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Talk:Concept/Archive 1

Various
The first sentence (as of July 21, 2008, 9:20pm ET) needs to defend its claim that the latin term for concept "is traced back to 1550-60". Traced by whom? Traced to whom? As far as I know, it goes back further than this. Medieval philosophers and theologians used the term 'conceptio', from 'conceptus', to refer to an intellectual item or product completing the act of understanding. E.g., St Thomas Aquinas, writing in the early 1270s (in his Compendium Theologiae), uses the term 'conceptio' among others often to refer to such an item.

I took away this below, not because its wrong, but because it might be copyrighted by Random House. The definition below, (from Random House Unabridged Dictionary) is how the word was used up until not too many years ago:

1. a general notion or idea; conception. 2. an idea of something formed by mentally combining all its characteristics or particulars; a construct. 3. a directly conceived or intuited object of thought.

In Fact, the word "concept" has many meanings, and this article needs a list of alternate meanings or a disambiguation page. DanielDemaret

---

I'm not sure about that first sentence. Does a "concept" have to identify a class or category? For example, I would classify "courage" as a concept. Any thoughts? Meelar 05:44, 30 May 2004 (UTC)

Well, you may call "courage" rescuing a little orphan from a burning building. For me "courage" could be having enough force of will to overcome great fear. So, the concept of courage would identify this class or type of feelings or actions. Chiquito

Regarding the phrase 'bearers of meaning' in the second paragraph: where 'bearer' has been redirected to 'hierarchy'. This confuses me. It can be reworded to state 'Concepts are hierarchy of meaning' and then will mean that there are many meanings. Which meaning is the most meaningful of the hierarchy?

I want to use the word concept in a writing for the encyclopedia but do not have a word to express what I mean by 'concept'. For my purposes a concept cannot be expressed in words, even when the words are in several languages to express a more generaalized word description. I want concept to refer to a mental construct which is not expressable in language. It seems to me that I often hold a concept which requires a search for words to express the concept but often find that the words cannot express the uppermost 'hierarchy' of meaning which I wish to convey by language.

Is it possible to refine the article on concept in order to express this generalization?

comments by O1thomas.

translation?
what is it that makes a dog "doggy"? Who's to say that a spaniard thinks of "chien" in the same way a German thinks of "Hund"? Or even that two people of the same culture have the same concept of "dog"? This is a classic example of why true translation is, in some sense, impossible... maybe the article can clarify this? What is the "concept" of a dog?

Can someone with a good philisophical grounding expand this article? Maybe it could include some history of the term and how various philosphers thought we obtain concepts -- Locke's tabula rasa and other empiricist ideas vs. "a priori" knowledge, aka Kant, Descartes, etc. I am unfortunately not knowledgable enough to do it.

Concept as object which exists psychically
I would like to suggest that one alternate meaning of concept can be derived from the definition of OBJECT (PHILOSOPHY) which is included in wikipedia. This is a meaning which I like to use.

O1thomas 14:17, 19 Nov 2004 (UTC)

Concept from Mathematical Category Theory
1. A concept has a name, for example, “Number” or “Set” are names of certain concepts. 2. Concepts have components, which are concepts, too. These components are used to construct a concept. 3. There are three fundamental principles how to combine such components * Conceptual Selection: requires one component * Conceptual Conjunction: requires one or two components * Conceptual Disjunction: requires two components 4. Concepts have instances (Examples), which have the following properties: * Instances have a name. * Instances have a value.

Kant
I added Kant's definition of a concept to the article because it seems, to me, to provide a very brief, clear, unambiguous meaning. The common attributes of certain objects make up a concept. You have a concept of "dog" when you see several different four-legged, furry, barking things that lick your hand, wag their tails, and fetch a thrown stick. The concept is that which is common to all of the different perceptual representations. It is a general, vague object that is present in the mind. It cannot be perceived. It is conceived. Differences between individual objects, such as color, size, and voice timbre, are abstracted or taken away.

It follows from Kant's definition that a word is only a sign of a concept. Words are not concepts. Therefore any word that is agreed upon by convention in any language can serve as a sign for a concept. The words "dog," "Hund," "perro," and "chien" all signify the same concept.Lestrade 20:42, 11 December 2005 (UTC)Lestrade

James's Conceptual Truth
According to William James, a concept is true if it results in a change in human behavior. If it has no effect on the way that humans act, then it is not true. This means that humans could agree, by general convention, that the word "Pamabawa" signifies an individual who controls the world. According to James, if everyone makes sacrifices to Pamabawa, then its concept is true. If everyone ignores Pamabawa, the the concept is false.Lestrade 12:57, 13 December 2005 (UTC)Lestrade

Saying Nothing
To say that a concept is an idea, notion, or entity is to communicate no information. This definition is similar to those that are given by people who do not understand what they are talking about. How many curious people have been disappointed by such answers to their questions? How many people have stopped thinking about such issues because they have received worthless answers?Lestrade 19:48, 17 December 2005 (UTC)Lestrade

Deleuze
How can philosophy be merely the making of concepts? I make a concept every time that I notice a similarity between two different objects. I see a lemon. I see a banana. They both have the same color. Now I have the concept that I designate by the word "yellow" or "jaune" or "amarillo" or "giallo" or "gelb." There is more to philosophy than this.Lestrade 21:16, 16 January 2006 (UTC)Lestrade

I don't see what the issue is. Philosophical ideas are simply more general and advanced than your everyday ones. Then again I'm no philosopher. Mgsloan 03:51, 11 October 2006 (UTC)

According to Deleuze and Guattari, philosophy is the activity of CREATING concepts, which implies that the concepts in question are new ones. That is, it does not mean that philosohy would consist in "coming up" with already existing concepts (such as yellow), or contemplating them (as is also suggested in the very superficial passage in the article). There's a lot more to it, but I suggest reading "What is Philosophy?" D&G give this definition of Philosophy at the very beginning.Telivuo (talk) 18:54, 26 April 2009 (UTC)

Extentions needed?

 * 1)  There are many more meanings to the word "concept" than are offered here. These should be included here or in a disambiguation page or by referring to a dictionary, such as wikidictionary.
 * 2) "Universal...idea" are rarely as universal, if one wants to be exact, as most people that only speak one language think they are. When translating even simple sentences one quickly runs into difficulties. What does "universal" have to do with "concept" apart from implying this fallacy?
 * 3) Since the usage of the word Concept by Kant, is strictly speaking a translation from German, then the exact usage implied from that translation should be described. The way I read Kant, the german word "Konzept" is not in my experience, the way most people around me use the english word "concept". DanielDemaret 13:52, 14 February 2006 (UTC)
 * Kant used the German word "Begriff." This word means, in English, "be-gripped." That is, several perceptions are grasped together. The grasping hand is the concept. It binds several different perceptions by uniting them according to what they have in common. Christian Wolff first used the German word "Begriff" to mean "Concept".64.12.116.204 02:10, 20 February 2006 (UTC)Lestrade

Conceptual Vagueness
The late Prof. George Schrader of Yale wrote a paper entitled "Kant's Theory of Concepts." In it, He asserted that empirical, a posteriori concepts are actually pure and a priori. In other words, when you see a Swiss, a Limburger, a Munster, a Gouda, a Monterey Jack, and a Cheddar, your concept of "cheese" was in your mind from birth and merely waiting to be activated by what you saw. Not surprisingly, he referred to Hegel several times in his paper. That philosopher also had a way of converting ideas into their opposite. As a matter of fact, the book in which Prof. Schrader's paper is printed was edited by Robert Paul Wolff, who turned into his opposite in a surprising way. This book also had an article entitled "Can Kant's Synthetic Judgments Be Made Analytic?" This is another attempt at a conversion.

References:
 * ''Kant. A Collection of Critical Essays. Edited by Robert Paul Wolff. Doubleday Anchor Original.
 * Autobiography of an Ex-White Man. Robert Paul Wolff. University of Rochester Press, New York.

List of scientific concepts
A comma separated list of 54 wikilinks is not exactly beautiful prose. Seeing as there is already a link to List of concepts in science I think we can trim this down considerably. -- N  scheffey   (T/C) 02:16, 27 June 2006 (UTC)

But where is the List of concepts ib science. The link provided only takes you to the List of Science topics and not to the "List of concepts in science. Topics and concepts cannot be equated. Charlie 04:13, 12 September 2006 (UTC)

Concept, content, and context
It may be that:

Concept : what would take shape in mind Content : what could take shape in mind Context : what helps take shape in mind

--ishiakkum 10:11, 13 August 2006 (UTC)

 * Er, huh? Sorry, but to be blunt, I don't think that makes any sense.  You'll have to clarify that. -- Bilbo1507 04:30, 11 September 2006 (UTC)

Sioraf (talk) 15:47, 3 February 2009 (UTC)
 * Cept is hypothetical and future tense
 * Tent is present tense pointing out what might happen in future
 * Text is present tense only

what FACT??
it is stated in the article that "The fact that concepts are in some sense independent of language makes translation possible - words in various languages have identical meaning, because they express one and the same concept." This is certainly not quite correct. because 1. if concepts are in some sense independent of language: then how is the concept of halal/haram (in islam) expressed in english (not translated). better examples are concepts appearing as axioms of things like religion. 2. what seems to be independent of language is: "the naming of objects" like dog which is not a concept but only an object. can someone please explain me the sentence in the article. kalash 3oct2006
 * A word is a sign that is used to designate a concept for the purpose of communication. Different languages use different words. English uses "tree," French uses "arbre," German uses "Baum," and Spanish uses "árbol." These words are only agreed-upon conventions that are a sign for the concept of a wooden thing that grows in the ground and has roots, leaves, and branches.Lestrade 01:39, 3 October 2006 (UTC)Lestrade
 * you are telling me the different names for the same object. "tree" does not determine a concept. it is only an object. from mathematical point of view, object is not the same as a concept. please look the examples i gave above. in philosophy too there is (as far as i know) no claim that "concepts are in some sense independent of language". by the way, a word is simply defined as "for any fixed set of presentation (i.e. letters of a language), a word is the name for an object constructed from the letters". different words may refer to the same object. irreducible words can be defined so that the asignment becomes unique. kalash3oct2006

