Rao in
"The Singularity," The New Humanists: Science at the Edge (2003)
Source: 1930s, On my Painting (1938), p. 16
quote by Van Doesburg, as cited in 'Great Masters of Art' in Eenheid no 392, 8 December 1917
1912 – 1919
And He Built a Crooked House (p. 33)
Short fiction, Off the Main Sequence (2005)
“The very fact that a Line is visible implies that it possesses yet another Dimension.”
Source: Flatland: A Romance of Many Dimensions (1884), PART II: OTHER WORLDS, Chapter 16. How the Stranger Vainly Endeavoured to Reveal to Me in Words the Mysteries of Spaceland
Source: Flatland: A Romance of Many Dimensions (1884), PART II: OTHER WORLDS, Chapter 19. How, Though the Sphere Showed Me Other Mysteries of Spaceland, I Still Desired More; and What Came of It
Context: I despair not that, even here, in this region of Three Dimensions, your Lordship's art may make the Fourth Dimension visible to me; just as in the Land of Two Dimensions my Teacher's skill would fain have opened the eyes of his blind servant to the invisible presence of a Third Dimension, though I saw it not.Let me recall the past. Was I not taught below that when I saw a Line and inferred a Plane, I in reality saw a Third unrecognized Dimension, not the same as brightness, called "height"? And does it not now follow that, in this region, when I see a Plane and infer a Solid, I really see a Fourth unrecognized Dimension, not the same as colour, but existent, though infinitesimal and incapable of measurement?
Source: Flatland: A Romance of Many Dimensions (1884), PART II: OTHER WORLDS, Chapter 22. How I Then Tried to Diffuse the Theory of Three Dimensions by Other Means, and of the Result
Context: I devoted several months in privacy to the composition of a treatise on the mysteries of Three Dimensions. Only, with the view of evading the Law, if possible, I spoke not of a physical Dimension, but of a Thoughtland whence, in theory, a Figure could look down upon Flatland and see simultaneously the insides of all things, and where it was possible that there might be supposed to exist a Figure environed, as it were, with six Squares, and containing eight terminal Points. But in writing this book I found myself sadly hampered by the impossibility of drawing such diagrams as were necessary for my purpose... my life was under a cloud. All pleasures palled upon me; all sights tantalized and tempted me to outspoken treason, because I could not but compare what I saw in Two Dimensions with what it really was if seen in Three, and could hardly refrain from making my comparisons aloud.' I neglected my clients and my own business to give myself to the contemplation of the mysteries which I had once beheld, yet which I could impart to no one, and found daily more difficult to reproduce even before my own mental vision.
“Time is not a line but a dimension, like the dimensions of space.”
Cat's Eye (1988)
