Page:Popular Science Monthly Volume 8.djvu/461

Rh not contradictory. If one should say that there is in the universe a circular triangle, we should deny it, not because the concept of a triangle is irreconcilable with the concept of a circle, as consistent in the same figure, which is quite true, but because they are contradictory. What is irreconcilable to you may be reconcilable to another mind, because "irreconcilable" indicates the relation of the concept to the individual intellect; but what is contradictory to the feeblest is contradictory to the mightiest mind, because "contradictory" represents the relation of the concepts to one another.

In the definition of a person there is nothing to exclude infinity, and in the definition of infinite there is nothing to exclude personality. There is no more exclusion between "person" and "infinite" than between "line" and "infinite;" and yet we talk of infinite lines, knowing the irreconcilability of the ideas, but never regarding them as contradictory.

Writers of great ability sometimes fall into this indiscrimination. For instance, a writer whom 1 greatly admire, Dr. Hill, former President of Harvard College, in one paragraph (on "The Uses of Mathesis," in Bibliotheca Sacra), seems twice to employ "contradictory" in an illogical sense, even when he is presenting an illustration which goes to show most clearly that in other sciences, as well as in theology, there are propositions which we cannot refuse to accept, because they are not contradictory, although they are irreconcilable; in other words, that there are irreconcilable concepts which are not contradictory, for we always reject one or the other of two contradictory concepts or propositions.

That is so striking an illustration of the mystery of the infinite that I will reproduce it. On a plane imagine a fixed line, pointing north and south. Intersect this at an angle of ninety degrees by another line, pointing east and west. Let this latter rotate at the point of intersection, and at the beginning be a foot long. At each approach of the rotating line toward the stationary line let the former double its length. Let each approach be made by bisecting the angle. At the first movement the angle would be forty-five degrees, and the line two feet in length; at the second, the angle twenty-two and one-half degrees, and the line four feet; at the third, the angle eleven and one-fourth degrees, and the line eight feet; at the fourth, the angle five and five-eighths degrees, and the line sixteen feet; at the fifth, the angle two and thirteen-sixteenths degrees, and the line thirty-two feet, and so on. Now, as this bisecting of the angle can go on indefinitely before the rotating line can touch the stationary line at all its points, it follows that before such contact the rotating line will have a length which cannot be stated in figures, and which defies all human computation. It can be mathematically demonstrated that a line so rotating, and increasing its length in the inverse ratio of its angle with the meridian, will have its end always receding from the meridian and