|
Results for canonical
|
On this page:
|
The standard or authoritative method. The term comes from "canon," which is the law or rules of the church. See canonical name and canonical synthesis.
adjective
Definition: accepted, recognized
Antonyms: unacceptable, unauthorized, uncanonical, unorthodox, unrecognized, unsanctioned
[very common; historically, ‘according to religious law’] The usual or standard state or manner of something. This word has a somewhat more technical meaning in mathematics. Two formulas such as 9 + x and x + 9 are said to be equivalent because they mean the same thing, but the second one is in canonical form because it is written in the usual way, with the highest power of x first. Usually there are fixed rules you can use to decide whether something is in canonical form. The jargon meaning, a relaxation of the technical meaning, acquired its present loading in computer-science culture largely through its prominence in Alonzo Church's work in computation theory and mathematical logic (see Knights of the Lambda Calculus). Compare vanilla.
Non-technical academics do not use the adjective ‘canonical’ in any of the senses defined above with any regularity; they do however use the nouns canon and canonicity (not **canonicalness or **canonicality). The canon of a given author is the complete body of authentic works by that author (this usage is familiar to Sherlock Holmes fans as well as to literary scholars). ‘The canon’ is the body of works in a given field (e.g., works of literature, or of art, or of music) deemed worthwhile for students to study and for scholars to investigate.
The word ‘canon’ has an interesting history. It derives ultimately from the Greek κανον (akin to the English ‘cane’) referring to a reed. Reeds were used for measurement, and in Latin and later Greek the word ‘canon’ meant a rule or a standard. The establishment of a canon of scriptures within Christianity was meant to define a standard or a rule for the religion. The above non-techspeak academic usages stem from this instance of a defined and accepted body of work. Alongside this usage was the promulgation of ‘canons’ (‘rules’) for the government of the Catholic Church. The techspeak usages (“according to religious law”) derive from this use of the Latin ‘canon’.
Hackers invest this term with a playfulness that makes an ironic contrast with its historical meaning. A true story: One Bob Sjoberg, new at the MIT AI Lab, expressed some annoyance at the incessant use of jargon. Over his loud objections, GLS and RMS made a point of using as much of it as possible in his presence, and eventually it began to sink in. Finally, in one conversation, he used the word canonical in jargon-like fashion without thinking. Steele: “Aha! We've finally got you talking jargon too!” Stallman: “What did he say?” Steele: “Bob just used ‘canonical’ in the canonical way.”
Of course, canonicality depends on context, but it is implicitly defined as the way hackers normally expect things to be. Thus, a hacker may claim with a straight face that ‘according to religious law’ is not the canonical meaning of canonical.
A canonical derivation in logic is one satisfying some set of conditions that are laid down: thus it may be important to show that if there is a derivation of B from A, there is a particular kind of derivation, en route to showing some result of proof theory. More widely the term may refer to a derivation which mirrors the structure of what is proved, as opposed to an indirect derivation that does not. A canonical description of a sentence would be one that revealed its basic structure or showed how the sentence is built by transformations from a basic structure.
Canonical is an adjective derived from canon. Canon comes from the Greek word kanon "rule" (perhaps originally from kanna "reed", cognate to cane) is used in various meanings.
basic, canonic, canonical: reduced to the simplest and most significant form possible without loss of generality, e.g. "a basic story line"; "a canonical syllable pattern"
This word is used by theologians and canon lawyers to refer to the canons of the Roman Catholic, Eastern Orthodox and Anglican Churches adopted by ecumenical councils. It also refers to later law developed by local churches and dioceses of these churches. The function of this collection of various "canons" is somewhat analogous to the precedents established in common law by case law.
In the 20th century, the Roman Catholic Church revised its canon law in 1917 and then again 1981 into the modern Code of Canon Law. This code is no longer merely a compilation of papal decrees and conciliar legislation, but a more completely developed body of international church law. It is analogous to the English system of Statute law.
Canonical can also mean "part of the canon", i.e., one of the books comprising the biblical canon, as opposed to apocryphal books. Canonization is the process by which a person is recognized as a saint.
It is used most often when describing bodies of literature or art: those books that all educated people have read make up the "canon", for example the Western canon. (See also canon (fiction)).
Mathematicians have for perhaps a century or more used the word canonical to refer to concepts that have a kind of uniqueness or naturalness, and are (up to trivial aspects) "independent of coordinates." Examples include the canonical prime factorization of positive integers, the Jordan canonical form of matrices (which is built out of the irreducible factors of the characteristic polynomial of the matrix), and the canonical decomposition of a permutation into a product of disjoint cycles. Various functions in mathematics are also canonical, like the canonical homomorphism of a group onto any of its quotient groups, or the canonical isomorphism between a finite-dimensional vector space and its double dual. Although a finite-dimensional vector space and its dual space are isomorphic, there is no canonical isomorphism. This lack of a canonical isomorphism can be made precise in terms of category theory, but one could say at a simpler level that "any isomorphism you can think of here depends on choosing a basis." As stated by Goguen, "To any canonical construction from one species of structure to another corresponds an adjunction between the corresponding categories." [1]
Being canonical in mathematics is stronger than being a conventional choice. For instance, the vector space Rn has a standard basis which is canonical in the sense that it is not just a choice which makes certain calculations easy; in fact most linear operators on Euclidean space take on a simpler form when written as a matrix relative to some basis other than the standard one (see Jordan form). In contrast, an abstract n-dimensional real vector space V would not have a canonical basis; it is isomorphic to Rn of course, but the choice of isomorphism is not canonical.
The word canonical is also used for a preferred way of writing something, see the main article canonical form.
