Alonzo Church (1903 – 1995) was a mathematician and logician who made major contributions to mathematical logic and the foundations of theoretical computer science. He created the lambda calculus which influenced the design of the LISP programming language and functional programming languages in general. Source: Alonzo Church. (n.d.). Retrieved December 22, 2014, from http://en.wikipedia.org/wiki/Alonzo_Church Stephen Cole Kleene (1909 – 1994) was an one of the students of Alonzo Church. He, along with others, founded the branch of mathematical logic known as recursion theory, which in turn provided foundations of theoretical computer science. Kleene's work is the basis of studying the computability of functions.
Kleene Star: Kleene Star is a mathematical unary operation (takes one input) that is applied to :
For example let A = { "Kleene", "Stephen", "Cole"}. The Kleene Star of A, denoted as A*, is the set of all strings that can be generated by concatenating zero or more strings in A. A* = { ε, KleeneKleene, KleeneStephen, KleeneCole, StephenKleene, StephenStephen, StephenCole, ColeKleene, ColeStephen, ColeCole, KleeneKleeneKleene...} 2. a set of symbols: "If B is a set of symbols or characters then B* (the Kleene Star of B) is the set of all strings over symbols in V, including the empty string ε." For example let B = {M, U, I} be a set containing the symbols of the MU system. The Kleene Star of B, denoted as B*, is the set of all finite length strings of symbols in B, including the empty string ε. B* = {ε, MM, MU, MI, UM, UU, UI, IM, IU, II, MMM, MMU, MMI...} Notice that the B* is an "infinite set" however each of the strings in it is finite. Source: Stephen Cole Kleene. (n.d.). Retrieved December 22, 2014, from http://en.wikipedia.org/wiki/Stephen_Cole_Kleene Kleene star | planetmath.org. (n.d.). Retrieved January 6, 2015, from http://planetmath.org/kleenestar
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Frame Analysis: An Essay on the Organization of Experience (1974) is Goffman's attempt to explain how conceptual frames – ways to organize experience – structure an individual's perception of society. Hence, the book is about the organization of people's experiences rather than the organization of society. A frame is a set of concepts and theoretical perspectives that organize experiences and guide the actions of individuals, groups and societies. Frame analysis, then, is the study of the organization of social experience. To illustrate the concept of the frame, Goffman gives the example of a picture frame: a person uses the frame (which represents structure) to hold together his picture (which represents the content) of what he is experiencing in his life.
Source: Wikipedia. Wikimedia Foundation. Web. 11 Jan. 2015. <http://en.wikipedia.org/wiki/Erving_Goffman#Frame_Analysis>. Are Quanta Real?: A Galilean Dialogue attempts to explain the concepts of quantum physics, especially the counter-intuitive ones.
The book is a dialogue between the same characters who appeared in Galileo's Dialogue on the Two Major Systems of the World, which attempted to explain the then revolutionary notion that the Earth is not the center of the Universe. The two principal characters' names are Simplicio and Salviati. Simplicio does not understand quantum physics and has some rather naive notions regarding how it works. Salviati understands it fully and is only too happy to point out Simplicio's errors. There is a third character, Sagredo, who appears a bit more sympathetic to Simplicio but nonetheless demurs to Salviati as the authority. Although Jauch is a bit rough on poor Simplicio, and sets up a few straw men to knock them down, the book is well worth reading. It explains quantum physics while maintaining a practical approach to its concepts. Are Quanta Real? was first published in Geneva in 1971, and then by Indiana University Press in 1973. Douglas R. Hofstadter uses the dialogue form in his book Gödel, Escher, Bach: An Eternal Golden Braid and claims Are Quanta Real? as the inspiration for it. 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 over mechanism. It claims that Gödel’s first incompleteness theorem shows that the human mind is not a computer. The argument has generated a great deal of discussion since then. The influential Computational Theory of Mind, which claims that the human mind is a computer, is false if Lucas’s argument succeeds. Furthermore, if Lucas’s argument is correct, then “strong artificial intelligence,” the view that it is possible at least in principle to construct a machine that has the same cognitive abilities as humans, is false.
Source: "Minds, Machines and Gödel." Wikipedia. Wikimedia Foundation. Web. 11 Jan. 2015. <http://en.wikipedia.org/wiki/Minds,_Machines_and_Gödel>. "Internet Encyclopedia of Philosophy." Internet Encyclopedia of Philosophy. Web. 11 Jan. 2015. <http://www.iep.utm.edu/lp-argue/>. Johann Sebastian Bach wrote over 200 cantatas (called Bachkantaten) of which at least 209 have survived.
While Bach was a Thomaskantor (cantor of the main churches of Leipzig) it was part of his job to perform a church cantata every Sunday and Holiday. Those cantats related to the readings prescribed by the Lutheran liturgy for the specific occasion. In his first years in Leipzig, he composed a new work every week and conducted soloists, the Thomanerchor and orchestra as part of the church service. Works from three annual cycles of cantatas have survived. A typical Bach cantata of his first year in Leipzig follows the scheme:
Source: Bach cantata. (n.d.). Retrieved January 11, 2015, from http://en.wikipedia.org/wiki/Bach_cantata |