Origin.

The source that popularized this pictorial maxim is a 17th-century carving over a door of the famous Tōshō-gū shrine in Nikkō, Japan. The carvings at Tōshō-gū Shrine were carved by Hidari Jingoro, and believed to have incorporated Confucius’s Code of Conduct, using the monkey as a way to depict man’s life cycle. There are a total of eight panels, and the iconic three wise monkeys picture comes from panel 2. The philosophy, however, probably originally came to Japan with a Tendai-Buddhist legend, from China in the 8th century (Nara Period). It has been suggested that the figures represent the three dogmas of the so-called middle school of the sect.  In Chinese, a similar phrase exists in the late "Analects of Confucius" from 2nd to 4th century B.C.: "Look not at what is contrary to propriety; listen not to what is contrary to propriety; speak not what is contrary to propriety; make no movement which is contrary to propriety" (). It may be this phrase that inspired the pictorial maxim after it was brought into Japan.  It is through the Kōshin rite of folk religion that the most significant examples are presented. The Kōshin belief or practice is a Japanese folk religion with Chinese Taoism origins and ancient Shinto influence. It was founded by Tendai Buddhist monks in the late 10th century. A considerable number of stone monuments can be found all over the eastern part of Japan around Tokyo. During the later part of the Muromachi period, it was customary to display stone pillars depicting the three monkeys during the observance of Kōshin.  Though the teaching had nothing to do with monkeys, the concept of the three monkeys originated from a simple play on words. The saying in Japanese is, where the "-zaru" is a negative conjugation on the three verbs, matching "zaru", the modified form of "monkey" used in compounds. Thus the saying (which does not include any specific reference to "evil") can also be interpreted as referring to three monkeys.  The shrine at Nikko is a Shinto shrine, and the monkey is an extremely important being in the Shinto religion. The monkey is believed to be the messenger of the Hie Shinto shrines, which also have connections with Tendai Buddhism. There are even important festivals that are celebrated during the year of the Monkey (occurring every twelve years) and a special festival is celebrated every sixteenth year of the Kōshin.  "The Three Mystic Apes" (Sambiki Saru) were described as "the attendants of Saruta Hito no Mikoto or Kōshin, the God of the Roads". The Kōshin festival was held on the 60th day of the calendar. It has been suggested that during the Kōshin festival, according to old beliefs, one's bad deeds might be reported to heaven "unless avoidance actions were taken...". It has been theorized that the three Mystic Apes, Not Seeing, Hearing, or Speaking, may have been the "things that one has done wrong in the last 59 days".  According to other accounts, the monkeys caused the "Sanshi" and "Ten-Tei" not to see, say or hear the bad deeds of a person. The are the Three Corpses living in everyone's body. The Sanshi keep track of the good deeds and particularly the bad deeds of the person they inhabit. Every 60 days, on the night called, if the person sleeps, the Sanshi will leave the body and go to, the Heavenly God, to report about the deeds of that person. Ten-Tei will then decide to punish bad people, making them ill, shortening their time alive, and in extreme cases putting an end to their lives. Those believers of Kōshin who have reason to fear will try to stay awake during Kōshin nights. This is the only way to prevent the Sanshi from leaving their body and reporting to Ten-Tei.  An ancient representation of the "no see, no hear, no say, no do" can be found in four golden figurines in the Zelnik Istvan Southeast Asian Gold Museum. These golden statues date from the 6th to 8th century. The figures look like tribal human people with not very precise body carvings and strong phallic symbols. This set indicates that the philosophy comes from very ancient roots.

Meaning of the proverb.

Just as there is disagreement about the origin of the phrase, there are differing explanations of the meaning of "see no evil, hear no evil, speak no evil".

Variations.

Sometimes there is a fourth monkey depicted, Shizaru, who symbolizes the principle of "do no evil", which fits with the full quote from Analects of Confucius. The monkey may be shown crossing his arms or covering his genitals. Yet another variation has the fourth monkey hold its nose to avoid a stench and has been dubbed "smell no evil" accordingly.  The opposite version of the three wise monkeys can also be found. In this case, one monkey holds its hands to its eyes to focus vision, the second monkey cups its hands around its ears to improve hearing, and the third monkey holds its hands to its mouth like a bullhorn. Those three monkeys might be considered unwise, but the fact that they intentionally select what they perceive is proof of wisdom, free will, and altruism. "Hear, see, and speak only good". It's the positive version of the three wise monkeys. Another modern interpretation is "Hear, see, and speak out loud for what you stand for".

Rajneesh movement.

According to Osho Rajneesh, the monkey symbolism originated in ancient Hindu tradition and Buddhist monks spread this symbolism across Asia. The original Hindu and Buddhist version has four monkeys and the fourth monkey covers his genitals. The Buddhist version means this as "Don't do anything evil".  In Hindu original version the meaning of the fourth monkey is totally different from the popular Buddhist version. It means, "Hide your pleasures. Hide your enjoyment, don't show it to anybody."  Osho Rajneesh gave his own meaning regarding this. The first monkey denotes 'Don't listen to the truth because it will disturb all your consoling lies'. The second monkey denotes 'Don't look at the truth; otherwise your God will be dead and your heaven and hell will disappear'. The third monkey denotes 'Don't speak the truth, otherwise you will be condemned, crucified, poisoned, tortured by the whole crowd, the unconscious people. The fourth monkey denotes "Keep your pleasures, your joys, hidden. Don't let anybody know that you are a cheerful man, a blissful man, an ecstatic man, because that will destroy your very life. It is dangerous".

Cultural influences.

The three wise monkeys, and the associated proverb, are known throughout Asia and outside Asia. They have been a motif in pictures, such as the ukiyo-e (Japanese woodblock printings) by Keisai Eisen, and are frequently represented in modern culture.  Mahatma Gandhi's one notable exception to his lifestyle of non-possession was a small statue of the three monkeys - Bapu, Ketan and Bandar. Today, a larger representation of the three monkeys is prominently displayed at the Sabarmati Ashram in Ahmedabad, Gujarat, where Gandhi lived from 1915 to 1930 and from where he departed on his famous salt march. Gandhi's statue also inspired a 2008 artwork by Subodh Gupta, "Gandhi's Three Monkeys".  The three monkeys are depicted in the trial scene in the 1968 "Planet of the Apes". An example of semiotics, as the judges mimic the see no evil, hear no evil, speak no evil monkeys.  In a spoof of this saying, Bob Dole quipped about a meeting of former US Presidents: "Carter, Ford and Nixon: see no evil, hear no evil and evil."  The maxim inspired an award-winning 2008 Turkish film by director Nuri Bilge Ceylan called "Three Monkeys" ("Üç Maymun").

Unicode characters.

Unicode provides emoji representations of the monkeys in the Emoticons block as follows:

The three wise monkeys are a Japanese pictorial maxim, embodying the proverbial principle "see no evil, hear no evil, speak no evil". The three monkeys are Mizaru, covering his eyes, who sees no evil; Kikazaru, covering his ears, who hears no evil and Iwazaru, covering his mouth, who speaks no evil.

Tři moudré opice, z nichž jedna si zakrývá uši, druhá ústa a třetí oči, svými gesty říkají „neslyším zlo, nevidím zlo, nemluvím zlo“. První opice, která si zakrývá oči a nevidí zlo, se jmenuje Mizaru. Druhá opice, která si zakrývá uši a nenaslouchá zlým řečem, se jmenuje Kikazaru. Třetí opice, která si zakrývá ústa a nepomlouvá, se jmenuje Iwazaru. Občas bývá znázorňována i čtvrtá opice Šizaru, která značí „nečiním zlo“, je zobrazována, jak si zakrývá břicho nebo oblast genitálií, nebo se zkříženýma rukama.


Life and career.

Saul Kripke is the oldest of three children born to Dorothy K. Kripke and Rabbi Myer S. Kripke. His father was the leader of Beth El Synagogue, the only Conservative congregation in Omaha, Nebraska; his mother wrote educational Jewish books for children. Saul and his two sisters, Madeline and Netta, attended Dundee Grade School and Omaha Central High School. Kripke was labeled a prodigy, teaching himself Ancient Hebrew by the age of six, reading Shakespeare's complete works by nine, and mastering the works of Descartes and complex mathematical problems before finishing elementary school. He wrote his first completeness theorem in modal logic at 17, and had it published a year later. After graduating from high school in 1958, Kripke attended Harvard University and graduated summa cum laude in 1962 with a bachelor's degree in mathematics. During his sophomore year at Harvard, he taught a graduate-level logic course at nearby MIT. Upon graduation he received a Fulbright Fellowship, and in 1963 was appointed to the Society of Fellows. Kripke later said, "I wish I could have skipped college. I got to know some interesting people but I can't say I learned anything. I probably would have learned it all anyway just reading on my own."  After briefly teaching at Harvard, in 1968 Kripke moved to Rockefeller University in New York City, where he taught until 1976. In 1978 he took a chaired professorship at Princeton University. In 1988 he received the university's Behrman Award for distinguished achievement in the humanities. In 2002 Kripke began teaching at the CUNY Graduate Center, and in 2003 he was appointed a distinguished professor of philosophy there.  Kripke has received honorary degrees from the University of Nebraska, Omaha (1977), Johns Hopkins University (1997), University of Haifa, Israel (1998), and the University of Pennsylvania (2005). He is a member of the American Philosophical Society and an elected Fellow of the American Academy of Arts and Sciences, and in 1985 was a Corresponding Fellow of the British Academy. He won the Schock Prize in Logic and Philosophy in 2001.  Kripke was married to philosopher Margaret Gilbert. He is the second cousin once removed of television writer, director, and producer Eric Kripke.

Work.

Kripke's contributions to philosophy include:  He has also contributed to recursion theory (see admissible ordinal and Kripke–Platek set theory).

Modal logic.

