Beyond Three Dimensions

“In One Dimensions, did not a moving Point produce a Line with two terminal points?

In two Dimensions, did not a moving Line produce a Square wit four terminal points?

In Three Dimensions, did not a moving Square produce - did not the eyes of mine behold it - that blessed being, a Cube, with eight terminal points?

And in Four Dimensions, shall not a moving Cube - alas, for Analogy, and alas for the Progress of Truth if it be not so - shall not, I say the motion of a divine Cube result in a still more divine organization with sixteen terminal points? Behold the infallible confirmation of the Series, 2, 4, 8, 16: is not this a Geometrical Progression? Is not this - if I might quote my Lord's own words - "Strictly according to Analogy"?

Again, was I not taught by my Lord that as in a Line there are two bonding points, and in a Square there are four bounding Lines, so in a Cube there must be six bounding Squares? Behold once more the confirming Series: 2, 4, 6: is not this an Arithmetical Progression? And consequently does it not of necessity follow that the more divine offspring of the divine Cube in the Land of Four Dimensions, must have eight bounding Cubes: and is not this also, as my Lord has taught me to believe, "strictly according to analogy"?”

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“My Lord, you own wisdom has taught me to aspire to One even more great, more beautiful, and more closely approximate to perfection than yourself. As you yourself, superior to all Flatland forms, combine many Circles in One, so doubtless there is One above you who combines many Spheres in One Supreme Existence, surpassing even the Solids of Spaceland. And even as we, who are now in Space, look down on Flatland and see the inside of all things, so of a certainly there is yet above us some higher, purer region, whither thou dost surely purpose to lead me - O Thou Whome 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 whome so much has already been vouchsafed.”