knew that, when we find our way stopped in the order of thought to which we have hitherto been confined, such experience is an indication that the time has come to investigate afresh the question of the relation between different orders of thought. By transferring the search for a relation between the hypothenuse and the sides to an order of dimensions higher than that involved in the original question, we find that there is a constant relation, one indeed of absolute equality, between the square on the hypothenuse and the squares on the sides.
Let us think with sympathy of the orthodox Geometricians. They thought, of course, that they had exhausted all the possibilities, and satisfactorily proved that the constant relation sought had no existence. And behold, here come dreamers, who claim the right to overthrow all established boundaries of knowledge; to evade difficulties by a mere trick; and to solve the question, declared unsolvable, by reference to some extra-linear order of ideas! We can well imagine their disgust. Alas for human short-sightedness! the defenders of orthodox methods are forgotten; and "the dreamers, the derided, the mad, blind men who saw" Truth, because they persisted in ignoring the cobweb barriers raised by intellectual timidity,—these heretics built the Temple dedicated by the Wise Man to The Great Unity; and they also founded the Geometry of the Future.
The moral of Euclid is this:—As long as we are investigating relations with no reference to any higher order of ideas than is obviously involved in those relations, we could make each discovery by some empirical method; a new order of thought begins at
