[So] few and far between are the occasions for forming notions whose specializations make up a continuous manifold, that the only simple notions whose specializations form a multiply extended manifold are the positions of perceived objects and colors.

~Riemann

Thus the colors with their various qualities and intensities fulfill the axioms of vector geometry if addition is interpreted as mixing; consequently, projective geometry applies to the color qualities.

~Weyl

A speck in the visual field, though it need not be red must have some color; it is, so to speak, surrounded by color-space. Notes must have some pitch, objects of the sense of touch some degree of hardness, and so on.

~Wittgenstein

We shall now recall the data of a classical theory as understood by physicists and then reinterpret them in geometrical form. Geometrically or mechanically we can interpret this data as follows. Imagine a structured particle, that is a particle which has a location at a point x of R_4 and an internal structure, or set of states, labeled by elements g of G.

## Extra dimensions

[So] few and far between are the occasions for forming notions whose specializations make up a continuous manifold, that the only simple notions whose specializations form a multiply extended manifold are the positions of perceived objects and colors.

~Riemann

Thus the colors with their various qualities and intensities fulfill the axioms of vector geometry if addition is interpreted as mixing; consequently, projective geometry applies to the color qualities.

~Weyl

A speck in the visual field, though it need not be red must have some color; it is, so to speak, surrounded by color-space. Notes must have some pitch, objects of the sense of touch some degree of hardness, and so on.

~Wittgenstein

We shall now recall the data of a classical theory as understood by physicists and then reinterpret them in geometrical form. Geometrically or mechanically we can interpret this data as follows. Imagine a structured particle, that is a particle which has a location at a point x of R_4 and an internal structure, or set of states, labeled by elements g of G.

~Atiyah