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Mathematical Universe Hypothesis
In physics and cosmology, the mathematical universe hypothesis (MUH), also known as the ultimate ensemble theory and struogony (from mathematical structure, Latin: struō), is a speculative "theory of everything" (TOE) proposed by cosmologist Max Tegmark. Description Tegmark's MUH is: ''Our external physical reality is a mathematical structure''. That is, the physical universe is not merely ''described by'' mathematics, but ''is'' mathematics (specifically, a mathematical structure). Mathematical existence equals physical existence, and all structures that exist mathematically exist physically as well. Observers, including humans, are "self-aware substructures (SASs)". In any mathematical structure complex enough to contain such substructures, they "will subjectively perceive themselves as existing in a physically 'real' world". The theory can be considered a form of Pythagoreanism or Platonism in that it proposes the existence of mathematical entities; a form of mathematicism ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Physics
Physics is the natural science that studies matter, its fundamental constituents, its motion and behavior through space and time, and the related entities of energy and force. "Physical science is that department of knowledge which relates to the order of nature, or, in other words, to the regular succession of events." Physics is one of the most fundamental scientific disciplines, with its main goal being to understand how the universe behaves. "Physics is one of the most fundamental of the sciences. Scientists of all disciplines use the ideas of physics, including chemists who study the structure of molecules, paleontologists who try to reconstruct how dinosaurs walked, and climatologists who study how human activities affect the atmosphere and oceans. Physics is also the foundation of all engineering and technology. No engineer could design a flat-screen TV, an interplanetary spacecraft, or even a better mousetrap without first understanding the basic laws of physic ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Jürgen Schmidhuber
Jürgen Schmidhuber (born 17 January 1963) is a German computer scientist most noted for his work in the field of artificial intelligence, deep learning and artificial neural networks. He is a co-director of the Dalle Molle Institute for Artificial Intelligence Research in Lugano, in Ticino in southern Switzerland. Following Google Scholar, from 2016 to 2021 he has received more than 100,000 scientific citations. He has been referred to as "father of modern AI," "father of AI," "dad of mature AI," "Papa" of famous AI products, "Godfather," and "father of deep learning." (Schmidhuber himself, however, has called Alexey Grigorevich Ivakhnenko the "father of deep learning.") Schmidhuber completed his undergraduate (1987) and PhD (1991) studies at the Technical University of Munich in Munich, Germany. His PhD advisors were Wilfried Brauer and Klaus Schulten. He taught there from 2004 until 2009 when he became a professor of artificial intelligence at the Università della Sviz ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Turing Machine
A Turing machine is a mathematical model of computation describing an abstract machine that manipulates symbols on a strip of tape according to a table of rules. Despite the model's simplicity, it is capable of implementing any computer algorithm. The machine operates on an infinite memory tape divided into discrete cells, each of which can hold a single symbol drawn from a finite set of symbols called the alphabet of the machine. It has a "head" that, at any point in the machine's operation, is positioned over one of these cells, and a "state" selected from a finite set of states. At each step of its operation, the head reads the symbol in its cell. Then, based on the symbol and the machine's own present state, the machine writes a symbol into the same cell, and moves the head one step to the left or the right, or halts the computation. The choice of which replacement symbol to write and which direction to move is based on a finite table that specifies what to do for each comb ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Decidability (logic)
In logic, a true/false decision problem is decidable if there exists an effective method for deriving the correct answer. Zeroth-order logic (propositional logic) is decidable, whereas first-order and higher-order logic are not. Logical systems are decidable if membership in their set of logically valid formulas (or theorems) can be effectively determined. A theory (set of sentences closed under logical consequence) in a fixed logical system is decidable if there is an effective method for determining whether arbitrary formulas are included in the theory. Many important problems are undecidable, that is, it has been proven that no effective method for determining membership (returning a correct answer after finite, though possibly very long, time in all cases) can exist for them. Decidability of a logical system Each logical system comes with both a syntactic component, which among other things determines the notion of provability, and a semantic component, which determines ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Piet Hut
Piet Hut (born September 26, 1952) is a Dutch-American astrophysicist, who divides his time between research in computer simulations of dense stellar systems and broadly interdisciplinary collaborations, ranging from other fields in natural science to computer science, cognitive psychology and philosophy. He is currently the Head of the Program in Interdisciplinary Studies at the Institute for Advanced Study (IAS) in Princeton, New Jersey, USA. Asteroid 17031 Piethut is named after him, in honor of his work in planetary dynamics and for co-founding the B612 Foundation, which focuses on prevention of asteroid impacts on Earth. Career In the Netherlands, Hut did a double PhD program, at Utrecht University, in particle physics under Martinus Veltman and in Amsterdam in astrophysics under Ed van den Heuvel, resulting in a PhD at the University of Amsterdam. Previously an assistant professor at the University of California, Berkeley, Hut was in 1985, at the age of 32, appointed as a ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
