Preference Quotes - page 2
I make a little mystique for myself. Since I have no preference or so-called sense of color, I could take almost everything that could be some accident of a previous painting. Or I set out to make a series. I take, for instance, some pictures where I take a color, some arbitrary color I took from some place. Well, this is gray maybe, and I mix the color for that, and then I find out that when I am through with getting the color the way I want it, I have six other colors in it, to get that color; and then I take those six colors and I use them also with this color. It is probably like a composer does a variation on a certain theme. But it isn't technical, it isn't just fun.
Willem de Kooning
Euclidean geometry can be easily visualized; this is the argument adduced for the unique position of Euclidean geometry in mathematics. It has been argued that mathematics is not only a science of implications but that it has to establish preference for one particular axiomatic system. Whereas physics bases this choice on observation and experimentation, i.e., on applicability to reality, mathematics bases it on visualization, the analogue to perception in a theoretical science. Accordingly, mathematicians may work with the non-Euclidean geometries, but in contrast to Euclidean geometry, which is said to be "intuitively understood," these systems consist of nothing but "logical relations" or "artificial manifolds". They belong to the field of analytic geometry, the study of manifolds and equations between variables, but not to geometry in the real sense which has a visual significance.
Hans Reichenbach