The marble index of a mind for ever Voyaging
through strange seas of Thought, alone. ~Wordsworth

Mach,
Weyl, Feynman, Dirac, EPR, Clark, Hughes, Bohm, Green, Cao, Langlands 

The science of colors becomes a speculation as truly mathematical as any other part of physics. ~Newton 

Steen Mach Weyl Feynman Dirac Born Grassmann Clark EPR Hughes Halmos 
In
Göttingen in 192526 Werner
Heisenberg and Erwin Schrödinger
created the theory of quantum mechanics. In Heisenberg's theory the
physical fact that certain atomic observations cannot be made
simultaneously was interpreted mathematically to mean that the
operations which represented these operations were not commutative.
Since the algebra of matrices is noncommutative, Heisenberg together
with Max Born and Pascual Jordan represented each physical quantity by
an appropriate (finite or infinite) matrix, called a transformation;
the set of possible values of the physical quantity was the spectrum of
the transformation. (So the spectrum of the energy of the atom was
precisely the spectrum of the atom.)
Schrödinger,
in contrast, advanced a less unorthodox theory based on his partial
differential wave equation. Following some initial surprise that
Schrödinger's "wave
mechanics" and Heisenberg's "matrix mechanics" — two
theories with substantially different hypotheses — should
yield the same results, Schrödinger
unified the two approaches by showing, in effect, that the eigenvalues
(or more generally, the spectrum) of the differential operator in Schrödinger's
wave equation determine the corresponding Heisenberg matrix. Similar
results were obtained simultaneously by the British physicist Paul A.
M. Dirac. Thus interest in spectral theory once again became quite
intense.
Steen When a
blind beetle crawls over the surface of the globe, A
color is a physical object a soon as we consider
The second principle of color mixing of lights is this: any color at all can be made from three different colors, in our case, red, green, and blue lights. By suitably mixing the three together we can make anything at all, as we demonstrated [...] Further, these laws are very interesting mathematically. For those who are interested in the mathematics of the thing, it turns out as follows. Suppose that we take our three colors, which were red, green, and blue, but label them A, B, and C, and call them our primary colors. Then any color could be made by certain amounts of these three: say an amount a of color A, an amount b of color B, and an amount c of color C makes X: Now
suppose another color Y is made from the same three colors:
Then it turns out that the mixture of the two lights (it is one of the consequences of the laws that we have already mentioned) is obtained by taking the sum of the components of X and Y: Feynman
Krantz
You can expect to gain a deep insight into the constitution of Σ in this way. After that you may start to investigate symmetric configurations of elements, i.e., configurations which are invariant under a certain subgroup of the group of all automorphisms. Weyl Simple CalabiYau space The
internal space defined at each spacetime point is called a fiber, and
the union of this internal space with spacetime is called fiberbundle
space.
Cao
The world as described by natural science has no obvious place for colors, tastes, or smells. Problems with sensory qualities have been philosophically and scientifically troublesome since ancient times, and in modern form at least since Galileo in 1623 identified some sensory qualities as characterizing nothing real in the objects themselves [...] The
qualities of size, figure (or shape), number, and motion are for
Galileo the only real properties of objects. All other qualities
revealed in sense perception—colors,
tastes, odours, sounds, and so
on—exist only in the sensitive body, and do not
qualify anything in
the objects themselves. They are the effects of the primary qualities
of things on the senses. Without the living animal sensing such things,
these 'secondary' qualities (to use the term introduced by Locke) would
not exist. Clark

The
mathematical machinery of quantum mechanics
became that of spectral analysis. ~Steen It
turned out that,
once these foundations had been The physical action only depends
If you
take a physical state and do
something to it — like
rotating it, or like waiting for some time t — you get a different state. We
say, "performing an operation on a state
produces a new state." We can express the same idea by an equation: _{}>
= A_{}>.
An operation on a
state produces another state. The operator A
stands for some particular operation. When this operation is performed
on any state, say _{}>,
it produces some other state _{}>.
Feynman
Similar light produces,
under like conditions, It seems useful to me to develop a little more precisely the "geometry" valid in the twodimensional manifold of perceived colors. For one can do mathematics also in the domain of these colors. The fundamental operation which can be performed upon them is mixing: one lets colored lights combine with one another in space [...] Weyl
[When]
a state is formed by the superposition of two other states, it
will have properties that are in some vague way intermediate between
those of the original states and that approach more or less closely to
those of either of them according to the greater or less 'weight'
attached to this state in the superposition process. The new state is
completely defined by the two original states when their relative
weights in the superposition process are known, together with a certain
phase difference, the exact meaning of weights and phases being
provided in the general case by the mathematical theory.
Dirac
Many of the foundations of wave mechanics are based on the
analyses and equations that Rayleigh
derived for the theory of acoustics in his book The Theory of Sound.
Erwin Schrödinger, a pioneer in quantum mechanics, studied this book
and was familiar with the perturbation methods it describes.
Masters
The suggestion that there may be such "hidden variables" is as old as the probabilistic interpretation of the state vector. It was made by Born [...] a few months after he first proposed that interpretation: "Anyone dissatisfied with these ideas may feel free to assume that there are additional parameters not yet introduced into the theory which determine the individual event." But almost as old is the denial that such hidden variables can exist. Hughes
In
view
of the preceding section, there is a natural onetoone correspondence
between subspaces and idempotent Hermitian operators. It is in
principle possible, therefore, to express all the geometric properties
of subspaces in terms of the algebraic properties of their projections.
Halmos Whatever the meaning assigned to the term complete, the following requirement for a complete theory seems to be a necessary one: every element of the physical reality must have a counterpart in the physical theory.
EPR
Now it may be asked why these hidden variables should have so long remained undetected. Bohm
Well, obviously the extra dimensions have to be different somehow because otherwise we would notice them. Green It was not until the advent of quantum mechanics in the twentieth century that absorbtion spectra were given a satisfactory theoretical explanation. They were shown to correspond with eigenvalues of appropriate Schrödinger operators. A given atom could absorb or emit light only at certain frequencies, corresponding to the energy levels of bound states represented by different eigenvalues. The mathematical spectra of differential operators thus carried fundamental information about the physical world, which even now seems almost magical. The analogy with number theory is through spectra of other differential operators. These are LaplaceBeltrami operators (and variants of higher degree) attached to certain Riemannian manifolds. The spectra of these and other operators are expected to carry fundamental information about the arithmetic world, a possibility that also seems quite magical. [...] The spectral data that is believed to be related to number theory is framed in the language of automorphic forms. Arthur
To monochromatic light corresponds in
the acoustic domain the simple tone.~Weyl 
color geometry superposition phase weight vector HVs complete dimension internal 