Two of Kripke's earlier works, "A Completeness Theorem in Modal Logic" (1959) and "Semantical Considerations on Modal Logic" (1963), the former written when he was a teenager, were on modal logic. The most familiar logics in the modal family are constructed from a weak logic called K, named after Kripke. Kripke introduced the now-standard Kripke semantics (also known as relational semantics or frame semantics) for modal logics. Kripke semantics is a formal semantics for non-classical logic systems. It was first made for modal logics, and later adapted to intuitionistic logic and other non-classical systems. The discovery of Kripke semantics was a breakthrough in the making of non-classical logics, because the model theory of such logics was absent before Kripke.  A Kripke frame or modal frame is a pair formula_1, where "W" is a non-empty set, and "R" is a binary relation on "W". Elements of "W" are called "nodes" or "worlds", and "R" is known as the accessibility relation. Depending on the properties of the accessibility relation (transitivity, reflexivity, etc.), the corresponding frame is described, by extension, as being transitive, reflexive, etc.  A Kripke model is a triple formula_2, where formula_1 is a Kripke frame, and formula_4 is a relation between nodes of "W" and modal formulas, such that:  We read formula_13 as ""w" satisfies "A"", ""A" is satisfied in "w"", or ""w" forces "A"". The relation formula_4 is called the "satisfaction relation", "evaluation", or "forcing relation". The satisfaction relation is uniquely determined by its value on propositional variables.  A formula "A" is valid in:  We define Thm("C") to be the set of all formulas that are valid in "C". Conversely, if "X" is a set of formulas, let Mod("X") be the class of all frames which validate every formula from "X".  A modal logic (i.e., a set of formulas) "L" is sound with respect to a class of frames "C", if "L" ⊆ Thm("C"). "L" is complete with respect to "C" if "L" ⊇ Thm("C").  Semantics is useful for investigating a logic (i.e., a derivation system) only if the semantical entailment relation reflects its syntactical counterpart, the "consequence" relation ("derivability"). It is vital to know which modal logics are sound and complete with respect to a class of Kripke frames, and for them, to determine which class it is.  For any class "C" of Kripke frames, Thm("C") is a normal modal logic (in particular, theorems of the minimal normal modal logic, "K", are valid in every Kripke model). However, the converse does not hold generally. There are Kripke incomplete normal modal logics, which is unproblematic, because most of the modal systems studied are complete of classes of frames described by simple conditions.  A normal modal logic "L" corresponds to a class of frames "C", if "C" = Mod("L"). In other words, "C" is the largest class of frames such that "L" is sound wrt "C". It follows that "L" is Kripke complete if and only if it is complete of its corresponding class.  Consider the schema T : formula_20. T is valid in any reflexive frame formula_1: if formula_22, then formula_13 since "w" "R" "w". On the other hand, a frame which validates T has to be reflexive: fix "w" ∈ "W", and define satisfaction of a propositional variable "p" as follows: formula_24 if and only if "w" "R" "u". Then formula_25, thus formula_26 by T, which means "w" "R" "w" using the definition of formula_4. T corresponds to the class of reflexive Kripke frames.  It is often much easier to characterize the corresponding class of "L" than to prove its completeness, thus correspondence serves as a guide to completeness proofs. Correspondence is also used to show "incompleteness" of modal logics: suppose "L" ⊆ "L" are normal modal logics that correspond to the same class of frames, but "L" does not prove all theorems of "L". Then "L" is Kripke incomplete. For example, the schema formula_28 generates an incomplete logic, as it corresponds to the same class of frames as GL (viz. transitive and converse well-founded frames), but does not prove the GL-tautology formula_29.

Canonical models.

For any normal modal logic "L", a Kripke model (called the canonical model) can be constructed, which validates precisely the theorems of "L", by an adaptation of the standard technique of using maximal consistent sets as models. Canonical Kripke models play a role similar to the Lindenbaum–Tarski algebra construction in algebraic semantics.  A set of formulas is "L"-"consistent" if no contradiction can be derived from them using the axioms of "L", and modus ponens. A "maximal L-consistent set" (an "L"-"MCS" for short) is an "L"-consistent set which has no proper "L"-consistent superset.  The canonical model of "L" is a Kripke model formula_2, where "W" is the set of all "L"-"MCS", and the relations "R" and formula_4 are as follows:  The canonical model is a model of "L", as every "L"-"MCS" contains all theorems of "L". By Zorn's lemma, each "L"-consistent set is contained in an "L"-"MCS", in particular every formula unprovable in "L" has a counterexample in the canonical model.  The main application of canonical models are completeness proofs. Properties of the canonical model of K immediately imply completeness of K with respect to the class of all Kripke frames. This argument does "not" work for arbitrary "L", because there is no guarantee that the underlying "frame" of the canonical model satisfies the frame conditions of "L".  We say that a formula or a set "X" of formulas is canonical with respect to a property "P" of Kripke frames, if  A union of canonical sets of formulas is itself canonical. It follows from the preceding discussion that any logic axiomatized by a canonical set of formulas is Kripke complete, and compact.  The axioms T, 4, D, B, 5, H, G (and thus any combination of them) are canonical. GL and Grz are not canonical, because they are not compact. The axiom M by itself is not canonical (Goldblatt, 1991), but the combined logic S4.1 (in fact, even K4.1) is canonical.  In general, it is undecidable whether a given axiom is canonical. We know a nice sufficient condition: H. Sahlqvist identified a broad class of formulas (now called Sahlqvist formulas) such that:  This is a powerful criterion: for example, all axioms listed above as canonical are (equivalent to) Sahlqvist formulas. A logic has the finite model property (FMP) if it is complete with respect to a class of finite frames. An application of this notion is the decidability question: it follows from Post's theorem that a recursively axiomatized modal logic L which has FMP is decidable, provided it is decidable whether a given finite frame is a model of L. In particular, every finitely axiomatizable logic with FMP is decidable.  There are various methods for establishing FMP for a given logic. Refinements and extensions of the canonical model construction often work, using tools such as filtration or unravelling. As another possibility, completeness proofs based on cut-free sequent calculi usually produce finite models directly.  Most of the modal systems used in practice (including all listed above) have FMP.  In some cases, we can use FMP to prove Kripke completeness of a logic: every normal modal logic is complete wrt a class of modal algebras, and a finite modal algebra can be transformed into a Kripke frame. As an example, Robert Bull proved using this method that every normal extension of S4.3 has FMP, and is Kripke complete.  Kripke semantics has a straightforward generalization to logics with more than one modality. A Kripke frame for a language with formula_38 as the set of its necessity operators consists of a non-empty set "W" equipped with binary relations "R" for each "i" ∈ "I". The definition of a satisfaction relation is modified as follows:

Carlson models.

A simplified semantics, discovered by Tim Carlson, is often used for polymodal provability logics. A Carlson model is a structure formula_41 with a single accessibility relation "R", and subsets "D" ⊆ "W" for each modality. Satisfaction is defined as:  Carlson models are easier to visualize and to work with than usual polymodal Kripke models; there are, however, Kripke complete polymodal logics which are Carlson incomplete.  In "Semantical Considerations on Modal Logic", published in 1963, Kripke responded to a difficulty with classical quantification theory. The motivation for the world-relative approach was to represent the possibility that objects in one world may fail to exist in another. If standard quantifier rules are used, however, every term must refer to something that exists in all the possible worlds. This seems incompatible with our ordinary practice of using terms to refer to things that exist contingently.  Kripke's response to this difficulty was to eliminate terms. He gave an example of a system that uses the world-relative interpretation and preserves the classical rules. However, the costs are severe. First, his language is artificially impoverished, and second, the rules for the propositional modal logic must be weakened.  Kripke's possible worlds theory has been used by narratologists (beginning with Pavel and Dolezel) to understand "reader's manipulation of alternative plot developments, or the characters' planned or fantasized alternative action series." This application has become especially useful in the analysis of hyperfiction.

Intuitionistic logic.

Kripke semantics for intuitionistic logic follows the same principles as the semantics of modal logic, but uses a different definition of satisfaction.  An intuitionistic Kripke model is a triple formula_44, where formula_45 is a partially ordered Kripke frame, and formula_4 satisfies the following conditions:  Intuitionistic logic is sound and complete with respect to its Kripke semantics, and it has the Finite Model Property.  Intuitionistic first-order logic  Let "L" be a first-order language. A Kripke model of "L" is a triple formula_61, where formula_45 is an intuitionistic Kripke frame, "M" is a (classical) "L"-structure for each node "w" ∈ "W", and the following compatibility conditions hold whenever "u" ≤ "v": Given an evaluation "e" of variables by elements of "M", we define the satisfaction relation formula_63: Here "e"("x"→"a") is the evaluation which gives "x" the value "a", and otherwise agrees with "e".

"Naming and Necessity".

