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Why, he can do tricks with all those new things they got on cars, tricks nobody ever did before or even thought about in the old days." "And more fundamental discoveries," the professor said. "Chadwick's Law of Dimensionality, Dvedkin and the Ontological Mean ... oh, I keep up with the literature. No matter what's happened to me, I keep up with the literature."
Prometheus up in Spaceland was bound for bringing down fire for mortals, but I poor Flatland Prometheus lie here in prison for bringing down nothing to my countrymen. Yet I existing the hope that these memoirs, in some manner, I know not how, may find their way to the minds of humanity in Some Dimension, and may stir up a race of rebels who shall refuse to be confined to limited Dimensionality.
They are not necessary to the cliff: they are necessary only to the climber. Dimensionality is the mind's method of mounting to the idea of the infinity of space. When we speak of the fourth dimension, what we mean is the fourth stage in the apprehension of that infinity.
Space is not measurable: we attribute dimensionality to space because such is the method of the mind; and that dimensionality we attribute to space is progressive because progression is a law of the mind. The so-called dimensions of space are to space itself as the steps that a climber cuts in the face of a cliff are to the cliff itself.
Far from the Higher Space Hypothesis complicating thought, it simplifies by synthesis and co-ordination in a manner analogous to that by which plane geometry is simplified when solid geometry becomes a subject of study. By immersing the mind in the idea of many dimensions, we emancipate it from the idea of dimensionality. But the mind moves most readily, as has been said, in ordered sequence.
And even as we, who are now in Space, look down on Flatland and see the insides of all things, so of a certainty there is yet above us some higher, purer region, whither thou dost surely purpose to lead me O Thou Whom I shall always call, everywhere and in all Dimensions, my Priest, Philosopher, and Friend some yet more spacious Space, some more dimensionable Dimensionality, from the vantage-ground of which we shall look down together upon the revealed insides of Solid things, and where thine own intestines, and those of thy kindred Spheres, will lie exposed to the view of the poor wandering exile from Flatland, to whom so much has already been vouchsafed.
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