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Bremermann's Limit
Bremermann's limit, named after Hans-Joachim Bremermann, is a limit on the maximum rate of computation that can be achieved in a self-contained system in the material universe. It is derived from Einstein's mass-energy equivalency and the Heisenberg uncertainty principle, and is '' c''2/'' h'' ≈ 1.36 × 1050 bits per second per kilogram. This value is important when designing cryptographic algorithms, as it can be used to determine the minimum size of encryption keys or hash values required to create an algorithm that could never be cracked by a brute-force search. For example, a computer with the mass of the entire Earth operating at Bremermann's limit could perform approximately 1075 mathematical computations per second. If one assumes that a cryptographic key can be tested with only one operation, then a typical 128-bit key could be cracked in under 10−36 seconds. However, a 256-bit key (which is already in use in some systems) would take about two minutes to cra ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Hans-Joachim Bremermann
Hans-Joachim Bremermann (1926–1996) was a German-American mathematician and biophysicist. He worked on computer science and evolution, introducing ideas of how mating generates new gene combinations. Bremermann's limit, named after him, is the maximum computational speed of a self-contained system in the material universe. Early life Bremermann was born in Bremen, Germany, to Bernard Bremermann and Berta Wicke. Bremermann undertook doctoral studies at the University of Münster, completing his Staatsexamen in mathematics and physics in 1951. In the same year his doctoral dissertation ''Die Charakterisierung von Regularitätsgebieten durch pseudokonvexe Funktionen'' and was to become a specialist in complex analysis. This was a special case of the Levi problem. Career He came to the United States in 1952 to a research associate position at Stanford University. In 1953, he was appointed a research fellow at Harvard University. He returned to Munster for 1954–55. After ret ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Quantum Memory
In quantum computing, quantum memory is the quantum-mechanical version of ordinary computer memory. Whereas ordinary memory stores information as binary states (represented by "1"s and "0"s), quantum memory stores a quantum state for later retrieval. These states hold useful computational information known as qubits. Unlike the classical memory of everyday computers, the states stored in quantum memory can be in a quantum superposition, giving much more practical flexibility in quantum algorithms than classical information storage. Quantum memory is essential for the development of many devices in quantum information processing, including a synchronization tool that can match the various processes in a quantum computer, a quantum gate that maintains the identity of any state, and a mechanism for converting predetermined photons into on-demand photons. Quantum memory can be used in many aspects, such as quantum computing and quantum communication. Continuous research and ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Cybernetics
Cybernetics is a wide-ranging field concerned with circular causality, such as feedback, in regulatory and purposive systems. Cybernetics is named after an example of circular causal feedback, that of steering a ship, where the helmsperson maintains a steady course in a changing environment by adjusting their steering in continual response to the effect it is observed as having. Cybernetics is concerned with circular causal processes such as steering however they are embodied,Ashby, W. R. (1956). An introduction to cybernetics. London: Chapman & Hall, p. 1. including in ecological, technological, biological, cognitive, and social systems, and in the context of practical activities such as designing, learning, managing, conversation, and the practice of cybernetics itself. Cybernetics' transdisciplinary and "antidisciplinary" character has meant that it intersects with a number of other fields, leading to it having both wide influence and diverse interpretations. Cybernetics ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Gennady Gorelik
Gennady Gorelik (born 1948, Lviv) is a research fellow at the Center for Philosophy and History of Science, Boston University. A physicist by education and historian by occupation, he published ten books and many articles on popular science and history of science, including in-depth biographies of 20th-century Russian physicists, Matvei Bronstein, Andrei Sakharov, and Lev Landau Lev Davidovich Landau (russian: Лев Дави́дович Ланда́у; 22 January 1908 – 1 April 1968) was a Soviet-Azerbaijani physicist of Jewish descent who made fundamental contributions to many areas of theoretical physics. His ac .... In his biography of Sakharov, he provides the documentary explanation of Sakharov's metamorphosis from a secret father of the Soviet H-bomb to most prominent advocate of human rights in the Soviet Union. In 1995, he received a Guggenheim Fellowship. Selected publications * Размерность пространства: историко-методо ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Ultrafinitism
In the philosophy of mathematics, ultrafinitism (also known as ultraintuitionism,International Workshop on Logic and Computational Complexity, ''Logic and Computational Complexity'', Springer, 1995, p. 31. strict formalism,St. Iwan (2000),On the Untenability of Nelson's Predicativism, ''Erkenntnis'' 53(1–2), pp. 147–154. strict finitism, actualism, predicativism, and strong finitism) is a form of finitism and intuitionism. There are various philosophies of mathematics that are called ultrafinitism. A major identifying property common among most of these philosophies is their objections to totality of number theoretic functions like exponentiation over natural numbers. Main ideas Like other finitists, ultrafinitists deny the existence of the infinite set N of natural numbers, i.e. there is a largest natural number. In addition, some ultrafinitists are concerned with acceptance of objects in mathematics that no one can construct in practice because of physical restrictions in ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Limits Of Computation
