Edward Sang addresses the Actuarial Society of Edinburgh

Edward Sang, as President, addressed the Actuarial Society of Edinburgh on 5 November 1868. An extract from his address was published in the Journal of the Institute of Actuaries and Assurance Magazine 15 (4) (1870), 257-270. We present below a short extract from the published article.

Address to the Actuarial Society of Edinburgh by Edward Sang

The only satisfactory data which can be obtained for the guidance of those engaged in the business of Life Assurance are to be found in the records of the offices. The dates of birth have been ascertained with very considerable precision, the influence of migration is reduced almost to zero, while the deaths, as well as the ages at death, are all authenticated; we only need a considerable number of cases at each age to make these records all that can be desired.

It is now more than the quarter of a century since the desirableness of combining their experience was urged upon the Scotch offices. The results of the experience of seventeen offices have been published, and now again we are on the eve of receiving a statement of the results obtained from the records of all the old establishments in the country.

It does not look to be a difficult affair, that of doing away with these spasmodic efforts, and of substituting for them a continuous system according to which each year's experience of all the institutions may be added to the past experience, and the results of the whole at once placed before us. Such a system would put us in possession at all times of the very latest information on the subject.

When we have to deal with confessedly imperfect data, we are forced to adopt some plan for smoothing down their irregularities. Now, if we knew the cause of the imperfection and the law according to which that cause operates, we could compute and allow for its effects; the data would then have ceased to be imperfect. For example, if we could estimate the relative attractions of the different ages, we could apply this law of preference to the tabulated numbers, and thus have made a true table. Hence, when we come to consider the matter deeply, the uncertainty is seen to be not in the numbers returned, but in our ignorance of the many causes which have combined to produce the return.

In the case, however, of the office records, which must be regarded as almost entirely freed from disturbing influences, it becomes a question whether it be or be not allowable to smooth the results. This question belongs to the general subject of observations made to determine physical laws, and we can hardly obtain a satisfactory answer to it if we confine our attention to one limited inquiry. Let us step out of our own department and take a look at other matters. Astronomers have set themselves to discover the manner of the earth's motion round the sun; they have observed the sun's apparent angular distance from a fixed line, and obtained his relative linear distance by micrometric measurements of his diameter at various times during the year. By combining these two sets of co-ordinate measurements they obtain a series of points representing the successive positions of the earth, and the line passing through these points is the earth's orbit. The operation is identical in principle with that which we follow in seeking the law of life. The line drawn through the points thus obtained will be uneven on account of the unavoidable errors of observation, and the astronomer will naturally set about to smooth it. Let us suppose him to be yet in ignorance of any law, and inquire on what principle he may proceed. Casting a glance over the general form of the observed path, he notices with Kepler its strong resemblance to an ellipse; he assumes the ellipse as representative of the true law of the earth's motion, seeks out from among all ellipses that one which passes most closely to his observed points, adopts that as the true orbit, and attributes the various deviations from this line to errors of observation.

Improved telescopes, larger and better divided circles, more accurate time-keepers, enable him greatly to reduce the errors of observation, and he finds that the deviations from the elliptic path are too great to be accounted for by these; the law is more complex than he at first thought; - the earth does not move round the sun in an ellipse, and the astronomer has to investigate the law of the deviation, or inequality as he calls it. Now it must be clear to you that if, instead of recording the actual observations, astronomers had been in the habit of previously smoothing them down to suit the supposed proper curve, we should never have been able to expiscate the true law of the variations, because the data from which alone it is to be found would have been .concealed.

It is the same in our business. There is, we must presume, a fundamental law of life accompanying the organisation of the human being; but this law is traversed by many artificial and accidental conditions; just as the disturbing attraction of the planets are combined with that of the sun. The disturbances caused by these conditions take the appearance of unevennesses in the life-line, and to smooth these down for the sake of accommodating them to any pre-conceived idea, is virtually to prevent our learning anything about them.

We can hardly over-estimate the influence of circumstances upon the duration of life. Think on the ravages of helminths and other parasites before the discovery of fire, and when all food was eaten raw; consider the catarrhs and bronchitis, and the nauseous skin-diseases when men wrapped themselves in untanned hides. Or, not to go so far back, remark the change which has been caused by the discovery of vaccination by Jenner, or the immunity from ague obtained by the use of quinine, from scurvy by that of lime-juice. Every improvement in life, every fluctuating fashion of dress, each new article of food, each new material for clothing, each change in our customs, must produce its effect, and leave its impress on the life-line; so that the sinuosities which we attribute to accidents in our observations, may in truth indicate the existence of active influences. Those of the irregularities which are due to minute errors in observation will gradually be compensated, while such as depend on changes in the state of society will continue to be represented in the returns for succeeding years; and hence, on all accounts, we must declare against the smoothing down of results obtained from trustworthy data.

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