No, I am telling you the different names for the same concept. A concept is the one common collection of properties that belong to several experienced objects. (I see many different shapes that all have fur, wagging tails, black noses, and four legs. I abstract their differences and, as a result, have the concept "dog".) A concept is general and abstract. In order to communicate with each other about a concept, we use a word that serves as a sign for it. Different languages use different words to designate a concept. As a result, concepts are independent of language because a concept is not a word.Lestrade 13:26, 3 October 2006 (UTC)Lestrade
 * 1. a dog is not a concept, it is an object that is common among different societies. on the other hand the concept of halal/haram does not exist in, for example, england. it can be explained in english though. but there is no fixed common THING available that can be uniquely asigned to the concept of halal. my point is that dog is not a concept. 2. for a trivial reason, there is no statement to the effect that "the concept x in the society y speaking the language z, has a (one-to-one) correspondence in the society y' speaking the language z'." i just don't see why you are implicitly assuming this and then try to explain to me the rest which is an obvious matter. 3. i agree with and dare to make the following statement: "for a fixed society y speaking the language z, a given concept x is independent of the way it is expressed." Moreover, "a translation of the concept x into the society y' speaking the language z' is merely a word for word substitution." kalash3oct2006

The disagreement in this section comes from the fact that the most text used for communication is ambiguous (=undefined). For example, The text "a dog is not a concept, it is an object" says nothing if the terms "concept" and "object" mean different things for the two authors. And because they don't say what they mean (it is not easy and practical in todays writtings to define every term we use), misunderstanding is a natural result. Kaseluris, Nikos (talk) 09:57, 25 August 2008 (UTC)

 * kalash3 is not distinguishing between perception and concept. An object is a perception. We directly experience the perception and assume that the perception is of some external thing. But we never directly know the external thing of which we are thinking. We only know the perception. A concept is a quality or qualities that we think are common to several perceptions. We take several perceptions and abstract all of their differences until we are left with common characteristics. These comprise the concept. We shouldn't talk about an object, because an object is only something that we assume. We should talk about concrete perceptions and abstract concepts. We directly know our perceptions. We generate our concepts through mental abstraction.Lestrade (talk) 14:21, 13 November 2008 (UTC)lestrade

Routt
If the author wishes to remove the material, why not let them? Banno 06:17, 22 October 2006 (UTC)

Author
Yes, let the author remove the material, please. It is irrelevant, after all.

Removed text from article
The following paragraph had been added to the very top of the article. I moved it here:

 * A Concept is a memory of a contextual relationship.A concept can demonstrate a small relationship such as the relative difference between big and small, or more complex relationships like the understanding of how a potato becomes the frenchfry you are eating via the whole process. The whole process Together from seed to mouth can be fixed into a single concept. A concept could be much bigger still taking into account all potatoes made into french fries in the world,thier distribution process,the consequences of consumers eating french fries, and the future possibilities of The frenchfry. We can also fix concepts that are smaller yet to an unknown limit, such as the concept of a single frenchfry in your hand. names are given to some of our concepts, but at present there are few in our lexicon. One worded example of a concept is "ecosystem". I summize that because there are so few concepts in our lexicon that worded Conceptualisations are relatively as new as our written languages, however, I infer that conceptualizing is neither new or exclusive to Human-kind because The ability to sence,compare, and rememder comprise a concept.
 * source: James Leon Zumwalt, Software developer Narssarssuaq 12:47, 23 April 2007 (UTC)

Ayn Rand's Theory of Concepts
I don't know how people here feel about Objectivism, but perhaps a short section on Ayn Rand's meaning of "concept" could be included, as her definition also exlains how the concept is formed in a summarized manner. It could possibly go as follows:

Rand considered concepts to be "...mental integration[s] of two or more units possessing the same distinguishing characteristic(s), with their particular measurements omitted." (Introduction to Objectivist Epistemology, Ch. 2, "Concept-formation"), with the distinguishing characteristic being a particular category of measurements within a commensurable characteristic, which Rand calls a "Conceptual Common Denominator" (ibid.), and Measurement-Omission being "...measurements exist, but are not specified"(ibid.).

Rand considered concepts as implicit until they are defined, as in the units of the concepts are differentiated from every other existent, and are integrated by a commensurable characteristic, which means that definition for Rand was the final step of concept-formation. She wrote that words, with the exception of proper nouns, are only perceptual concertes that represent concepts, and could have no meaning besides the meaning of the concept.(ibid., Ch. 5, "Definitions")Rodfitts 06:28, 31 May 2007 (UTC)

Rand shouldn't in this article because, though her supporters might want to think of her as some deep philosopher, she's not even a reputed egoist. She basically dismisses Aristotelian and Kantian ethics while giving reductio ad absurdum arguments about human nature. She shouldn't be in this article. If you Rand supporters want to talk about Randian concepts, go ahead, but keep it out of here. — Preceding unsigned comment added by 76.173.193.112 (talk) 16:21, 3 January 2012 (UTC)

http://en.wikipedia.org/wiki/Objectivism_%28Ayn_Rand%29#Intellectual_impact Read this. She's no more of a philosopher than Anton Lavey. Furthermore, serious philosophers don't cite their own fiction characters, John Galt, to make philosophical points. She has a cult following, and her cult following tries to make her seem more intellectually deep than she really is. — Preceding unsigned comment added by 76.173.193.112 (talk) 16:28, 3 January 2012 (UTC)

Pask's work on Concepts
Gordon Pask defined a concept as "A procedure for bringing about a relation." (Conversation, Cognition and Learning 1975). He developed his Conversation Theory to describe how analogies ("the value of a conversation is analogy and any analogy has a generalisation") are produced by the differences of shared concepts. In his Interaction of Actors Theory he extended his definition of concept into all media making it panpsychic. He was a celebrated cybernetician. Does anyone have a view on where would it fit in this article?--Nick Green (talk) 15:21, 17 November 2007 (UTC)

Nonsense
A number of sections of this article make no sense whatsoever, and even more have no decipherable sources.

 * Conceptual structure
 * Has something that looks like a reference copied from another reference, and refers to opinions of people.
 * One possible and likely structure
 * No references, one person's name, not very understandable.
 * The dual nature of concepts
 * Weaselly, probably devoid of content, although it does have one malformatted link to a Wikipedia page, which I'm now going to fix.
 * The first concept
 * No references or content, as noted by an anon.
 * One is two and three
 * No references or content, as noted by an anon.

IS A UNIT OF KNOWLEDGE — Preceding unsigned comment added by 69.242.173.77 (talk) 01:19, 22 November 2011 (UTC)

Now, it's possible that some of the sections had content at one point, but were vandalized. — Arthur Rubin (talk) 22:40, 29 April 2011 (UTC)

Ayn Rand
Ayn Rand created a theory of epistemology, (which was a part of her philosophy she called Objectivism). She's very popular with the general public among philosophers. The fall 1991 Book-of-the-Month Club and the Library of Congress' Center poll found that when they asked Americans what book made the biggest difference in their lives, Atlas Shrugged got second place (behind the Bible) with about 10%. It's selling today better than it ever has. I'd say this makes her opinion of what a concept is notable enough. Heck, if you want to include 20 more definitions by less popular philosophers, that's fine with me. Why should we not include a unique definition of concept just because it's from relatively unknown philosophers? If they get their own article, then that should be notability enough.

I'm also really not sure why "WordNet" is more notable than Ayn Rand. byelf2007 (talk) 19 February 2012
 * It's a question of editorial weight. Rand and her writings are certainly popular, and indeed increasingly a subject of academic scrutiny. However, that's not the threshold for inclusion in a top-level philosophical encyclopaedia entry; I would be extremely surprised to see Rand's theory of concepts covered in a general philosophical dictionary, for instance, or an epistemology textbook published by a reputable university press. There is a strong case for covering Rand's theories in an entry on a serious academic subject like ethical egoism, because they make up a crucial variant of the historical development of the position, but I am far from convinced that one couldn't have a thorough knowledge of the idea of concepts without knowing of Rand's work. Skomorokh  04:35, 20 February 2012 (UTC)
 * I understand. What about wordnet? I don't see how that's hit this threshold. byelf2007 (talk) 19 February 2012

Inferring a concept?
One of the article’s lead sentences is: “Philosophers generally agree that a concept is an idea formed from inference.” This sentence has two major problems. (1) Obviously, we want to know exactly who are all of these philosophers and where in their works have they written such a definition; (2) Is it true that a concept is an idea formed from inference? Problem (2) results from the fact that many people would not know the difference between a concept and an idea, especially an idea that is not formed from inference. Also, conclusions, not concepts, are formed from inference through the use of reasoning. This is an exercise in logic. Concepts, on the other hand, are not inferred. Conception, concept formation, or conceiving is not a logical process. Concepts are formed by the brain’s activity when it perceives several different perceptions or other concepts that are experienced as having a common element. This common element is imaginatively formed or conceived and is therefore a concept or conception.Lestrade (talk) 17:32, 14 April 2012 (UTC)Lestrade

Major Rewrite - especially definitions section
Hi editing community! I plan on doing some pretty big changes to this page :D Particularly, I would like to focus on the definitions section and put in subheadings to structure it according to the philosophical history of conceptual definitions. The subheadings will be: Classical Theory, Prototype Theory, Theory-Theory, as well as an argument against any definition. I also want to add a little historical background from Hume and Kant. Below is my proposed bibiliography - a start of the list of sources I will use. Feel free to contact me with suggestions either here or non my talk page!! This is my fist wiki-edit, so help would be appreciated!

