title: Big Bad Beetleborgs

text: Shout! Factory began putting the series out on DVD with the October 16, 2012 release of "Beetleborgs: Season 1, Part 1". "Season 1, Part 2" was released on February 12, 2013. "Season 2, Part 1" was released on June 11, 2013. "Season 2, Part 2" was released on May 5, 2015.


title: Iker Muniain

text: Iker Muniain Goñi (, ; born 19 December 1992) is a Spanish footballer who plays for Athletic Bilbao, where he is captain, mainly as a left winger.


title: Iker Muniain

text: Due to his style of play and stature, he was dubbed "the Spanish Messi" by the media. He has spent all of his professional career with Athletic Bilbao after debuting in 2009 as their youngest player in a competitive match. He helped the team reach the final of the UEFA Europa League in 2012 as well as four Copa del Rey finals in nine years, though finished on the losing side each time; in 2022 he became the sixth player to make 500 appearances for the club.


title: Iker Muniain

text: Muniain made 59 appearances for Spain at youth level, winning the European Under-21 Championship in 2011 and 2013. He also featured at the 2012 Olympics, in the same year as his senior Spain debut. He was selected again in 2019, gaining a second international cap seven years after the first.


title: Iker Muniain

text: Born in Pamplona, Navarre, Muniain was a product of Basque giants Athletic Bilbao's youth ranks after joining at the age of 12. In January 2009, he made his debut for the reserve team Bilbao Athletic in the Segunda División B, aged 16 years and 16 days, and scored his first goal at that level 19 days later.


title: Iker Muniain

text: Muniain made his first-team debut on 30 July 2009, in a UEFA Europa League qualifying match against BSC Young Boys: he entered the field as a 59th-minute substitute for Gaizka Toquero in an eventual 1–0 home defeat, thus becoming the youngest player in 94 years to wear Athletic's shirt in an official game at 16 years, 7 months and 11 days old, only behind Domingo Acedo who scored on his debut in 1914. One week later, in the return leg in Switzerland, he netted his first goal, in a 2–1 win that qualified for the playoff rounds; he again entered the club's record books as the joint-second-youngest player to find the net (16 years, 7 months and 18 days) in a competitive match – behind Acedo and level with Agustín Gaínza– and the youngest ever in a European match.


title: Iker Muniain

text: Another record fell on 30 August 2009, as Muniain started in the 1–0 home victory over RCD Espanyol, 2009–10's opener, becoming the youngest player to have donned the club's shirt in La Liga (overtaking Patxi Ferreira). Two weeks later he scored again in European competition, 3–0 at home against FK Austria Wien, after a good team move involving Andoni Iraola and veteran Joseba Etxeberria.


title: Iker Muniain

text: On 4 October 2009, Muniain became the youngest player to score in a first division match as he achieved that feat in a 2–2 draw at Real Valladolid, aged 16 years and 289 days– that record was surpassed by Málaga CF's Fabrice Olinga in August 2012. On 1 December he signed his first professional contract, running until June 2015. On the 6th, after nearly one month out due to injury, he returned to action, scoring as a 51st-minute substitute to give his team the lead, albeit in a 2–1 loss to Valencia CF. He set up both goals in the next game, a 2–1 win at Real Zaragoza, and finished his first senior season with 35 appearances and six goals across all competitions.


title: Iker Muniain

text: Muniain was an undisputed starter in the 2010–11 campaign, featuring as a left winger for the Joaquín Caparrós-led side. On 17 April 2011, he scored a last-minute goal in a 2–1 away defeat of CA Osasuna in his hometown; he was initially booked for taking his hand to his ear during his celebrations (before signing for Athletic he played for UDC Txantrea in Pamplona, and always considered Osasuna a rival organisation. He did clarify that, just because he had affection for a particular organisation, it did not mean he held any animosity towards any others) which meant a suspension for his fifth yellow card of the season, but it was later lifted. Now allowed to take part in the following matchday, the derby against Real Sociedad, he netted another in a 2–1 home victory.


title: Iker Muniain

text: Muniain took part in 58 games overall in 2011–12, scoring on nine occasions as the "Lions" reached both the Europa League and the Copa del Rey finals. In early 2012, he was linked with a move away from Athletic, although a move never materialised as he did not push for a move with three years still left on his contract. He scored just once in 33 league appearances the following campaign, netting the only goal on 10 March 2013 in a home win over Valencia which eased doubts over a possible relegation battle.


title: Iker Muniain

text: On 1 December 2013, Muniain was again the sole name on the scoresheet at the new San Mamés Stadium, to hand FC Barcelona their first league loss of that season. Eighteen days later, he celebrated his 21st birthday by grabbing a brace in a 4–0 domestic cup home victory against RC Celta de Vigo, which signified his team progressed through to the round of 16 4–1 on aggregate. In that period, media reports suggested that his progression as a footballer in his 20s had slowed after showing such high potential as a young teenager.


title: Iker Muniain

text: On 4 April 2015, during a game against Sevilla FC, Muniain suffered the first serious injury of his career, being sidelined for several months with an anterior cruciate ligament ailment to his left knee– this meant he was unable to take any part in the year's Spanish Cup or Supercopa de España finals. After suffering some setbacks in his recovery process he returned to action on 20 December, replacing Iñaki Williams for the last minutes of a 2–0 home defeat of Levante UD.


title: Iker Muniain

text: Muniain successfully regained his first-team place in December 2015 and made 86 further appearances between then and 28 September 2017, when he suffered another serious ACL injury (this time to his right knee) in the closing stages of a Europa League fixture at home to FC Zorya Luhansk, potentially ending his season. After an absence of just over six months, he returned to action as a substitute in a domestic league match against Villarreal CF on 9 April 2018, scoring his side's third in a 3–1 away win.