The three lectures that form "Naming and Necessity" constitute an attack on descriptivist theory of names. Kripke attributes variants of descriptivist theories to Frege, Russell, Wittgenstein and John Searle, among others. According to descriptivist theories, proper names either are synonymous with descriptions, or have their reference determined by virtue of the name's being associated with a description or cluster of descriptions that an object uniquely satisfies. Kripke rejects both these kinds of descriptivism. He gives several examples purporting to render descriptivism implausible as a theory of how names get their references determined (e.g., surely Aristotle could have died at age two and so not satisfied any of the descriptions we associate with his name, but it would seem wrong to deny that he was still Aristotle).  As an alternative, Kripke outlined a causal theory of reference, according to which a name refers to an object by virtue of a causal connection with the object as mediated through communities of speakers. He points out that proper names, in contrast to most descriptions, are rigid designators: that is, a proper name refers to the named object in every possible world in which the object exists, while most descriptions designate different objects in different possible worlds. For example, "Richard Nixon" refers to the same person in every possible world in which Nixon exists, while "the person who won the United States presidential election of 1968" could refer to Nixon, Humphrey, or others in different possible worlds.  Kripke also raised the prospect of "a posteriori necessities" — facts that are necessarily true, though they can be known only through empirical investigation. Examples include "Hesperus is Phosphorus", "Cicero is Tully", "Water is HO" and other identity claims where two names refer to the same object.  Finally, Kripke gave an argument against identity materialism in the philosophy of mind, the view that every mental particular is identical with some physical particular. Kripke argued that the only way to defend this identity is as an "a posteriori" necessary identity, but that such an identity — e.g., that pain is C-fibers firing — could not be necessary, given the (clearly conceivable) possibility that pain could be separate from the firing of C-fibers, or the firing of C-fibers be separate from pain. (Similar arguments have since been made by David Chalmers.) In any event, the psychophysical identity theorist, according to Kripke, incurs a dialectical obligation to explain the apparent logical possibility of these circumstances, since according to such theorists they should be impossible.  Kripke delivered the John Locke Lectures in philosophy at Oxford in 1973. Titled "Reference and Existence", they were in many respects a continuation of "Naming and Necessity", and deal with the subjects of fictional names and perceptual error. In 2013 Oxford University Press published the lectures as a book, also titled "Reference and Existence".  In a 1995 paper, philosopher Quentin Smith argued that key concepts in Kripke's new theory of reference originated in the work of Ruth Barcan Marcus more than a decade earlier. Smith identified six significant ideas in the New Theory that he claimed Marcus had developed: (1) that proper names are direct references that do not consist of contained definitions; (2) that while one can single out a single thing by a description, this description is not equivalent to a proper name of this thing; (3) the modal argument that proper names are directly referential, and not disguised descriptions; (4) a formal modal logic proof of the necessity of identity; (5) the concept of a rigid designator, though Kripke coined that term; and (6) "a posteriori" identity. Smith argued that Kripke failed to understand Marcus's theory at the time but later adopted many of its key conceptual themes in his New Theory of Reference.  Other scholars have subsequently offered detailed responses arguing that no plagiarism occurred.

"A Puzzle about Belief".

Kripke's main propositions about proper names in "Naming and Necessity" are that the meaning of a name simply is the object it refers to and that a name's referent is determined by a causal link between some sort of "baptism" and the utterance of the name. Nevertheless, he acknowledges the possibility that propositions containing names may have some additional semantic properties, properties that could explain why two names referring to the same person may give different truth values in propositions about beliefs. For example, Lois Lane believes that Superman can fly, although she does not believe that Clark Kent can fly. This can be accounted for if the names "Superman" and "Clark Kent", though referring to the same person, have distinct semantic properties.  But in his article "A Puzzle about Belief" Kripke seems to oppose even this possibility. His argument can be reconstructed as follows: The idea that two names referring to the same object may have different semantic properties is supposed to explain that coreferring names behave differently in propositions about beliefs (as in Lois Lane's case). But the same phenomenon occurs even with coreferring names that obviously have the same semantic properties: Kripke invites us to imagine a French, monolingual boy, Pierre, who believes that ""Londres est joli"" ("London is beautiful"). Pierre moves to London without realizing that London = Londres. He then learns English the same way a child would learn the language, that is, not by translating words from French to English. Pierre learns the name "London" from the unattractive part of the city where he lives, and so comes to believe that London is not beautiful. If Kripke's account is correct, Pierre now believes both that "Londres" is "joli" and that London is not beautiful. This cannot be explained by coreferring names having different semantic properties. According to Kripke, this demonstrates that attributing additional semantic properties to names does not explain what it is intended to.

Wittgenstein.

First published in 1982, Kripke's "Wittgenstein on Rules and Private Language" contends that the central argument of Wittgenstein's "Philosophical Investigations" centers on a devastating rule-following paradox that undermines the possibility of our ever following rules in our use of language. Kripke writes that this paradox is "the most radical and original skeptical problem that philosophy has seen to date", and that Wittgenstein does not reject the argument that leads to the rule-following paradox, but accepts it and offers a "skeptical solution" to ameliorate the paradox's destructive effects.  Most commentators accept that "Philosophical Investigations" contains the rule-following paradox as Kripke presents it, but few have agreed with his attributing a skeptical solution to Wittgenstein. Kripke himself expresses doubts in "Wittgenstein on Rules and Private Language" as to whether Wittgenstein would endorse his interpretation of "Philosophical Investigations." He says that the work should not be read as an attempt to give an accurate statement of Wittgenstein's views, but rather as an account of Wittgenstein's argument "as it struck Kripke, as it presented a problem for him".  The portmanteau "Kripkenstein" has been coined for Kripke's interpretation of "Philosophical Investigations". Kripkenstein's main significance was a clear statement of a new kind of skepticism, dubbed "meaning skepticism": the idea that for an isolated individual there is no fact in virtue of which he/she means one thing rather than another by the use of a word. Kripke's "skeptical solution" to meaning skepticism is to ground meaning in the behavior of a community.  Kripke's book generated a large secondary literature, divided between those who find his skeptical problem interesting and perceptive, and others, such as Gordon Baker and Peter Hacker, who argue that his meaning skepticism is a pseudo-problem that stems from a confused, selective reading of Wittgenstein. Kripke's position has been defended against these and other attacks by the Cambridge philosopher Martin Kusch, and Wittgenstein scholar David G. Stern considers Kripke's book "the most influential and widely discussed" work on Wittgenstein since the 1980s.

Truth.

In his 1975 article "Outline of a Theory of Truth", Kripke showed that a language can consistently contain its own truth predicate, something deemed impossible by Alfred Tarski, a pioneer in formal theories of truth. The approach involves letting truth be a partially defined property over the set of grammatically well-formed sentences in the language. Kripke showed how to do this recursively by starting from the set of expressions in a language that do not contain the truth predicate, and defining a truth predicate over just that segment: this action adds new sentences to the language, and truth is in turn defined for all of them. Unlike Tarski's approach, however, Kripke's lets "truth" be the union of all of these definition-stages; after a denumerable infinity of steps the language reaches a "fixed point" such that using Kripke's method to expand the truth-predicate does not change the language any further. Such a fixed point can then be taken as the basic form of a natural language containing its own truth predicate. But this predicate is undefined for any sentences that do not, so to speak, "bottom out" in simpler sentences not containing a truth predicate. That is, " 'Snow is white' is true" is well-defined, as is "'"Snow is white" is true' is true," and so forth, but neither "This sentence is true" nor "This sentence is not true" receive truth-conditions; they are, in Kripke's terms, "ungrounded."  Nevertheless, it has been shown by Gödel that self-reference cannot be avoided naively, since propositions about seemingly unrelated objects (such as integers) can have an informal self-referential meaning, and this idea – manifested by the diagonal lemma – is the basis for Tarski's theorem that truth cannot be consistently defined. It has thus been claimed that Kripke's suggestion does lead to contradiction: while its truth predicate is only partial, it does give truth value (true/false) to propositions such as the one built in Tarski's proof, and is therefore inconsistent. There is still a debate about whether Tarski's proof can be implemented to every variation of such a partial truth system, but none has been shown to be consistent by acceptable proving methods used in mathematical logic.  Kripke's proposal is also problematic in the sense that while the language contains a "truth" predicate of itself (at least a partial one), some of its sentences – such as the liar sentence ("this sentence is false") – have an undefined truth value, but the language does not contain its own "undefined" predicate. In fact it cannot, as that would create a new version of the liar paradox, called the "strengthened liar paradox" ("this sentence is false or undefined"). Thus while the liar sentence is undefined in the language, the language cannot express that it is undefined.

Religious views.

Kripke is an observant Jew. On how his religious views influenced his philosophical views, he has said: "I don't have the prejudices many have today. I don't believe in a naturalist worldview. I don't base my thinking on prejudices or a worldview and do not believe in materialism."

Saul Kripke Center.

The Saul Kripke Center at the Graduate Center of the City University of New York is dedicated to preserving and promoting Kripke's work. Its director is Gary Ostertag. The Saul Kripke Center holds events related to Kripke's work and is creating a digital archive of previously unpublished recordings of Kripke's lectures, lecture notes, and correspondence dating back to the 1950s. In his favorable review of Kripke's "Philosophical Troubles", the Stanford philosopher Mark Crimmins wrote, "That four of the most admired and discussed essays in 1970s philosophy are here is enough to make this first volume of Saul Kripke's collected articles a must-have... The reader's delight will grow as hints are dropped that there is a great deal more to come in this series being prepared by Kripke and an ace team of philosopher-editors at the Saul Kripke Center at The Graduate Center of the City University of New York."

Saul Aaron Kripke (; born November 13, 1940) is an American philosopher and logician in the analytic tradition. He is a Distinguished Professor of Philosophy at the Graduate Center of the City University of New York and emeritus professor at Princeton University. Since the 1960s, Kripke has been a central figure in a number of fields related to mathematical logic, modal logic, philosophy of language, philosophy of mathematics, metaphysics, epistemology, and recursion theory. Much of his work remains unpublished or exists only as tape recordings and privately circulated manuscripts.

Saul Aaron Kripke (* 13. listopadu 1940 Omaha, Nebraska) je americko-židovský filosof a logik, emeritní profesor university Princeton, jeden z nejvýznamnějších žijících filosofů, alespoň v anglosaském světě a analytické filosofii.


Methods.

Three methods are used in electrology: Galvanic, thermolysis, and blend. All three methods have their own merits, and one method is not better than another. The success depends on the skill of the electrologist, the type of hair being removed, the condition of the skin and the pain threshold of the client. All three methods, when properly performed, can be thorough at destroying the hair matrix cells, and leaving follicles incapable of regrowing hair.

Galvanic method.

This method is named after Luigi Galvani and uses a person's body as an electrolytic cell. Galvanic electrolysis was first reported in medical literature in 1875 by ophthalmologist Charles Michel as a method for removing ingrown eyelashes. A galvanic hair remover is essentially a positive ground power supply that delivers 0-3 milliamperes through the body. The follicular probe is the cathode of an electrolytic cell. Sodium hydroxide formed at the cathode by the process of chemical electrolysis kills the hair matrix cells. Modern galvanic hair removers automatically adjust the voltage to maintain constant current.