Bibiliography

 * Armstrong, S. L., Gleitman, L. R., & Gleitman, H. (1999). what some concepts might not be. In E. Margolis, & S. Lawrence, Concepts (pp. 225-261). Massachusetts: MIT press.
 * Carey, S. (1999). knowledge acquisition: enrichment or conceptual change? In E. Margolis, & S. Lawrence, concepts: core readings (pp. 459-489). Massachusetts: MIT press.
 * Fodor, J. A., Garrett, M. F., Walker, E. C., & Parkes, C. H. (1999). against definitions. In E. Margolis, & S. Lawrence, concepts: core readings (pp. 491-513). Massachusetts: MIT press.
 * Fodor, J., & LePore, E. (1996). the pet fish and the red Herring: why concept still can't be prototypes. cognition, 253-270.
 * Hume, D. (1739). book one part one: of the understanding of ideas, their origin, composition, connexion, abstraction etc. In D. Hume, a treatise of human nature. England.
 * Murphy, G. (2004). Chapter 2. In G. Murphy, a big book of concepts (pp. 11 - 41). Massachusetts: MIT press.
 * Murphy, G., & Medin, D. (1999). the role of theories in conceptual coherence. In E. Margolis, & S. Lawrence, concepts: core readings (pp. 425-459). Massachusetts: MIT press.
 * Prinz, J. J. (2002). Desiderata on a Theory of Concepts. In J. J. Prinz, Furnishing the Mind: Concepts and their Perceptual Basis (pp. 1-23). Massechusettes: MIT press.
 * Putnam, H. (1999). is semantics possible? In E. Margolis, & S. Lawrence, concepts: core readings (pp. 177-189). Massachusetts: MIT press.
 * Quine, W. (1999). two dogmas of empiricism. In E. Margolis, & S. Lawrence, concepts: core readings (pp. 153-171). Massachusetts: MIT press.
 * Rey, G. (1999). Concepts and Stereotypes. In E. Margolis, & S. Laurence (Eds.), Concepts: Core Readings (pp. 279-301). Cambridge, Massachusetts: MIT Press.
 * Rosch, E. (1977). Classification of real-world objects: Origins and representations in cognition. In P. Johnson-Laird, & P. Wason, Thinking: Readings in Cognitive Science (pp. 212-223). Cambridge: Cambridge University Press.
 * Rosch, E. (1999). Principles of Categorization. In E. Margolis, & S. Laurence (Eds.), Concepts: Core Readings (pp. 189-206). Cambridge, Massechusetts: MIT Press.
 * Wittgenstein, L. (1999). philosophical investigations: sections 65-78. In E. Margolis, & S. Lawrence, concepts: core readings (pp. 171-175). Massachusetts: MIT press.

With-silver-luck (talk) 22:57, 15 October 2012 (UTC)
 * Your outline sounds promising. My only hesitation is with some of the sources (I don't know all of them). Wittgenstein, Quine and Hume, for example, sound like they would be used as primary sources. Remember that Wikipedia is a tertiary source, so you need to summary secondary sources. That is, you need to summarize what scholars have said are the most important definitions, not summarize the actual philosophy yourself, otherwise you will be doing original research. Does that make sense? Wadewitz (talk) 18:00, 17 October 2012 (UTC)
 * I think then that I am definitely confused as to the difference in the case of philosophy. Isn't the primary source in this case my experience of mental language (concepts) or someone else's description of this, rather than the original theories/definitions given by philosophers on the subject - do I have to find people who summarise these theories and then cite them? With-silver-luck (talk) 19:31, 17 October 2012 (UTC)
 * Perhaps let's check with a philosopher and see what they think about the primary/secondary. I think if your article were about the arguments of a philosopher then this would be an issue but because you are talking about their ideas about concepts I am not sure. I'll ask around to see what I can find out for you. Clevwiki (talk) 19:38, 22 October 2012 (UTC)
 * In the case of philosophy, primary sources are the original theories, so, yes, you have to find summaries of them. Think of it this way. You cannot pick and choose which theories to put in the article yourself because you are not an expert. You must find peer-reviewed articles that explain the important definitions and use those. You cannot decide which theories are important. Does that make sense? Wadewitz (talk) 22:09, 22 October 2012 (UTC)
 * Yes. Can I find an article that says which theories are important and then summarize and cite the original sources from there or is a cliffnotes summary style-thing really preferable to returning to the original? With-silver-luck (talk) 04:20, 24 October 2012 (UTC)
 * Yes, it is required, because returning to the original is original research, as you would be interpreting it yourself. Just don't use Cliff Notes, use reputable sources! Wadewitz (talk) 20:42, 31 October 2012 (UTC)

Proposed Outline

 * Opening paragraph
 * Better definition (source tbd) which includes 'mental language'
 * Historical/Philosophical Background
 * Under Definitions
 * Classical Theory
 * Prototype Theory
 * Theory-Theory
 * No Definition? — Preceding unsigned comment added by With-silver-luck (talk • contribs) 21:37, 23 October 2012 (UTC)

PS. New list of sources to follow With-silver-luck (talk) 21:39, 23 October 2012 (UTC)
 * This looks like it will be a very good addition and the new sources look good. Wadewitz (talk) 20:42, 31 October 2012 (UTC)

New/additional Source List
With-silver-luck (talk) 04:17, 24 October 2012 (UTC)
 * Margolis, Eric and Laurence, Stephen, "Concepts", The Stanford Encyclopedia of Philosophy (Fall 2012 Edition), Edward N. Zalta (ed.), URL = .
 * Brown, R. (1978). A New Paradigm of Reference. In G. Miller, & E. Lenneberg, Psychology and Biology of Language and Thought (pp. 151-167). New York: Academic Press.
 * Murphy's "The Big Book of Concepts"
 * Thanks for all your work on finding new sources. Your list of proposed changes seems to be the right amount to be manageable. Your original list of references might work well as a suggested readings for those who are interested.Clevwiki (talk) 23:12, 2 November 2012 (UTC)

Planned Deletions
Because they are not cited properly, I plan on deleting most of what is currently under "notable definitions", and I'm planning on deleting what is in that section in order to rework it. I will post what I delete on this page, and anyone who finds that something significant has been deleted can find a way to incorporate it back into the new framework. I will also probably change the heading of this section to "Notable Theories on the Structure of Concepts". With-silver-luck (talk) 18:59, 5 November 2012 (UTC)
 * I have deleted the section I warned about. I have also updated the introduction, and will try to make it more easily readable. I wanted the language stuff as a new paragraph, but it wouldn't do it (help pls?). I moved some stuff from that section to the A priori kant section because it fit there better. I also deleted the origin section because it was wrong. Philosophers have been discussing concepts for much longer than Karl Jung. Below is what I deleted/moved:
 * Origin

Carl Jung argues that concepts may be attributed to space other than within the inside boundaries of any body or mass or material formation of living creatures. Notable definitions John Locke's description of a general idea corresponds to a description of a concept. According to Locke, a general idea is created by abstracting, drawing away, or removing the uncommon characteristic or characteristics from several particular ideas. The remaining common characteristic is that which is similar to all of the different individuals. For example, the abstract general idea or concept that is designated by the word "red" is that characteristic which is common to apples, cherries, and blood. The abstract general idea or concept that is signified by the word "dog" is the collection of those characteristics which are common to Airedales, Collies, and Chihuahuas.

John Stuart Mill argued that general conceptions are formed through abstraction. A general conception is the common element among the many images of members of a class. "...[W]hen we form a set of phenomena into a class, that is, when we compare them with one another to ascertain in what they agree, some general conception is implied in this mental operation" (A System of Logic, Book IV, Ch. II). Mill did not believe that concepts exist in the mind before the act of abstraction. "It is not a law of our intellect, that, in comparing things with each other and taking note of their agreement, we merely recognize as realized in the outward world something that we already had in our minds. The conception originally found its way to us as the result of such a comparison. It was obtained (in metaphysical phrase) by abstraction from individual things" (Ibid.).

Philosopher Arthur Schopenhauer argued that concepts are "mere abstractions from what is known through intuitive perception, and they have arisen from our arbitrarily thinking away or dropping of some qualities and our retention of others." (Parerga and Paralipomena, Vol. I, "Sketch of a History of the Ideal and the Real"). In his On the Will in Nature, "Physiology and Pathology," Schopenhauer said that a concept is "drawn off from previous images ... by putting off their differences. This concept is then no longer intuitively perceptible, but is denoted and fixed merely by words." Nietzsche, who was heavily influenced by Schopenhauer, wrote: "Every concept originates through our equating what is unequal. No leaf ever wholly equals another, and the concept 'leaf' is formed through an arbitrary abstraction from these individual differences, through forgetting the distinctions..."

By contrast to the above philosophers, Immanuel Kant held that the account of the concept as an abstraction of experience is only partly correct. He called those concepts that result from abstraction "a posteriori concepts" (meaning concepts that arise out of experience). An empirical or an a posteriori concept is a general representation (Vorstellung) or non-specific thought of that which is common to several specific perceived objects (Logic, I, 1., §1, Note 1)

A concept is a common feature or characteristic. Kant investigated the way that empirical a posteriori concepts are created.

Kant's description of the making of a concept has been paraphrased as "...to conceive is essentially to think in abstraction what is common to a plurality of possible instances..." (H.J. Paton, Kant's Metaphysics of Experience, I, 250). In his discussion of Kant, Christopher Janaway wrote: "...generic concepts are formed by abstraction from more than one species."

