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" "Your Lordship tempts his servant to see whether he remembers the revelations imparted to him. Trifle not with me, my Lord; I crave, I thirst, for more knowledge. Doubtless we cannot see that other higher Spaceland now, because we have no eye in our stomachs. But, just as there was the realm of Flatland, though that poor puny Lineland Monarch could neither turn to left nor right to discern it, and just as there was close at hand, and touching my frame, the land of Three Dimensions, though I, blind senseless wretch, had no power to touch it, no eye in my interior to discern it, so of a surety there is a Fourth Dimension, which my Lord perceives with the inner eye of thought. And that it must exist my Lord himself has taught me. Or can he have forgotten what he himself imparted to his servant? In 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 this eye 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 bounding 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 8 bounding Cubes: and is not this also, as
Edwin Abbott Abbott (20 December 1838 – 12 October 1926) was an English schoolmaster and theologian, most famous as the author of the social satire Flatland (1884), widely noted for its use of mathematical dimensions in religious and political allegories.
Biography information from Wikiquote
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Osserva quella miserabile creatura. Quel Punto è un Essere come noi, ma confinato nel baratro adimensionale. Egli stesso è tutto il suo Mondo, tutto il suo Universo; egli non può concepire altri fuor di se stesso: egli non conosce lunghezza, né larghezza, né altezza, poiché non ne ha esperienza; non ha cognizione nemmeno del numero Due; né ha un'idea della pluralità, poiché egli è in se stesso il suo Uno e il suo Tutto, essendo in realtà Niente. Eppure nota la sua soddisfazione totale, e traine questa lezione: che l'essere soddisfatti di sé significa essere vili e ignoranti, e che è meglio aspirare a qualcosa che essere ciecamente, e impotentemente, felici.