|(quoted from Symposium)|
"And, Zed," said O doubtfully, "every one of those elements is shaky. We are unable to separate space from one of its elements—shape. We do not know whether the particular distortion we live in is one of shape or of space. For instance, with us, the relation of the ring to the tendon of a circle is three and a continuing decimal to one.. But we know from Scripture, and also from the geometry of Jordman, that in undistorted space or shape the relation would be exactly three to one. Now, if we were in such an undistorted space or shape, might we not think undistorted thoughts? It is certain that we would think in a different manner and that every object of our thoughts would differ from the present. We would not have the same grammar or conventions."
"There is no undistorted space, O," Wye said solidly. "Distortion is a necessary element. If I be not distorted, then I be not at all. The shape of space depends on the amount of matter in the universe. Matter is the distortion, but no matter is nothing. The amount of matter posits its own mathematics. There cannot be theoretical mathematics, only the mathematics of an actual universe. But, should the mass of the universe increase by only an ounce (Nictitating nebulas!—that's a little too slight), should it increase by no more than a thousand galaxies, then every mathematical property would change. The ratio of the ring to the tendon of a circle might then become three and a half, or five, or nine, or one. There might then be thirteen whole numbers between one and ten.
"For my part, I believe that we do live in a universe of changing mass, and that every property changes with it. Do you know why nobody discovered certain simple relationships before Pythagoras did so? It was because they had only just then become true relationships. Do you know why nobody discovered the three laws of motion before Newton discovered them? Because—they had not been true the day before."