History 3: Russell, Whitehead, Pauli, Bohm, Bell, Feynman, Lockwood, Churchland
What we see depends on light entering the eye. Furthermore we do not even perceive what enters the eye. The things transmitted are waves or—as Newton thought—minute particles, and the things seen are colors. Locke met this difficulty by a theory of primary and secondary qualities. Namely, there are some attributes of the matter which we do perceive. These are the primary qualities, and there are other things which we perceive, such as colors, which are not attributes of matter, but are perceived by us as if they were such attributes. These are the secondary qualities of matter.
Why should we perceive secondary qualities? It seems an unfortunate arrangement that we should perceive a lot of things that are not there. Yet this is what the theory of secondary qualities in fact comes to. There is now reigning in philosophy and in science an apathetic acquiescence in the conclusion that no coherent account can be given of nature as it is disclosed to us in sense-awareness, without dragging in its relation to mind.
For the invisible reality, of which we have small pieces of evidence in both quantum physics and the psychology of the unconscious, a symbolic psychophysical unitary language must ultimately be adequate, and this is the far goal which I actuallyaspire. I am quite confident that the finalobjective is the same, independent of whether one starts from the psyche (ideas) or from physis (matter). Therefore, I consider the old distinction between materialism and idealism as obsolete.
John S Bell
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.
Take some range of phenomenal qualities. Assume that these qualities can be arranged according to some abstract n-dimensional space, in a way that is faithful to their perceived similarities and degrees of similarity — just as, according to Land, it is possible to arrange the phenomenal colors in his three-dimensional color solid. Then my Russellian proposal is that there exists, within the brain, some physical system, the states of which can be arranged in some n-dimensional state space [...] And the two states are to be equated with each other: the phenomenal qualities are identical with the states of the corresponding physical system.
These predictions will be drawn, in a standard and unproblematic way, from the assumptions of what deserves to be called the Standard Model of how color is processed and represented within the human brain [...] I am thus posig only as a consumer of of existing cognitive neuroscience, not as an advocate of a new theory. But standard or not, this familiar 'color-opponency' theory of chromatic information processing has some unexpected and unappreciated consequences concerning the full range of neuronal activity possible, in an extreme, for the human visual system. From there, one needs only the tentative additional assumption of a systematic identity between neuronal coding vectors on the one hand, and subjective color qualia on the other—a highly specific material assumption in the spirit of classical identity theory, and in the spirit of intertheoretic reductions generally—to formally derive the unexpected but qualia-specific predictions at issue.
A trained-up network is one in which, for appropriate input vectors, the network gives the correct response, expressed in terms of an output vector. Training up a network involves adjusting the many weights so that this end is achieved. This might be done in a number of different ways. One might hand-set the weights, or the weights might be set by a back-propagation of error or by an unsupervised algorithm. Weight configurations too are characterizable in terms of vectors, and at any given time the complete set of synaptic values defines a weight state space, with points on each axis specifying the size of a particular weight. [...]
It is conceptually efficient to see the final resting region in weight space as embodying the total knowledge stored in the network. Notice that all incoming vectors go through the matrix of synaptic connections specified by that weight-space point. [...]
A matrix is an array of values, and the elements of an incoming vector can be operated on by some function to produce an output vector.
In May 1926 Schrödinger published a proof that matrix and wave mechanics gave equivalent results: mathematically they were the same theory. He also argued for the superiority of wave mechanics over matrix mechanics. This provoked an angry reaction, especially from Heisenberg, who insisted on the existence of discontinuous quantum jumps rather than a theory based on continuous waves.
Alfred North Whitehead
Thus "this is red," "this is earlier than that," are atomic propositions.
Russell & Whitehead
[What] is proved by impossibility proofs is lack of imagination...
Well, obviously the extra dimensions have to be different somehow because otherwise we would notice them.
Now it may be asked why these hidden variables should have so long remained undetected.
It is shown that the matrix models which give non-perturbative definitions of string and M-theory may be interpreted as non-local hidden variables theories in which the quantum observables are the eigenvalues of the matrices while their entries are the non-local hidden variables.
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.
[The] tensor calculus emerges as the natural framework with which to address such matters.
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.
Fourier's theorem is probably the most far-reaching principle of mathematical physics.
theorem tells us that every curve, no matter what its nature may be, or
in what way it was originally obtained, can be exactly reproduced by
superposing a sufficient number of simple harmonic curves —in brief,
every curve can be built up by piling up waves.
History 4: Atiyah, Green, Schwarz, Witten, Ramond, Weinberg, Salam, Greene, Calabi-Yau