PRO & CON
I am free to imagine a horse with or without wings.
Meditations V (1641)
A horse is a horse for everybody... Representation according to nature is not itself nature; moreover, art is not nature.
Natural Reality and Abstract Reality (1919-1920)
OLD REALITIES IN NEW DREAMS
Lewis Carroll took the nineteenth century into a dream world that
was as startling as that of Bosch, but built on reverse
principles. Alice in Wonderland offers as norm that continuous
time and space that had created consternation in the Renaissance.
Pervading this uniform Euclidean world of familiar space-and-time, Carroll
drove a fantasia of discontinuous space-and-time
that anticipated Kafka, Joyce, and Eliot. Carroll, the
mathematical contemporary of Clerk Maxwell, was quite avant-garde
enough to know about the non-Euclidean geometries coming into
vogue in his time. He gave the confident Victorians a playful
foretaste of Einsteinian time-and-space in Alice in Wonderland.
Bosch had provided his era a foretaste of the new continuous
time-and-space of uniform perspective. Bosch looked ahead to the
modern world with horror, as Shakespeare did in King Lear, and as
Pope did in The Dunciad. But Lewis Carroll greeted the electronic
age of space-time with a cheer.
Mathematics in Western Culture (1953)
But I have resolved to quit only abstract Geometry, that is to say the research of questions that serve only to exercise the mind; this in order to have more leisure to cultivate another sort of Geometry, whose purpose is to explain questions about the phenomena of nature. If it pleases Desargues to consider what I've written about salt, about snow, about the rainbow etc., he knows well that all of my Physics is nothing other than Geometry.
Letter to Mersenne (27 July 1638)
I undertake to prove that God, in creating the universe and regulating the order of the cosmos, had in view the five regular bodies of geometry as known since the days of Pythagoras and Plato, and that he has fixed according to those dimensions, the number of the heavens, their proportions, and the relations of their movements.
Mystery of the Cosmos (1596)
It is my impression that the very special serenity of the starry sky is due to the geometrical relation of the stars to each other. -PIET MONDRIAN Natural Reality and Abstract Reality (1919-1920)
By way of analogy we can now say that although it is not possible to squeeze a four-dimensional body into a three-dimensional space without some parts sticking out, one can speak of the projections of various four-dimensional figures in our space of only three dimensions. But one must remember that just as the plane projections of three-dimensional bodies are two-dimensional or plane figures, so the projections of four-dimensional superbodies in our ordinary space will be represented by space-figures.
One, Two, Three, ... Infinity (1947)