With-silver-luck (talk) 22:56, 6 November 2012 (UTC)

Finished my editing process (maybe) and call for improvement further
I have just about finished the plans I had for the article (I decided not to add a section about concepts not having structure - these cover the major points, I'm not sure its necessary- though it would be nice to have a section on conceptual atomism). I would still ideally like to add criticism sections for the prototype and theorytheory sections (but it is most important to have it for classic because that was the most longstanding understanding and it was revolutionary to say anything else). I would suggest for further improvement to clean up the "issues" section, and maybe add a section about ontology with the stuff I deleted above. I just don't have the knowledge base for that kind of remodel. My stuff probably could also do with a few more wikilinks. It's been fun wikipedia. See you soon. With-silver-luck (talk) 08:31, 7 November 2012 (UTC)

Referencing Murphy
Much of the article uses "The big book of concepts" by GL Murphy. The referencing to this book has no page numbers, so it makes it difficult to check what it says. I can see nowhere where Murphy says "a dog can still be a dog with only four legs" or anything like it. What, indeed, does it mean? Myrvin (talk) 19:57, 21 November 2012 (UTC)
 * I don't have the murphy book with me any more (rented from library as an attempt at finding secondary sources as suggested above)but you're right, it was a typo and should have read "three legs" I have changed it to reflect the correct information. With-silver-luck (talk) 04:03, 27 November 2012 (UTC)

The introduction was much too biased
I have changed the introduction because it was simply much too biased to cognitive science/mental representation. Wikipedia should not propagate one thinking, but should be a balanced introduction different points of view. The article even quoted Stanford Encyclopedia as if there was one modern and correct way of thinking concepts. I have changed the introduction only, but it further changes if the article should give an all-round introduction to the philosophy of concept. — Preceding unsigned comment added by Bjerke (talk • contribs) 07:36, 2 December 2012 (UTC)
 * I restored the old intro from November. Bhny (talk) 23:01, 30 December 2012 (UTC)
 * User:Gregbard reverted my restoration Bhny (talk) 02:08, 31 December 2012 (UTC)
 * It's true. I made some other modifications too, so please make further edits preserving the format, as they are consistent with the philosophy Manual of style. Greg Bard (talk) 02:22, 31 December 2012 (UTC)

title: Talk:Concept/Archive 1


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Kamehameha V

Kamehameha V (Lota Kapuāiwa Kalanimakua Aliʻiōlani Kalanikupuapaʻīkalaninui; December 11, 1830 – December 11, 1872 ), reigned as the fifth monarch of the Kingdom of Hawaiʻi from 1863 to 1872. His motto was "Onipaʻa": immovable, firm, steadfast or determined; he worked diligently for his people and kingdom and was described as the last great traditional chief.

Early life
He was born and given the name Lot Kapuāiwa December 11, 1830. His mother was Elizabeth Kīnaʻu and father was Mataio Kekūanaōʻa. His siblings included David Kamehameha, Moses Kekūāiwa, Alexander Liholiho, and Victoria Kamāmalu. He also was a grandson of Kamehameha I. Kapu āiwa means mysterious kapu or sacred one protected by supernatural powers. He was adopted using the ancient Hawaiian tradition called hānai by Princess Nāhiʻenaʻena, but she died in 1836. He was then adopted by his grandmother Queen Kalākua Kaheiheimālie and step-grandfather High Chief Ulumāheihei Hoapili. His childhood was difficult; he felt that his hānai parents treated him as a stranger in their house, and that the adoption had deprived him the love of his mother. Throughout his life he would have a deep dislike for this tradition as it could be later seen by his anger at his half-sister Ruth Keelikolani giving away her second son Keolaokalani to Bernice Pauahi Bishop.

It was planned that he would be Hoapili's heir as Governor of Maui, although this never happened. Since King Kamehameha III declared him eligible for the throne, he was educated at the Royal School like his cousins and siblings. He was betrothed to Bernice Pauahi at birth, but she chose to marry American Charles Reed Bishop instead.

After leaving school, he traveled abroad with his brother Alexander Liholiho. With the supervision of their guardian Dr. Judd, Lot and his brother sailed to San Francisco in September 1849. After their tour of California, they continued on to Panama, Jamaica, New York City and Washington, D.C. They toured Europe and met with various heads of state including French president Louis Napoleon, British prince consort Albert, and US president Zachary Taylor and vice president Millard Fillmore.

Career
From 1852 to 1855 he served on the Privy Council of State, and from 1852 to 1862 in the House of Nobles. He was Minister of the Interior from 1857 to 1863, chief justice of the supreme court from 1857 to 1858, and held other offices. His more charismatic younger brother Prince Alexander Liholiho was chosen to become King Kamehameha IV in 1854. In 1862, he was officially added to the line of succession in an amendment to the 1852 Constitution of the Kingdom of Hawaii. Lot and his heirs, follow by his sister Princess Victoria and her heirs, would succeed in the case his brother died without any legitimate heirs. The change was made shortly before the death of Prince Albert Kamehameha, the only son of Kamehameha IV, on August 23, 1862.

New constitution and new laws
He came to power on November 30, 1863, after his brother's death, but refused to uphold the previous constitution of 1852. He objected, in particular, to that constitution's grant of universal male suffrage in elections for the lower House of Representatives. In May 1864 he called for a constitutional convention. On July 7, 1864, he proposed a new constitution rather than amending the old one. The convention ran smoothly until the 62nd article. It limited voters to being residents who passed a literacy test and possessed property or had income qualifications. On August 20, 1864, he signed the 1864 Constitution of the Kingdom of Hawaii and took an oath to protect it.

The constitution was based on the original draft, but 20 articles were deleted. When he appointed Charles de Varigny, a French national, as minister of finance in December 1863, Americans in Hawaiʻi were convinced that he had adopted an anti-American policy. In reality, his foreign policy remained the same. Later de Varigny became minister of foreign affairs from 1865 to 1869.

He was the first king to encourage revival of traditional practices. Under his reign, the laws against "kahunaism" were repealed. A Hawaiian Board of Medicine was established, with kahuna members, and la'au lapa'au or Hawaiian medicine was again practiced. He brought kahuna practitioners to Honolulu to document their remedies.

In 1865, a bill was brought before the legislature giving foreign merchants the right to sell liquor directly to Native Hawaiians. Kamehameha V surprised supporters of the bill by refusing to grant his assent, saying: "I will never sign the death warrant of my people." Alcoholism was one of the many causes of the already declining population of the native Hawaiians.

Growth in travel to Hawaii
Growth in travel to the islands increased during Kamehameha's reign. Mark Twain came in March 1866 aboard the merchantman Ajax. He stayed for four months under his real name, Samuel Clemens, writing letters back to the Sacramento Union describing the islands. Twain described the king:

"He was a wise sovereign; he had seen something of the world; he was educated & accomplished, & he tried hard to do well by his people, & succeeded. There was no trivial royal nonsense about him; He dressed plainly, poked about Honolulu, night or day, on his old horse, unattended; he was popular, greatly respected, and even beloved."

Queen Victoria sent her second son Prince Alfred, Duke of Edinburgh on a state visit in 1869. He appealed to Kaiser Wilhelm I of Germany, who sent Henri Berger to organize the Royal Hawaiian Band, a gift of music from the king to his people.

Succession
His sister and only named Heir Apparent to the throne, Crown Princess Victoria Kamāmalu had died childless in 1866 and through the remainder of his reign, Kamehameha V did not name a successor. He died on December 11, 1872, while the preparations for his birthday celebration were underway. As Lot lay bedstricken, he answered those that came to visit him: "It is hard to die on my birthday, but God's will be done". He offered the throne to his cousin Bernice Pauahi Bishop who refused, and died an hour later without designating an heir. Lot Kapuāiwa had a daughter Keanolani (July 7, 1847 – June 30, 1902) with Abigail Maheha. However, her illegitimate birth prevented her from succeeding to the Hawaiian throne. Lot was buried in the Royal Mausoleum of Hawaii at Mauna ʻAla.

He was the last ruling monarch of the House of Kamehameha styled under the Kamehameha name. Before his death Kamehameha V stated:

"The throne belongs to Lunalilo; I will not appoint him, because I consider him unworthy of the position. The constitution, in case I make no nomination, provides for the election of the next King; let it be so."

With no heir at his death, the next monarch would be elected by the legislature. Kamehameha V's cousin William Charles Lunalilo, a Kamehameha by birth from his mother, demanded a general election and won. The legislature agreed and Lunalilo became the first elected King of the Hawaiian Kingdom.

Legacy
He founded the Royal Order of Kamehameha I society on April 11, 1865, named to honor his grandfather.

The Prince Lot Hula Festival is named for him. It was held the third Saturday in July since 1977 at his former home called Moanalua Gardens.

In February 1847, a female student at the Royal School, Abigail Maheha, was expelled and wed in a hastily arranged marriage due to a scandalous pregnancy. Some speculate that the sixteen year-old Kamehameha V or his seventeen-year-old brother Moses Kekūāiwa was the father of Abigail's daughter Keanolani, who left living descendants. Evidence to support this claim include his financial support of Abigail's husband Keaupuni, veiled conversations the Cookes had with Abigail and Lot dated months before the pregnancy was discovered, and entries from the period which were torn out of his school journal.

Honours

 * Kingdom of Hawaii: Founder of the Order of Kamehameha I, April 11, 1865
 * Mexican Empire: Grand Cross of the Order of Guadalupe, 1865
 * Grand Duchy of Hesse: Grand Cross of the Order of Philip the Magnanimous, December 1, 1869

license: Creative Commons - Attribution Share-Alike - https://creativecommons.org/licenses/by-sa/4.0/

title: Kamehameha V


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Edge coloring

In graph theory, a proper edge coloring of a graph is an assignment of "colors" to the edges of the graph so that no two incident edges have the same color. For example, the figure to the right shows an edge coloring of a graph by the colors red, blue, and green. Edge colorings are one of several different types of graph coloring. The edge-coloring problem asks whether it is possible to color the edges of a given graph using at most $k$ different colors, for a given value of $k$, or with the fewest possible colors. The minimum required number of colors for the edges of a given graph is called the chromatic index of the graph. For example, the edges of the graph in the illustration can be colored by three colors but cannot be colored by two colors, so the graph shown has chromatic index three.

By Vizing's theorem, the number of colors needed to edge color a simple graph is either its maximum degree $Δ$ or $Δ+1$. For some graphs, such as bipartite graphs and high-degree planar graphs, the number of colors is always $Δ$, and for multigraphs, the number of colors may be as large as $3Δ/2$. There are polynomial time algorithms that construct optimal colorings of bipartite graphs, and colorings of non-bipartite simple graphs that use at most $Δ+1$ colors; however, the general problem of finding an optimal edge coloring is NP-hard and the fastest known algorithms for it take exponential time. Many variations of the edge-coloring problem, in which an assignments of colors to edges must satisfy other conditions than non-adjacency, have been studied. Edge colorings have applications in scheduling problems and in frequency assignment for fiber optic networks.

