| Smart Remarks 1: Einstein, Bohr, Bohm, Feynman, Dirac, Atiyah & Weyl | ||||||
We are accustomed to regarding as real
those sense perceptions which are common to different individuals, and
which therefore are, in a measure, impersonal. The natural sciences,
and in particular, the most fundamental of them, physics, deal with
such sense perception.
Einstein
  Bohr
Every great and deep difficulty bears
in itself its own solution. It forces us to change our thinking in order to find it.  |
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I believe that the first step in the setting of a "real external world" is the formation of the concept of bodily objects and of bodily objects of
various kinds. Out of the multitude of our sense experiences we take,
mentally and arbitrarily, certain repeatedly occurring complexes of
sense impression (partly in conjunction with sense impressions which are interpreted as signs for sense experiences of others), and we attribute to them a meaning—the meaning of the bodily object. Considered logically
this concept is not identical with the totality of sense impressions
referred to; but it is an arbitrary creation of the human (or animal)
mind. On the other hand, the
concept owes its meaning and its justification exclusively to the
totality of the sense impressions which we associate with it.
Einstein |
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| Bohr Bohm |
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Bohr suggests that thought involves such small amounts of energy that quantum- theoretical limitations play an essential role in determining its character. Bohm  |
color quantum |
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wave | |||||
Feynman Weyl |
It is just like the mathematics of the addition of vectors, where (a, b, c) are the components of one vector, and (a', b', c' ) are those of another vector, and the new light Z is then the "sum" of the vectors. This subject has always appealed to physicists and mathematicians. In fact, Schrödinger wrote a wonderful paper on color vision in which he developed this theory of vector analysis as applied to the mixing of colors.
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. 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 
Gauge
theory first appeared in physics in the early attempt by H. Weyl to
unify general relativity and electro-magnetism. Weyl had noticed the
conformal invariance of Maxwell's equations and sought to exploit this
fact by interpreting the Maxwell field as the distortion of
relativistic length produced by moving around a closed path. Weyl's
interpretation was disputed by Einstein and never generally accepted. However
after the advent of quantum mechanics with its all-important complex
wave-functions it became clear that phase rather than scale was the
correct concept for Maxwell's equations, or in modern language that the
gauge group was the circle rather than the multiplicative numbers.
Atiyah
Holonomy Group
Our discussion will focus on
compactified string theory, which as we shall see, requires the compact
portion of space-time to meet certrain stringent constraints. Although
there are more general solutions, we shall study the case in which the
extra “curled-up” dimensions fill out an n-dimensional manifold that
has the following properties:
where d = n/2. For much of these
lectures, n will be 6 and hence d = 3. Manifolds which meet these
conditions are known as Calabi-Yau manifolds, for reasons which will
become clear shortly.
Greene
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To monochromatic light corresponds in the acoustic domain the simple tone. Out of different kinds of monochromatic light composite light may be mixed, just as tones combine to a composite sound. This takes place by superposing simple oscillations of different frequency with definite intensities. Weyl
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 
Dirac
The characteristic of an n-dimensional
manifold is that each of the elements composing it (in our examples,
single points, conditions of a gas, colors, tones) may be specified by
the giving of n quantities, the "co-ordinates," which are continuous
functions within the manifold.
Weyl
Weyl
Epistemologically
it is not without interest that in addition to ordinary space there
exists quite another domain of intuitively given entities, namely the
colors, which forms a continuum capable of geometric treatment.
§
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. |
light neural nets sound |
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Dirac Atiyah Calabi Yau Greene |
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manifold phase |
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| Calabi-Yau |
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| More smartness 2: Einstein, Noether, Russell, Helmholtz, Lockwood, Churchland, Atiyah, Weyl | ||||||
