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Binocular Rivalry Described By Quantum Formalism
Binocular rivalry is a visual phenomenon wherein one experiences alternating perceptions due to the occurrence of different stimuli presented to the corresponding retinal regions of the two eyes and their competition for perceptual dominance. As they compete, alternations between stimuli typically occur after a few seconds of steady vision. Neuroscientists have used binocular rivalry as a means to test neural responses and have found that the time intervals for these responses correlate with the alternations in perceptual dominance. A famous example of the phenomenon as described by Giambattista della Porta in the sixteenth-century, was to try reading two pages, each from a different book. The reader is to train an eye on each page and attempt to read one without disruption from the other eye. However, the rivalry is not always triggered; sometimes the stimuli blend together in a superposition of the original two stimuli or they fuse into a stable average. The rivalry is easily tr ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Binocular Rivalry
Binocular rivalry is a phenomenon of visual perception in which perception alternates between different images presented to each eye. When one image is presented to one eye and a very different image is presented to the other (also known as dichoptic presentation), instead of the two images being seen superimposed, one image is seen for a few moments, then the other, then the first, and so on, randomly for as long as one cares to look. For example, if a set of vertical lines is presented to one eye, and a set of horizontal lines to the same region of the retina of the other, sometimes the vertical lines are seen with no trace of the horizontal lines, and sometimes the horizontal lines are seen with no trace of the vertical lines. At transitions, brief, unstable composites of the two images may be seen. For example, the vertical lines may appear one at a time to obscure the horizontal lines from the left or from the right, like a traveling wave, switching slowly one image for the ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Giambattista Della Porta
Giambattista della Porta (; 1535 – 4 February 1615), also known as Giovanni Battista Della Porta, was an Italian scholar, polymath and playwright who lived in Naples at the time of the Renaissance, Scientific Revolution and Reformation. Giambattista della Porta spent the majority of his life on scientific endeavors. He benefited from an informal education of tutors and visits from renowned scholars. His most famous work, first published in 1558, is entitled ''Magia Naturalis (Natural Magic).'' In this book he covered a variety of the subjects he had investigated, including occult philosophy, astrology, alchemy, mathematics, meteorology, and natural philosophy. He was also referred to as "professor of secrets". Childhood Giambattista della Porta was born at Vico Equense, near Naples, to the nobleman Nardo Antonio della Porta. He was the third of four sons and the second to survive childhood, having an older brother Gian Vincenzo and a younger brother Gian Ferrante.Giambattist ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Hilbert Space
In mathematics, Hilbert spaces (named after David Hilbert) allow generalizing the methods of linear algebra and calculus from (finite-dimensional) Euclidean vector spaces to spaces that may be infinite-dimensional. Hilbert spaces arise naturally and frequently in mathematics and physics, typically as function spaces. Formally, a Hilbert space is a vector space equipped with an inner product that defines a distance function for which the space is a complete metric space. The earliest Hilbert spaces were studied from this point of view in the first decade of the 20th century by David Hilbert, Erhard Schmidt, and Frigyes Riesz. They are indispensable tools in the theories of partial differential equations, quantum mechanics, Fourier analysis (which includes applications to signal processing and heat transfer), and ergodic theory (which forms the mathematical underpinning of thermodynamics). John von Neumann coined the term ''Hilbert space'' for the abstract concept that under ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Orthogonal Basis
In mathematics, particularly linear algebra, an orthogonal basis for an inner product space V is a basis for V whose vectors are mutually orthogonal. If the vectors of an orthogonal basis are normalized, the resulting basis is an orthonormal basis. As coordinates Any orthogonal basis can be used to define a system of orthogonal coordinates V. Orthogonal (not necessarily orthonormal) bases are important due to their appearance from curvilinear orthogonal coordinates in Euclidean spaces, as well as in Riemannian and pseudo-Riemannian manifolds. In functional analysis In functional analysis, an orthogonal basis is any basis obtained from an orthonormal basis (or Hilbert basis) using multiplication by nonzero scalars. Extensions Symmetric bilinear form The concept of an orthogonal basis is applicable to a vector space V (over any field) equipped with a symmetric bilinear form \langle \cdot, \cdot \rangle, where '' orthogonality'' of two vectors v and w means \langle v, w \rangle = ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Operator (mathematics)
In mathematics, an operator is generally a mapping or function that acts on elements of a space to produce elements of another space (possibly and sometimes required to be the same space). There is no general definition of an ''operator'', but the term is often used in place of ''function'' when the domain is a set of functions or other structured objects. Also, the domain of an operator is often difficult to be explicitly characterized (for example in the case of an integral operator), and may be extended to related objects (an operator that acts on functions may act also on differential equations whose solutions are functions that satisfy the equation). See Operator (physics) for other examples. The most basic operators are linear maps, which act on vector spaces. Linear operators refer to linear maps whose domain and range are the same space, for example \R^n to \R^n. Such operators often preserve properties, such as continuity. For example, differentiation and indef ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Binocular Rivalry
