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Elegance
Elegance is beauty that shows unusual effectiveness and simplicity. Elegance is frequently used as a standard of tastefulness, particularly in visual design, decorative arts, literature, science, and the aesthetics of mathematics. Elegant things often exhibit refined grace and suggest maturity, and in the case of mathematics, a deep mastery of the subject matter. General concept Essential components of the concept include simplicity and consistency of design, focusing on the essential features of an object. In art of any kind one might also require dignified grace, or restrained beauty of style. Visual stimuli are frequently considered elegant, if a small number of colors and stimuli are used, emphasizing the remainder. In philosophy of science In the philosophy of science, there are two concepts referring to two aspects of simplicity: elegance (syntactic simplicity), which means the number and complexity of hypotheses, and parsimony (ontological simplicity), which is th ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Computer Algorithm
In mathematics and computer science, an algorithm () is a finite sequence of rigorous instructions, typically used to solve a class of specific problems or to perform a computation. Algorithms are used as specifications for performing calculations and data processing. More advanced algorithms can perform automated deductions (referred to as automated reasoning) and use mathematical and logical tests to divert the code execution through various routes (referred to as automated decision-making). Using human characteristics as descriptors of machines in metaphorical ways was already practiced by Alan Turing with terms such as "memory", "search" and "stimulus". In contrast, a heuristic is an approach to problem solving that may not be fully specified or may not guarantee correct or optimal results, especially in problem domains where there is no well-defined correct or optimal result. As an effective method, an algorithm can be expressed within a finite amount of space and t ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Ontological Simplicity
Occam's razor, Ockham's razor, or Ocham's razor ( la, novacula Occami), also known as the principle of parsimony or the law of parsimony ( la, lex parsimoniae), is the problem-solving principle that "entities should not be multiplied beyond necessity". It is generally understood in the sense that with competing theories or explanations, the simpler one, for example a model with fewer parameters, is to be preferred. The idea is frequently attributed to English Franciscan friar William of Ockham (), a Scholasticism, scholastic philosopher and theologian, although he never used these exact words. This philosophical razor advocates that when presented with competing hypothesis, hypotheses about the same prediction, one should select the solution with the fewest assumptions, and that this is not meant to be a way of choosing between hypotheses that make different predictions. Similarly, in science, Occam's razor is used as an Abductive reasoning, abductive heuristic in the development ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Beauty
Beauty is commonly described as a feature of objects that makes these objects pleasurable to perceive. Such objects include landscapes, sunsets, humans and works of art. Beauty, together with art and taste, is the main subject of aesthetics, one of the major branches of philosophy. As a positive aesthetic value, it is contrasted with ugliness as its negative counterpart. Along with truth and goodness it is one of the transcendentals, which are often considered the three fundamental concepts of human understanding. One difficulty in understanding beauty is because it has both objective and subjective aspects: it is seen as a property of things but also as depending on the emotional response of observers. Because of its subjective side, beauty is said to be "in the eye of the beholder". It has been argued that the ability on the side of the subject needed to perceive and judge beauty, sometimes referred to as the "sense of taste", can be trained and that the verdicts of experts ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Simplicity
Simplicity is the state or quality of being simple. Something easy to understand or explain seems simple, in contrast to something complicated. Alternatively, as Herbert A. Simon suggests, something is simple or complex depending on the way we choose to describe it. In some uses, the label "simplicity" can imply beauty, purity, or clarity. In other cases, the term may suggest a lack of nuance or complexity relative to what is required. The concept of simplicity is related to the field of epistemology and philosophy of science (e.g., in Occam's razor). Religions also reflect on simplicity with concepts such as divine simplicity. In human lifestyles, simplicity can denote freedom from excessive possessions or distractions, such as having a simple living style. Some other information In some contextual uses, "simplicity" can imply beauty, purity, or clarity. In other cases, the term may have negative connotations, as when referring to people as simpletons. In philosophy of sci ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Occam's Razor
Occam's razor, Ockham's razor, or Ocham's razor ( la, novacula Occami), also known as the principle of parsimony or the law of parsimony ( la, lex parsimoniae), is the problem-solving principle that "entities should not be multiplied beyond necessity". It is generally understood in the sense that with competing theories or explanations, the simpler one, for example a model with fewer parameters, is to be preferred. The idea is frequently attributed to English Franciscan friar William of Ockham (), a scholastic philosopher and theologian, although he never used these exact words. This philosophical razor advocates that when presented with competing hypotheses about the same prediction, one should select the solution with the fewest assumptions, and that this is not meant to be a way of choosing between hypotheses that make different predictions. Similarly, in science, Occam's razor is used as an abductive heuristic in the development of theoretical models rather than as a rigoro ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Mathematics
