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Inventor's Paradox
The inventor's paradox is a phenomenon that occurs in seeking a solution to a given problem. Instead of solving a specific type of problem, which would seem intuitively easier, it can be easier to solve a more general problem, which covers the specifics of the sought-after solution. The ''inventor's paradox'' has been used to describe phenomena in mathematics, programming, and logic, as well as other areas that involve critical thinking. History In the book ''How to Solve It'', Hungarian mathematician George Pólya introduces what he defines as the inventor's paradox: Or, in other words, to solve what one desires to solve, one may have to solve more than that in order to get a properly working flow of information. When solving a problem, the natural inclination typically is to remove as much excessive variability and produce limitations on the subject at hand as possible. Doing this can create unforeseen and intrinsically awkward parameters.Tate, et al., p. 110 The goal is to f ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Critical Thinking
Critical thinking is the analysis of available facts, evidence, observations, and arguments to form a judgement. The subject is complex; several different definitions exist, which generally include the rational, skeptical, and unbiased analysis or evaluation of factual evidence. Critical thinking is self-directed, self-disciplined, self- monitored, and self- corrective thinking. It presupposes assent to rigorous standards of excellence and mindful command of their use. It entails effective communication and problem-solving abilities as well as a commitment to overcome native egocentrism and sociocentrism. History The earliest records of critical thinking are the teachings of Socrates recorded by Plato. These included a part in Plato's early dialogues, where Socrates engages with one or more interlocutors on the issue of ethics such as question whether it was right for Socrates to escape from prison. The philosopher considered and reflected on this question and came to the conc ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
How To Solve It
''How to Solve It'' (1945) is a small volume by mathematician George Pólya describing methods of problem solving. Four principles ''How to Solve It'' suggests the following steps when solving a mathematical problem: # First, you have to ''understand the problem''. # After understanding, ''make a plan''. pp. 8–12 # ''Carry out the plan''. # ''Look back'' on your work. How could it be better? If this technique fails, Pólya advises: "If you cannot solve the proposed problem, try to solve first some related problem. Could you imagine a more accessible related problem?" First principle: Understand the problem "Understand the problem" is often neglected as being obvious and is not even mentioned in many mathematics classes. Yet students are often stymied in their efforts to solve it, simply because they don't understand it fully, or even in part. In order to remedy this oversight, Pólya taught teachers how to prompt each student with appropriate questions, depending on the ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
George Pólya
George Pólya (; hu, Pólya György, ; December 13, 1887 – September 7, 1985) was a Hungarian mathematician. He was a professor of mathematics from 1914 to 1940 at ETH Zürich and from 1940 to 1953 at Stanford University. He made fundamental contributions to combinatorics, number theory, numerical analysis and probability theory. He is also noted for his work in heuristics and mathematics education. He has been described as one of The Martians, an informal category which included one of his most famous students at ETH Zurich, John Von Neumann. Life and works Pólya was born in Budapest, Austria-Hungary, to Anna Deutsch and Jakab Pólya, Hungarian Jews who had converted to Christianity in 1886. Although his parents were religious and he was baptized into the Catholic Church upon birth, George eventually grew up to be an agnostic. He was a professor of mathematics from 1914 to 1940 at ETH Zürich in Switzerland and from 1940 to 1953 at Stanford University. He remained a Pr ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Bruce Tate
Bruce A. Tate is an American author on the topic of the Java, Ruby, and Elixir programming languages and other computer software. He is also the CTO of icanmakeitbetter.com and the editor of Elixir books for the Pragmatic Bookshelf. Works * ''Adopting Elixir'' * ''Better, Faster, Lighter Java'' * ''Beyond Java: A Glimpse at the Future of Programming Languages'' * ''Bitter EJB'', co-authored a critical analysis of Java EJBs * ''Bitter Java'', a critical analysis of Java * ''Deploying Rails Applications'' * ''From Java to Ruby: Things Every Manager Should Know'' * ''Programming Phoenix'' * ''Rails: Up and Running'' * ''Seven Languages in Seven Weeks'' * ''Seven More Languages in Seven Weeks'' References External links Review of Tate's book Beyond JavaWeblog''Amazon book review and listings''interview in the free Prolog Prolog is a logic programming language associated with artificial intelligence and computational linguistics. Prolog has its roots in first-order logic, a f ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Visual Basic , an Active Scripting language