Thermolysis.

Another method is known as thermolysis, also called radio frequency (RF), shortwave or diathermy. Thermolysis was developed in the 1920s and first reported in medical literature by Henri Bordier. A thermolytic hair remover is essentially a radio transmitter, usually with an output of about 0-8 watts at a frequency of 13.56. RF energy emanates from the probe tip to tissue within about a millimeter. Thermolysis works by heating the hair matrix cells to about, causing electrocoagulation.

Blend method.

The galvanic method and thermolysis are often combined in the blend method, developed by Arthur Hinkel in 1948, which uses both RF and direct current, combining many of the advantages of both methods.

Technique.

The practitioner selects a metal probe that slides easily into the hair follicle, usually the same diameter as the hair shaft or smaller. The probe is typically 50 to 150 μm (0.002 to 0.006 inches) for all three modalities. Care is needed to insert the probe at the same angle as the hair is growing out of the skin. The probe is inserted to the depth of the hair matrix, the site where hair is formed. The power and duration of the electricity are started at the lowest setting, then gradually increased until the hair comes out as easily as possible. If the patient experiences significant discomfort, the settings can be lowered.

Treatment duration.

Most practitioners will advise that complete removal of male pattern facial hair takes between 1 and 4 years, with an average treatment length of 2 years in case of one session per week, one hour per session. Removal of body hair works considerably faster.

Status of profession.

In the United States, electrolysis is regulated in many states, requiring training and licensing.  Electrolysis as a profession faced new competition in the 1990s after laser hair removal was developed and promoted as a quicker and easier way to remove hair. However, the U.S. Food and Drug Administration (FDA) declared laser can only claim to reduce hair growth, not permanently remove it.

Electrology is the practice of electrical hair removal to permanently remove human hair from the body. Electrolysis is the actual process of removing hair using electricity.

Elektrolýza je metoda elektrické depilace, která vede k trvalému odstranění kořínků chlupů na lidském těle. Slovo elektrolýza znamená samotný proces odstraňování, který probíhá vsunováním pevné kovové sondy o tloušťce lidského vlasu do každého jednotlivého vlasového folikulu. Při správném provedení nedochází k propíchnutí kůže, ale vlasový folikul je zničen a chlup trvale odstraněn.


Finnic languages.

In the Finnic languages, such as Finnish and Estonian, this case is often used to express unknown identities and irresultative actions. For example, it is found in the following circumstances, with the characteristic ending of "-a" or "-ta":  Where not mentioned, the accusative case would be ungrammatical. For example, the partitive must always be used after singular numerals.  As an example of the irresultative meaning of the partitive, "ammuin karhun" (accusative) means "I shot the bear (dead)", whereas "ammuin karhua" (partitive) means "I shot (at) the bear" without specifying if it was even hit. Notice that Finnish has no native future tense, so that the partitive provides an important reference to the present as opposed to the future. Thus "luen kirjaa" means "I am reading a/the book" whereas "luen kirjan" means "I will read a/the book". Thus "luen" can mean "I am reading" or "I will read" depending on the case form of the word that follows. The partitive form "kirjaa" indicates incompleted action and hence the meaning of the verb form is present tense. The accusative form "kirjan" indicates completed action when used with the past tense verb but indicates planned future action when used with a verb in the present tense. Hence "luen kirjan" means "I will read the book". The case with an unspecified identity is "onko teillä kirjoja", which uses the partitive, because it refers to unspecified books, as contrasted to nominative "onko teillä (ne) kirjat?", which means "do you have (those) books?"  The partitive case comes from the older ablative case. This meaning is preserved e.g. in "kotoa" (from home), "takaa" (from behind), where it means "from".  A Western Finnish dialectal phenomenon seen in some dialects is the assimilation of the final "-a" into a preceding vowel, thus making the chroneme the partitive marker. For example, "suurii" → "suuria" "some big --".  In Estonian, the system is generally similar. In Estonian grammatical tradition, the term "accusative" is not used, since like in Finnish, the total object form coincides with the genitive in the singular, and the partitive in the plural.  In many Estonian words, the difference between the full and partial object cases is only in vowel or consonant quantity (long vs overlong), which is not marked in writing, except for stop consonants. Thus, the distinction between a total and partial object may be apparent in speech but not in writing. For example, the sentence "Linn ehitab kooli" would mean "The city will build a/the school" when pronounced with a long vowel "o" in "kooli" "school (genitive case)", and "The city is building a/the school" with an overlong "o" (partitive case).  For many verbs in Estonian, an additional adverb is almost always added when a completed action is meant - for example, "ma söön leiba" "I'm eating bread", vs "ma söön leiva ära" "I will eat the (whole) bread". Since Estonian, unlike Finnish, has words where the genitive and partitive singular are identical even in pronunciation, this can provide disambiguation in those cases - e.g "ma söön kala" "I'm eating fish", vs "ma söön kala ära" "I will eat (all of) the fish".

Sámi.

Of the Sámi languages, Inari and Skolt Sámi still have a partitive, although it is slowly disappearing and its function is being taken over by other cases.

Skolt Sámi.

The partitive is used only in the singular and can always be replaced by the genitive. The partitive marker is "-d".  1. It appears after numbers larger than 6:  This can be replaced with "kää ́uc čâustõõǥǥ".  2. It is also used with certain postpositions:  This can be replaced with "kuä ́đ vuâstta".  3. It can be used with the comparative to express that which is being compared:  This would nowadays more than likely be replaced by "pue ́rab ko kå ́ll"

Russian.

The Russian language usually uses the genitive case to express partialness. However, some Russian mass nouns have developed a distinct partitive case, also referred to as the "second genitive case". The partitive arose from the merger of the declensions of "*-ŏ" and "*-ŭ" stem nouns in Old East Slavic, which left the former "*-ŭ" stem genitive suffix available for a specialized use. In modern Russian, use of the partitive case is often facultative. In many situations, the partitive and the genitive can be used almost synonymously:,'(partitive) and'(genitive) both mean "a cup of tea";,'(partitive) and'(genitive) both mean "lots of smoke". The partitive variant is preferred with verbs:, ', "to have a drink of tea". The genitive variant is used more frequently when the mass noun is modified by an adjective: ', "a cup of hot tea".

The partitive case (abbreviated or more ambiguously ) is a grammatical case which denotes "partialness", "without result", or "without specific identity". It is also used in contexts where a subgroup is selected from a larger group, or with numbers.

Partitiv (zkratka "PART" nebo "PTV") je mluvnický pád, který označuje „část celku“, „neurčité množství něčeho“. Je typický pro baltofinské jazyky, jako např. finština nebo sámština. V češtině, polštině a dalších jazycích se vyskytuje také tzv. partitivní genitiv (př.: "nabrat vody").


Biography.

Bevk was born in the mountain village of Zakojca (Coizza during Italian rule, now part of the Municipality of Cerkno) in the County of Gorizia and Gradisca of what was then the Austro-Hungarian Empire, now in Slovenia. He was the oldest of eight children born to the tenant farmer and shoemaker Ivan Bevk and his wife Katarina (née Čufer).  Bevk attended school in Bukovo until 1904, and then in Kranj (1905), Koper (1908), and Gorizia (1909), and became a teacher in the Slovene Littoral. His first teaching position was in the village of Orehek. During the First World War he was a soldier on the Eastern Front and for a while at a military school in Hungary.  After the war he worked for various newspapers in Ljubljana. In 1920 he moved to Gorizia dedicating himself to cultural and political activism in the Slovene Littoral, then under Italian rule. He was frequently prosecuted by Italian Fascist authorities and interned for his activities. In 1935 he had to leave the Julian March and moved to Ljubljana, in the Kingdom of Yugoslavia. There, he came in contact with the vibrant cultural life of the Slovenian capital, becoming friends with figures such as the painter Zoran Mušič, writer Vladimir Bartol, political activist and author Lavo Čermelj, literary critic Josip Vidmar and art historian France Stele.  After the Axis invasion of Yugoslavia in April 1941, he was imprisoned by the Italian occupation authorities due to his public Anti-Fascist stance. In 1943, he escaped from prison and joined the Slovene Partisans. After the end of World War II, he moved to Trieste and later back to Ljubljana. In 1953 he became a member of the Slovenian Academy of Sciences and Arts. He received the Prešeren Award, the most prestigious award for artistic achievements in Slovenia, twice, in 1949 and in 1954. He died in Ljubljana on his 80th birthday.

Work.

Bevk started writing at the age of sixteen with encouragement from the influential feminist editor Zofka Kveder. In his early poems, Bevk was influenced by the vitalist poetry of Oton Župančič and Maurice Maeterlinck. After the experience of World War I, he came under the influence of Christian expressionism which represented a strong literary and artistic current in interwar Slovenia. Some of its most talented representatives, such as the poet Joža Lovrenčič and Ivan Pregelj, came from Bevk's native region of Goriška. At first, he followed their examples, but later moved to social realism. He became known in the 1930s with his novels describing the struggle of the Slovene people from the Julian March to maintain their identity against the Fascist Italianization. His best-known work was the novel "Kaplan Martin Čedermac" (The Vicar Martin Čedermac), in which he described the inner struggles of a Roman Catholic priest in the westernmost Slovene ethnic region known as Venetian Slovenia. The novel was published under a pseudonym by the publishing house "Slovenska matica" in 1938 and soon became a best-seller. The term "Čedermac" is still used in Slovene to refer to the Roman Catholic clergy in the Slovene Littoral that struggled to defend the Slovene identity of their flock under the Italian Fascist regime.  Later in his life, Bevk devoted himself largely to children's literature. He was a very prolific author: when a complete bibliography was made on the occasion of his 70th birthday, it was determined that Bevk had written over 100 books.