Examples
A cycle graph may have its edges colored with two colors if the length of the cycle is even: simply alternate the two colors around the cycle. However, if the length is odd, three colors are needed.

A complete graph $K_{n}$ with $n$ vertices is edge-colorable with $K_{8}$ colors when $n$ is an even number; this is a special case of Baranyai's theorem. provides the following geometric construction of a coloring in this case: place $n$ points at the vertices and center of a regular $n − 1$-sided polygon. For each color class, include one edge from the center to one of the polygon vertices, and all of the perpendicular edges connecting pairs of polygon vertices. However, when $n$ is odd, $n$ colors are needed: each color can only be used for $(n − 1)$ edges, a $(n − 1)/2$ fraction of the total.

Several authors have studied edge colorings of the odd graphs, $n$-regular graphs in which the vertices represent teams of $1/n$ players selected from a pool of $n$ players, and in which the edges represent possible pairings of these teams (with one player left as "odd man out" to referee the game). The case that $(n − 1)$ gives the well-known Petersen graph. As explains the problem (for $n − 1$), the players wish to find a schedule for these pairings such that each team plays each of its six games on different days of the week, with Sundays off for all teams; that is, formalizing the problem mathematically, they wish to find a 6-edge-coloring of the 6-regular odd graph $n = 3$. When $2n − 1$ is 3, 4, or 8, an edge coloring of $n = 6$ requires $O_{6}$ colors, but when it is 5, 6, or 7, only $n$ colors are needed.

Definitions
As with its vertex counterpart, an edge coloring of a graph, when mentioned without any qualification, is always assumed to be a proper coloring of the edges, meaning no two adjacent edges are assigned the same color. Here, two distinct edges are considered to be adjacent when they share a common vertex. An edge coloring of a graph $n$ may also be thought of as equivalent to a vertex coloring of the line graph $O_{n}$, the graph that has a vertex for every edge of $G$ and an edge for every pair of adjacent edges in $G$.

A proper edge coloring with $G$ different colors is called a (proper) $k$-edge-coloring. A graph that can be assigned a $k$-edge-coloring is said to be $k$-edge-colorable. The smallest number of colors needed in a (proper) edge coloring of a graph $k$ is the chromatic index, or edge chromatic number, $n + 1$. The chromatic index is also sometimes written using the notation $L(G)$; in this notation, the subscript one indicates that edges are one-dimensional objects. A graph is $G$-edge-chromatic if its chromatic index is exactly $k$. The chromatic index should not be confused with the chromatic number $χ′(G)$ or $χ_{1}(G)$, the minimum number of colors needed in a proper vertex coloring of $k$.

Unless stated otherwise all graphs are assumed to be simple, in contrast to multigraphs in which two or more edges may be connecting the same pair of endpoints and in which there may be self-loops. For many problems in edge coloring, simple graphs behave differently from multigraphs, and additional care is needed to extend theorems about edge colorings of simple graphs to the multigraph case.

Relation to matching
A matching in a graph $G$ is a set of edges, no two of which are adjacent; a perfect matching is a matching that includes edges touching all of the vertices of the graph, and a maximum matching is a matching that includes as many edges as possible. In an edge coloring, the set of edges with any one color must all be non-adjacent to each other, so they form a matching. That is, a proper edge coloring is the same thing as a partition of the graph into disjoint matchings.

If the size of a maximum matching in a given graph is small, then many matchings will be needed in order to cover all of the edges of the graph. Expressed more formally, this reasoning implies that if a graph has $G$ edges in total, and if at most $χ(G)$ edges may belong to a maximum matching, then every edge coloring of the graph must use at least $χ_{0}(G)$ different colors. For instance, the 16-vertex planar graph shown in the illustration has $β$ edges. In this graph, there can be no perfect matching; for, if the center vertex is matched, the remaining unmatched vertices may be grouped into three different connected components with four, five, and five vertices, and the components with an odd number of vertices cannot be perfectly matched. However, the graph has maximum matchings with seven edges, so $m/β$. Therefore, the number of colors needed to edge-color the graph is at least 24/7, and since the number of colors must be an integer it is at least four.

For a regular graph of degree $m$ that does not have a perfect matching, this lower bound can be used to show that at least $m = 24$ colors are needed. In particular, this is true for a regular graph with an odd number of vertices (such as the odd complete graphs); for such graphs, by the handshaking lemma, $k$ must itself be even. However, the inequality $β = 7$ does not fully explain the chromatic index of every regular graph, because there are regular graphs that do have perfect matchings but that are not k-edge-colorable. For instance, the Petersen graph is regular, with $k + 1$ and with $χ′ ≥ m/β$ edges in its perfect matchings, but it does not have a 3-edge-coloring.

Vizing's theorem
The edge chromatic number of a graph $k$ is very closely related to the maximum degree $m = 15$, the largest number of edges incident to any single vertex of $G$. Clearly, $β = 5$, for if $Δ(G)$ different edges all meet at the same vertex $G$, then all of these edges need to be assigned different colors from each other, and that can only be possible if there are at least $χ′(G) ≥ Δ(G)$ colors available to be assigned. Vizing's theorem (named for Vadim G. Vizing who published it in 1964) states that this bound is almost tight: for any graph, the edge chromatic number is either $Δ$ or $Δ$. When $Δ(G)$, G is said to be of class 1; otherwise, it is said to be of class 2.

Every bipartite graph is of class 1, and almost all random graphs are of class 1. However, it is NP-complete to determine whether an arbitrary graph is of class 1.

proved that planar graphs of maximum degree at least eight are of class one and conjectured that the same is true for planar graphs of maximum degree seven or six. On the other hand, there exist planar graphs of maximum degree ranging from two through five that are of class two. The conjecture has since been proven for graphs of maximum degree seven. Bridgeless planar cubic graphs are all of class 1; this is an equivalent form of the four color theorem.

Regular graphs
A 1-factorization of a k-regular graph, a partition of the edges of the graph into perfect matchings, is the same thing as a k-edge-coloring of the graph. That is, a regular graph has a 1-factorization if and only if it is of class 1. As a special case of this, a 3-edge-coloring of a cubic (3-regular) graph is sometimes called a Tait coloring.

Not every regular graph has a 1-factorization; for instance, the Petersen graph does not. More generally the snarks are defined as the graphs that, like the Petersen graph, are bridgeless, 3-regular, and of class 2.

According to the theorem of, every bipartite regular graph has a 1-factorization. The theorem was stated earlier in terms of projective configurations and was proven by Ernst Steinitz.

Multigraphs
For multigraphs, in which multiple parallel edges may connect the same two vertices, results that are similar to but weaker than Vizing's theorem are known relating the edge chromatic number $Δ(G) + 1$, the maximum degree $χ′(G) = Δ(G)$, and the multiplicity $χ′(G)$, the maximum number of edges in any bundle of parallel edges. As a simple example showing that Vizing's theorem does not generalize to multigraphs, consider a Shannon multigraph, a multigraph with three vertices and three bundles of $Δ(G)$ parallel edges connecting each of the three pairs of vertices. In this example, $μ(G)$ (each vertex is incident to only two out of the three bundles of $μ(G)$ parallel edges) but the edge chromatic number is $Δ(G) = 2μ(G)$ (there are $μ(G)$ edges in total, and every two edges are adjacent, so all edges must be assigned different colors to each other). In a result that inspired Vizing, showed that this is the worst case: $3μ(G)$ for any multigraph $v$. Additionally, for any multigraph $G$, $3μ(G)$, an inequality that reduces to Vizing's theorem in the case of simple graphs (for which $χ′(G) ≤ (3/2)Δ(G)$).

Algorithms
Because the problem of testing whether a graph is class 1 is NP-complete, there is no known polynomial time algorithm for edge-coloring every graph with an optimal number of colors. Nevertheless, a number of algorithms have been developed that relax one or more of these criteria: they only work on a subset of graphs, or they do not always use an optimal number of colors, or they do not always run in polynomial time.

Optimally coloring special classes of graphs
In the case of bipartite graphs or multigraphs with maximum degree $χ′(G) ≤ Δ(G) + μ(G)$, the optimal number of colors is exactly $μ(G) = 1$. showed that an optimal edge coloring of these graphs can be found in the near-linear time bound $Δ$, where $G$ is the number of edges in the graph; simpler, but somewhat slower, algorithms are described by and. The algorithm of begins by making the input graph regular, without increasing its degree or significantly increasing its size, by merging pairs of vertices that belong to the same side of the bipartition and then adding a small number of additional vertices and edges. Then, if the degree is odd, Alon finds a single perfect matching in near-linear time, assigns it a color, and removes it from the graph, causing the degree to become even. Finally, Alon applies an observation of, that selecting alternating subsets of edges in an Euler tour of the graph partitions it into two regular subgraphs, to split the edge coloring problem into two smaller subproblems, and his algorithm solves the two subproblems recursively. The total time for his algorithm is $Δ$.

For planar graphs with maximum degree $O(m log Δ)$, the optimal number of colors is again exactly $O(m log m)$. With the stronger assumption that $Δ ≥ 7$, it is possible to find an optimal edge coloring in linear time.

For d-regular graphs which are pseudo-random in the sense that their adjacency matrix has second largest eigenvalue (in absolute value) at most $Δ$, d is the optimal number of colors.

Algorithms that use more than the optimal number of colors
and describe polynomial time algorithms for coloring any graph with $Δ ≥ 9$ colors, meeting the bound given by Vizing's theorem; see Misra & Gries edge coloring algorithm.

