Essence-Function

Essence-Function or Essence and Function, or else Substance and Function (體用, Chinese pinyin: tǐ yòng, Korean: che-yong) is a key concept in Chinese philosophy and other Far-Eastern philosophies (Japanese philosophy, Korean philosophy, Vietnamese philosophy).

The notions appear already in the Zhongyong (Doctrine of the Mean) attributed to Zi Si, the grandson of Confucius. The first philosopher to systematically use the ti yong schema for the analysis and explanation of deep relationships, was Wang Bi (226-249) in his commentary to Daodejing, chapter 22, when he discussed the metaphysical relation between non-being (wu) and being (you). Subsequently the notion has been borrowed from the Neo-Daoist philosophy to other schools of Chinese philosophy, including Hua-yen and other schools of Buddhism, and Neo-Confucianism of Cheng Yi and Zhu Xi, and served as a basic tool of interpretation of various philosophical relations in compound and dynamic events. With these schools it has travelled to Korea, Japan and Vietnam, and has been developed there. Wing-tsit Chan is one of the first scholars to open the discourse in English on this notion within the Chinese Neo-Confucian philosophy (in his Reflections on Things at Hand, 1967).

Function

Function may refer to:

Math, computing and engineering

Music

Other uses

See also

Minkowski's question mark function

In mathematics, the Minkowski question mark function (or the slippery devil's staircase), denoted by ?(x), is a function possessing various unusual fractal properties, defined by Hermann Minkowski (1904, pages 171–172). It maps quadratic irrationals to rational numbers on the unit interval, via an expression relating the continued fraction expansions of the quadratics to the binary expansions of the rationals, given by Arnaud Denjoy in 1938. In addition, it maps rational numbers to dyadic rationals, as can be seen by a recursive definition closely related to the Stern–Brocot tree.

Definition

If is the continued fraction representation of an irrational number x, then

whereas:

If is a continued fraction representation of a rational number x, then

Intuitive explanation

To get some intuition for the definition above, consider the different ways of interpreting an infinite string of bits beginning with 0 as a real number in [0,1]. One obvious way to interpret such a string is to place a binary point after the first 0 and read the string as a binary expansion: thus, for instance, the string 001001001001001001001001... represents the binary number 0.010010010010..., or 2/7. Another interpretation views a string as the continued fraction [0; a₁, a₂, … ], where the integers a_i are the run lengths in a run-length encoding of the string. The same example string 001001001001001001001001... then corresponds to [0; 2, 1, 2, 1, 2, 1, …] = √3 − 1/2. If the string ends in an infinitely long run of the same bit, we ignore it and terminate the representation; this is suggested by the formal "identity":

Function (mathematics)

In mathematics, a function is a relation between a set of inputs and a set of permissible outputs with the property that each input is related to exactly one output. An example is the function that relates each real number x to its square x². The output of a function f corresponding to an input x is denoted by f(x) (read "f of x"). In this example, if the input is −3, then the output is 9, and we may write f(−3) = 9. Likewise, if the input is 3, then the output is also 9, and we may write f(3) = 9. (The same output may be produced by more than one input, but each input gives only one output.) The input variable(s) are sometimes referred to as the argument(s) of the function.

Functions of various kinds are "the central objects of investigation" in most fields of modern mathematics. There are many ways to describe or represent a function. Some functions may be defined by a formula or algorithm that tells how to compute the output for a given input. Others are given by a picture, called the graph of the function. In science, functions are sometimes defined by a table that gives the outputs for selected inputs. A function could be described implicitly, for example as the inverse to another function or as a solution of a differential equation.

Essence (disambiguation)

Essence is the attribute (or set of attributes) that make an object or substance what it fundamentally is.

Essence may also refer to:

Essence (The X-Files)

"Essence" is the twentieth and penultimate episode of the eighth season and the 181st episode overall of the science fiction television series The X-Files. The episode first aired in the United States on May 13, 2001 on Fox, and subsequently aired in the United Kingdom. It was written by executive producer Chris Carter and directed by Kim Manners. "Essence" earned Nielsen rating of 7.7 and was viewed by 12.8 million viewers. The episode received largely positive reviews from critics.

The show centers on FBI special agents John Doggett (Robert Patrick) and Dana Scully (Gillian Anderson)—as well as ex-FBI agent Fox Mulder (David Duchovny)—who work on cases linked to the paranormal, called X-Files. In this episode, Mulder, Walter Skinner (Mitch Pileggi), and Doggett come up against the horrible consequences of the Syndicate’s pact with the aliens, as Billy Miles (Zachary Ansley)—reprogrammed as a soldier—attempts to erase all evidence of the tests—including Scully's soon-to-be-born baby. The men call on Monica Reyes (Annabeth Gish) to help them.

Essence (Don Ellis album)

Essence is an album by trumpeter Don Ellis recorded in 1962 and released on the Pacific Jazz label.

Reception

Reviewed in the January 3, 1963 issue of Down Beat magazine, jazz critic Richard B. Hadlock said that "Over and over throughout the 44 remarkable minutes of this recording the force of Ellis' extraordinary musicianship makes itself felt. Indeed, at times his complete mastery of the horn almost seems to get in the way. But this is a brilliant young musician with original ideas to offer..."

The Allmusic site awarded the album 4 stars stating "Ellis, who sought during this period to transfer ideas and concepts from modern classical music into adventurous jazz, often experimented with time, tempos and the use of space while still swinging... This is thought-provoking music that was certainly way overdue to be reissued."The Penguin Guide to Jazz said "The group is a fine one; even the little-known drummers play with authority and seem equal to Ellis's developing rhythmic obsessions. ...Bley is fascinating and Peacock his usual authoritative self."