Legacy.

Although Bevk is still revered as the author of the popular novel "The Vicar Martin Čedermac", he is mostly remembered as an author of children's literature. The regional library in Nova Gorica is named after him, as well as the central square in the town.

France Bevk () (17 September 1890 – 17 September 1970) was a Slovene writer, poet and translator. He also wrote under the pseudonym Pavle Sedmak.

France Bevk (17. září 1890 Zakojca u Cerkenem – 17. září 1970 Lublaň) byl slovinský realistický prozaik a básník, překladatel z bulharštiny. Psal také pod pseudonymem Pavle Sedmak.


Production and composition.

"OMG" was written and produced by The Black Eyed Peas frontman, will.i.am. The tune was recorded at Chung King Studios, New York City. Dylan "3-D" Dresdow mixed the record at Paper V.U. Studios, North Hollywood. The vocal sample of a crowd shouting "owowowo" supposedly taken from Deep Purple's Live at Olympia '96. The song was recorded by will.i.am while performing with The Black Eyed Peas on the French TV show Taratata.  "OMG" is a midtempo pop song, drawing from the subgenres of dance-pop and synthpop, and is also influenced by R&B. The song also infuses hints of Eurodance. Several lines feature the Auto-Tune vocal effect, and makes use of "hypnotic" hand claps, and "Jock Jams"-esque arena chanting. The song is set in common time, and has a tempo of 130 beats per minute. It is written in the key of E minor, and Usher's vocals span from the low note of G to high note of E. It follows the chord progression Em–D–Bm–C. According to James Reed of "The Boston Globe", Usher is featured in a staccato delivery over the song's minimalist dance beat." will.i.am begins the song with the line, "Oh my gosh" then Usher starts singing the chorus. He performs his verse and the second chorus, before will.i.am gives his verse. "OMG" concludes with an extended final chorus. Mikael Wood of "The Los Angeles Times" said that the lyrics of the song detail Usher's encounter with a woman in a club.

Reception.

Critical.

The song has garnered mixed reception, with most critics disapproving of the auto-tuned vocals, and the production and appearance by will.i.am. Edna Gundersen of "USA Today" said that Usher seemed "disengaged" on the song, and allowed will.i.am. to "bludgeon" the song with auto-tune. Greg Kot of the "Chicago Tribune" said the song was one of the tracks where production fell short on "Raymond v. Raymond", calling the song another auto-tuned "formulaic chant" by will.i.am. "The New York Daily News" said that the song is "as annoying as the tech-speak it mimics." Andrew Winistorfer of "Prefix Magazine" preferred "Lil Freak" to be the album's big single, stating that the song "doesn't come close to matching the filthy heights of "Little Freak," "[sic]" but the sports arena chanting thing hasn't been done this well since the '90s when "Jock Jams" were enormous." Winistorfer also said that Usher brought back his "bad taste" in collaborators since Lil Jon on "Yeah!", saying that having the latter on this song would be an improvement.  James Reed of the "Boston Globe" said that Usher "fares better" on the collaboration. Mikael Wood of "The Los Angeles Times" commended the song's "thumping" groove. Gail Mitchell of "Billboard" said that Usher "pumps up the beat on the infectious club anthem." Caroline Sullivan of "The Guardian", called the track "irresistible". Monica Herrera of "Billboard" magazine said the song, like "Yeah!", appealed to a broader audience and attuned to clubs. Herrera also said that "the lyrics are hypnotic hand claps and soccer-game chants that fade in and out to keep the party going".

Controversy.

In 2010, WYOY disc jockeys compared part of Usher's verse to a song sung by Homer Simpson in "Dude, Where's My Ranch?", a 2003 episode of television comedy "The Simpsons". The cadences of the line, "Honey got a booty like pow, pow, pow. Honey got some boobies like wow, oh wow" were compared to those of Homer's tune, "Christmas in December, wow wow wow. Give me tons of presents, now now now." Simon Vozick-Levinson of "Entertainment Weekly" disagreed, calling the likenesses "a random coincidence".

Chart performance.

The song debuted at number fourteen on the "Billboard" Hot 100 selling 130,000 units in its first week. The song became the third-highest debut on the "Billboard" Hot 100 of Usher's career, behind 1997's "Nice & Slow" at number nine, and 1998's "My Way" at eight. For the week ending May 15, 2010, the song lifted to number one on the chart, becoming Usher's ninth number-one single and Will.i.am's first number one single as a solo artist (or without his group, The Black eyed Peas). The song collected airplay and digital gainer honors, moving fourteen to seven on the Hot 100 Airplay chart, and two to one on the Hot Digital Songs chart. The song later topped both charts. By March 2011, the song has reached 4 million in sales, and as of May 2013, the song has sold 4,719,000 copies.  With the song, Usher tied with the Bee Gees, Elton John, and Paul McCartney for ninth among artists all time with the most Hot 100 hits. Usher also became the third male solo artist, behind McCartney and Michael Jackson to collect at least one number-one single from five consecutive albums. The song made Usher the first artist in the 2010s to have a number-one single in three consecutive decades, Usher's being the 1990s, 2000s and 2010s. He became only the fifth artist of all time to accomplish this, the others being Stevie Wonder in the 1960s, 1970s and 1980s; Michael Jackson in the 1970s, 1980s, and 1990s; and Madonna and Janet Jackson in the 1980s, 1990s and 2000s. "OMG" was the second shortest title to lead the chart, tying Jackson's "Ben", "Bad", and "ABC" with the Jackson 5, with Britney Spears' "3" being the chart-topper with the shortest title.  The song charted at number three on the R&B/Hip-Hop Songs chart, two on the Pop Songs chart, and three on the Hot Dance Club Play chart. It also topped the Rhythmic Top 40, making Usher the first artist to collect ten number ones on the chart, above 50 Cent, Beyoncé, Nelly, T-Pain, and Mariah Carey, each with seven. Usher led first on the chart with "You Make Me Wanna" for thirteen weeks from 1997–1998 and "Love in This Club" featuring Young Jeezy in 2008.  "OMG" reached number two in Canada, and was certified Platinum by the Canadian Recording Industry Association. It was later upgraded to 2x Platinum for shipments over 160,000 copies. It sold 223,000 copies during 2010 in Canada. Internationally, "OMG" charted across Europe, reaching number one in the Ireland, and United Kingdom where it became the third best selling song of 2010. It also charted moderately in other countries, allowing it to reach a peak of six on the European Hot 100. In Australia and New Zealand the song placed at the top of the charts. It was certified 2× Platinum by the Australian Recording Industry Association, and Platinum in New Zealand by the Recording Industry Association of New Zealand for shipments of 15,000 units. It was later upgraded to 6× Platinum in Australia for shipments over 420,000 copies.

Music video.

Background.

Usher and will.i.am shot the video the weekend of March 6, 2010. The video was directed by Anthony Mandler. In an interview with "Rap-Up", Mandler said about the concept of the video: "...The video is a spectacle. It really emphasizes what we love about Usher and the character and the icon that he is, and most importantly, it's really a video that showcases his superstardom". The video was released on March 30, 2010, on VEVO and AMTV. According to Mandler, the original idea for the video was citing Max Headroom, a fictional artificial intelligence character from 1980s British television and film. The reference is made when Usher is seen on a flickering television at the beginning of the video. Mandler specified, commenting, "Max Headroom was always in his room," he continued, "this unidentifiable room, '80s shapes. I used that for inspiration." Usher stated that he wanted to do something theatrical and fun, and that while will.i.am. brought the international sound, he wanted to bring the producer into his world, "working off of each other and playing off of each other as artists, but the cinematography would be artistic and incredible." Mandler described the visuals in the clip as "Hitchcock-ian", as well as simply capturing Usher in his element, as he said he wanted the R&B singer's talent to take over. He further explained, stating, "The concept was to create a world where we put Usher in a space where he does what I think he does better than anyone else in the world, which is perform at a level and magnitude of a superstar and take us, the viewer, whether audible or visually, on a journey, not a ride. And, in that, I wanted to create an unpredictability, so one set leads to another and another, and you never know what's gonna happen. Along the way, Usher becomes our guide. We're so focused on him, we don't notice the change. The thing is unfolding little by little, and you can't quite see far enough ahead to know what's gonna come next."

Synopsis and reception.

The video begins with Usher flickering on a television in a room, before we see him in a scene dancing with blue flashing lights, and will.i.am. is shown in a similar room with red flashing lights. Usher is then shown with female background dancers in a white room. In the scene he dons a pair of glasses which show the dancers performing through the lens. Usher then dances outside in front of a concrete wall, with male background dancers appearing as shadows. As will.i.am. performs his verse, he and Usher are seen in their corresponding rooms with flashing lights. After this, Usher puffs a cigar and dances with male background dancers in an arena-like area, whilst he is also joined by female dancers with flashing lights on the floor, with the video ending with Usher shown on the flashing television.  In a review of the video, Brad Wete of "Entertainment Weekly" said, "For a song with such a title, it sure does take a minute for its video to build up to wow-worthy moments. After some clean dance sequences, the magic begins. Usher grooves with shadows, puffs out O's with cigar smoke, and then links back up with his ladies on a primary colored dance floor to show off his steps." Chris Ryan of "MTV News" compared the video's flashing lights to the music video for "Yeah!", and called the song an answer track to Trey Songz's "LOL". At the 2010 MTV Video Music Awards, the clip was nominated for Best Dance Video, Best Choreography, and Best Male Video.

Live performances.

