As these two luminous rays are bent out of their paths in space by the gravitation of the stars, and as they are differently affected in this way because they are at different distances from the stars, it follows necessarily that they will cease to be parallel (in the Euclidean sense of the word) and will finally meet; or at least that they cease to realise the first condition of parallelism—coexistence—in the same local plane. In a word, if we consider the matter, not within the ridiculously limited field of experiment in the laboratory, but in the vast field of celestial space, the real universe is not Euclidean, because in it light does not travel in a straight line. Kant regarded the truths—to be accurate, the deductive affirmations—of the Euclidean geometry as “synthetic judgments _a priori_,” or self-evident propositions. As we have seen, Kant was wrong, not only from the point of view of theoretical geometry, but also from the point of view of real geometry. The etymology of the word “geometry” (which means “measuring the earth”) is enough of itself to show that it was originally, and chiefly, a practical science. That is a sufficient justification for our asking which geometry is most in accord with the real universe. Gauss, a profound thinker, asked the question long ago, in the last century, and he made certain delicate experiments to measure if the sum of the angles of a triangle is really equal to two right angles, as the Euclidean geometry says. With this view he took a vast triangle, the apices of which were formed by the highest peaks of three widely separated mountains. One of them was the famous Brocken. With his assistants he took simultaneous sights of each peak in relation to the other two, and he found that the sum of the three angles of the triangle only differed from 180 degrees to an extent that might be put down to error in observation. There were many philosophers who ridiculed Gauss and his experiments. With the _a priori_ dogmatism that one so often encounters amongst these people they said that his measurements, even if they had had a different result, would have proved nothing to the detriment of Euclid’s theorems, but would merely have shown that some disturbing cause bent the luminous rays between the three apices of the triangle. This is true, but it does not matter. If Gauss had found that the sum of the angles of the triangle in question was larger than two right angles, it would have proved that real geometry is not the geometry of Euclid. The question which Gauss asked was profound and reasonable. The philosophers who ridiculed it might have been challenged to define real straight lines, natural straight lines, in any other terms than those of the passage of light.