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Visual Basic is a name for a family of programming languages from Microsoft. It may refer to: * Visual Basic .NET (now simply referred to as "Visual Basic"), the current version of Visual Basic launched in 2002 which runs on .NET * Visual Basic (classic), the original Visual Basic supported from 1991–2008 * Embedded Visual Basic, the classic version geared toward embedded applications * Visual Basic for Applications, an implementation of Visual Basic 6 built into programs such as Microsoft Office and used for writing macros * VBScript VBScript (''"Microsoft Visual Basic Scripting Edition"'') is an Active Scripting language developed by Microsoft that is modeled on Visual Basic. It allows Microsoft Windows system administrators to generate powerful tools for managing computers ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Apache HTTP Server
The Apache HTTP Server ( ) is a free and open-source cross-platform web server software, released under the terms of Apache License 2.0. Apache is developed and maintained by an open community of developers under the auspices of the Apache Software Foundation. The vast majority of Apache HTTP Server instances run on a Linux distribution, but current versions also run on Microsoft Windows, OpenVMS, and a wide variety of Unix-like systems. Past versions also ran on NetWare, OS/2 and other operating systems, including ports to mainframes. Originally based on the NCSA HTTPd server, development of Apache began in early 1995 after work on the NCSA code stalled. Apache played a key role in the initial growth of the World Wide Web, quickly overtaking NCSA HTTPd as the dominant HTTP server. In 2009, it became the first web server software to serve more than 100 million websites. , Netcraft estimated that Apache served 23.04% of the million busiest websites, while Nginx served 22. ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Abstraction
Abstraction in its main sense is a conceptual process wherein general rules and concepts are derived from the usage and classification of specific examples, literal ("real" or "concrete") signifiers, first principles, or other methods. "An abstraction" is the outcome of this process—a concept that acts as a common noun for all subordinate concepts and connects any related concepts as a ''group'', ''field'', or ''category''. Suzanne K. Langer (1953), ''Feeling and Form: a theory of art developed from Philosophy in a New Key'' p. 90: " Sculptural form is a powerful abstraction from actual objects and the three-dimensional space which we construe ... through touch and sight." Conceptual abstractions may be formed by filtering the information content of a concept or an observable phenomenon, selecting only those aspects which are relevant for a particular purpose. For example, abstracting a leather soccer ball to the more general idea of a ball selects only the information on gen ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Generalization
A generalization is a form of abstraction whereby common properties of specific instances are formulated as general concepts or claims. Generalizations posit the existence of a domain or set of elements, as well as one or more common characteristics shared by those elements (thus creating a conceptual model). As such, they are the essential basis of all valid deductive inferences (particularly in logic, mathematics and science), where the process of verification is necessary to determine whether a generalization holds true for any given situation. Generalization can also be used to refer to the process of identifying the parts of a whole, as belonging to the whole. The parts, which might be unrelated when left on their own, may be brought together as a group, hence belonging to the whole by establishing a common relation between them. However, the parts cannot be generalized into a whole—until a common relation is established among ''all'' parts. This does not mean that the p ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
A New Aspect Of Mathematic Method
A, or a, is the first letter and the first vowel of the Latin alphabet, used in the modern English alphabet, the alphabets of other western European languages and others worldwide. Its name in English is ''a'' (pronounced ), plural ''aes''. It is similar in shape to the Ancient Greek letter alpha, from which it derives. The uppercase version consists of the two slanting sides of a triangle, crossed in the middle by a horizontal bar. The lowercase version can be written in two forms: the double-storey a and single-storey ɑ. The latter is commonly used in handwriting and fonts based on it, especially fonts intended to be read by children, and is also found in italic type. In English grammar, " a", and its variant " an", are indefinite articles. History The earliest certain ancestor of "A" is aleph (also written 'aleph), the first letter of the Phoenician alphabet, which consisted entirely of consonants (for that reason, it is also called an abjad to distinguish it fro ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Decision-making Paradoxes
In psychology, decision-making (also spelled decision making and decisionmaking) is regarded as the cognitive process resulting in the selection of a belief or a course of action among several possible alternative options. It could be either rational or irrational. The decision-making process is a reasoning process based on assumptions of values, preferences and beliefs of the decision-maker. Every decision-making process produces a final choice, which may or may not prompt action. Research about decision-making is also published under the label problem solving, particularly in European psychological research. Overview Decision-making can be regarded as a problem-solving activity yielding a solution deemed to be optimal, or at least satisfactory. It is therefore a process which can be more or less rational or irrational and can be based on explicit or tacit knowledge and beliefs. Tacit knowledge is often used to fill the gaps in complex decision-making processes. Usually, both of ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
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