Binocular rivalry is a phenomenon of visual perception in which perception alternates between different images presented to each eye. When one image is presented to one eye and a very different image is presented to the other (also known as dichoptic presentation), instead of the two images being seen superimposed, one image is seen for a few moments, then the other, then the first, and so on, randomly for as long as one cares to look. For example, if a set of vertical lines is presented to one eye, and a set of horizontal lines to the same region of the retina of the other, sometimes the vertical lines are seen with no trace of the horizontal lines, and sometimes the horizontal lines are seen with no trace of the vertical lines. At transitions, brief, unstable composites of the two images may be seen. For example, the vertical lines may appear one at a time to obscure the horizontal lines from the left or from the right, like a traveling wave, switching slowly one image for the ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Neural Correlates Of Consciousness
The neural correlates of consciousness (NCC) refer to the relationships between mental states and neural states and constitute the minimal set of neuronal events and mechanisms sufficient for a specific conscious percept. Neuroscientists use empirical approaches to discover neural correlates of subjective phenomena; that is, neural changes which necessarily and regularly correlate with a specific experience. The set should be ''minimal'' because, under the materialist assumption that the brain is sufficient to give rise to any given conscious experience, the question is which of its components is necessary to produce it. Neurobiological approach to consciousness A science of consciousness must explain the exact relationship between subjective mental states and brain states, the nature of the relationship between the conscious mind and the electro-chemical interactions in the body (mind–body problem). Progress in neuropsychology and neurophilosophy has come from focusing on the ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Hermitian Operator
In mathematics, a self-adjoint operator on an infinite-dimensional complex vector space ''V'' with inner product \langle\cdot,\cdot\rangle (equivalently, a Hermitian operator in the finite-dimensional case) is a linear map ''A'' (from ''V'' to itself) that is its own adjoint. If ''V'' is finite-dimensional with a given orthonormal basis, this is equivalent to the condition that the matrix of ''A'' is a Hermitian matrix, i.e., equal to its conjugate transpose ''A''. By the finite-dimensional spectral theorem, ''V'' has an orthonormal basis such that the matrix of ''A'' relative to this basis is a diagonal matrix with entries in the real numbers. In this article, we consider generalizations of this concept to operators on Hilbert spaces of arbitrary dimension. Self-adjoint operators are used in functional analysis and quantum mechanics. In quantum mechanics their importance lies in the Dirac–von Neumann formulation of quantum mechanics, in which physical observables such as positi ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Fourier Series
A Fourier series () is a summation of harmonically related sinusoidal functions, also known as components or harmonics. The result of the summation is a periodic function whose functional form is determined by the choices of cycle length (or ''period''), the number of components, and their amplitudes and phase parameters. With appropriate choices, one cycle (or ''period'') of the summation can be made to approximate an arbitrary function in that interval (or the entire function if it too is periodic). The number of components is theoretically infinite, in which case the other parameters can be chosen to cause the series to converge to almost any ''well behaved'' periodic function (see Pathological and Dirichlet–Jordan test). The components of a particular function are determined by ''analysis'' techniques described in this article. Sometimes the components are known first, and the unknown function is ''synthesized'' by a Fourier series. Such is the case of a discrete-ti ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Schrödinger Equation
The Schrödinger equation is a linear partial differential equation that governs the wave function of a quantum-mechanical system. It is a key result in quantum mechanics, and its discovery was a significant landmark in the development of the subject. The equation is named after Erwin Schrödinger, who postulated the equation in 1925, and published it in 1926, forming the basis for the work that resulted in his Nobel Prize in Physics in 1933. Conceptually, the Schrödinger equation is the quantum counterpart of Newton's second law in classical mechanics. Given a set of known initial conditions, Newton's second law makes a mathematical prediction as to what path a given physical system will take over time. The Schrödinger equation gives the evolution over time of a wave function, the quantum-mechanical characterization of an isolated physical system. The equation can be derived from the fact that the time-evolution operator must be unitary, and must therefore be generated by t ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Planck’s Constant
The Planck constant, or Planck's constant, is a fundamental physical constant of foundational importance in quantum mechanics. The constant gives the relationship between the energy of a photon and its frequency, and by the mass-energy equivalence, the relationship between mass and frequency. Specifically, a photon's energy is equal to its frequency multiplied by the Planck constant. The constant is generally denoted by h. The reduced Planck constant, or Dirac constant, equal to the constant divided by 2 \pi, is denoted by \hbar. In metrology it is used, together with other constants, to define the kilogram, the SI unit of mass. The SI units are defined in such a way that, when the Planck constant is expressed in SI units, it has the exact value The constant was first postulated by Max Planck in 1900 as part of a solution to the ultraviolet catastrophe. At the end of the 19th century, accurate measurements of the spectrum of black body radiation existed, but the distribution ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Quantum Mechanics
Quantum mechanics is a fundamental theory in physics that provides a description of the physical properties of nature at the scale of atoms and subatomic particles. It is the foundation of all quantum physics including quantum chemistry, quantum field theory, quantum technology, and quantum information science. Classical physics, the collection of theories that existed before the advent of quantum mechanics, describes many aspects of nature at an ordinary (macroscopic) scale, but is not sufficient for describing them at small (atomic and subatomic) scales. Most theories in classical physics can be derived from quantum mechanics as an approximation valid at large (macroscopic) scale. Quantum mechanics differs from classical physics in that energy, momentum, angular momentum, and other quantities of a bound system are restricted to discrete values ( quantization); objects have characteristics of both particles and waves (wave–particle duality); and there are limits to ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
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