For multigraphs, present the following algorithm, which they attribute to Eli Upfal. Make the input multigraph $m$ Eulerian by adding a new vertex connected by an edge to every odd-degree vertex, find an Euler tour, and choose an orientation for the tour. Form a bipartite graph $G$ in which there are two copies of each vertex of $H$, one on each side of the bipartition, with an edge from a vertex $G$ on the left side of the bipartition to a vertex $u$ on the right side of the bipartition whenever the oriented tour has an edge from $v$ to $u$ in $v$. Apply a bipartite graph edge coloring algorithm to $G$. Each color class in $H$ corresponds to a set of edges in $H$ that form a subgraph with maximum degree two; that is, a disjoint union of paths and cycles, so for each color class in $G$ it is possible to form three color classes in $H$. The time for the algorithm is bounded by the time to edge color a bipartite graph, $d^{1−ε}$ using the algorithm of. The number of colors this algorithm uses is at most $$3 \left\lceil\frac\Delta2\right\rceil$$, close to but not quite the same as Shannon's bound of $$\left\lfloor\frac{3\Delta}2\right\rfloor$$. It may also be made into a parallel algorithm in a straightforward way. In the same paper, Karloff and Shmoys also present a linear time algorithm for coloring multigraphs of maximum degree three with four colors (matching both Shannon's and Vizing's bounds) that operates on similar principles: their algorithm adds a new vertex to make the graph Eulerian, finds an Euler tour, and then chooses alternating sets of edges on the tour to split the graph into two subgraphs of maximum degree two. The paths and even cycles of each subgraph may be colored with two colors per subgraph. After this step, each remaining odd cycle contains at least one edge that may be colored with one of the two colors belonging to the opposite subgraph. Removing this edge from the odd cycle leaves a path, which may be colored using the two colors for its subgraph.

A greedy coloring algorithm that considers the edges of a graph or multigraph one by one, assigning each edge the first available color, may sometimes use as many as $Δ + 1$ colors, which may be nearly twice as many number of colors as is necessary. However, it has the advantage that it may be used in the online algorithm setting in which the input graph is not known in advance; in this setting, its competitive ratio is two, and this is optimal: no other online algorithm can achieve a better performance. However, if edges arrive in a random order, and the input graph has a degree that is at least logarithmic, then smaller competitive ratios can be achieved.

Several authors have made conjectures that imply that the fractional chromatic index of any multigraph (a number that can be computed in polynomial time using linear programming) is within one of the chromatic index. If these conjectures are true, it would be possible to compute a number that is never more than one off from the chromatic index in the multigraph case, matching what is known via Vizing's theorem for simple graphs. Although unproven in general, these conjectures are known to hold when the chromatic index is at least $$\Delta+\sqrt{\Delta/2}$$, as can happen for multigraphs with sufficiently large multiplicity.

Exact algorithms
It is straightforward to test whether a graph may be edge colored with one or two colors, so the first nontrivial case of edge coloring is testing whether a graph has a 3-edge-coloring. As showed, it is possible to test whether a graph has a 3-edge-coloring in time $O(m log Δ)$, while using only polynomial space. Although this time bound is exponential, it is significantly faster than a brute force search over all possible assignments of colors to edges. Every biconnected 3-regular graph with $G$ vertices has $2Δ − 1$ 3-edge-colorings; all of which can be listed in time $O(1.344^{n})$ (somewhat slower than the time to find a single coloring); as Greg Kuperberg observed, the graph of a prism over an $O(2^{n/2})$-sided polygon has $O(2^{n/2})$ colorings (lower instead of upper bound), showing that this bound is tight.

By applying exact algorithms for vertex coloring to the line graph of the input graph, it is possible to optimally edge-color any graph with $n$ edges, regardless of the number of colors needed, in time $n/2$ and exponential space, or in time $Ω(2^{n/2})$ and only polynomial space.

Because edge coloring is NP-complete even for three colors, it is unlikely to be fixed parameter tractable when parametrized by the number of colors. However, it is tractable for other parameters. In particular, showed that for graphs of treewidth $m$, an optimal edge coloring can be computed in time $2^{m}m^{O(1)}$, a bound that depends superexponentially on $w$ but only linearly on the number $w$ of vertices in the graph.

formulate the edge coloring problem as an integer program and describe their experience using an integer programming solver to edge color graphs. However, they did not perform any complexity analysis of their algorithm.

Additional properties
A graph is uniquely $n$-edge-colorable if there is only one way of partitioning the edges into $k$ color classes, ignoring the $O(2.2461^{m})$ possible permutations of the colors. For $O(nw(6w)^{w(w + 1)/2})$, the only uniquely $k$-edge-colorable graphs are paths, cycles, and stars, but for $G(9,2)$ other graphs may also be uniquely $k$-edge-colorable. Every uniquely 3-edge-colorable graph has exactly three Hamiltonian cycles (formed by deleting one of the three color classes) but there exist 3-regular graphs that have three Hamiltonian cycles and are not uniquely 3-colorable, such as the generalized Petersen graphs $k!$ for $k ≠ 3$. The only known nonplanar uniquely 3-colorable graph is the generalized Petersen graph $k = 3$, and it has been conjectured that no others exist.

investigated the non-increasing sequences of numbers $G(6n + 3, 2)$ with the property that there exists a proper edge coloring of a given graph $k$ with $n ≥ 2$ edges of the first color, $G(9,2)$ edges of the second color, etc. They observed that, if a sequence $G$ is feasible in this sense, and is greater in lexicographic order than a sequence $P$ with the same sum, then $Q$ is also feasible. For, if $m_{1}, m_{2}, m_{3}, ...$ in lexicographic order, then $Q$ can be transformed into $P$ by a sequence of steps, each of which reduces one of the numbers $m_{1}$ by one unit and increases another later number $m_{2}$ with $P > Q$ by one unit. In terms of edge colorings, starting from a coloring that realizes $Q$, each of these same steps may be performed by swapping colors $P$ and $i$ on a Kempe chain, a maximal path of edges that alternate between the two colors. In particular, any graph has an equitable edge coloring, an edge coloring with an optimal number of colors in which every two color classes differ in size by at most one unit.

The De Bruijn–Erdős theorem may be used to transfer many edge coloring properties of finite graphs to infinite graphs. For instance, Shannon's and Vizing's theorems relating the degree of a graph to its chromatic index both generalize straightforwardly to infinite graphs.

considers the problem of finding a graph drawing of a given cubic graph with the properties that all of the edges in the drawing have one of three different slopes and that no two edges lie on the same line as each other. If such a drawing exists, then clearly the slopes of the edges may be used as colors in a 3-edge-coloring of the graph. For instance, the drawing of the utility graph $m_{i}$ as the edges and long diagonals of a regular hexagon represents a 3-edge-coloring of the graph in this way. As Richter shows, a 3-regular simple bipartite graph, with a given Tait coloring, has a drawing of this type that represents the given coloring if and only if the graph is 3-edge-connected. For a non-bipartite graph, the condition is a little more complicated: a given coloring can be represented by a drawing if the bipartite double cover of the graph is 3-edge-connected, and if deleting any monochromatic pair of edges leads to a subgraph that is still non-bipartite. These conditions may all be tested easily in polynomial time; however, the problem of testing whether a 4-edge-colored 4-regular graph has a drawing with edges of four slopes, representing the colors by slopes, is complete for the existential theory of the reals, a complexity class at least as difficult as being NP-complete.

As well as being related to the maximum degree and maximum matching number of a graph, the chromatic index is closely related to the linear arboricity $m_{j}$ of a graph $j$, the minimum number of linear forests (disjoint unions of paths) into which the graph's edges may be partitioned. A matching is a special kind of linear forest, and in the other direction, any linear forest can be 2-edge-colored, so for every $G$ it follows that $i < j$. Akiyama's conjecture (named for Jin Akiyama) states that $$\mathop{\mathrm{la}}(G) \leq \left\lceil\frac{\Delta+1}{2}\right\rceil$$, from which it would follow more strongly that $K_{3,3}$. For graphs of maximum degree three, $la(G)$ is always exactly two, so in this case the bound $la(G) ≤ χ′(G) ≤ 2 la(G)$ matches the bound given by Vizing's theorem.

Other types
The Thue number of a graph is the number of colors required in an edge coloring meeting the stronger requirement that, in every even-length path, the first and second halves of the path form different sequences of colors.

The arboricity of a graph is the minimum number of colors required so that the edges of each color have no cycles (rather than, in the standard edge coloring problem, having no adjacent pairs of edges). That is, it is the minimum number of forests into which the edges of the graph may be partitioned into. Unlike the chromatic index, the arboricity of a graph may be computed in polynomial time.

List edge-coloring is a problem in which one is given a graph in which each edge is associated with a list of colors, and must find a proper edge coloring in which the color of each edge is drawn from that edge's list. The list chromatic index of a graph $G$ is the smallest number $G$ with the property that, no matter how one chooses lists of colors for the edges, as long as each edge has at least $k$ colors in its list, then a coloring is guaranteed to be possible. Thus, the list chromatic index is always at least as large as the chromatic index. The Dinitz conjecture on the completion of partial Latin squares may be rephrased as the statement that the list edge chromatic number of the complete bipartite graph $2 la(G) − 2 ≤ χ′(G) ≤ 2 la(G)$ equals its edge chromatic number, $k$. resolved the conjecture by proving, more generally, that in every bipartite graph the chromatic index and list chromatic index are equal. The equality between the chromatic index and the list chromatic index has been conjectured to hold, even more generally, for arbitrary multigraphs with no self-loops; this conjecture remains open.

Many other commonly studied variations of vertex coloring have also been extended to edge colorings. For instance, complete edge coloring is the edge-coloring variant of complete coloring, a proper edge coloring in which each pair of colors must be represented by at least one pair of adjacent edges and in which the goal is to maximize the total number of colors. Strong edge coloring is the edge-coloring variant of strong coloring, an edge coloring in which every two edges with adjacent endpoints must have different colors. Strong edge coloring has applications in channel allocation schemes for wireless networks.