Usher performed the song with will.i.am. on the ninth season of "American Idol", appearing in a black bowler and matching black suit with silver lapels, accompanied by flames and other pyrotechnics. They then performed the song together on "The Oprah Winfrey Show" on May 10, 2010. The song has also been performed live in Australia on "Hey Hey it's Saturday" on May 19, 2010, as well as on "Sunrise" on May 21, 2010. Usher later performed the song on "The Ellen DeGeneres Show", "So You Think You Can Dance", "Good Morning America" and live in the United Kingdom on "Britain's Got Talent". On August 6, 2010, he performed the song alongside other hits at his New Look Foundation's inaugural World Leadership Awards in Atlanta, where his protege Justin Bieber and R&B singer Ciara also performed. Another event the song was performed at was the Activision E3 Event. The song was performed alongside "DJ Got Us Fallin' in Love" during the 2010 MTV Video Music Awards. VMA executive producer Dave Sirulnick told MTV News, "We said to him, 'We want to do the best televised dance routine that you've done in years. Let's show why you're the king.'" MTV Buzzworthy writer, Tamar Antai was present at the rehearsal for the show, and commented that the VMA crew was about to "pull off visual feats not just previously unseen and unparalleled at the VMAs, but unseen and unparalleled on TV."  The performance was received with critical acclaim. On Usher specifically Antai said the performance was like "liquid magic", saying, "He took it to the level that comes after the next level. The penthouse level." He was aided by about a dozen background dancers, the males in skeleton-like costumes, and the females donning a one-piece, gloves and boots. The "OMG" performance was accompanied by red laser lights, making an illusion as if the stage disappeared. The lights spelled out "O.M.G" as well as "Usher", as dancers lowered from the ceiling. Jayson Rodriguez of MTV News commented, "The singer moved and grooved, proving that he's the R&B star that everyone pays attention to for the big moments." Rochell D. Thomas, also of the site said "Call it what you will: talent, swag, skills...When he steps on the dance floor, some mysterious thing comes out of him and puts the G in groove." Thomas went on to say that Usher's dance moves would make "the late great Michael Jackson jealous" in the stage production "that included more special-effects bells and whistles than a summer blockbuster." Chris Ryan of MTV Buzzworthy also compared the performance to Jackson, calling it overall, "One part "Tron," one part laser show, one part Michael Jackson choreo tribute, and all spectacle." Usher appeared with The Black Eyed Peas to perform the song during the Super Bowl XLV halftime show.

Personnel.

Source:

"OMG" is a song by American recording artist Usher and American rapper will.i.am, who also wrote and produced the song. It uses the auto-tune effect in several lines, as well as "Jock Jams"-esque sports arena chanting. It was released on March 22, 2010 as the first worldwide single off his sixth studio album, "Raymond v. Raymond", and the fourth single overall, following the three US singles "Papers", "Hey Daddy (Daddy's Home)", and "Lil Freak". The song was met with a mixed reception from critics, who criticized the use of auto-tune, but commended the song's dance and club vibe. The song marks the second time that Usher has collaborated with will.i.am, following the single "What's Your Name", from his previous album "Here I Stand" (2008).

„OMG“ je píseň amerického R&B zpěváka Ushera. Píseň pochází z jeho šestého studiového alba "Raymond v. Raymond". Produkce se ujal producent Will.i.am. S touto písní mu vypomohl americký R&B zpěvák Will.i.am člen kapely Black Eyed Peas


History.

Formative seasons.

Despite winning the 1966 Memorial Cup, the Edmonton Oil Kings' owner, Bill Hunter, was growing concerned about the state of junior hockey in western Canada. Each of the West's four provinces had its own junior league, and Hunter felt that this put them at a disadvantage when competing nationally against the powerful leagues in Ontario and Quebec. Desiring stronger competition, Hunter's Oil Kings competed in the Alberta Senior Hockey League rather than the Alberta Junior Hockey League. During the 1966 Memorial Cup, Hunter made newspaper headlines when he stated his vision for a nation-wide junior ice hockey league competing for the Memorial Cup. The Canadian Amateur Hockey Association (CAHA) second vice-president Lloyd Pollock responded by saying that the idea would be nothing more than a pipe dream, and would not be feasible while the CAHA was renegotiating a development agreement with the National Hockey League.  The CAHA informed the Oil Kings that they were required to play in a junior hockey league for the 1966–67 season or would be held ineligible to compete for the Memorial Cup. This led Hunter to form a new league with five former members of the Saskatchewan Junior Hockey League (SJHL), the Estevan Bruins, Regina Pats, Saskatoon Blades, Moose Jaw Canucks, and Weyburn Red Wings, to leave the SJHL and join the Oil Kings and the Calgary Buffaloes in a new league known as the Canadian Major Junior Hockey League. Despite concerns that this new league would see the demise of the Alberta and Saskatchewan leagues, the governing bodies in both provinces sanctioned the new league. The CAHA did not, however, declaring the CMJHL to be an "outlaw league" and suspending all teams and players from participation in CAHA sanctioned events. The new league accused the CAHA of overstepping its boundaries and with the support of the players and their families, chose to play the season regardless. The CMJHL began legal action against the CAHA executive in March 1967, since the CAHA had suspended CMJHL teams and ruled the teams ineligible for the Memorial Cup playoffs.  In May 1967, the CMJHL renamed itself to the Western Canada Junior Hockey League (WCJHL). Initially, the new league deliberately avoided including the term "Western" in its moniker, as some of its founders wanted to keep open the possibility of inviting top Eastern junior clubs to join in a national elite junior league in case negotiations with the CAHA reached a complete impasse. The new CAHA-NHL development agreement came into effect July 1, 1967. The new pact ended direct sponsorship of junior teams by the NHL which then paid development fees to the CAHA, and junior players became eligible for the NHL Entry Draft at age 20. In May 1968, Bill Hunter announced the league would use an age limit of 21 in defiance of the CAHA and NHL agreement. The WCJHL stopped short of declaring independence from the CAHA, and claimed that the lower age limit would decrease its talent pool and negatively affect ticket sales. In response, the CAHA suspended league and its players.  On June 10, 1968, the WCJHL announced a name change to the Western Canada Hockey League (WCHL), and that it was leaving the CAHA to affiliate with the rival Canadian Hockey Association (CHA). Hunter became chairman of the board for the WCHL, and Ron Butlin became president of the WCHL and the CHA. Four new teams were added in 1968 to total 11 as the league stretched east into Manitoba. Concerns over the WCHL's relationship with the CAHA led the Pats, Canucks and Red Wings to withdraw before the 1968–69 season, returning to the SJHL.  When the CAHA reorganized junior hockey in 1971, it reunited with the WCHL making it one of three Tier I Major-Junior leagues, along with the Ontario Hockey Association's Tier I division (now the Ontario Hockey League) and the Quebec Major Junior Hockey League.

Early years.

The first decade of the WCHL saw constant expansion and franchise movement as the league spread throughout the West. The Flin Flon Bombers became the league's first powerhouse team, led by future NHL stars Bobby Clarke and Reggie Leach. The Brandon Wheat Kings and Swift Current Broncos joined in 1967, the Medicine Hat Tigers in 1970. The WCHL truly became a western league in 1971 when Estevan moved to B.C. to become the New Westminster Bruins, joined by expansion franchises the Victoria Cougars and Vancouver Nats.  In the mid 1970s, the New Westminster Bruins became the WCHL's first true dynasty, capturing four consecutive championships between 1975 and 1978. The Bruins also won back-to-back Memorial Cups in 1977 and 1978.  In 1976, the Oil Kings succumbed to the competing Edmonton Oilers of the World Hockey Association and relocated to Portland to become the Winter Hawks, the WCHL's first American franchise. With the addition of American teams in Seattle and Billings a year later, the WCHL shortened its name to the "Western Hockey League".

The Brawling '80s.

The 1980s were marked by several brawls that involved police intervention, one of the most bizarre trades in hockey history, and the tragic deaths of four players in a bus crash.  Early in the 1980–81 WHL season, Medicine Hat Tigers GM/Coach Pat Ginnell traded blows with a linesman during a bench clearing brawl against the Lethbridge Broncos. Ginnell was found guilty of assault, fined $360, and suspended for 36 games by the WHL. In March 1982 a violent brawl between the Regina Pats and Calgary Wranglers saw the two teams collectively fined $2250 and players suspended for 73 games combined. Pats coach Bill LaForge would end up in a courtroom later that season when he got into an altercation with a fan. LaForge was acquitted when the judge noted that it was hard to convict a man for assault when faced with "an obnoxious person trying to get into the coach's area." LaForge resigned following the season after serving three separate suspensions.  On January 19, 1983, the Seattle Breakers dealt Tom Martin and $35,000 to the Victoria Cougars for the Cougars' team bus. The deal made perfect sense upon further examination: the Breakers were unable to sign Martin, who wanted to play in his home town of Victoria, and the Cougars were unable to use the bus (which they had purchased from the folded Spokane Flyers) because they were unwilling to pay the taxes and duties required to register the vehicle in Canada.  On December 30, 1986, tragedy struck the Swift Current Broncos when their bus slid off an icy highway and rolled on the way to Regina for a game. Scott Kruger, Trent Kresse, Brent Ruff, and Chris Mantyka were killed. The Broncos retired their numbers, and still wear a commemorative patch in remembrance of the four players who died. The WHL later renamed its award for most valuable player as the Four Broncos Memorial Trophy in their honour.

The 1990s to today.

