ‘any formula will do if it fits’ was meaningless without some definition of the word ’fit‘. A test for graduation was usually undertaken with the idea that the observations were a sample and that the purpose of the graduation was to remove random variations due to sampling. One attitude, therefore, might be that if the random variations had been removed from a mortality experience so far as could be judged the object had been achieved, regardless of whether the graduation method used would be suitable for another experience. He did not think that that attitude need deny reality to the graduation process. The other attitude was that of seeking something which was common to more than one mortality experience, and naturally involved the consideration of common features of graduation formulae which had been successful and the attempt to construct formulae which would be successful in more than one instance. The idea of a law of mortality necessitated that more searching attitude to the problem. He was sure that the use of a quotation from Gompertz as the title of the paper was more than a mild literary conceit, in spite of the modest statement in paragraph 77 that the method must take its place beside the others of all kinds. The title, it would be noted, postulated that there was a law of mortality, and it distinguished human mortality. In what sense were they to understand ‘law’ ? The author pointed out that there had been a change in attitude with regard to the function expressive of the postulated law, that in the early tables attention had been directed primarily to the number of survivors, and that it was only later that the law had been thought of in terms first of a rate, and then of a force operating on the number alive at a given age. During the same period, ideas had changed as to the meaning of ‘law’, To Gompertz, a natural law must have seemed a much more definite statement than it did in the middle of the twentieth