Contrast Quotes - page 4
The landscapes of Ruysdael present the greatest possible contrast to those of Claude, showing how powerfully, from the most opposite directions, genius may command our homage. In Claude's pictures, with scarcely an exception, the sun ever shines. Ruysdael, on the contrary, delighted in, and has made delightful to our eyes, those solemn days, peculiar to his country and to ours, when without storm, large rolling clouds scarcely permit a ray of sunlight to break the shades of the forest.
John Constable
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