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Dualism Duality EM 
In
dualism, ‘mind’ is
contrasted with ‘body,’ but at different times, different aspects of
the mind have been the centre of attention. In the classical and
mediaeval periods, it was the intellect that was thought to be most
obviously resistant to a materialistic account: from Descartes on, the
main stumbling block to materialist monism was supposed to be
‘consciousness,’ of which phenomenal consciousness or sensation came to
be considered as the paradigm instance.
The principle of duality in
projective geometry states that we can interchange point and line in a
theorem about figures lying in one plane and obtain a meaningful
statement. Moreover, the new or dual statement will itself be a theorem
— that is, it can be proven. On the basis of what has been presented
here we cannot see why this must always be the case for the dual
statement. However, it is possible to show by one proof that every
rephrasing of a theorem of projective geometry in accordance with the
principle of duality must be a theorem. This principle is a remarkable
characteristic of projective geometry. It reveals the symmetry in the
roles that point and line play in the structure of that geometry.
Kline
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
The two main approaches for the description of sound fields are methods derived from solutions of the wave equation and geometric methods based on analogies to ray optics. Their mathematical representations are reviewed and it is shown that representations by projective geometry and descriptions by Fourier acoustics lead to similar parametric representations of sound fields. Annibale et al.
Very recently, in
the last two years,Witten and his collaborators (mainly Kapustin and
Gukov, two young Russians) have managed to deduce what is required for
the geometric Langlands program from nonabelian dualities in physics.
The kind of dualities they use are close to the dualities in
Donaldson’s theory and to the dualities in the mirror symmetry, and are
based (at least) on the electricmagnetic duality. The original
dualities in physics are those between electricity and magnetism.
Atiyah
A. Stationary states are determined by complex valued wave functions (q), which remain finite everywhere in qspace. B. The functions satisfy a differential equation in which the operator H is obtained from the classical Hamiltonian H(p; q) by replacing every momentum p by C. The eigenvalues E are the energy values. To these three hypotheses, Schrödinger added Bohr’s postulate: D.
This theory was presented in Schrödinger’s first and second communications on “Quantisierung als Eigenwertproblem” in Annalen der Physik 79. The first communication was received on 27 January, and the second on 23 February 1926. On the other hand, matrix mechanics was invented by Heisenberg in June 1925, and presented in a fully developed form in Dirac’s first paper on quantum mechanics(received 7 November 1925) and also in the famous “threemen’s paper” of Born, Heisenberg and Jordan (received 16 November 1925). This theory was based upon four mechanical hypotheses and two radiation hypotheses. The mechanical hypotheses are: 1. The behaviour of a mechanical system is determinedby the matrices p and q (one matrix q forevery coordinate q, and one p for every momentum p). 2. if p belongs to the same coordinate q, otherwise equal to 0. 3. H(p, q) = W = diagonal matrix, having diagonal elements E_{n}, the energy values. 4. Equations of motion: ~BL van der Waerden [PDF]
Mathematics has introduced the name isomorphic representation for the relation which according to Helmholtz exists between objects and their signs. I should like to carry out the precise explanation of this notion between the points of the projective plane and the color qualities [...] the projective plane and the color continuum are isomorphic with one another. Every theorem which is correct in the one system _{1} is transferred unchanged to the other _{2}. A science can never determine its subject matter except up to an isomorphic representation. The idea of isomorphism indicates the self understood, insurmountable barrier of knowledge. It follows that toward the "nature" of its objects science maintains complete indifference. This for example what distinguishes the colors from the points of the projective plane one can only know in immediate alive intuition... Weyl All chemical binding is electromagnetic in origin, and so are all phenomena of nerve impulses. Salam
Fundamental electromagnetic interactions occur between any two particles that have electric charge. These interactions involve the exchange or production of photons. Thus, photons are the carrier particles of electromagnetic interactions. I would
like to again impress you with the vast range of phenomena that the
theory of quantum electrodynamics describes: It's easier to say it
backwards: the theory describes all the phenomena of the physical world
except the gravitational effect [...] and radioactive phenomena, which
involve nuclei shifting in their energy levels. So if we leave out
gravity and radioactivity (more properly, nuclear physics) what have we
got left? Gasoline burning in automobiles, foam and bubbles, the
hardness of salt or copper, the stiffness of steel. In fact, biologists
are trying to interpret as much as they can about life in terms of
chemistry, and as I already explained, the theory behind chemistry is quantum
electrodynamics.
Feynman


Energy 
It
followed from the special theory of relativity that mass and energy are
both but different manifestations of the same thing  a somewhat
unfamiliar conception for the average mind. Furthermore, the equation E
= mc², in which energy is put equal to mass, multiplied by the square
of the velocity of light, showed that very small amounts of mass may be
converted into a very large amount of energy and vice versa.
Einstein


EPR 
A
theory that yields "maybe" as an answer should be recognized as an
inaccurate theory. 't Hooft Can
it really be true that Einstein, in any significant sense, was a
profoundly "wrong" as the followers of Bohr maintain? I do not
believe so. I would, myself, side strongly with Einstein in his belief
in a submiscroscopic reality, and with his conviction that presentday
quantum mechanics is fundamentally incomplete.
Penrose
In attempting to judge the success of a physical theory, we may ask ourselves two questions: (1) “Is the theory correct?” and (2) “Is the description given by the theory complete?” It is only in the case in which positive answers may be given to both of these questions, that the concepts of the theory may be said to be satisfactory. The correctness of the theory is judged by the degree of agreement between the conclusions of the theory and human experience... 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 Thus "this is red," "this is earlier than that," are atomic propositions. Russell & Whitehead
Einstein
The world as described by natural science
has no obvious place for colors, tastes, or smells.
Until recently my view about these things was pretty similar to Feynman’s with maybe a bit of Dirac’s; namely: Quantum mechanics is so confusing that I can’t even tell if there is a problem, but maybe it’s all ok because it works. There is probably not much profit in thinking about “interpretations” and even less in arguing about them. But over the last two years I’ve come to see it differently. Now I feel that our current views of quantum mechanics are provisional; it’s the best we can do without a much deeper understanding of its connection with gravity, but it’s not final. The reason involves a very particular development, the so called ER = EPR principle. ER = EPR tells us that the immensely complicated network of entangled subsystems that comprises the universe is also an immensely complicated (and technically complex) network of EinsteinRosen bridges. To me it seems obvious that if ER = EPR is true it is a very big deal, and it must affect the foundations and interpretation of quantum mechanics. Susskind


Eye 
The processes on
the retina produce excitations which are conducted to the brain in the
optic nerves, maybe in the form of electric currents. Even here we are
still in the real sphere. But between the physical processes which are
released in the terminal organ of the nervous conductors in the central
brain and the image which thereupon appears to the perceiving subject,
there gapes a hiatus, an abyss which no realistic conception of the
world can span. It is the transition from the world of being to the
world of appearing image or of consciousness.
Weyl