Acyclic edge coloring is the edge-coloring variant of acyclic coloring, an edge coloring for which every two color classes form an acyclic subgraph (that is, a forest). The acyclic chromatic index of a graph $$G$$, denoted by $$a'(G)$$, is the smallest number of colors needed to have a proper acyclic edge coloring of $$G$$. It has been conjectured that $$a'(G) \le \Delta + 2 $$, where $$\Delta$$ is the maximum degree of $$G$$. Currently the best known bound is $$a'(G) \le \lceil 3.74 (\Delta -1) \rceil$$. The problem becomes easier when $$G$$ has large girth. More specifically, there is a constant $$c$$ such that if the girth of $$G$$ is at least $$ c \Delta \log \Delta$$, then $$a'(G) \le \Delta + 2$$. A similar result is that for all $$\epsilon > 0$$ there exists an $$g$$ such that if $$G$$ has girth at least $$g$$, then $$a'(G) \le (1+\epsilon) \Delta$$.

studied 3-edge-colorings of cubic graphs with the additional property that no two bichromatic cycles share more than a single edge with each other. He showed that the existence of such a coloring is equivalent to the existence of a drawing of the graph on a three-dimensional integer grid, with edges parallel to the coordinate axes and each axis-parallel line containing at most two vertices. However, like the standard 3-edge-coloring problem, finding a coloring of this type is NP-complete.

Total coloring is a form of coloring that combines vertex and edge coloring, by requiring both the vertices and edges to be colored. Any incident pair of a vertex and an edge, or an edge and an edge, must have distinct colors, as must any two adjacent vertices. It has been conjectured (combining Vizing's theorem and Brooks' theorem) that any graph has a total coloring in which the number of colors is at most the maximum degree plus two, but this remains unproven.

If a 3-regular graph on a surface is 3-edge-colored, its dual graph forms a triangulation of the surface which is also edge colored (although not, in general, properly edge colored) in such a way that every triangle has one edge of each color. Other colorings and orientations of triangulations, with other local constraints on how the colors are arranged at the vertices or faces of the triangulation, may be used to encode several types of geometric object. For instance, rectangular subdivisions (partitions of a rectangular subdivision into smaller rectangles, with three rectangles meeting at every vertex) may be described combinatorially by a "regular labeling", a two-coloring of the edges of a triangulation dual to the subdivision, with the constraint that the edges incident to each vertex form four contiguous subsequences, within each of which the colors are the same. This labeling is dual to a coloring of the rectangular subdivision itself in which the vertical edges have one color and the horizontal edges have the other color. Similar local constraints on the order in which colored edges may appear around a vertex may also be used to encode straight-line grid embeddings of planar graphs and three-dimensional polyhedra with axis-parallel sides. For each of these three types of regular labelings, the set of regular labelings of a fixed graph forms a distributive lattice that may be used to quickly list all geometric structures based on the same graph (such as all axis-parallel polyhedra having the same skeleton) or to find structures satisfying additional constraints.

A deterministic finite automaton may be interpreted as a directed graph in which each vertex has the same out-degree $n$, and in which the edges are $d$-colored in such a way that every two edges with the same source vertex have distinct colors. The road coloring problem is the problem of edge-coloring a directed graph with uniform out-degrees, in such a way that the resulting automaton has a synchronizing word. solved the road coloring problem by proving that such a coloring can be found whenever the given graph is strongly connected and aperiodic.

Ramsey's theorem concerns the problem of $d$-coloring the edges of a large complete graph $la(G)$ in order to avoid creating monochromatic complete subgraphs $χ′(G) ≤ 2 la(G)$ of some given size $k$. According to the theorem, there exists a number $K_{n,n}$ such that, whenever $K_{n}$, such a coloring is not possible. For instance, $K_{s}$, that is, if the edges of the graph $R_{k}(s)$ are 2-colored, there will always be a monochromatic triangle.

A path in an edge-colored graph is said to be a rainbow path if no color repeats on it. A graph is said to be rainbow colored if there is a rainbow path between any two pairs of vertices. An edge-colouring of a graph G with colours 1. . . t is an interval t coloring if all colours are used, and the colours of edges incident to each vertex of G are distinct and form an interval of integers.

Applications
Edge colorings of complete graphs may be used to schedule a round-robin tournament into as few rounds as possible so that each pair of competitors plays each other in one of the rounds; in this application, the vertices of the graph correspond to the competitors in the tournament, the edges correspond to games, and the edge colors correspond to the rounds in which the games are played. Similar coloring techniques may also be used to schedule other sports pairings that are not all-play-all; for instance, in the National Football League, the pairs of teams that will play each other in a given year are determined, based on the teams' records from the previous year, and then an edge coloring algorithm is applied to the graph formed by the set of pairings in order to assign games to the weekends on which they are played. For this application, Vizing's theorem implies that no matter what set of pairings is chosen (as long as no teams play each other twice in the same season), it is always possible to find a schedule that uses at most one more weekend than there are games per team.

Open shop scheduling is a problem of scheduling production processes, in which there are a set of objects to be manufactured, each object has a set of tasks to be performed on it (in any order), and each task must be performed on a specific machine, preventing any other task that requires the same machine from being performed at the same time. If all tasks have the same length, then this problem may be formalized as one of edge coloring a bipartite multigraph, in which the vertices on one side of the bipartition represent the objects to be manufactured, the vertices on the other side of the bipartition represent the manufacturing machines, the edges represent tasks that must be performed, and the colors represent time steps in which each task may be performed. Since bipartite edge coloring may be performed in polynomial time, the same is true for this restricted case of open shop scheduling.

study the problem of link scheduling for time-division multiple access network communications protocols on sensor networks as a variant of edge coloring. In this problem, one must choose time slots for the edges of a wireless communications network so that each node of the network can communicate with each neighboring node without interference. Using a strong edge coloring (and using two time slots for each edge color, one for each direction) would solve the problem but might use more time slots than necessary. Instead, they seek a coloring of the directed graph formed by doubling each undirected edge of the network, with the property that each directed edge $s$ has a different color from the edges that go out from $uv$ and from the neighbors of $v$. They propose a heuristic for this problem based on a distributed algorithm for $n ≥ R(s)$-edge-coloring together with a postprocessing phase that reschedules edges that might interfere with each other.

In fiber-optic communication, the path coloring problem is the problem of assigning colors (frequencies of light) to pairs of nodes that wish to communicate with each other, and paths through a fiber-optic communications network for each pair, subject to the restriction that no two paths that share a segment of fiber use the same frequency as each other. Paths that pass through the same communication switch but not through any segment of fiber are allowed to use the same frequency. When the communications network is arranged as a star network, with a single central switch connected by separate fibers to each of the nodes, the path coloring problem may be modeled exactly as a problem of edge coloring a graph or multigraph, in which the communicating nodes form the graph vertices, pairs of nodes that wish to communicate form the graph edges, and the frequencies that may be used for each pair form the colors of the edge coloring problem. For communications networks with a more general tree topology, local path coloring solutions for the star networks defined by each switch in the network may be patched together to form a single global solution.

Open problems
list 23 open problems concerning edge coloring. They include:
 * The conjecture of that the chromatic index and fractional index are within one of each other, which would allow the chromatic index to be approximated within one color in polynomial time.
 * Several conjectures of Jakobsen and others on the structure of critical graphs for edge coloring, graphs of class 2 such that any subgraph either has smaller maximum degree or is of class 1. Jakobsen originally conjectured that all critical graphs have an odd number of vertices, but this was eventually disproved. Several other conjectures weakening this one, or bounding the numbers of vertices of critical graphs and critical multigraphs, remain open.
 * Vizing's problem of classifying the maximum degrees that are possible for class 2 planar graphs.
 * The overfull subgraph conjecture of A. J. W. Hilton, stating that graphs with degree at least $R_{2}(3) = 6$ are either of class 1 or contain a subgraph with the same degree $K_{6}$ as the original graph, and with an odd number $v$ of vertices, such that the number of edges in the subgraph is greater than $(Δ + 1)$, and a similar conjecture by Herbert Grötzsch and Paul Seymour concerning planar graphs in place of high-degree graphs.
 * A conjecture of Amanda Chetwynd and Anthony Hilton (possibly going back earlier to the work of Gabriel Andrew Dirac) that regular graphs with an even number $k$ of vertices and with degree at least $n/3$ are of class 1.
 * A conjecture of Claude Berge and D. R. Fulkerson that the 6-regular multigraphs formed by doubling every edge of a bridgeless 3-regular simple graph may be edge-colored with six colors.
 * A conjecture of Fiorini and Wilson that every triangle-free planar graph, other than the claw K1,3, is not uniquely 3-edge-colorable.
 * A 2012 conjecture that if $Δ$ is a $Δ(k − 1)/2$-regular planar multigraph, then $n/2$ is $G$-edge-colorable if and only if $d$ is oddly $G$-edge-connected. This conjecture is a generalization of the four color theorem, which arises at $d$=3. Maria Chudnovsky, Katherine Edwards, and Paul Seymour proved that an 8-regular planar multigraph has an edge chromatic number of 8.

title: Edge coloring


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Virgil Bogue

Virgil Gay Bogue (1846–1916) was an American civil engineer who worked initially in his home state of New York before taking jobs internationally and in the western and northwestern United States. He primarily worked for railroads, though also became involved in city planning.

Civil engineering
Bogue was born in Norfolk, New York, on July 16, 1846, the son of George Charles and Mary W. (Perry) Bogue. He received a degree in civil engineering from the Rensselaer Polytechnic Institute in Troy, New York, in 1868.

Bogue worked consecutively on Oroya Railway in Peru to 1879, the Northern Pacific Railway to 1886. On the Northern Pacific, he named Pasco, Washington after a region known for vicious sandstorms he had seen while in South America; built the Northern Pacific and Puget Sound Shore Railroad connecting Tacoma, Washington to Seattle, Washington; and discovered Stampede Pass.

After the Northern Pacific, Bogue served as chief engineer of the Union Pacific Railroad until 1891. Following this, he was also chief engineer on the Western Maryland Railway and headed up the construction of the Western Pacific Railroad through California's rugged Feather River Canyon.