title: Iker Muniain

text: Muniain signed a new deal with Athletic Bilbao in November 2018 to run until summer 2024, as his link was set to expire; unusually, it did not include any buyout clause. He said: "I didn’t want a release clause because I do not want to have a price or be for sale. I want to go hand in hand with Athletic to the end... I want to be here for the rest of my career helping the club achieve nice things." Following the departures of Ander Iturraspe and Markel Susaeta in summer 2019 he was appointed as the club captain, and also reached the milestone of ten years with the first team.


title: Iker Muniain

text: On 19 January 2020, Muniain became the 18th player in Athletic's history to play 400 official games, against Celta. In July of that year, his 420th match set the club record for a player from Navarre, surpassing Ismael Urzaiz. On 8 November, he made his 430th appearance to enter its top 10 (equalling Julen Guerrero's total) at the age of 27.


title: Iker Muniain

text: In early 2021, with the team playing a more attacking style under new coach Marcelino García Toral, Muniain recorded eight assists in three competitions between 17 January and 15 February (bettering his total for some entire seasons previously), including two in the Spanish Supercup final as his team won the trophy. During April of that year he took the field in the 2020 (delayed due to the COVID-19 pandemic) and 2021 Spanish Cup finals, both played in an empty Estadio de la Cartuja – the same venue as the Supercup win – due to the pandemic restrictions. Athletic lost the first match 1–0 to Real Sociedad, with Muniain breaking a footballing superstition before kick-off by touching the trophy (considered to be 'bad luck') but praised for his sportsmanship for staying on the pitch after the final whistle to applaud the winners. A pre-match injury doubt for the second final two weeks later, he stated to the press "Cups and trophies are not won or lost because one touches it or not. They are won on the pitch, and that is the only reality", but this time it was noted he kept his hands well away from the prize; nevertheless his team were defeated 4–0 by Barcelona and he was withdrawn at half-time with the score at 0–0 and did not feature again that season, missing the last eight league fixtures.


title: Iker Muniain

text: On 31 October 2021, Muniain scored a late equaliser in the Basque derby via a free kick and was again conspicuous for his sportsmanship in consoling the opposing goalkeeper Álex Remiro, a former Athletic player whose error had contributed to the goal. In February 2022, it was assessed that he had created 60 scoring chances in that league campaign and 72 in all competitions, the most by any player by both counts.


title: Iker Muniain

text: Muniain made his 500th appearance for Athletic on the first matchday of 2022–23 against RCD Mallorca, reaching the milestone at a younger age than the five other players to do so. He was honoured in a reception after that match, and was presented with a momento by two of those men – José Ángel Iribar and Susaeta – on the pitch before the next fixture against Valencia six days later.


title: Iker Muniain

text: On 8 February 2011, at the age of only 18, Muniain made his debut with the Spain under-21 team in a match against Denmark, replacing Adrián López. Subsequently, he was selected by manager Luis Milla to the squad that appeared in the 2011 UEFA European Championship, appearing in all the games as the nation won its third title in the category and qualified to the 2012 Summer Olympics.


title: Iker Muniain

text: On 24 February 2012, Muniain was called up to the senior side for the first time, for a friendly with Venezuela. Five days later, he came on for Cesc Fàbregas in the 74th minute of the 5–0 win in Málaga. Later that year, at the Summer Olympic Games in London, he made two appearances as Spain exited in the group stage without scoring a goal.


title: Iker Muniain

text: Muniain earned 31 caps for the under-21s, which was a national record for three years before being surpassed by Gerard Deulofeu. In 2019, after showing fine form for his club, he was selected in the senior squad for two UEFA Euro 2020 qualifying matches; he played his second match more than seven years after the first, as well as his competitive debut, as a substitute in a 2–0 victory over Malta on 26 March.


title: Iker Muniain

text: Muniain has two older cousins who are also footballers, were both Athletic youth players and were briefly his teammates at Bilbao Athletic. Adrien Goñi, a midfielder, made a handful of first-team appearances before embarking on a career in the Spanish third division. Winger Julen Goñi eventually moved to Barakaldo CF also in that tier, but departed when they were relegated and did not find another club at that level.


title: Iker Muniain

text: Muniain's son was born in February 2015, with the player announcing his girlfriend's pregnancy in August 2014 by gesturing while celebrating his goal against S.S.C. Napoli in the play-off of the UEFA Champions League. He is an admirer of Sergio Agüero, and named his pet Labrador "Kun" after the Argentina international; Muniain's own nickname, Bart Simpson, was given to him by Fernando Amorebieta due to his mischievous personality as well as his diminutive stature and fair hair.


title: Iker Muniain

text: Having vowed to have the Europa League trophy tattooed on his body if Athletic Bilbao won the 2012 final, which did not happen, Muniain did have the Supercopa de España trophy 'inked' on his leg in 2015 following the team's victory (albeit he took no part in the matches due to injury). Another tattoo on the rear of his neck, "XIX", (19 in Roman numerals) refers to his birth date and that of his brother, and was his original Athletic squad number for several seasons although he wore 27 as a promoted youth player in his breakthrough campaign, and in 2016 changed to the traditional playmaker's number 10.


title: Saul Kripke

text: Saul Aaron Kripke (; November 13, 1940 – September 15, 2022) was an American philosopher and logician in the analytic tradition. He was 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.


title: Saul Kripke

text: Kripke made influential and original contributions to logic, especially modal logic. His principal contribution is a semantics for modal logic involving possible worlds, now called Kripke semantics. He received the 2001 Schock Prize in Logic and Philosophy.


title: Saul Kripke

text: Kripke was also partly responsible for the revival of metaphysics after the decline of logical positivism, claiming necessity is a metaphysical notion distinct from the epistemic notion of "a priori", and that there are necessary truths that are known "a posteriori", such as that water is HO. A 1970 Princeton lecture series, published in book form in 1980 as "Naming and Necessity", is considered one of the most important philosophical works of the 20th century. It introduces the concept of names as rigid designators, true in every possible world, as contrasted with descriptions. It also contains Kripke's causal theory of reference, disputing the descriptivist theory found in Gottlob Frege's concept of sense and Bertrand Russell's theory of descriptions.