Since the early 1990s, the WHL has seen another period of expansion and the return of the league to Western Canada's major cities. The Kamloops Blazers became the WHL's second dynasty in the early 1990s when they won both the WHL Championship and Memorial Cup three times in four years between 1992 and 1995. The Kelowna Rockets became the third dynasty, winning three WHL titles in 2003, 2005, and 2009; and winning the Memorial Cup as host city in 2004. The Portland Winter Hawks won their second Memorial Cup in 1998.  In 1995, the Calgary Hitmen, founded by a group of investors including Bret "the Hitman" Hart from whom the team got its name, were granted an expansion franchise. Despite early fears that the WHL could not succeed in an NHL city, the Hitmen were a success, averaging as many as 10,000 fans per game in 2004–05. The Hitmen were followed one year later by the Edmonton Ice, but failed after only two seasons because of conflicts with the Edmonton Oilers. The team became the Kootenay Ice and had better success in Cranbrook, British Columbia, despite being one of the smallest markets in the league including winning the 2002 Memorial Cup.  In the 2000s, the league expanded with four more teams — the Vancouver Giants in 2001, the Everett Silvertips in 2003, the Chilliwack Bruins in 2005 (who relocated in 2011 to become the Victoria Royals), and the Edmonton Oil Kings in 2007, as the Oilers have taken an interest in cultivating a junior team within their home market in the Alberta capital.  Since 2006 Shaw TV has become the television partner with the league in Canada airing a game every Friday Night and other select games throughout the season as well as one round of every playoff series. From 2008 to 2015, FSN Northwest (now Root Sports Northwest) aired some games throughout the northwest United States.  On February 21, 2011, the Calgary Hitmen hosted the Regina Pats, Canada's oldest major junior hockey team, at McMahon Stadium for an outdoor game in conjunction with the 2011 Heritage Classic. The WHL teams wore retro inspired jerseys. The Spokane Chiefs also hosted the Kootenay Ice outdoors on January 15, 2011. The 2010–11 season was the first for the league to be featured in video game, EA Sports' "NHL 11", and included all the teams and rosters.  On January 29, 2019, the Kootenay Ice announced the team would be relocated to Winnipeg for the 2019–20 season as the Winnipeg Ice.

Member teams.

For the 2017–18 season, the WHL comprises 22 teams divided into two conferences, making it the largest league in the CHL; the Ontario Hockey League has 20 teams and the Quebec Major Junior Hockey League has 18. The WHL has member teams across four Canadian provinces, and two American states. The Eastern Conference comprises teams from Manitoba, Saskatchewan, and Alberta. The Western Conference is made up of teams based in British Columbia, Washington and Oregon.  The top eight teams in each conference qualify for the playoffs, with the division winners declared the top two seeds in the first round of the post-season. The four remaining teams in each conference are reseeded by regular season points in the second round of the playoffs. The Saskatoon Blades, one of the original WHL teams, are the only team to never have won a league championship since their inception in 1966.

Timeline of franchises (since 1966).

Education.

The WHL has taken a much greater role in its players educational needs in recent years. The league operates a scholarship program that offers one full year of tuition, textbooks and compulsory fees for each season they play in the WHL. Since the program was introduced in 1993, more than 3000 scholarships of this calibre have been handed out at a total value of C$9 million. Each team maintains an academic advisor, who monitors the academic progress of all players along with the league's Director of Education Services.  Canadian universities and colleges recruit extensively from the WHL, affording graduating players the opportunity to continue playing hockey as they attend post-secondary institutions. The U.S. National Collegiate Athletic Association (NCAA), though, considers graduates of the WHL (and the other two CHL members, the OHL and QMJHL) to be professionals and thus ineligible to participate in college hockey programs in the United States. Players hoping to receive scholarships to, and play for, American universities must play Junior A hockey in one of the Canadian Junior Hockey League's member organizations or the United States Hockey League to retain their NCAA eligibility.

Player eligibility.

The WHL Bantam Draft is an annual event which teams select players from bantam hockey league age groups, 14 or 15 years old. The order of selection depends on the final standings of the teams, the last place team selects first the second to last will choose second and so on.  Players aged 15–20 are eligible to play in the WHL, though 15-year-olds are permitted to play only five games unless their midget team's season has ended. Also, each team is allowed to have only three 20-year-olds on their rosters, unless there is an expansion team, in which case five 20-year-olds are eligible to play. Each team is permitted to carry only two non-North American players. Each of the CHL's three member leagues are granted exclusive territorial rights to players from within North America. The WHL holds rights to players from the four western provinces, the U.S. Pacific Northwest, all other U.S. states west of the Mississippi River (except Missouri), and the Yukon, Northwest Territories and Nunavut.

Memorial Cup champions.

The Memorial Cup has been captured by a WHL team 19 times since the league's founding.

Records.

Individual  Team

The Western Hockey League (WHL) is a major junior ice hockey league based in Western Canada and the Northwestern United States. The WHL is one of three leagues that constitutes the Canadian Hockey League (CHL) as the highest level of junior hockey in Canada. Teams play for the Ed Chynoweth Cup, with the winner moving on to play for the Memorial Cup, Canada's national junior championship. WHL teams have won the Memorial Cup 19 times since the league became eligible to compete for the trophy. Many players have been drafted from WHL teams, and have found success at various levels of professional hockey, including the National Hockey League (NHL).

Western Hockey League (užívá zkratku WHL, česky Západní hokejová liga) je jedna z trojice nejprestižnějších juniorských lig v Kanadě a USA. Dalšími soutěžemi jsou Ontario Hockey League a Quebec Major Junior Hockey League. V těchto soutěžích působí největší talenty zámořského hokeje, v posledních letech mají se tendenci do nich přesouvat i mladí Evropané. V soutěži smí hrát hráči od 16 let (v případě velkého talentu se udělují výjimky). Hokejista v lize působnost ukončí v sezoně, na jejímž konci je mu 21 let.


Playing career.

As a youth, Francis played in the 1975 and 1976 Quebec International Pee-Wee Hockey Tournaments with a minor ice hockey team from Sault Ste. Marie, Ontario.  Francis was drafted by the Hartford Whalers in the first round, fourth overall, of the 1981 NHL Entry Draft. He was a model of consistency and durability, averaging more than a point a game in over 1,700 games in 23 seasons, and (not counting the lockout-shortened 1994–95 season) averaging just under 77 games played a season. His three Lady Byng Trophies attest to his gentlemanly conduct on and off the ice. Francis stands second all-time in career assists behind Wayne Gretzky with 1,249, fifth in career points (1,798), third in games played (1,731), and twenty-sixth in career goals (549).  Francis played almost ten seasons with the Whalers, serving as captain for almost six and setting nearly every offensive record in franchise history. He was traded to the Pittsburgh Penguins on March 4, 1991 with Ulf Samuelsson and Grant Jennings, in exchange for Jeff Parker, Zarley Zalapski, and John Cullen. The trade became a coup for Pittsburgh, where he centred a formidable second line behind Mario Lemieux, as the Penguins won their first Stanley Cup less than three months later. The threat posed by the Francis-centered second line, formidable in its own right, often required opposing teams to throw their best defenseman against two lines, instead of zeroing in on Lemieux's line, thus creating more opportunities for both top lines. Francis was also known as one of the best face-off men in the NHL in this period, in both the offensive and defensive ends. In power-play and empty-net situations, his key face-off wins often led to Penguin goals.  Francis was indispensable the following year, as Pittsburgh repeated as champions, in leading the team during the absence of Lemieux in the 1992 playoffs – and in scoring the Cup-clinching goal against the Chicago Blackhawks. At the same time, the trade that brought him to Pittsburgh is considered to be one of the most one-sided trades in NHL history (though "The Hockey News" suggested that Hartford had gotten the better end of the trade at the time); the players Hartford acquired never approached the numbers or impact Francis produced there or with Pittsburgh. Francis would spend seven seasons in Pittsburgh, captaining the team twice, and becoming the first Penguin to win the Selke Trophy in 1995.  Francis returned to his original organization as a free agent for 1998–99, signing with the Carolina Hurricanes (who had moved from Hartford the previous season). He spent the next 5.5 seasons padding his franchise records. He still ranks first all-time in Whalers/Hurricanes history in points, goals, assists and games played. At the time of his retirement, his 1,175 points were more than double those of then-runner up Kevin Dineen. He captained the Hurricanes to a surprise appearance in the 2002 Stanley Cup Finals and scored the winning goal for the Hurricanes in overtime of Game 1, before losing to the Detroit Red Wings in five games.  Francis finished his career with a brief stint with the Toronto Maple Leafs, traded there by the Hurricanes in March 2004 to allow him one last run at the Stanley Cup. He retired from the NHL before the 2005–06 season and assumed a position with the Raleigh Youth Hockey Association.

Management career.

In June 2011, Francis assumed the position of director of hockey operations with the Carolina Hurricanes before later being named general manager of the team in 2014. On March 7, 2018, Francis was named president of hockey operations by new Hurricanes' majority owner Thomas Dundon. His Hurricanes contract was terminated on April 30, 2018. On July 18, 2019, Francis was named the first general manager of the upcoming Seattle NHL team.

Personal life.

Francis is married to the former Mary Lou Robie, a native of Stamford, Connecticut whom he met in Hartford during his tenure with the Whalers. They married in 1986 and have three children: Kaitlyn (b. 1991), Michael (b. 1993), and Connor (b. 1996). Francis is considered a popular sports figure in Hartford, Pittsburgh and Raleigh, and is also noted for his humanitarian and charity work. Francis also has the distinction of being the first ice hockey player inducted into the North Carolina Sports Hall of Fame. Francis was born in Sault Ste. Marie, Ontario, Canada. He is second cousin with Mike Liut.

Awards and achievements.

Francis won two Stanley Cups, in 1990–91 and the following season, with the Pittsburgh Penguins. Statistically, his best season was 1995–96, when he recorded 119 points; that season, he led the NHL in assists, with 92. The previous season, he had not only led the League in assists with 48 over the lockout-shortened, half-season schedule, but became the first player to win both the Frank J. Selke Trophy and the Lady Byng Trophy in the same season.  Francis' Whalers number 10 jersey was raised at the Hartford Civic Center on January 6, 2006 (though not officially retired, the Whalers organization no longer existing to retire it), along with Ulf Samuelsson's number 5 and Kevin Dineen's number 11. Additionally, his Hurricanes number 10 jersey was retired by the Carolina organization on January 28, 2006. He was also pictured in the Pittsburgh Penguins Ring of Honor that formerly circled the upper level of the Pittsburgh Civic Arena.  On June 28, 2007, Francis was selected to enter the Hockey Hall of Fame in his first year on the ballot. He was formally inducted on November 12, 2007.