As a consulting engineer, Bogue worked on Columbia River Navigation, Commencement Bay and Grays Harbor, the New Zealand Railway, the New York Department of Public Works, and finally, shortly before his death, the Greater Seattle Plan. Bogue died at sea aboard the steamship Esperanza on October 14, 1916.

His "Bogue Plan" was rejected by voters on March 5, 1912, by a 10,000-vote margin. It would have established Seattle's first comprehensive plan and a variety of improvements, including a civic center in the new Denny Regrade area. The civic center was eventually realized five decades later as Seattle Center, more or less in the location Bogue proposed.

title: Virgil Bogue


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Category:Anime

The term anime in English is generally taken to refer to Japanese animation; it is also sometimes used to refer to animation from elsewhere which has been drawn in that style.

title: Category:Anime


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Frye Art Museum

The Frye Art Museum is a modern and contemporary art museum in the First Hill neighborhood of Seattle, Washington. It was founded in 1952 to house the collection of Charles and Emma Frye and has since grown to include rotating temporary exhibitions of emerging and contemporary artists.

History
The museum emphasizes painting and sculpture from the nineteenth century to the present. Its holdings originated from the private collection of Charles H. Frye (1858–1940) and Emma Lamp Frye (d. 1934). The Fryes' were first-generation Americans of German descent who collected primarily German and Austrian artwork, often purchased directly from studios in Munich.

Charles Frye was the owner of a local meatpacking plant in Seattle. He set aside money in his will for a museum to house the Fryes' collection of 232 paintings. The Fryes' collection was first offered to the Seattle Art Museum but it was declined due to restrictions stipulated in the will which specified that the artwork must be on permanent display, be shown under natural light, not be shown with abstract work, and that admission to view the works remain free of charge. After Charles and Emma Frye had both died and following the sale of their home in 1941, many of their collected paintings, overseen by Walser Greathouse, were moved to the meat plant on Airport Way in SoDo, Seattle. The stored artwork survived a major fire at the plant on Feb. 18, 1943, following the crash of a B-29 bomber prototype, then a top-secret military project.

The Frye Art Museum was built in Seattle's First Hill neighborhood and opened to the public in 1952 as a free art museum.

The Fryes' historic collection consisted of representational art works, with a tendency toward "the dark, the dramatic, and the psychological" rather than "the genteel". The museum's permanent collection reflects Charles Frye's relatively conservative artistic tastes, and initially, the museum continued to be dedicated to representational art, both in its acquisitions and its exhibits. This conservatism reflected the artistic and social values of its first director, Walser Greathouse (d. 1966) and of his widow and successor Ida Kay Greathouse, who ran the museum until 1993.

After 2007 the artwork presented and collected by the museum shifted, contrary to the restrictions stipulated in Charles Frye's will, to include more contemporary forms such as Conceptual Art, eliciting comparisons to Seattle's Henry Art Gallery.

Architecture
The building for the Frye Art Museum was originally designed by architect Paul Thiry. In the mid 1990s the museum was expanded and renovated by architect Rick Sundberg of Olson Sundberg Kundig Allen Architects. The museum added a 142-seat auditorium and an education studio as part of the renovation.

Exhibitions and programs
Exhibitions have included "Subspontaneous: Francesca Lohmann and Rob Rhee," featuring sculptures involving natural forces and ecological growth, "Agnieszka Polska: Love Bite," and "Unsettling Femininity: Selections from the Frye Art Museum Collection." The museum often redeploys its permanent collection, experimenting with exhibiting it in different arrangements. In 2018, the museum had 109,249 total attendees and a membership base of 2,383.

Contemporary artists and groups exhibited at The Frye have included the performance group Degenerate Art Ensemble, First Nations indigenous artist Duane Linklater, American painter Christina Quarles, and African-American filmmaker and multimedia artist Cauleen Smith.

In 2020, amid the COVID-19 pandemic, the museum temporarily closed for in-person visits and provided online art viewing and educational opportunities through the Frye From Home program. On August 28, 2020, the museum announced its expectation to reopen for in-person visits in October 2020.

Collection
The Frye Art Museum's collection highlights many kinds of paintings, prints, works on paper, and sculptures. Artists represented in the museum's collection include Eugène Boudin, Nicolai Fechin, William-Adolphe Bouguereau, Félix Ziem, Eugène Isabey, Franz von Lenbach, Tim Lowly, Fritz von Uhde (Picture Book), Hermann Corrodi (Venice), Ludwig von Zumbusch, Leopold Schmutzler, and Franz Stuck (Judgment of Paris).

Library
The Frye Art Museum library contains more than 2,000 books. It specializes in 19th and 20th century American and German art.

title: Frye Art Museum


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Tigernmas

Tigernmas, son of Follach, son of Ethriel, a descendant of Érimón, was, according to medieval Irish legend and historical traditions, an early High King of Ireland.

According to the Lebor Gabála Érenn he became king when he overthrew his predecessor Conmáel in the Battle of Óenach Macha, and within a year of his accession had won twenty-seven battles against the descendants of Eber Finn, almost completely destroying Eber's line. It is said that during his reign gold was first smelted in Ireland, by the wright Iuchadán. Tigernmas was the first king to give drinking-horns to his followers, and the first to have clothes dyed purple, blue and green and decorated with brooches, fringes and ornaments. Seven lakes and three rivers burst from the ground during his reign. After reigning for seventy-seven years (or 100 years according to the Book of Fenagh, P 23), he and three-quarters of the men of Ireland died on Magh Slécht while worshipping Crom Cruach, a cruel deity propitiated with human sacrifice. According to the Annals of the Four Masters, Ireland was without a High King for seven years after his death, before Eochaid Étgudach took the kingship.

The Lebor Gabála synchronises his reign with the deaths of Thineas and Decylas, kings of Assyria, and the reigns of David and Solomon in Israel; the Laud Synchronisms with the Judean kings Asa and Jehoshaphat and the Assyrian king Pertiades (Pyriatides) 985 B.C. The Annals of the Four Masters dates his reign to 1621–1544 BC; Geoffrey Keating to 1209–1159 BC.

title: Tigernmas


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Bounty (chocolate bar)

Bounty is a coconut-filled, chocolate-enrobed candy bar manufactured by Mars, Incorporated, introduced in 1951 in the United Kingdom and Canada. It is a direct emulation of the Mounds bar introduced by Peter Paul in 1936, and also copies the milk chocolate enrobing of Hershey's Almond Joy, introduced in 1948. It is no longer domestically sold within the United States, only being available via import sales.

Flavours
Bounty has a coconut filling, enrobed with milk chocolate (in a blue wrapper) or dark chocolate (in a red wrapper) and is usually sold as two small bars wrapped in one package.

Since 2006, a cherry-flavoured version has also been available in Australia. This was initially a limited edition flavour, but remained available as of 2013. In Europe, a limited edition mango flavour was available in 2004-05 and in Russia and Ukraine in 2010. A pineapple-flavoured edition was available in Russia during 2014.

Although Bounty is no longer distributed by Mars in the United States, similar products, such as Mounds and Almond Joy, are marketed by Hershey's.

On 3 November 2022, it was announced that Bounty bars would be removed from some Celebrations tubs in the United Kingdom after the manufacturers found that 40% of people hated them. A limited run of "No Bounty" tubs would be available, in the weeks before Christmas. But a final decision had not been made after 18% of people named the Bounty as their favourite.

Since November 2022 the dark chocolate Bounty has not been available. Mars UK said in September 2023 that "we have temporarily had to delist Bounty Dark for operational reasons and we’re working hard to bring the product back when we can".

Advertising
In the 1970s the bar was promoted in television adverts showing a tropical beach scene and the tag-line "The Bounty hunters — They came in search of paradise." In 1996 the format was radically changed, after a £2m investment from the manufacturer.

title: Bounty (chocolate bar)


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Nang yai

Nang yai (หนังใหญ่, ) is a form of shadow play found in Thailand. Puppets are made of painted buffalo hide, while the story is narrated by songs, chants and music.

Nang means "leather" ("leather puppet" in this case), and in common usage refers to a dance-drama shadow puppet show. Nang yai, whose name specifically means "large shadow puppet", features life-size puppets, while nang talung (a similar tradition of shadow puppetry whose name derives from Pattalung, a southern city where the tradition has long been popular) features much smaller puppets. Both are particularly popular in southern Thailand. According to James Brandon, most scholars believe that nang yai came to Thailand via Java and the Malay Peninsula from India.

Nang yai and nang talung incorporate various episodes of the Indian epic Ramayana (known as the Ramakien in Thailand). The art form's traditions originated around the beginning of the 15th century. Nang yai performances were a popular means of entertainment during the Ayudhaya period and are mentioned in a poem called "Bunnovat Khamchan", written by the Buddhist monk Mahanag sometime around the years 1751 to 1758, at the end of King Boromakot's reign. The earliest known mention of nang yai in Thai records is from 1458, according to Brandon. Performances are traditionally held in open spaces such as a lawn or village dirt space. A white cloth screen about 16 m long and 6 m high, with a decorated border, is stretched across the stage. Behind the screen, a bonfire is lit to project the puppets' shadows (electric lights are often used instead now). During the show, a Thai instrumental ensemble (usually a piphat) plays music appropriate to each episode, synchronized with the puppets' action. Offstage reciters tell the story in a sort of heightened speech. The puppet figures are made from perforated cow or buffalo hide, each weighing about three or four kilograms. The biggest puppet is one which characterizes a place, weighing around five to seven kilograms.

Nang yai influenced that khon, a dance-drama art form from Thailand which involves masked pantomime.

Nang yai can be found throughout Thailand. For example, in central Thailand, nang yai is performed at Wat Khanon in Ratchaburi, Wat Plub in Petchaburi, Wat Sawang Arom in Singburi, and Wat Pumarin in Samut Songkhram, while in eastern Thailand it can be found at Wat Donin in Rayong Province.

title: Nang yai