I groaned with horror, doubting whether I was not out of my senses; but the Stranger continued: "Surely you must now see that my explanation, and no other, suits the phenomena. What you call Solid things are really superficial; what you call Space is really nothing but a great Plane. I am in Space, and look down upon the insides of the things of which you only see the outsides. You could leave this Plane yourself, if you could but summon up the necessary volition. A slight upward or downward motion would enable you to see all that I can see.
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Chapter 17. How the Sphere, Having in Vain Tried Words, Resorted to DeedsEdwin Abbot
My Lord, your 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 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.
Edwin Abbot
Were I to give the Sphere's explanation of these matters, succinct and clear though it was, it would be tedious to an inhabitant of Space, who knows these things already. Suffice it, that by his lucid statements, and by changing the position of objects and lights, and by allowing me to feel the several objects and even his own sacred Person, he at last made all things clear to me, so that I could now readily distinguish between a Circle and a Sphere, a Plane Figure and a Solid.
Edwin Abbot
Since one cannot create "real depth" by carving a hole in the picture, and since one should not attempt to create the illusion of depth by tonal gradation, depth as a plastic reality must be two dimensions in a formal sense as well in the sense of color. "Depth" is not created on a flat surface as an illusion, but as a plastic reality. The nature of the picture plane makes it possible to achieve depth without destroying the two-dimensional essence of the picture plane. ... A plane is a fragment in the architecture of space. When a number of planes are opposed one to another, a spatial effect results. A plane functions in the same manner as the walls of a building. ... Planes organized within a picture create the pictorial space of its composition. ... The old masters were plane-consciousness. This makes their pictures restful as well as vital...
Hans Hofmann
To paint space, I owe it to myself to go there, to that very space... without illusions or tricks, nor with a plane or a parachute or a rocket ship: the painter of space must go there with his own means, with an independent individual force, in a word, he must be capable of levitation. (1960)
Yves Klein
My aim is always to get hold of the magic of reality and to transfer this reality in painting – to make the invisible visible through reality… …What helps me most in this task is the penetration of space. Height, width and depth are the three phenomena which I must transfer into one plane to form the abstract surface of the picture, and thus to protect myself from the infinity of space. My figures come and go, suggested by fortune or misfortune. I try to fix them divested of their apparent accidental quality.
Max Beckmann
Abbot, Edwin
Abbot, Jack
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