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Vertical and horizontal lines are the expression of two opposing forces; they exist everywhere and dominate everything; their reciprocal action constitutes ‘life’. I recognized that the equilibrium of any particular aspect of nature rests on the equivalence of its opposites.
--
Plastic Art and Pure Plastic Art, Piet Mondrian, New York: Wittenborn 1945, p. 13; as quoted in Astract Expressionist Painting in America, W.C, Seitz, Cambridge Massachusetts, 1983, p. 55

 

Piet Mondrian

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As you can see this is a composition of vertical and horizontal lines which will (in an abstract manner) have to express the idea of rising upwards, of magnitude. This is the same idea which used, for example, to be the guiding principle in the construction of cathedrals. Since only the manner of expression and not the representation has to express this general idea, I have not given any title. An abstract human mind will, of itself, receive the intended impression. I always confine myself to expressing the general.

 

Piet Mondrian

 

Thus the universe is to be conceived as attaining the active self-expression of its own variety of opposites of its own freedom and its own necessity, of its own multiplicity and its own unity, of its own imperfection and its own perfection. All the opposites are elements in the nature of things, and are incorrigibly there. The concept of God is the way in which we understand this incredible fact that what cannot be, yet is.

 

Alfred North Whitehead

 

Let us honour if we can
The vertical man
Though we value none
But the horizontal one.

 

Wystan Hugh Auden

 

The vertical is in my spirit. It helps me to define precisely the direction of lines, and in quick sketches I never indicate a curve, that of a branch in landscape for example, without being aware of its relationship to the vertical.
My curves are not mad.

 

Henri Matisse

 

[One of the company... said: ...is not this the direct contrary of what we admitted before--that out of the greater came the less and out of the less the greater, and that opposites are simply generated from opposites; whereas now this seems to be utterly denied.] ...then we were speaking of opposites in the concrete, and now of the essential opposite which, as is affirmed, neither in us nor in nature can ever be at variance with itself... these essetial opposites will never, as we maintain, admit of generation into or out of one another.

 

Socrates