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Action 
The
calculus of variations incorporates—and, historically speaking,
arises from—the important idea of 'least action,' which Maupertuis
and Leibniz independently pioneered by extending Fermat's approach to
refraction. The principal of least action says the physical path taken
by an object moving under given physical conditions can be found
mathematically by minimising the object's 'action.' The mathematical
method is the same as that used in the calculus of variations for
minimising time in the brachistochrone problem, but minimising the
'action' refers specifically to economising on some 'active' quality of
the motion, like its velocity, rather than simply minimising time or
distance. Mary [Somerville] described the amazing way in which the
principle can produce, purely
mathematically, the basic Newtonian 'laws of
motion.'
Arianrhod Hamilton's approach arose in 1835 in his unification of the language of optics and mechanics. It too had a usefulness far beyond its origin, and the Hamiltonian is now most familiar as the operator in quantum mechanics which determines the evolution in time of the wave function. Shapiro Roughly speaking, force is the space derivative of energy and the time derivative of momentum. You can take one more step up the ladder: energy and momentum are both derivatives of action: energy is its time derivative, momentum its space derivative. Wilczek
It is a
most beautiful and aweinspiring fact that all the fundamental laws of
Classical Physics can be understood in terms of one mathematical
construct called the Action. It
yields the classical equations of motion, and analysis of its
invariances leads to quantities conserved in the course of the
classical motion. In addition, as Dirac and Feynman have shown, the
Action acquires its full importance in Quantum Physics.
Ramond
It is increasingly clear
that the symmetry
group
of nature is the deepest thing that we understand about nature today.
Weinberg
How
does yellow change under translations, rotations and reflections?
If you ask a physicist
what is his idea of yellow light, he will tell you that it is
transversal electromagnetic waves of wavelength in the neighborhood of
590 millimicrons. If you ask him: But where does yellow come in? he
will say: In my picture not at all, but these kinds of vibrations, when
they hit the retina of a healthy eye, give the person whose eye it is
the sensation of yellow.


It was found possible to
account for the atomic stability, as well as for the empirical laws
governing the spectra of the elements, by assuming that any reaction of
the atom resulting in a change of its energy involved a complete
transition between two socalled stationary quantum states and that, in
particular, the spectra were emitted by a steplike process in which
each transition is accompanied by the emission of a monochromatic light quantum of
an energy just equal to that of an Einstein photon.
Bohr 

Audition 
The fact
that the formalism describing the brain microprocess is identical with
the physical microprocess allows two interpretations: (a) The neural
microprocess is in fact based on relations among microphysical quantum
events, and (b) that the laws describing quantum physics are applicable
to certain macrophysical interactions when these attain some special
characteristics.”
Pribram
Consider
the field of the data of sense—a field of universal interest—and
fundamental. We are here in the domain of sights and sounds and motions
among other things ... Do the colors constitute a group? ... Let us
pass from colors to figures or shapes—to figures or shapes, I mean, of
physical or material objects—rocks, chairs, trees, animals and the
like—as known to sense perception ... And what of sounds—sensations of
sound? Are sounds combinable? Is the result always a sound or is it
sometimes silence? If we agree to regard silence as a species of
sound—as the zero of sound—has the system of sounds the property of a
group?
Keyser


Brain 
There
have been many models based on quantum theories, but many of them are
rather philosophically oriented. The article by Burns [...] provides a
detailed list of papers on the subject of consciousness, including
quantum models. The incorrect perception that the quantum system has
only microscopic manifestations considerably confused this subject. As
we have seen in preceding sections, manifestation of ordered states is
of quantum origin. When we recall that almost all of the macroscopic
ordered states are the result of quantum field theory, it seems natural
to assume that macroscopic ordered states in biological systems are
also created by a similar mechanism.
Umezawa 

Cerebellum 
In academic research, Pellionisz, as professor of New York University was the originator of a pioneering informationgeometric approach to Neural Nets, Tensor Network Theory. TNT explains the function of 25% of the brain (the cerebellum) in terms of tensor analysis, the intrinsic mathematical language of Biological Neural Nets. Pellionisz 

Cerebrum 
The cerebrum makes up about 85% of the weight of the human brain. A large groove called the longitudinal fissure divides the cerebrum into halves called the left cerebral hemisphere and the right cerebral hemisphere. The hemispheres are connected by bundles of nerve fibres, the largest of which is the corpus callosum. 

Color 
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 lightss combine with one another in space [...]
Weyl
A color is a physical
object a soon as we consider its dependence, for instance, upon its
luminous source, upon temperatures, and so forth.
Mach 

Computer: Quantum 
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 [...] 

Cortex 
