[1573]. Analytical and graphical treatment of statistics is employed by the economist, the philanthropist, the business expert, the actuary, and even the physician, with the most surprisingly valuable results; while symbolic language involving mathematical methods has become a part of wellnigh every large business. The handling of pig-iron does not seem to offer any opportunity for mathematical application. Yet graphical and analytical treatment of the data from long-continued experiments with this material at Bethlehem, Pennsylvania, resulted in the discovery of the law that fatigue varied in proportion to a certain relation between the load and the periods of rest. Practical application of this law increased the amount handled by each man from twelve and a half to forty-seven tons per day. Such study would have been impossible without preliminary acquaintance with the simple invariable elements of mathematics.—Karpinsky, L.
High School Education (New York, 1912), chap. 6, p. 134.
[1574]. They [computation and arithmetic] belong then, it seems, to the branches of learning which we are now investigating;—for a military man must necessarily learn them with a view to the marshalling of his troops, and so must a philosopher with the view of understanding real being, after having emerged from the unstable condition of becoming, or else he can never become an apt reasoner.
That is the fact he replied.
But the guardian of ours happens to be both a military man and a philosopher.
Unquestionably so.
It would be proper then, Glaucon, to lay down laws for this branch of science and persuade those about to engage in the most important state-matters to apply themselves to computation, and study it, not in the common vulgar fashion, but with the view of arriving at the contemplation of the nature of numbers by the intellect itself,—not for the sake of buying and selling as anxious merchants and retailers, but for war also, and that the soul may acquire a facility in turning itself from what is in the course of generation to truth and real being.—Plato.
Republic [Davis], Bk. 7, p. 525.
[1575]. The scientific part of Arithmetic and Geometry would be of more use for regulating the thoughts and opinions of men than all the great advantage which Society receives from the general application of them: and this use cannot be spread through the Society by the practice; for the Practitioners, however dextrous, have no more knowledge of the Science than the very instruments with which they work. They have taken up the Rules as they found them delivered down to them by scientific men, without the least inquiry after the Principles from which they are derived: and the more accurate the Rules, the less occasion there is for inquiring after the Principles, and consequently, the more difficult it is to make them turn their attention to the First Principles; and, therefore, a Nation ought to have both Scientific and Practical Mathematicians.—Williamson, James.
Elements of Euclid with Dissertations (Oxford, 1781).