Ronald Michael Francis Jr. (born March 1, 1963) is a Canadian former professional ice hockey centre. He is the general manager of the upcoming Seattle NHL team that plans to play its first season in 2021. Drafted fourth overall in the 1981 NHL Entry Draft, Francis played 23 seasons in the NHL for the Hartford Whalers, Pittsburgh Penguins, Carolina Hurricanes and Toronto Maple Leafs. Upon retiring from professional ice hockey in 2004, Francis stood second all-time in career assists (1,249), behind only Wayne Gretzky; fifth in career points (1,798); third in games played (1,731); and 27th in career goals (549).

Ron Francis (* 1. března 1963, Sault Ste. Marie, Kanada) je bývalý kanadský hokejista. V National Hockey League odehrál 23 sezón a v historickém pořadí produktivity NHL patří k nejlepším hráčům. U příležitosti 100. výročí NHL byl v lednu 2017 vybrán jako jeden ze sta nejlepších hráčů historie ligy. Je generálním manažerem nadcházejícího týmu NHL Seattle.


Design.

The first eight submarines initially deployed with the Polaris A-2 missile, later being refitted with the longer ranged Polaris A-3, with having the A-3 missile from the start. In the mid-1970s all were upgraded to carry the Poseidon C3 missile; their missile tubes were slightly larger than the "Ethan Allen" and "George Washington" classes and Poseidon was designed to take advantage of this. Unlike twelve of the similar "James Madison" and "Benjamin Franklin" classes, none of the "Lafayette"-class submarines were refitted with Trident I (C4) missiles.  The "Lafayette"s and their successors were equipped with a hovering system to manage trim more effectively when firing missiles; this increased the missile rate of fire from one per minute to four per minute.  "Daniel Webster" was originally built with diving planes mounted on a "mini-sail" near the bow, leading to her nickname "Old Funny Fins". This configuration, unique to US submarines, was an attempt to reduce the effect of porpoising. While successful, the "mini-sail" required to contain the operating mechanism reduced hydrodynamic efficiency and lowered her overall speed. During a mid-1970s overhaul these unusual planes were removed and standard fairwater planes were installed.

Fate.

The "Lafayette"s were decommissioned between 1986 and 1992, due to a combination of SALT II treaty limitations as the SSBNs entered service, age, and the collapse of the Soviet Union. One ("Daniel Webster") remains out of commission but converted to a Moored Training Ship (MTS-626) with the missile compartment removed. She is stationed at Nuclear Power Training Unit Charleston, South Carolina, along with.

Boats in class.

Submarines of the "Lafayette" class:

The "Lafayette" class of submarine was an evolutionary development from the of fleet ballistic missile submarine, slightly larger and generally improved. This class, together with the,,, and classes, composed the "41 for Freedom," the Navy's primary contribution to the nuclear deterrent force through the late 1980s. The "James Madison" and "Benjamin Franklin" classes are combined with the "Lafayette"s in some references.

Třída Lafayette byla americká třída raketonosných ponorek s jaderným pohonem z éry studené války. V letech 1961–1964 bylo postaveno celkem devět ponorek této třídy. Američané je provozovali v letech 1963–1994. Vyřazovány byly počínaje rokem 1986. Jako poslední byl v roce 1994 vyřazen "Woodrow Wilson". Po vyřazení bylo prvních osm jednotek odesláno do recyklačního programu k sešrotování, zatímco ponorka "Daniel Webster" se dochovala jako muzejní loď.


General mechanism.

When a solution of nitrate ions is mixed with aqueous sodium hydroxide, adding Devarda's alloy and heating the mixture gently, liberates ammonia gas. After conversion under the form of ammonia, the total nitrogen is then determined by Kjeldahl method.  The reduction of nitrate by the Devarda's alloy is given by the following equation:

Distinction between NO and NO with spot tests.

To distinguish between nitrate and nitrite dilute HCl must be added to the nitrate. The Brown Ring Test can also be used.

Similarity with the Marsh test.

Devarda's alloy is a reducing agent that was commonly used in wet analytical chemistry to produce so-called nascent hydrogen under alkaline conditions "in situ". In the Marsh test, used for arsenic determination, hydrogen is generated by contacting zinc powder with hydrochloric acid. So, hydrogen can be conveniently produced at low or high pH, according to the volatility of the species to be detected. Acid conditions in the Marsh test promote the fast escape of the arsine gas (AsH), while in hyperalkaline solution, the degassing of the reduced ammonia (NH) is greatly facilitated.

Long-debated question of the nascent hydrogen.

Since the mid-19th century the existence of true nascent hydrogen has repeatedly been challenged. It was assumed by the supporters of this theory that, before two hydrogen atoms can recombine into a more stable H molecule, the labile H· free radicals are more reactive than molecular H, a relatively weak reductant in the absence of a metal catalyst. Nascent hydrogen was supposed to be responsible for the reduction of arsenate or nitrate in arsine or ammonia respectively. Nowadays, isotopic evidence has closed the nascent hydrogen debate, presently considered to be a "Gedanken" artifact of romanticism.

Devarda's alloy (CAS # 8049-11-4), is an alloy of aluminium (44% – 46%), copper (49% – 51%) and zinc (4% – 6%).

někdy nesprávně též Dewardova slitina či Dewarova slitina je slitina mědi, zinku a hliníku. Autorem je Arturo Devarda (1859-1944). Složení:


Formula.

The Hagenbach-Bischoff quota may be given as:  where:  The Droop quota's formula is slightly different in that the quotient arrived at by dividing the total vote by the number of seats plus 1 is rounded up if it is fractional, or if it is a whole number, 1 is added, so that in either case the quotient is increased to the next whole number.

An example of use in STV.

To see how the Hagenbach-Bischoff quota would work in an STV election imagine an election in which there are 2 seats to be filled and 3 candidates: Andrea, Carter, Brad. There are 100 voters who vote as follows:  Because there are 100 votes cast, and 2 seats, the Hagenbach-Bischoff is:  To begin the count the first preferences cast for each candidate are tallied and are as follows:  Andrea has more than 331⁄3 votes. She therefore has reached the quota and is declared elected. She has 112⁄3 votes more than the quota. These votes are transferred to Carter so the tallies become:  Carter has now reached the quota so he is declared elected. The winners are therefore Andrea and Carter.

Advantage over the Droop quota.

Some voting systems experts, such as Christine Cierra Danica, have observed that in an STV election held under the Droop quota it is sometimes possible for a group of candidates supported by a majority of voters to receive only a minority of seats. Such an outcome is far more likely under the older Hare quota but can still occur under the Droop quota in rare circumstances. It is a possibility that is only completely eliminated by use of the Hagenbach-Bischoff quota. The problem is best illustrated by an example.

Scenario.

Imagine an election in which there are 7 seats to be filled. There are 8 candidates standing, in two groups: Andrea, Carter, Brad and Delilah are members of the Alpha party; Scott, Jennifer, Matt and Susan are members of the Beta party. There are 104 voters and they vote as follows:  It can be seen that supporters of the Alpha party all rank all four Alpha party candidates higher than any of the Beta party candidates (the last four preferences of the voters are not shown above because they will not affect the result of the election). Similarly, voters who support the Beta party all give their first four preferences to Beta party candidates. Overall, the Alpha party receives 53 votes out of a total of 104. The Alpha party therefore has a majority of one. The Beta party receives a minority share of the vote.  Below the election results are shown first under the Droop and then under the Hagenbach-Bischoff quota. It can be seen that under the Droop quota, despite having the support of a majority of voters, the Alpha party receives only a minority of seats. When the same election is conducted under the Hagenbach-Bischoff quota, however, the Alpha party's majority is rewarded with a majority of seats.

Count under the Hagenbach-Bischoff quota.

The elected candidates are Andrea, Carter, Brad and "Delilah" (from the Alpha party) and Scott, Jennifer and Matt (from the Beta party).

Disadvantage of Hagenbach-Bischoff quota.

In STV-like system with larger quotas (such as Hare or Droop), the typical rule is that candidates are elected when their number of votes "equals or exceeds" the quota. If this rule is used with the Hagenbach-Bischoff quota, it is possible that more candidates are elected than there are seats. Imagine an election with three candidates for two positions where the 300 votes are  The Hagenbach-Bischoff quota is 300/(2+1) = 100. In the first round Andrea is elected with 200 preferences, while Brad (75) and Carter (25) remain in contention. Andrea's surplus of 100 is transferred: 25 to Brad and 75 to Carter, bringing each of them to 100. So all three have achieved the quota and so should be elected even though there are only two positions to fill.  This problem is easily resolved, as suggested by Irwin Mann in 1973, by adjusting the rule so candidates are only elected when their number of votes strictly "exceeds" the quota (not necessarily by so large a fraction as to reach the Droop quota).  Alternatively, B. L. Meek proposed treating the result as an n+1-way tie, and eliminating one of the candidates at random; still another solution would call for a runoff between the candidates.

The Hagenbach-Bischoff quota (also known as the Newland-Britton quota or the exact Droop quota, as opposed to the more common rounded Droop quota) is a formula used in some voting systems based on proportional representation (PR). It is used in some elections held under the largest remainder method of party-list proportional representation as well as in a variant of the D'Hondt method known as the Hagenbach-Bischoff system. The Hagenbach-Bischoff quota is named for its inventor, Swiss professor of physics and mathematics Eduard Hagenbach-Bischoff (1833–1910)

Hagenbach-Bischoffova kvóta je typem volební kvóty, podle níž se provádí výpočet "volebního (mandátového) čísla", tedy určení minimální hranice množství hlasů potřebných k zisku mandátu v rámci prvního skrutinia, a to ve vícemandátových volebních obvodech. Jedná se o jednoduchý matematický model. Název získala po švýcarském matematikovi a fyzikovi Eduardu Hagenbach-Bischoffovi.