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On the Rejection of the Fractions of a Pound in extensive Valuations

Published online by Cambridge University Press:  18 August 2016

A. De Morgan
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Extract

When a mass of results are to be calculated and added up, it generally happens that a small fraction is of little consequence in each item, except as the little of which many make a mickle. The money calculator knows nothing of the principle that it is very hard, next to impossible, practically quite impossible, to get a mickle out of positives and negatives, when both are sure to occur in equal numbers in the long run, and with equal quantities. Generally speaking, the items of money calculations are determinable, and accuracy to the penny below the true result is a matter of contract. But in life contingencies, in which a certain amount of inaccuracy is known to lurk in the fundamental tables, no real truth is gained by tacking shillings, pence, and farthings, on to hundreds of pounds. If the nearest pound be always taken, granting that the calculated result shall be thereby a little altered, no man alive can say whether that alteration shall be approach to, or recession from, what we should call absolute truth, if our tables were perfect: it is as likely to be one as the other.

Type
Research Article
Information
Journal of the Institute of Actuaries , Volume 10 , Issue 5 , October 1862 , pp. 247 - 251
Copyright
Copyright © Institute and Faculty of Actuaries 1863

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References

page 248 note * A word is much wanted for this creature. Physical philosopher is unobjectionable, but too long. Philosopher, by itself, a word which has been used, is not only proved to be too wide, but, in the revival of philosophy proper which is taking place, will go near to be thought so shortly. Physician has irrevocably lost its original sense; and so has naturalist. Physicist is coming into use: it was a word invented in Pandemonium as a salute to Satan when he returned from his inquiry into nature, undertaken with a view of creating confusion by the introduction of his own notions; and Milton has made the natural mistake of supposing that he was hissed. One good distinctive word is empiric, follower of experience; but the physician has appropriated it to medical practitioners who are, rightly or wrongly, wise above what is written. But pirastic would do very well; and would prevent the experimentalist from carrying about a collar of SS.

page 249 note * I suppose that such a formula as (1–rA): (1 + r) must needs present all digits equally in the long run, there being no law in the values of A as to digits. But no such thing is to be inferred of numbers which are not accidentally arranged. In Mr. Shanks's ratio of the circumference of a circle to its diameter, or 4(1-⅓+⅕-1/7+…), to 608 figures, the nine digits and cipher occur as follows:—

The exceptional character of the 7 is remarkable.