The limits of computation are governed by a number of different factors. In particular, there are several physical and practical limits to the amount of computation or data storage that can be performed with a given amount of mass, volume, or energy. Hardware limits or physical limits Processing and memory density * The Bekenstein bound limits the amount of information that can be stored within a spherical volume to the entropy of a black hole with the same surface area. * Thermodynamics limit the data storage of a system based on its energy, number of particles and particle modes. In practice, it is a stronger bound than the Bekenstein bound. Processing speed * Bremermann's limit is the maximum computational speed of a self-contained system in the material universe, and is based on mass–energy versus quantum uncertainty constraints. Communication delays * The Margolus–Levitin theorem sets a bound on the maximum computational speed per unit of energy: 6 × 1033 ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Transcomputational Problem
In computational complexity theory, a transcomputational problem is a problem that requires processing of more than 1093 bits of information. Any number greater than 1093 is called a transcomputational number. The number 1093, called Bremermann's limit, is, according to Hans-Joachim Bremermann, the total number of bits processed by a hypothetical computer the size of the Earth within a time period equal to the estimated age of the Earth.Bremermann, H.J. (1962''Optimization through evolution and recombination''In: Self-Organizing systems 1962, edited M.C. Yovitts et al., Spartan Books, Washington, D.C. pp. 93–106. The term ''transcomputational'' was coined by Bremermann. Examples Testing integrated circuits Exhaustively testing all combinations of an integrated circuit with 309 boolean inputs and 1 output requires testing of a total of 2309 combinations of inputs. Since the number 2309 is a transcomputational number (that is, a number greater than 1093), the problem of testing s ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Kolmogorov Complexity
In algorithmic information theory (a subfield of computer science and mathematics), the Kolmogorov complexity of an object, such as a piece of text, is the length of a shortest computer program (in a predetermined programming language) that produces the object as output. It is a measure of the computational resources needed to specify the object, and is also known as algorithmic complexity, Solomonoff–Kolmogorov–Chaitin complexity, program-size complexity, descriptive complexity, or algorithmic entropy. It is named after Andrey Kolmogorov, who first published on the subject in 1963 and is a generalization of classical information theory. The notion of Kolmogorov complexity can be used to state and prove impossibility results akin to Cantor's diagonal argument, Gödel's incompleteness theorem, and Turing's halting problem. In particular, no program ''P'' computing a lower bound for each text's Kolmogorov complexity can return a value essentially larger than ''P'''s own len ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Bekenstein Bound
In physics, the Bekenstein bound (named after Jacob Bekenstein) is an upper limit on the thermodynamic entropy ''S'', or Shannon entropy ''H'', that can be contained within a given finite region of space which has a finite amount of energy—or conversely, the maximal amount of information required to perfectly describe a given physical system down to the quantum level. It implies that the information of a physical system, or the information necessary to perfectly describe that system, must be finite if the region of space and the energy are finite. In computer science this implies that non-finite models such as Turing machines are not realizable as finite devices. Equations The universal form of the bound was originally found by Jacob Bekenstein in 1981 as the inequality : S \leq \frac, where ''S'' is the entropy, ''k'' is the Boltzmann constant, ''R'' is the radius of a sphere that can enclose the given system, ''E'' is the total mass–energy including any rest masses, ''ħ ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Landauer's Principle
Landauer's principle is a physical principle pertaining to the lower theoretical limit of energy consumption of computation. It holds that "any logically irreversible manipulation of information, such as the erasure of a bit or the merging of two computation paths, must be accompanied by a corresponding entropy increase in non-information-bearing degrees of freedom of the information-processing apparatus or its environment".. Another way of phrasing Landauer's principle is that if an observer loses information about a physical system, heat is generated and the observer loses the ability to extract useful work from that system. A so-called logically reversible computation, in which no information is erased, may in principle be carried out without releasing any heat. This has led to considerable interest in the study of reversible computing. Indeed, without reversible computing, increases in the number of computations per joule of energy dissipated must eventually come to a ha ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Margolus–Levitin Theorem
The Margolus–Levitin theorem states that the processing rate of all forms of computation (including quantum computation) cannot be higher than about 6 × 1033 operations per second per joule of energy. The theorem is named for Norman Margolus and Lev B. Levitin, who derived this fundamental limit on the rate of computation. Stating the bound for one bit is as follows: :A quantum system of energy ''E'' needs at least a time of \frac to go from one state to an orthogonal state, where ''h'' is the Planck constant () and ''E'' is average energy. See also * Bekenstein bound * Bremermann's limit * Landauer's principle * Kolmogorov complexity * Koomey's law * Limits to computation * Moore's law References * * * * Lloyd, Seth; Ng, Y. Jack,Black Hole Computers, ''Scientific American ''Scientific American'', informally abbreviated ''SciAm'' or sometimes ''SA'', is an American popular science magazine. Many famous scientists, including Albert Einstein and Nikola Tesla ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Norman Margolus
Norman H. Margolus (born 1955) is a Canadian-American physicist and computer scientist, known for his work on cellular automata and reversible computing.. He is a research affiliate with the Computer Science and Artificial Intelligence Laboratory at the Massachusetts Institute of Technology. Education and career Margolus received his Ph.D. in physics in 1987 from the Massachusetts Institute of Technology (MIT) under the supervision of Edward Fredkin. He founded and was chief scientist for Permabit, an information storage device company. Research contributions Margolus was one of the organizers of a seminal research meeting on the connections between physics and computation theory, held on Mosquito Island in 1982. He is known for inventing the block cellular automaton and the Margolus neighborhood for block cellular automata, which he used to develop cellular automaton simulations of billiard-ball computers.. Reprinted in . In the same work, Margolus also showed that the bi ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
