A Cubism Dream

β€œIn One Dimension, did not a moving Point produce a Line with two terminal points?

In Two Dimensions, did not a moving Line produce a Square with 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”?”

― Edwin A. Abbott, Flatland: A Romance of Many Dimensions

Taken with a6000, ISO 800. October 18, 2017.

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