title: Saul Kripke

text: Kripke also gave an original reading of Ludwig Wittgenstein, known as "Kripkenstein", in his "Wittgenstein on Rules and Private Language". The book contains his rule-following argument, a paradox for skepticism about meaning.


title: Saul Kripke

text: Saul Kripke was 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."


title: Saul Kripke

text: After briefly teaching at Harvard, Kripke moved in 1968 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.


title: Saul Kripke

text: 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 was 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.


title: Saul Kripke

text: Kripke was married to philosopher Margaret Gilbert. He is the second cousin once removed of television writer, director, and producer Eric Kripke.


title: Saul Kripke

text: 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.


title: Saul Kripke

text: 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.


title: Saul Kripke

text: 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:


title: Saul Kripke

text: 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.


title: Saul Kripke

text: 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".


title: Saul Kripke

text: 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").


title: Saul Kripke

text: 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.


title: Saul Kripke

text: 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.


title: Saul Kripke

text: 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.


title: Saul Kripke

text: 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.


title: Saul Kripke

text: 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.


title: Saul Kripke

text: 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.


title: Saul Kripke

text: 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.


title: Saul Kripke

text: 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:


title: Saul Kripke

text: 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.


title: Saul Kripke

text: 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".


title: Saul Kripke

text: We say that a formula or a set "X" of formulas is canonical with respect to a property "P" of Kripke frames, if


title: Saul Kripke

text: 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.


title: Saul Kripke

text: 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.


title: Saul Kripke

text: 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:


title: Saul Kripke

text: 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.


title: Saul Kripke

text: 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.


title: Saul Kripke

text: 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.


title: Saul Kripke

text: Kripke semantics has a straightforward generalization to logics with more than one modality. A Kripke frame for a language with


title: Saul Kripke

text: 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:


title: Saul Kripke

text: 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:


title: Saul Kripke

text: 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.


title: Saul Kripke

text: 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. But if standard quantifier rules are used, 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.


title: Saul Kripke

text: 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. But the costs are severe. First, his language is artificially impoverished, and second, the rules for the propositional modal logic must be weakened.


title: Saul Kripke

text: 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.


title: Saul Kripke

text: Kripke semantics for intuitionistic logic follows the same principles as the semantics of modal logic, but uses a different definition of satisfaction.


title: Saul Kripke

text: formula_44, where formula_45 is a partially ordered Kripke frame, and formula_4 satisfies the following conditions:


title: Saul Kripke

text: Intuitionistic logic is sound and complete with respect to its Kripke semantics, and it has the Finite Model Property.


title: Saul Kripke

text: (classical) "L"-structure for each node "w" ∈ "W", and the following compatibility conditions hold whenever "u" ≤ "v":


title: Saul Kripke

text: Given an evaluation "e" of variables by elements of "M", we define the satisfaction relation formula_63:


title: Saul Kripke

text: 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).


title: Saul Kripke

text: 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.


title: Saul Kripke

text: 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.


title: Saul Kripke

text: 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.


title: Saul Kripke

text: 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".


title: Saul Kripke

text: 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.


title: Saul Kripke

text: 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.


title: Saul Kripke

text: But in his article "A Puzzle about Belief" (1988) 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 jolie"" ("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 "jolie" 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.


title: Saul Kripke

text: 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.


title: Saul Kripke

text: 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".


title: Saul Kripke

text: 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 isolated individuals there is no fact in virtue of which they mean 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.


title: Saul Kripke

text: 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, Peter Hacker, and Colin McGinn, 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.


title: Saul Kripke

text: 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."


title: Saul Kripke

text: Gödel's first incompleteness theorem demonstrates 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. But Kripke's truth predicate does not give a truth value (true/false) to propositions such as the one built in Tarski's proof, since it is provable by induction that it is undefined at stage formula_84 for every finite formula_84.


title: Saul Kripke

text: Kripke's proposal is 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, 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.


title: Saul Kripke

text: 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 Romina Padro. 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."


title: Aoshima, Ehime

text: , also known as , is an island in Ehime Prefecture, Japan, known for its large number of feline residents. Felines have been reported by news outlets to outnumber humans by ratios between 6:1 and 10:1, but as elderly inhabitants of the island have died, the ratio has greatly increased to almost 36:1. Felines were introduced to combat rodents on fishing boats, but remained on the island and reproduced in large numbers.


title: Aoshima, Ehime

text: The feline inhabitants of Aoshima are fed by food donations from all over Japan. The cats also eat the small creatures of the island and some food from visitors.


title: Aoshima, Ehime

text: The human population has decreased since sardine fisheries depleted and jobs moved to cities. As of February 2019, only six human residents live on Aoshima.


title: Aoshima, Ehime

text: In 1945, the island was a fishing village with a population of approximately 900. In 2013, the island was estimated to be home to 50 residents. In 2018, "Ehime Shimbun" reported that the population had decreased to 13 with an average age of "over 75". In 2019, "Globe" reported that only six residents remained on the island. The island attracts tourists who visit the cats and give them food.


title: Aoshima, Ehime

text: In February 2018, it was reported by "Ehime Shimbun" that all cats on the island would be spayed or neutered in order to lower the feline population as a response to the declining human population. By October, 210 cats had been spayed and neutered, with another estimated 10 cats uncaptured that had been hidden by an old resident who opposed the program.


title: Aoshima, Ehime

text: Aoshima is accessible via a ferry departing from in front of JR Iyo-Nagahama Station in Port Nagahama, which takes around 30 minutes.


title: Itsukushima Shrine

text: The Itsukushima shrine is one of Japan's most popular tourist attractions. It is most famous for its dramatic gate, or "torii" on the outskirts of the shrine, the sacred peaks of Mount Misen, extensive forests, and its ocean view. The shrine complex itself consists of two main buildings: the Honsha shrine and the Sessha Marodo-jinja, as well as 17 other different buildings and structures that help to distinguish it.


