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Shadows Of The Mind
''Shadows of the Mind: A Search for the Missing Science of Consciousness'' is a 1994 book by mathematical physicist Roger Penrose that serves as a followup to his 1989 book '' The Emperor's New Mind: Concerning Computers, Minds and The Laws of Physics''. Penrose hypothesizes that: *Human consciousness is non-algorithmic, and thus is not capable of being modelled by a conventional Turing machine type of digital computer. *Quantum mechanics plays an essential role in the understanding of human consciousness; specifically, he believes that microtubules within neurons support quantum superpositions. *The objective collapse of the quantum wavefunction of the microtubules is critical for consciousness. *The collapse in question is physical behaviour that is non-algorithmic and transcends the limits of computability. *The human mind has abilities that no Turing machine could possess because of this mechanism of non-computable physics. Argument Mathematical thought In 1931, th ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Roger Penrose
Sir Roger Penrose (born 8 August 1931) is an English mathematician, mathematical physicist, philosopher of science and Nobel Laureate in Physics. He is Emeritus Rouse Ball Professor of Mathematics in the University of Oxford, an emeritus fellow of Wadham College, Oxford, and an honorary fellow of St John's College, Cambridge and University College London. Penrose has contributed to the mathematical physics of general relativity and cosmology. He has received several prizes and awards, including the 1988 Wolf Prize in Physics, which he shared with Stephen Hawking for the Penrose–Hawking singularity theorems, and one half of the 2020 Nobel Prize in Physics "for the discovery that black hole formation is a robust prediction of the general theory of relativity". He is regarded as one of the greatest living physicists, mathematicians and scientists, and is particularly noted for the breadth and depth of his work in both natural and formal sciences. Early life and education Bor ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Quantum Gravity
Quantum gravity (QG) is a field of theoretical physics that seeks to describe gravity according to the principles of quantum mechanics; it deals with environments in which neither gravitational nor quantum effects can be ignored, such as in the vicinity of black holes or similar compact astrophysical objects, such as neutron stars. Three of the four fundamental forces of physics are described within the framework of quantum mechanics and quantum field theory. The current understanding of the fourth force, gravity, is based on Albert Einstein's general theory of relativity, which is formulated within the entirely different framework of classical physics. However, that description is incomplete: describing the gravitational field of a black hole in the general theory of relativity leads physical quantities, such as the spacetime curvature, to diverge at the center of the black hole. This signals the breakdown of the general theory of relativity and the need for a theory that goes b ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Space-time Curvature
General relativity, also known as the general theory of relativity and Einstein's theory of gravity, is the geometric theory of gravitation published by Albert Einstein in 1915 and is the current description of gravitation in modern physics. General relativity generalizes special relativity and refines Newton's law of universal gravitation, providing a unified description of gravity as a geometric property of space and time or four-dimensional spacetime. In particular, the ' is directly related to the energy and momentum of whatever matter and radiation are present. The relation is specified by the Einstein field equations, a system of second order partial differential equations. Newton's law of universal gravitation, which describes classical gravity, can be seen as a prediction of general relativity for the almost flat spacetime geometry around stationary mass distributions. Some predictions of general relativity, however, are beyond Newton's law of universal gravitat ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Quantum Linear Superposition
Quantum superposition is a fundamental principle of quantum mechanics. It states that, much like waves in classical physics, any two (or more) quantum states can be added together ("superposed") and the result will be another valid quantum state; and conversely, that every quantum state can be represented as a sum of two or more other distinct states. Mathematically, it refers to a property of solutions to the Schrödinger equation; since the Schrödinger equation is linear, any linear combination of solutions will also be a solution(s) . An example of a physically observable manifestation of the wave nature of quantum systems is the interference peaks from an electron beam in a double-slit experiment. The pattern is very similar to the one obtained by diffraction of classical waves. Another example is a quantum logical qubit state, as used in quantum information processing, which is a quantum superposition of the "basis states" , 0 \rangle and , 1 \rangle . Here , 0 \ra ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Quantum State
In quantum physics, a quantum state is a mathematical entity that provides a probability distribution for the outcomes of each possible measurement on a system. Knowledge of the quantum state together with the rules for the system's evolution in time exhausts all that can be predicted about the system's behavior. A mixture of quantum states is again a quantum state. Quantum states that cannot be written as a mixture of other states are called pure quantum states, while all other states are called mixed quantum states. A pure quantum state can be represented by a ray in a Hilbert space over the complex numbers, while mixed states are represented by density matrices, which are positive semidefinite operators that act on Hilbert spaces. Pure states are also known as state vectors or wave functions, the latter term applying particularly when they are represented as functions of position or momentum. For example, when dealing with the energy spectrum of the electron in a hydrogen at ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
