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Mental phenomena, all mental phenomena whether conscious or unconscious, visual or auditory, pains, tickles, itches, thoughts, indeed, all our mental life, are caused by processes going on in the brain.


The prevailing view in philosophy, psychology and artificial intelligence, is one which emphasises the analogies between the functioning of the human brain and the functioning of digital computers.




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The calculus of variations incorporatesand, historically speaking, arises fromthe 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.' 



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.


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.

action equation

It is a most beautiful and awe-inspiring 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.


Furthermore, and now this is the point, this is the punch line, the symmetries determine the action. This action, this form of the dynamics, is the only one consistent with these symmetries [...] This, I think, is the first time that this has happened in a dynamical theory: that the symmetries of the theory have completely determined the structure of the dynamics, i.e., have completely determined the quantity that produces the rate of change of the state vector with time.

It is increasingly clear that the of nature is the deepest thing that we understand about nature today.

gold sphere

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.

energy levels

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 so-called stationary quantum states and that, in particular, the spectra were emitted by a step-like 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.



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wave interference

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.”

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?



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Brain areas

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.



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In academic research, Pellionisz, as professor of New York University was the originator of a pioneering information-geometric 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.



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. 

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color geometry


It seems useful to me to develop a little more precisely the "geometry" valid in the two-dimensional 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 [...]


A color is a physical object a soon as we consider its dependence, for instance, upon its luminous source, upon temperatures, and so forth.


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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 [...]


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.

For a few years, scientists have been predicting that computers exploiting the quantum properties of matter will carry out computations billions of times faster than today's supercomputers. Yet the technical challenges are so daunting that such quantum computers may not be feasible for decades.

Now, researchers have developed a new, yet less exotic computing method that may be as good as quantum computing for certain tasks, such as searching databases. The method relies entirely on classical physics, say Ian Walmsley and his colleagues of the University of Rochester in New York. To convert their ideas into hardware, the Rochester scientists have built an optical device and successfully demonstrated the method.

The group reported its results at the Lasers and Electro-Optics/Quantum Electronics and Laser Science conference in Baltimore last week.

Researchers expect quantum processors to work incredibly fast thanks in part to particles' wavelike interactions, including interference. The processors would take advantage of another, stranger effect known as entanglement, in which two or more particles share one quantum state.


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