title: Itsukushima Shrine

text: It is said to have been erected in 593 supposedly by Saeki Kuramoto during the reign of Empress Suiko (592–628 CE). However, the present shrine has been popularly attributed to Taira no Kiyomori, a prominent noble of the Imperial Court and later Chancellor (Daijō-daijin), who contributed heavily to the construction of the shrine during his time as governor of Aki Province in 1168. Another renowned patron of the shrine was Mori Motonari, lord of Chōshū Domain, who was responsible for rebuilding the honden in 1571. It is important to note, however, that as a result of waging war against Sue Takafusa there in 1555, Motonari is said to have tainted the island's grounds by battling on the island. Spilling blood violated the strict taboos meant to preserve the sacred purity associated with Shinto shrines. The only surviving structure in Itsukushima shrine from the Kamakura period is the Kyakuden or "Guest-God's Shrine".


title: Itsukushima Shrine

text: It was not uncommon during the 12th century for the nobility to build shrines or take on other architectural projects in order to "reflect their power and splendor." The Taira are known specifically for their involvement in maritime trade with the Song dynasty (960–1279) and for attempting to monopolize overseas trade along the Inland Sea.


title: Itsukushima Shrine

text: Kiyomori was at the height of his power when he established the Taira dominion over the island. He "ordered construction of the main hall of Itsukushima shrine as a display of reverence for the tutelary god of navigation and to serve as a base for maritime activities..." Miyajima soon became the Taira family shrine. Supposedly, Kiyomori chose the location also for the reason to further establish himself in the Heian aristocracy as one who deviated from the social norms of Shinto pilgrimage . He lavished great wealth upon Itsukushima, and he enjoyed showing the place to his friends and colleagues, or even to royal personages..."


title: Itsukushima Shrine

text: It is also said that Kiyomori rebuilt the shrine on account of a dream he had of an old monk who promised him dominion over Japan if he constructed a shrine on the island of Miyajima, and pay homage to its kami who are enshrined there for his success in life. The renovations funded by the Taira allowed for Itsukushima to "grow into an important religious complex."


title: Itsukushima Shrine

text: The Itsukushima shrine is dedicated to the three daughters of Susano-o no Mikoto: Ichikishimahime no mikoto, Tagorihime no mikoto, and Tagitsuhime no mikoto. Otherwise known as the "sanjoshin" or "three female deities", these Shinto deities are the goddesses of seas and storms. Kiyomori believed the goddesses to be "manifestations of Kannon," therefore the island was understood as the home of the bodhisattva. In Japanese, he word Itsukushima translates to "island dedicated to the gods." The island itself is also considered to be a god, which is why the shrine was built on the outskirts of the island. Adding to its sanctity, Mount Misen is the tallest peak at about 1,755 feet. Tourists can either hike or take a ropeway to the top.


title: Itsukushima Shrine

text: Its treasures include the celebrated Heike Nōkyō, or "Sutras dedicated by the House of Taira." These consist of thirty-two scrolls, on which the Lotus, Amida, and Heart sutras have been copied by Kiyomori, his sons, and other members of the family, each completing the transcription of one scroll, and it was "decorated with silver, gold, and mother-of-pearl by himself [Kiyomori] and other members of his clan."


title: Itsukushima Shrine

text: Originally Itsukushima was a pure Shinto shrine "where no births or deaths were allowed to cause pollution. Because the island itself has been considered sacred, commoners were not allowed to set foot on it throughout much of its history to maintain its purity. Retaining the purity of the shrine is so important that since 1878, no deaths or births have been permitted near it. To this day, pregnant women are supposed to retreat to the mainland as the day of delivery approaches, as are the terminally ill or the very elderly whose passing has become imminent. Burials on the island are forbidden. To allow pilgrims to approach, the shrine was built like a pier over the water, so that it appeared to float, separate from the land. The red entrance gate, or "torii", was built over the water for much the same reason. Commoners had to steer their boats through the "torii" before approaching the shrine.


title: Itsukushima Shrine

text: Japan has gone to great lengths to preserve the twelfth-century-style architecture of the Shrine throughout history. The shrine was designed and built according to the "Shinden-zukuri" style, equipped with pier-like structures over the Matsushima bay in order to create the illusion of floating on the water, separate from island, which could be approached by the devout "like a palace on the sea." This idea of intertwining architecture and nature is reflective of a popular trend during the 16th century as well as the Heian period in which Japanese structures tended to "follow after their environment," often allowing trees, water, and other forms of natural beauty to enter into the decor of homes and buildings. This led to a far more intimate relationship between the two.


title: Itsukushima Shrine

text: The most recognizable and celebrated feature of the Itsukushima shrine, is its fifty-foot tall vermilion otorii gate ("great gate"), built of decay-resistant camphor wood. The placement of an additional leg in front of and behind each main pillar identifies the "torii" as reflecting the style of "Ryōbu Shintō" (dual Shinto), a medieval school of esoteric Japanese Buddhism associated with the Shingon Sect. The "torii" appears to be floating only at high tide. When the tide is low, it is only approachable by foot from the island. Gathering shellfish near the gate is also popular at low tide. At night, powerful lights on the shore illuminate the "torii." Although the gate has been in place since 1168, the current gate dates back only to 1875.


title: Itsukushima Shrine

text: Shinto architecture has many distinct parts, most of which include the shrine's "honden" (main hall) and the unusually long "haiden" (main oratory), and its equally long "heiden" (offertory hall). The "honden" "is an eight-by-four bay structure with a kirizuma roof surfaced in cypress bark." Its walls are decorated in white stucco; they were constructed using a process requiring fifteen coats of white stucco, with vermilion woodwork.


title: Itsukushima Shrine

text: Extending from the sides of the "haraiden" of the main shrine is a "noh" stage which dates from 1590. "Noh" theater performances have long been used to pay homage to the gods through the ritual acting out of key events in Shinto myth.