Some circles in the field of computer science have borrowed this usage from mathematicians. It has come to mean "the usual or standard state or manner of something"; for example, "the canonical way to organize a file system is as a hierarchy, with extensions to make it a directed graph". XML Signature defines canonicalization as the process of converting XML content to a canonical form, to take into account changes that can invalidate a signature over that data (from JWSDP 1.6).
For an illuminating story about the word's use among computer scientists, see the Jargon File's entry for the word[1].
Some people have been known to use the noun canonicality; others use canonicity. In fields other than computer science, canonicity is this word's canonical form.
In theoretical physics, the concept of canonical (or conjugate, or canonically conjugate) variables is of major importance. They always occur in complementary pairs, such as spatial location x and linear momentum p, angle φ and angular momentum L, and energy E and time t. They can be defined as any coordinates whose Poisson brackets give a Kronecker delta (or a Dirac delta in the case of continuous variables). The existence of such coordinates is guaranteed under broad circumstances as a consequence of Darboux's theorem. Canonical variables are essential in the Hamiltonian formulation of physics, which is particularly important in quantum mechanics. For instance, the Schrödinger equation and the Heisenberg uncertainty relation always incorporate canonical variables. Canonical variables in physics are based on the aforementioned mathematical structure and therefore bear a deeper meaning than being just convenient variables. One facet of this underlying structure is expressed by Noether's theorem, which states that a (continuous) symmetry in a variable implies an invariance of the conjugate variable, and vice versa; for instance symmetry under spatial displacement leads to conservation of momentum, and time-independence implies energy conservation.
In statistical mechanics, the canonical ensemble, the grand canonical ensemble, and the microcanonical ensemble are archetypal probability distributions for the (unknown) microscopic state of a thermal system, applying respectively in the physical cases of:- a closed system at fixed temperature (able to exchange energy with its environment); an open system at fixed temperature (able to exchange both energy and particles); and a closed thermally isolated system (able to exchange neither). These probability distributions can be applied directly to practical problems in thermodynamics.
This entry is from Wikipedia, the leading user-contributed encyclopedia. It may not have been reviewed by professional editors (see full disclaimer)
Dansk (Danish)
adj. - kanonisk, vedtaget
Nederlands (Dutch)
canoniek, kanonikaal, (mv)priestergewaad
Français (French)
adj. - canonique
Deutsch (German)
adj. - kanonisch, verbindlich, (Mus.) in Kanonform, Chorherren-
Ελληνική (Greek)
adj. - (θρησκ.) κανονικός
Português (Portuguese)
adj. - canônico, legal
Русский (Russian)
канонический
Español (Spanish)
adj. - canónico
Svenska (Swedish)
adj. - kanonisk, vedertagen
中文（简体） (Chinese (Simplified))
根据教会法的, 权威的, 标准的, 牧师礼服, 法服
中文（繁體） (Chinese (Traditional))
adj. - 根據教會法的, 權威的, 標準的
n. pl. - 牧師禮服, 法服
한국어 (Korean)
adj. - 교회법에 의한, 정전으로 인정 받은, 규범적인
n. pl. - 성직자의 제의
日本語 (Japanese)
adj. - 教会法による, 正統的な
n. - 法衣
العربيه (Arabic)
(صفه) قانوني, معترف به بالشرع
עברית (Hebrew)
adj. - סמכותי, מקובל, לפי החוק הקנוני, קנוני
n. pl. - סמכותי, מקובל, לפי החוק הקנוני, קנוני
If you are unable to view some languages clearly, click here.
To select your translation preferences click here.
Some good "canonical" pages on the web:
 Math mathworld.wolfram.com |
Join the WikiAnswers Q&A community. Post a question or answer questions about "canonical" at WikiAnswers.
Copyrights:
 |
 | Dictionary. The American Heritage® Dictionary of the English Language, Fourth Edition Copyright © 2007, 2000 by Houghton Mifflin Company. Updated in 2007. Published by Houghton Mifflin Company. All rights reserved. Read more |
 |
| Computer Desktop Encyclopedia. THIS COPYRIGHTED DEFINITION IS FOR PERSONAL USE ONLY. All other reproduction is strictly prohibited without permission from the publisher. © 1981-2008 Computer Language Company Inc. All rights reserved. Read more |
 |
| Thesaurus. Roget's II: The New Thesaurus, Third Edition by the Editors of the American Heritage® Dictionary Copyright © 1995 by Houghton Mifflin Company. Published by Houghton Mifflin Company. All rights reserved. Read more |
 |
| Antonyms. © 1999-2008 by Answers Corporation. All rights reserved. Read more |
 |
| Hacker Slang. The Jargon File. Copyright © 2007. Read more |
 |
| Philosophy Dictionary. The Oxford Dictionary of Philosophy. Copyright © 1994, 1996, 2005 by Oxford University Press. All rights reserved. Read more |
 |
| Word Tutor. Copyright © 2004-present by eSpindle Learning, a 501(c) nonprofit organization. All rights reserved. eSpindle provides personalized spelling and vocabulary tutoring online; free trial. Read more |
 |
| Wikipedia. This article is licensed under the GNU Free Documentation License. It uses material from the Wikipedia article "Canonical". Read more |
|
| Misspellings. © 1999-2008 by Answers Corporation. All rights reserved. Read more |
 |
| Translations. Copyright © 2007, WizCom Technologies Ltd. All rights reserved. Read more |
Search for answers directly from your browser with the FREE Answers.com Toolbar!
Click here to download now. 
Get Answers your way! Check out all our free tools and products.
Mentioned In:
