What they really thought of each other was known only to themselves and to their immediate domestic circles.
Naturally Professor Marmion was well aware that his elevation to the higher plane of N4 gave him an enormous advantage over his adversary, for now he could, if he chose, smite him hip and thigh, in a strictly scientific sense, and reduce him to utter confusion and public ridicule, and the question which he had come to discuss with himself was: In how far, if at all, was he justified in so using the extra-human powers with which he had been endowed?
The moment that he began to do this he became conscious of another curious complication of his recent development.

On the higher plane he had argued the matter out with no more emotion than a calculating machine would have betrayed, and he had come to a conclusion that was absolutely luminous and just: but now that he came to argue the same question on the lower plane he found that he was doing it under human limitations, and therefore with human feelings.
"No," he said in the peculiar low, musing tone which was habitual to him during these monologues, "no; after all, I do not see that there would be any harm in that.

Wrong, nay, sinful it would undoubtedly be to prove to demonstration that religious, social, and physical laws, may, under certain changing circumstances, be both true and false at the same time.
I am, or was--or whatever it is--perfectly right in considering that to deliberately produce such a chaos as that would do would be the most colossal crime that a man could commit against humanity, as far as this plane is concerned, but there can be no harm in making a few mathematical experiments." He took a few more turns up and down the room, pulling slowly at his pipe, and with his mind not wholly unoccupied with speculations as to what Professor Van Huysman's feelings might be if he were watching the said experiments.

Then he began again: "At the worst I shall only be carrying certain investigations a few steps farther, and developing theories which have been seriously discussed by the hardest-headed scholars in the world.

Both the Greek and the Alexandrian philosophers speculated on the possibility of a state of four dimensions; and didn't Cayley, before this very Society, deliberately say that at the present rate of progress in the Higher Mathematics, the eye of Intellect might ere long see across the border of tri-dimensional space?
"Surely I cannot do any very great harm by carrying his arguments to their logical conclusions--if I can.