title: Itsukushima Shrine

text: On September 5, 2004, the shrine was severely damaged by Typhoon Songda. The boardwalks and roof were partially destroyed, and the shrine was temporarily closed for repairs. Today anyone can go visit the shrine for 300 yen.


title: Fearsome critters

text: In North American folklore, fearsome critters were tall tale animals jokingly said to inhabit the wilderness in or around logging camps, especially in the Great Lakes region. Today, the term may also be applied to similar fabulous beasts.


title: Fearsome critters

text: Fearsome critters were an integral part of oral tradition in North American logging camps during the turn of the twentieth century, principally as a means to pass time (such as in tall tales) or as a jest for hazing newcomers. In a typical fearsome critter gag, a person would casually remark about a strange noise or sight they encountered in the wild, and another accomplice would join in with a similar anecdote. Meanwhile, an eavesdropper would begin to investigate, as Henry H. Tryon recorded in his book, "Fearsome Critters" (1939) —


title: Fearsome critters

text: Lumberjacks, who regularly traveled between camps, would stop to swap stories, which eventually disseminated these myths across the continent. Many fearsome critters were simply the products of pure exaggeration; however, a number were used either jokingly or seriously as explanations for both unexplained and natural phenomena. For example, the hidebehind served to account for loggers who failed to return to camp, while the treesqueak offered justification for strange noises heard in the woods. A handful whether intentionally or unknowing mirrored descriptions of actual animals. The mangrove killifish, which takes up shelter in decaying branches after leaving the water, exhibits similarities to the upland trout, a legendary fish purported to nest in trees. In addition, the story of the fillyloo, about a mythical crane that flies upside-down, may have been inspired by observations of the wood stork, a bird that has been witnessed briefly flying in this manner. In particular instances more elaborate ruses were created using taxidermy or trick photography.


title: Fearsome critters

text: The character of the fearsome critters themselves was usually more comical than frightful. Often the greater emphasis is placed on behavioral traits with little or no detail mentioned on their appearance, as in the cases of the hidebehind, teakettler, squidgicum-squee, and hangdown. Some fearsome critters like flittericks or the goofus appeared to be ordinary animals that just behaved out of the ordinary. The more physically emphasized and improbable creatures seem to be distinguished by how far the storyteller could push the boundaries of biomechanics. Both the tripodero and snoligoster demonstrate facets more in common with mechanical apparatuses than animals, and the hugag and sidehill gouger seem to be more a play on applied physics than fanciful inspiration. While much of the literature that has been written on the subject echoes a naturalist's perspective, commonly specifying a range of distribution, behavioral habits, and physical appearance, many of these myths were never as widespread as others. Consequently, it is common to find a lack of consensus on a specific fearsome critter, if not clear contradictions. To illustrate, the wampus cat differs widely in appearance depending on region. For instance, in Henry H. Tryon's "Fearsome Critters", the wampus cat is described as having pantographic forelimbs while in Vance Randolph's "We Always Lie to Strangers," it is portrayed a supernatural, aquatic panther.


title: Fearsome critters

text: The tendency to description of behavior without image is used to eerie literary effect by Manly Wade Wellman in employing a number of fearsome critters in his 1952 science fiction folk tale "The Desrick on Yandro," as well as commenting specifically on the lack of physical description for one of the beasts: "The Behinder flung itself on his shoulders. Then I knew why nobody's supposed to see one. I wish I hadn't. To this day I can see it, as plain as a fence at noon, and forever I will be able to see it. But talking about it's another matter. Thank you, I won't try."


title: Fearsome critters

text: In his 1939 book, "Fearsome Critters," Henry H. Tryon recounted that "... much true folk-lore was born, lived and died with no chance of ever becoming a part of our permanent records. Without doubt this has happened to a good bit of woods lore." Consequently, firsthand records on fearsome critters are few in number. However, among some of the more significant sources to record fearsome critter stories directly from loggers, hunters and other forest tradesmen, listed chronologically, are:


title: Fearsome critters

text: Additionally, in 1922 and 1925, veteran guide Art Childs published an illustrated newspaper column entitled, "Yarns of the Big Woods" that featured fearsome critters from oral traditions. Additionally, many of the aforementioned texts has since been made freely available online, yet others are still under copyright.


title: Sierra Nevada (Spain)

text: Sierra Nevada (; meaning "mountain range covered in snow") is a mountain range in the Andalusian province of Granada in Spain. It contains the highest point of continental Spain: Mulhacén, at above sea level.


title: Sierra Nevada (Spain)

text: It is a popular tourist destination, as its high peaks make skiing possible in one of Europe's most southerly ski resorts, in an area along the Mediterranean Sea predominantly known for its warm temperatures and abundant sunshine. At its foothills is found the city of Granada, and a little further south, Almería and Málaga.


title: Sierra Nevada (Spain)

text: Parts of the range have been included in the Sierra Nevada National Park. The range has also been declared a biosphere reserve. The Sierra Nevada Observatory and the IRAM radiotelescope are located on the northern slopes at an elevation of .


title: Sierra Nevada (Spain)

text: The Sierra Nevada was formed during the Alpine Orogeny, a mountain-building event that also formed the European Alps to the east and the Atlas Mountains of northern Africa across the Mediterranean Sea to the south. The Sierra as observed today formed during the Paleogene and Neogene Periods (66 to 1.8 million years ago) from the collision of the African and Eurasian continental plates.


title: Sierra Nevada (Spain)

text: Central to the mountain range is a ridge running broadly west-south-west - east-north-east. For a substantial distance, the watershed stays consistently above . This is sufficient altitude for the peaks to be consistently snow-covered.


title: Sierra Nevada (Spain)

text: On the southern side of the range, several long, narrow river valleys lead off towards the south-west, separated by a number of subsidiary ridges.


title: Sierra Nevada (Spain)

text: On the steeper and craggier northern side, the valleys have less regular orientations. This side is dominated by the Rio Genil which starts near Mulhacén and into which many of the other rivers flow.


title: Sierra Nevada (Spain)

text: Geologically, the range is composed chiefly of soft micaceous schists, sloping steeply to the north, but more gradually to the south and south-east.


title: Sierra Nevada (Spain)

text: According to the Köppen climate classification, Sierra Nevada has a Mediterranean climate, with different variations depending on the altitude. Above the climate is Mediterranean subalpine (Dsc), due to the location's high elevation and low summer precipitation. With June and September being around the threshold of in mean temperature to avoid the subarctic classification, the climate at a slightly lower elevation is continental highland climate. At an elevation slightly lower than that classification area; where February means average above ; it falls into the normal cool-summer mediterranean classification transitioning with the hot-summer variety in surrounding lowland areas. This renders Sierra Nevada's climate a highland cooled-down variety of a typical mediterranean climate. Summer and winter daytime temperatures are some 12° C cooler than found in Granada, differences that are even greater in spring as Sierra Nevada takes longer to approach the short summers. In May daytime highs in Sierra Nevada are around with Granada having an average of . The yearly temperature of at the ski station of Pradollano is in stark contrast to Granada's and coastal Málaga's .


title: Tribe of Dan

text: The Tribe of Dan (, "Judge") was one of the twelve tribes of Israel, according to the Torah. They were allocated a coastal portion of land when the people of Israel entered the Promised Land, later moving northwards.


title: Tribe of Dan

text: In the Biblical census of the Book of Numbers, the tribe of Dan is portrayed as the second largest Israelite tribe (after Judah). Some textual scholars regard the census as being from the Priestly Source, dating it to around the 7th century BC, and more likely to reflect the biases of its authors. In the "Blessing of Moses", which some textual scholars regard as dating from only slightly earlier than the deuteronomist, Dan is prophesied to "leap from Bashan"; scholars are uncertain why this should be since the tribe did not live in the Bashan plain, east of the Jordan River.


title: Tribe of Dan

text: According to the biblical narrative, following the completion of the conquest of Canaan by the Israelite tribes after about 1200 BC, Joshua allocated the land among the twelve tribes. Dan was the last tribe to receive its territorial inheritance. The land originally allocated to Dan was a small enclave in the central coastal area of Canaan, between Judah, Benjamin, Ephraim and the Philistines.


title: Tribe of Dan

text: To the north the territory of Dan abutted Joppa, the modern Jaffa. This territory, not very extensive originally, was soon diminished by its dangerous neighbors, the Philistines. The tribe was only able to camp in the hill country overlooking the Sorek Valley, the camp location becoming known as "Mahaneh Dan" ("Camp of Dan"). () The region they were trying to settle extended south into the Shephelah in the area of Timnah; as a result, the modern state of Israel refers to the region as Gush Dan ("the Dan area").


title: Tribe of Dan

text: From after the conquest of the land by Joshua until the formation of the first united Kingdom of Israel in c. 1050 BC, the Tribe of Dan was a part of a loose confederation of Israelite tribes. No central government existed, and in times of crisis the people were led by ad hoc leaders known as Judges.


title: Tribe of Dan

text: The most celebrated Danite was Samson, a Danite judge from the period of settlement in the lands allotted by Joshua. Pnina Galpaz-Feller sees similarities between the story of Samson and Denyen tribal legends. Excavations conducted at Tel Dan by David Ilan of the Hebrew Union College show support for the Danites' potential Aegean connections.


title: Tribe of Dan

text: As a consequence of the pressure from the Philistines, a portion of the tribe abandoned hopes of settling near the central coast, instead migrating to the north of Philistine territory, and after conquering Laish, refounded it as the city of "Dan" (). Thus their territory in the end lay northeast of that of Naphtali, east of the upper Jordan River, near its eastern sources, and defining the northern extent of the land of the Israelites. A number of biblical texts thus refer to "All Israel, from Dan to Beersheba".


title: Tribe of Dan

text: With the growth of the threat from Philistine incursions, the Israelite tribes decided to form a strong centralised monarchy to meet the challenge, and the Tribe of Dan joined the new kingdom with Saul as the first king. After the death of Saul, all the tribes other than Judah remained loyal to the House of Saul. But after the death of Ish-bosheth, Saul's son and successor to the throne of Israel, the Tribe of Dan joined the other northern Israelite tribes in making David, who was then the king of Judah, king of a re-united Kingdom of Israel. The tribe provided substantial military support for the kingdom in the form of 28,600 soldiers, being considered "experts in war".


title: Tribe of Dan

text: However, on the accession of Rehoboam, David's grandson, in c. 930 BC the northern tribes split from the House of David to re-form a Kingdom of Israel as the Northern Kingdom.


title: Tribe of Dan

text: As part of the Kingdom of Israel, the territory of Dan was conquered by the Assyrians and exiled; the manner of their exile led to their further history being lost.


title: Tribe of Dan

text: A 15th-century Latin chronicle, "Chronicon Holsatiae vetus", found in Gottfried Leibniz's "Accessiones historicae" (1698),  states the Danes were of the Tribe of Dan. The antiquarian Henry Spelman in 1620 had made a similar claim that the Danes were the Israelite Tribe of Dan, based on the apparent similarity in name. Additionally, proponents of Nordic and British Israelism have made similar claims about descent from the tribe of Dan. British Israelite authors such as John Cox Gawler and J. H. Allen identified the Tribe of Dan with Denmark. While another prominent British Israelite author, Edward Hine, took the view that the tribe of Dan had originated in Denmark and then migrated to the British Isles.


title: Tribe of Dan

text: Some Ethiopian Jews, also known as Beta Israel, claim descent from the Tribe of Dan, whose members migrated south along with members of the tribes of Gad, Asher, and Naphtali, into the Kingdom of Kush, now Ethiopia and Sudan, during the destruction of the First Temple. This position is supported by former Sephardic Chief Rabbi Ovadia Yosef. They are said to have fought with the natives.