General Relativity
General relativity, also known as the general theory of relativity and Einstein's theory of gravity, is the geometric theory of gravitation published by Albert Einstein in 1915 and is the current description of gravitation in modern physics. General relativity generalizes special relativity and refines Newton's law of universal gravitation, providing a unified description of gravity as a geometric property of space and time or four-dimensional spacetime. In particular, the ' is directly related to the energy and momentum of whatever matter and radiation are present. The relation is specified by the Einstein field equations, a system of second order partial differential equations. Newton's law of universal gravitation, which describes classical gravity, can be seen as a prediction of general relativity for the almost flat spacetime geometry around stationary mass distributions. Some predictions of general relativity, however, are beyond Newton's law of universal gravitat ... [...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] |
John Lucas (philosopher)
John Randolph Lucas (18 June 1929 – 5 April 2020) was a British philosopher. Biography Lucas was educated at Winchester College and then, as a pupil of R.M. Hare, among others, at Balliol College, Oxford. He studied first mathematics, then Greats (Greek, Latin, Philosophy and Ancient History), obtaining first class honours in both. He sat for Finals in 1951, and took his MA in 1954. He spent the 1957–58 academic year at Princeton University, studying mathematics and logic. For 36 years, until his 1996 retirement, he was a Fellow and Tutor of Merton College, Oxford, and he remained an emeritus member of the University Faculty of Philosophy. He was a Fellow of the British Academy. Lucas is perhaps best known for his paper "Minds, Machines and Gödel," arguing that an automaton cannot represent a human mathematician, attempting to refute computationalism. An author with diverse teaching and research interests, Lucas wrote on the philosophy of mathematics, especially the ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Minds, Machines And Gödel
"Minds, Machines and Gödel" is J. R. Lucas's 1959 philosophical paper in which he argues that a human mathematician cannot be accurately represented by an algorithmic automaton. Appealing to Gödel's incompleteness theorem, he argues that for any such automaton, there would be some mathematical formula which it could not prove, but which the human mathematician could both see, and show, to be true. The paper is a Gödelian argument against mechanism. Lucas presented the paper in 1959 to the Oxford Philosophical Society. It was first printed in ''Philosophy'', XXXVI, 1961, then reprinted in ''The Modeling of Mind'', Kenneth M. Sayre and Frederick J. Crosson, eds., Notre Dame Press, 1963, and in ''Minds and Machines'', ed. Alan Ross Anderson, Prentice-Hall, 1964, . See also *Artificial intelligence *Philosophy of artificial intelligence The philosophy of artificial intelligence is a branch of the philosophy of technology that explores artificial intelligence and its implica ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
The Emperor's New Mind
''The Emperor's New Mind: Concerning Computers, Minds and The Laws of Physics'' is a 1989 book by the mathematical physicist Sir Roger Penrose. Penrose argues that human consciousness is non-algorithmic, and thus is not capable of being modeled by a conventional Turing machine, which includes a digital computer. Penrose hypothesizes that quantum mechanics plays an essential role in the understanding of human consciousness. The Wave function collapse, collapse of the quantum wavefunction is seen as playing an important role in brain function. Most of the book is spent reviewing, for the scientifically-minded lay-reader, a plethora of interrelated subjects such as Newtonian physics, special relativity, special and general relativity, the philosophy and limitations of mathematics, quantum physics, physical cosmology, cosmology, and the nature of time. Penrose intermittently describes how each of these bears on his developing theme: that consciousness is not "algorithmic". Only the ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Artificial General Intelligence
Artificial general intelligence (AGI) is the ability of an intelligent agent to understand or learn any intellectual task that a human being can. It is a primary goal of some artificial intelligence research and a common topic in science fiction and futures studies. AGI is also called strong AI,: Kurzweil describes strong AI as "machine intelligence with the full range of human intelligence." full AI, or general intelligent action, although some academic sources reserve the term "strong AI" for computer programs that experience sentience or consciousness. Strong AI contrasts with ''weak AI'' (or ''narrow AI''), which is not intended to have general cognitive abilities; rather, weak AI is any program that is designed to solve exactly one problem. (Academic sources reserve "weak AI" for programs that do not experience consciousness or do not have a mind in the same sense people do.) A 2020 survey identified 72 active AGI R&D projects spread across 37 countries. Characteristics ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
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