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The progression of a painter’s work, as it travels in time from point to point, will be toward clarity: toward the elimination of all obstacles between the painter and the idea, and between the idea and the observer. As examples of such obstacles, I give (among others) memory, history or geometry, which are swamps of generalization from which one might pull out parodies of ideas (which are ghosts) but never an idea in itself. To achieve this clarity is, inevitably, to be understood.
--
Tiger’s Eye, vol 1, no 9, October 1949; as quoted in Abstract Expressionism Creators and Critics, edited by Clifford Ross, Abrams Publishers New York 1990, p. 170

 

Mark Rothko

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A painter makes patterns with shapes and colours, a poet with words. A painting may embody an ‘idea’, but the idea is usually commonplace and unimportant. In poetry, ideas count for a good deal more; but, [...] the importance of ideas in poetry is habitually exaggerated: '... Poetry is no the thing said but a way of saying it.' [In poetry,] the poverty of the ideas seems hardly to affect the beauty of the verbal pattern.

 

G. H. Hardy

 

If you are a man of learning, fight in the skull, kill ideas and create new ones. God hides in every idea as in every cell of flesh. Smash the idea, set him free! Give him another, a more spacious idea in which to dwell.

 

Nikos Kazantzakis

 

The Art of painting is itself an intensely personal activity. It may be labouring the obvious to say so but it is too little recognised in art journalism now that a picture is a unique and private event in the life of the painter: an object made alone with a man and a blank canvas... A real painting is something which happens to the painter once in a given minute; it is unique in that it will never happen again and in this sense is an impossible object. It is judged by the painter simply as a success or failure without qualification. And it is something which happens in life not in art: a picture which was merely the product of art would not be very interesting and could tell us nothing we were not already aware of. The old saying, “what you don’t know can’t hurt you”, expresses the opposite idea to that which animates the painter before his canvas. It is precisely what he does not know which may destroy him.

 

Patrick Swift

 

He (Jasper Johns, fh) and I were each other’s first serious critics. Actually he was the first painter I ever shared ideas with, or had discussions with about painting. No, not the first. Cy Twombly was the first. But Cy and I were not critical. I did my work and he did his. Cy’s direction was always so personal that you could only discuss it after the fact. But Jasper and I literally traded ideas. He would say, ‘I’ve got a terrific idea for you, ‘ and then I’d have to find one for him. (remark on his cooperative relation with Jasper Johns, to his biographer Calvin Tomkins)

 

Robert Rauschenberg

 

It is remarkable that this generalization of plane geometry to surface geometry is identical with that generalization of geometry which originated from the analysis of the axiom of parallels. ...the construction of non-Euclidean geometries could have been equally well based upon the elimination of other axioms. It was perhaps due to an intuitive feeling for theoretical fruitfulness that the criticism always centered around the axiom of parallels. For in this way the axiomatic basis was created for that extension of geometry in which the metric appears as an independent variable. Once the significance of the metric as the characteristic feature of the plane has been recognized from the viewpoint of Gauss' plane theory, it is easy to point out, conversely, its connection with the axiom of parallels. The property of the straight line as being the shortest connection between two points can be transferred to curved surfaces, and leads to the concept of straightest line; on the surface of the sphere the great circles play the role of the shortest line of connection... analogous to that of the straight line on the plane. Yet while the great circles as "straight lines" share the most important property with those of the plane, they are distinct from the latter with respect to the axiom of the parallels: all great circles of the sphere intersect and therefore there are no parallels among these "straight lines". ...If this idea is carried through, and all axioms are formulated on the understanding that by "straight lines" are meant the great circles of the sphere and by "plane" is meant the surface of the sphere, it turns out that this system of elements satisfies the system of axioms within two dimensions which is nearly identical in all of it statements with the axiomatic system of Euclidean geometry; the only exception is the formulation of the axiom of the parallels. The geometry of the spherical surface can be viewed as the realization of a two-dimensional non-Euclidean geometry: the denial of the axiom of the parallels singles out that generalization of geometry which occurs in the transition from the plane to the curve surface.

 

Hans Reichenbach