title: Tribe of Dan

text: Their primary trade characteristic was seafaring, unusual for the Israelite tribes. In the Song of Deborah the tribe is said to have stayed on their ships with their belongings.


title: Tribe of Dan

text: Modern artists use the "scales of justice" to represent the Tribe of Dan due to referencing Dan "shall achieve justice for his kindred". More traditional artists use a snake to represent Dan, based upon Genesis 49:17, "Let Dan be a serpent by the roadside, a horned viper by the path, That bites the horse's heel, so that the rider tumbles backward."


title: Tribe of Dan

text: Revelation 7:4–8 mentions that people from the twelve tribes of Israel will be sealed. The selection of the twelve tribes does not include the names of Ephraim and Dan, although their names were used for the twelve tribes that settled in the Promised Land. It has been suggested that this could be because of their pagan practices. This led Irenaeus, Hippolytus of Rome and some Millennialists to propose that the Antichrist will come from the tribe of Dan.


title: Detonator

text: A detonator, frequently a blasting cap, is a device used to trigger an explosive device. Detonators can be chemically, mechanically, or electrically initiated, the last two being the most common.


title: Detonator

text: The commercial use of explosives uses electrical detonators or the capped fuse which is a length of safety fuse to which an ordinary detonator has been joined. Many detonators' primary explosive is a material called ASA compound. This compound is formed from lead azide, lead styphnate and aluminium and is pressed into place above the base charge, usually TNT or tetryl in military detonators and PETN in commercial detonators.


title: Detonator

text: Other materials such as DDNP (diazo dinitro phenol) are also used as the primary charge to reduce the amount of lead emitted into the atmosphere by mining and quarrying operations. Old detonators used mercury fulminate as the primary, often mixed with potassium chlorate to yield better performance.


title: Detonator

text: A blasting cap is a small sensitive primary explosive device generally used to detonate a larger, more powerful and less sensitive secondary explosive such as TNT, dynamite, or plastic explosive.


title: Detonator

text: Blasting caps come in a variety of types, including non-electric caps, electric caps, and fuse caps. They are used in commercial mining, excavation, and demolition. Electric types are set off by a short burst of current sent by a blasting machine via a long wire to the cap to ensure safety. Traditional fuse caps have a fuse which is ignited by a flame source, such as a match or a lighter.


title: Detonator

text: The need for detonators such as blasting caps came from the development of safer explosives. Different explosives require different amounts of energy (their activation energy) to detonate. Most commercial explosives are formulated with a high activation energy, to make them stable and safe to handle so they will not explode if accidentally dropped, mishandled, or exposed to fire. These are called secondary explosives. However they are correspondingly difficult to detonate intentionally, and require a small initiating explosion. This is provided by a detonator.


title: Detonator

text: A detonator contains an easy-to-ignite primary explosive that provides the initial activation energy to start the detonation in the main charge. Explosives commonly used in detonators include mercury fulminate, lead azide, lead styphnate, tetryl, and DDNP. Blasting caps and some detonators are stored separately and not inserted into the main explosive charge until just before use, keeping the main charge safe.


title: Detonator

text: Early blasting caps also used silver fulminate, but it has been replaced with cheaper and safer primary explosives.


title: Detonator

text: Detonators are hazardous for untrained personnel to handle since they contain primary explosive. They are sometimes not recognized as explosives due to their appearance, leading to injuries.


title: Detonator

text: Ordinary detonators usually take the form of ignition-based explosives. While they are mainly used in commercial operations, ordinary detonators are still used in military operations. This form of detonator is most commonly initiated using a safety fuse, and used in non time-critical detonations e.g. conventional munitions disposal. Well known detonators are lead azide [Pb(N)], silver azide [AgN] and mercury fulminate [Hg(ONC)].


title: Detonator

text: There are three categories of electrical detonators: instantaneous electrical detonators (IED), short period delay detonators (SPD) and long period delay detonators (LPD). SPDs are measured in milliseconds and LPDs are measured in seconds. In situations where nanosecond accuracy is required, specifically in the implosion charges in nuclear weapons, exploding-bridgewire detonators are employed. The initial shock wave is created by vaporizing a length of a thin wire by an electric discharge. A new development is a slapper detonator, which uses thin plates accelerated by an electrically exploded wire or foil to deliver the initial shock. It is in use in some modern weapons systems. A variant of this concept is used in mining operations, when the foil is exploded by a laser pulse delivered to the foil by optical fiber.


title: Detonator

text: A non-electric detonator is a shock tube detonator designed to initiate explosions, generally for the purpose of demolition of buildings and for use in the blasting of rock in mines and quarries. Instead of electric wires, a hollow plastic tube delivers the firing impulse to the detonator, making it immune to most of the hazards associated with stray electric current. It consists of a small diameter, three-layer plastic tube coated on the innermost wall with a reactive explosive compound, which, when ignited, propagates a low energy signal, similar to a dust explosion. The reaction travels at approximately 6,500 ft/s (2,000 m/s) along the length of the tubing with minimal disturbance outside of the tube. Non-electric detonators were invented by the Swedish company Nitro Nobel in the 1960s and 1970s, and launched to the demolitions market in 1973.


title: Detonator

text: In civil mining, electronic detonators have a better precision for delays. Electronic detonators are designed to provide the precise control necessary to produce accurate and consistent blasting results in a variety of blasting applications in the mining, quarrying, and construction industries. Electronic detonators may be programmed in millisecond or sub-millisecond increments using a dedicated programming device.


title: Detonator

text: Wireless electronic detonators are beginning to be available in the civil mining market. Encrypted radio signals are used to communicate the blast signal to each detonator at the correct time. While currently expensive, wireless detonators can enable new mining techniques as multiple blasts can be loaded at once and fired in sequence without putting humans in harm's way.