String Theory Landscape
The string theory landscape or landscape of vacua refers to the collection of possible false vacua in string theory,The number of metastable vacua is not known exactly, but commonly quoted estimates are of the order 10500. See M. Douglas, "The statistics of string / M theory vacua", ''JHEP'' 0305, 46 (2003). ; S. Ashok and M. Douglas, "Counting flux vacua", ''JHEP'' 0401, 060 (2004). together comprising a collective "landscape" of choices of parameters governing compactifications. The term "landscape" comes from the notion of a fitness landscape in evolutionary biology. It was first applied to cosmology by Lee Smolin in his book '' The Life of the Cosmos'' (1997), and was first used in the context of string theory by Leonard Susskind. Compactified Calabi–Yau manifolds In string theory the number of flux vacua is commonly thought to be roughly 10^, but could be 10^ or higher. The large number of possibilities arises from choices of Calabi–Yau manifolds and choices of gen ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Halting Problem
In computability theory, the halting problem is the problem of determining, from a description of an arbitrary computer program and an input, whether the program will finish running, or continue to run forever. Alan Turing proved in 1936 that a general algorithm to solve the halting problem for all possible program–input pairs cannot exist. For any program that might determine whether programs halt, a "pathological" program , called with some input, can pass its own source and its input to ''f'' and then specifically do the opposite of what ''f'' predicts ''g'' will do. No ''f'' can exist that handles this case. A key part of the proof is a mathematical definition of a computer and program, which is known as a Turing machine; the halting problem is '' undecidable'' over Turing machines. It is one of the first cases of decision problems proven to be unsolvable. This proof is significant to practical computing efforts, defining a class of applications which no programming inventi ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Undecidable Problem
In computability theory and computational complexity theory, an undecidable problem is a decision problem for which it is proved to be impossible to construct an algorithm that always leads to a correct yes-or-no answer. The halting problem is an example: it can be proven that there is no algorithm that correctly determines whether arbitrary programs eventually halt when run. Background A decision problem is any arbitrary yes-or-no question on an infinite set of inputs. Because of this, it is traditional to define the decision problem equivalently as the set of inputs for which the problem returns ''yes''. These inputs can be natural numbers, but also other values of some other kind, such as strings of a formal language. Using some encoding, such as a Gödel numbering, the strings can be encoded as natural numbers. Thus, a decision problem informally phrased in terms of a formal language is also equivalent to a set of natural numbers. To keep the formal definition simple, it is ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Formal System
A formal system is an abstract structure used for inferring theorems from axioms according to a set of rules. These rules, which are used for carrying out the inference of theorems from axioms, are the logical calculus of the formal system. A formal system is essentially an "axiomatic system". In 1921, David Hilbert proposed to use such a system as the foundation for the knowledge in mathematics. A formal system may represent a well-defined abstraction, system of abstract thought. The term ''formalism'' is sometimes a rough synonym for ''formal system'', but it also refers to a given style of notation, for example, Paul Dirac's bra–ket notation. Background Each formal system is described by primitive Symbol (formal), symbols (which collectively form an Alphabet (computer science), alphabet) to finitely construct a formal language from a set of axioms through inferential rules of formation. The system thus consists of valid formulas built up through finite combinations of the ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Linked Open Data
In computing, linked data (often capitalized as Linked Data) is structured data which is interlinked with other data so it becomes more useful through semantic queries. It builds upon standard Web technologies such as HTTP, RDF and URIs, but rather than using them to serve web pages only for human readers, it extends them to share information in a way that can be read automatically by computers. Part of the vision of linked data is for the Internet to become a global database. Tim Berners-Lee, director of the World Wide Web Consortium (W3C), coined the term in a 2006 design note about the Semantic Web project. Linked data may also be open data, in which case it is usually described as Linked Open Data. Principles In his 2006 "Linked Data" note, Tim Berners-Lee outlined four principles of linked data, paraphrased along the following lines: #Uniform Resource Identifiers (URIs) should be used to name and identify individual things. #HTTP URIs should be used to allow these thin ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Digital Library Of Mathematical Functions
The Digital Library of Mathematical Functions (DLMF) is an online project at the National Institute of Standards and Technology (NIST) to develop a database of mathematical reference data for special functions and their applications. It is intended as an update of '' Abramowitz's and Stegun's Handbook of Mathematical Functions'' (A&S). It was published online on 7 May 2010, though some chapters appeared earlier. In the same year it appeared at Cambridge University Press under the title ''NIST Handbook of Mathematical Functions''. In contrast to A&S, whose initial print run was done by the U.S. Government Printing Office and was in the public domain, NIST asserts that it holds copyright to the DLMF under Title 17 USC 105 of the U.S. Code. See also * NIST Dictionary of Algorithms and Data Structures The NIST ''Dictionary of Algorithms and Data Structures'' is a reference work maintained by the U.S. National Institute of Standards and Technology. It defines a large number of te ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