Mathematics is an area of knowledge that includes the topics of numbers, formulas and related structures, shapes and the spaces in which they are contained, and quantities and their changes. These topics are represented in modern mathematics with the major subdisciplines of number theory, algebra, geometry, and analysis, respectively. There is no general consensus among mathematicians about a common definition for their academic discipline. Most mathematical activity involves the discovery of properties of abstract objects and the use of pure reason to prove them. These objects consist of either abstractions from nature orin modern mathematicsentities that are stipulated to have certain properties, called axioms. A ''proof'' consists of a succession of applications of deductive rules to already established results. These results include previously proved theorems, axioms, andin case of abstraction from naturesome basic properties that are considered true starting points of ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Surprise (emotion)
Surprise () is a brief mental and physiological state, a startle response experienced by animals and humans as the result of an unexpected event. Surprise can have any valence; that is, it can be neutral/moderate, pleasant, unpleasant, positive, or negative. Surprise can occur in varying levels of intensity ranging from very-surprised, which may induce the fight-or-flight response, or little-surprise that elicits a less intense response to the stimuli. Construct Surprise is intimately connected to the idea of acting in accordance with a set of rules. When the rules of reality generating events of daily life separate from the rule-of-thumb expectations, surprise is the outcome. Surprise represents the difference between expectations and reality, the gap between our assumptions and expectations about worldly events and the way that those events actually turn out. This gap can be deemed an important foundation on which new findings are based since surprises can make people awar ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Mathematical Proof
A mathematical proof is an inferential argument for a mathematical statement, showing that the stated assumptions logically guarantee the conclusion. The argument may use other previously established statements, such as theorems; but every proof can, in principle, be constructed using only certain basic or original assumptions known as axioms, along with the accepted rules of inference. Proofs are examples of exhaustive deductive reasoning which establish logical certainty, to be distinguished from empirical arguments or non-exhaustive inductive reasoning which establish "reasonable expectation". Presenting many cases in which the statement holds is not enough for a proof, which must demonstrate that the statement is true in ''all'' possible cases. A proposition that has not been proved but is believed to be true is known as a conjecture, or a hypothesis if frequently used as an assumption for further mathematical work. Proofs employ logic expressed in mathematical symbols ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Theorem
In mathematics, a theorem is a statement that has been proved, or can be proved. The ''proof'' of a theorem is a logical argument that uses the inference rules of a deductive system to establish that the theorem is a logical consequence of the axioms and previously proved theorems. In the mainstream of mathematics, the axioms and the inference rules are commonly left implicit, and, in this case, they are almost always those of Zermelo–Fraenkel set theory with the axiom of choice, or of a less powerful theory, such as Peano arithmetic. A notable exception is Wiles's proof of Fermat's Last Theorem, which involves the Grothendieck universes whose existence requires the addition of a new axiom to the set theory. Generally, an assertion that is explicitly called a theorem is a proved result that is not an immediate consequence of other known theorems. Moreover, many authors qualify as ''theorems'' only the most important results, and use the terms ''lemma'', ''proposition'' and ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Mathematical Elegance
Mathematical beauty is the aesthetic pleasure derived from the abstractness, purity, simplicity, depth or orderliness of mathematics. Mathematicians may express this pleasure by describing mathematics (or, at least, some aspect of mathematics) as beautiful or describe mathematics as an art form, e.g., a position taken by G. H. Hardy) or, at a minimum, as a creative activity. Comparisons are made with music and poetry. In method Mathematicians describe an especially pleasing method of proof as ''elegant''. Depending on context, this may mean: * A proof that uses a minimum of additional assumptions or previous results. * A proof that is unusually succinct. * A proof that derives a result in a surprising way (e.g., from an apparently unrelated theorem or a collection of theorems). * A proof that is based on new and original insights. * A method of proof that can be easily generalized to solve a family of similar problems. In the search for an elegant proof, mathematicians oft ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Frédéric Soulacroix - Elegance Of The Epoque
Frédéric and Frédérick are the French versions of the common male given name Frederick. They may refer to: In artistry: * Frédéric Back, Canadian award-winning animator * Frédéric Bartholdi, French sculptor * Frédéric Bazille, Impressionist painter best known for his depiction of figures * Frédéric Mariotti, actor In politics: * Frédéric Bamvuginyumvira, 1st Vice-President of Burundi * Frédéric Ngenzebuhoro, Vice-President of Burundi from 11 November 2004 to 26 August 2005 * Frédéric Bastiat, political economist and member of the French assembly In literature: * Frédéric Beigbeder, French writer, commentator critic and pundit * Frédéric Berat, French poet and songwriter * Frédéric Mistral, French poet In science: * Frédéric Cailliaud, French mineralogist * Frédéric Joliot-Curie, French physicist and Nobel laureate In sport: * Frédéric Bourdillon (born 1991), French-Israeli basketball player in the Israel Basketball Premier League * Frédérick ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Computer Program
A computer program is a sequence or set of instructions in a programming language for a computer to execute. Computer programs are one component of software, which also includes documentation and other intangible components. A computer program in its human-readable form is called source code. Source code needs another computer program to execute because computers can only execute their native machine instructions. Therefore, source code may be translated to machine instructions using the language's compiler. ( Assembly language programs are translated using an assembler.) The resulting file is called an executable. Alternatively, source code may execute within the language's interpreter. If the executable is requested for execution, then the operating system loads it into memory and starts a process. The central processing unit will soon switch to this process so it can fetch, decode, and then execute each machine instruction. If the source code is requested for execution, ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
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