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Hidden Variables to Neuroscience

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elements of reality

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.

It seems clear that the present quantum mechanics is not in its final form [...] I think it very likely, or at any rate quite possible, that in the long run Einstein will turn out to be correct.


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.

The aspects of things that are most important for us are hidden because of their simplicity and familiarity.


Where does the yellow come in?

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.


spectral theory

The mathematical machinery of quantum mechanics
became that of spectral analysis.

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.


sense awareness

Identity Theory (Mind/Brain)

The whole duality of mind and matter, according to this theory, is a mistake; there is only one kind of stuff out of which the world is made, and this stuff is called mental in one arrangement, physical in the other


The solution that appears most plausible to me, and that is consistent with a thoroughgoing naturalism, is an identity theory of the mental and the physical, as follows: Certain neurophysiological terms denote (refer to) the very same events that are also denoted (referred to) by certain phenomenal terms ... I take these referents to be the immediately experienced qualities, or their configurations in the various phenomenal fields.

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.

A color is a physical object as soon as we consider its dependence, for instance, upon its luminous source, upon temperatures, upon spaces, and so forth. When we consider, however, its dependence upon the retina, [,,,] it is a psychological object, a sensation. Not the subject matter, but the direction of our investigation, is different in the two domains.


For the invisible reality, of which we have small pieces of evidence in both quantum physics and the psychology of the unconscious, a symbolic psycho- physical unitary language must ultimately be adequate, and this is the far goal which I actually aspire. I am quite confident that the final objective 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.

We can also find information embodied in conscious experience. The pattern of color patches in a visual field, for example, can be seen as analogous to that of pixels covering a display screen. Intriguingly, it turns out that we find the same information states embodied in conscious experience and in underlying physical processes in the brain. The three-dimensional encoding of color spaces, for example, suggests that the information state in a color experience correspond directly to an information state in the brain. We might even regard the two states as distinct aspects of a single information state, which is simultaneously embodied in both physical processing and conscious experience.



"One day I had a drink with some machine-learning researchers, and we suddenly said, 'Oh, it's not noise,' because noise implies something's wrong," says Pouget. "We started to realize then that what looked like noise may actually be the brain's way of running at optimal performance."

Bayesian computing can be done most efficiently when data is formatted in what's called "Poisson distribution."

And the neural noise, Pouget noticed, looked suspiciously like this optimal distribution.



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It is a little hard to understand the significance of Klein's contributions to geometry. This is not because it is strange to us today, quite the reverse, it has become so much a part of our present mathematical thinking that it is hard for us to realise the novelty of his results and also the fact that they were not universally accepted by all his contemporaries. [...]

During his time at Göttingen in 1871 Klein made major discoveries regarding geometry. He published two papers On the so-called Non-Euclidean Geometry in which he showed that it was possible to consider euclidean geometry and non-Euclidean geometry as special cases a projective surface with a specific conic section adjoined. This had the remarkable corollary that non-Euclidean geometry was consistent if and only if Euclidean geometry was consistent. The fact that non-Euclidean geometry was at the time still a controversial topic now vanished. Its status was put on an identical footing to euclidean geometry. Cayley never accepted Klein's ideas, believing his arguments to be circular.

Klein's synthesis of geometry as the study of the properties of a space that are invariant under a given group of transformations, known as the Erlanger Program (1872), profoundly influenced mathematical development. This was written for the occasion of Klein's inaugural address when he was appointed professor at Erlangen in 1872 although it was not actually the speech he gave on that occasion. The Erlanger Programm gave a unified approach to geometry which is now the standard accepted view.

J J O'Connor and E F Robertson



Thus the colors with their various qualities and intensities fulfill the
of vector geometry if addition is interpreted as mixing; consequently, 
projective geometry applies to the color qualities. ~Weyl

So few and far between are the occasions for forming notions whose specializations
makeup a continuous manifold, that the only simple notions whose specializations form a
multiply extended manifold are the positions of perceived objects and colors. ~Riemann

Riemann calls a system in which one individual can be  determined by n measurments an n fold extended aggregate,  or an aggregate of n dimensions. Thus the space in which we  live is a threefold, a surface is a twofold, and a line is a simple  extended aggregate of points. Time also is an aggregate of  one  dimension. The system of colors is an aggrgate of three dimensions, inasmuch as each color, according to the  investigations of Thomas Young and Clerk Maxwell, may be  represented as a mixture of three primary colors in definite  quantities.

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.


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.


Altogether it is a great tour de force and one of the most exciting things happening in the last few years. It is a non-trivial, very deep operation, and it is quite spectacular that the electric-magnetic duality should be  behind the duality which is used in this Langlands program, itself born out of number theory.

It turns out that these automorphic sheaves "live" on a certain space attached to a Riemann surface X and the group G, called the moduli space of G-bundles on X.

Riemann stereographic


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mxn matrix


M-theory is a name for a more unified theory that has the different string theories, as we know them, as limits, and which also can reduce, under appropriate conditions, to eleven-dimensional supergravity. There's this picture that we all have to draw where different string theories are limits of this M theory, where M stands for Magic, Mystery or Matrix, but it also sometimes is seen as standing for Murky, because the truth about M theory is Murky.


While a proper understanding of M-theory still eludes us, much is now known about it. In particular the various geometric results that have emerged from string theory become related in interesting but mysterious ‘dualities’ whose real meaning has yet to be discovered.

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.


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.


projective geometry


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Mass and energy are both but different manifestations of the same thing—a somewhat unfamiliar conception for the average mind.

The stuff of which the world of our experience is composed is, in my belief, neither mind nor matter, but something more primitive than either. Both mind and matter seem to be composite, and the stuff of which they are compounded lies in a sense between the two, in a sense above them both, like a common ancestor.

Bertrand Russell

Most versions of neutral monism are versions of noneliminativist reductionism. Mental and physical phenomena are real but reducible to/constructible from the underlying neutral level. It differs from other versions of reductionism—be they materialistic or mentalistic, eliminative or noneliminative—by insisting on the neutrality of the basis. And its reductionism sets it apart from certain versions of nonreductive theories—emergentism and the dual aspect theory come to mind—with which it is sometimes compared or identified.

Neural Nets

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Artificial Neural Net (ANN)

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.
NNs with Java


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Among the many biological objects a particularly interesting one is the brain. For any theory to be able to claim itself as a brain theory, it should be able to explain the origin of such fascinating properties as the mechanism for creation and recollection of memories and consciousness.

For many years it was believed that brain function is controlled solely by the classical neuron system which provides the pathway for neural impulses. This is frequently called the neuron doctrine. The most essential one among many facts is the nonlocality of memory function discovered by Pribram [...]

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.