title: Detonator

text: A number 8 test blasting cap is one containing 2 grams of a mixture of 80 percent mercury fulminate and 20 percent potassium chlorate, or a blasting cap of equivalent strength. An equivalent strength cap comprises 0.40-0.45 grams of PETN base charge pressed in an aluminum shell with bottom thickness not to exceed to 0.03 of an inch, to a specific gravity of not less than 1.4 g/cc, and primed with standard weights of primer depending on the manufacturer.


title: Detonator

text: The oldest and simplest type of cap, fuse caps are a metal cylinder, closed at one end. From the open end inwards, there is first an empty space into which a pyrotechnic fuse is inserted and crimped, then a pyrotechnic ignition mix, a primary explosive, and then the main detonating explosive charge.


title: Detonator

text: The primary hazard of pyrotechnic blasting caps is that for proper usage, the fuse must be inserted and then crimped into place by crushing the base of the cap around the fuse. If the tool used to crimp the cap is used too close to the explosives, the primary explosive compound can detonate during crimping. A common hazardous practice is crimping caps with one's teeth; an accidental detonation can cause serious injury to the mouth.


title: Detonator

text: Fuse type blasting caps are still in active use today. They are the safest type to use around certain types of electromagnetic interference, and they have a built in time delay as the fuse burns down.


title: Detonator

text: Solid pack electric blasting caps use a thin bridgewire in direct contact (hence solid pack) with a primary explosive, which is heated by electric current and causes the detonation of the primary explosive. That primary explosive then detonates a larger charge of secondary explosive.


title: Detonator

text: Some solid pack fuses incorporate a small pyrotechnic delay element, up to a few hundred milliseconds, before the cap fires.


title: Detonator

text: Match type blasting caps use an electric match (insulating sheet with electrodes on both sides, a thin bridgewire soldered across the sides, all dipped in ignition and output mixes) to initiate the primary explosive, rather than direct contact between the bridgewire and the primary explosive. The match can be manufactured separately from the rest of the cap and only assembled at the end of the process.


title: Detonator

text: This type of detonator was invented in the 1940s as part of the Manhattan Project to develop nuclear weapons. The design goal was to produce a detonator which acted very rapidly and predictably. Both Match and Solid Pack type electric caps take a few milliseconds to fire, as the bridgewire heats up and heats the explosive to the point of detonation. Explosive bridgewire or EBW detonators use a higher voltage electric charge and a very thin bridgewire, .04 inch long, .0016 diameter, (1 mm long, 0.04 mm diameter). Instead of heating up the explosive, the EBW detonator wire is heated so quickly by the high firing current that the wire actually vaporizes and explodes due to electric resistance heating. That electrically driven explosion then fires the detonator's initiator explosive (usually PETN).


title: Detonator

text: Some similar detonators use a thin metal foil instead of a wire, but operate in the same manner as true bridgewire detonators.


title: Detonator

text: In addition to firing very quickly when properly activated, EBW detonators are safe from stray static electricity and other electric current. Enough current and the bridgewire may melt, but it is small enough that it cannot detonate the initiator explosive unless the full high-voltage high-current charge passes through the bridgewire. EBW detonators are used in many civilian applications where radio signals, static electricity, or other electrical hazards might cause accidents with conventional electric detonators.


title: Detonator

text: Slapper detonators are an improvement on EBW detonators. Slappers, instead of directly using the exploding foil to detonate the initiator explosive, use the electrical vaporization of the foil to drive a small circle of insulating material such as PET film or kapton down a circular hole in an additional disc of insulating material. At the far end of that hole is a pellet of conventional initiator explosive.


title: Detonator

text: The conversion efficiency of energy from electricity into kinetic energy of the flying disk or slapper can be 20–40%.


title: Detonator

text: Since the slapper impacts a wide area - 40 thousandths of an inch (roughly one mm) across - of the explosive, rather than a thin line or point as in an exploding foil or bridgewire detonator, the detonation is more regular and requires less energy. Reliable detonation requires raising a minimum volume of explosive to temperatures and pressures at which detonation starts. If energy is deposited at a single point, it can radiate away in the explosive in all directions in rarefaction or expansion waves, and only a small volume is efficiently heated or compressed. The flier disc loses impact energy at its sides to rarefaction waves, but a conical volume of explosive is efficiently shock compressed.


title: Detonator

text: Slapper detonators are used in nuclear weapons. These components require large quantities of energy to initiate, making them extremely unlikely to accidentally discharge.


title: Detonator

text: In this type, a pulse from a laser passes down an optical fiber to strike and thus initiate a carbon-doped explosive. These initiators are highly reliable. Unintentional initiation is very difficult as the explosive can only be detonated by the attached laser, which is precisely tuned to do so, or a completely independent laser that matches.


title: Detonator

text: The first blasting cap or detonator was demonstrated in 1745 when British physician and apothecary William Watson showed that the electric spark of a friction machine could ignite black powder, by way of igniting a flammable substance mixed in with the black powder.


title: Detonator

text: In 1750, Benjamin Franklin in Philadelphia made a commercial blasting cap consisting of a paper tube full of black powder, with wires leading in both sides and wadding sealing up the ends. The two wires came close but did not touch, so a large electric spark discharge between the two wires would fire the cap.


title: Detonator

text: In 1832, a hot wire detonator was produced by American chemist Robert Hare, although attempts along similar lines had earlier been attempted by the Italians Volta and Cavallo. Hare constructed his blasting cap by passing a multistrand wire through a charge of gunpowder inside a tin tube; he had cut all but one fine strand of the multistrand wire so that the fine strand would serve as the hot bridgewire. When a strong current from a large battery (which he called a "deflagrator" or "calorimotor") was passed through the fine strand, it became incandescent and ignited the charge of gunpowder.


title: Detonator

text: In 1863, Alfred Nobel realized that although nitroglycerin could not be detonated by a fuse, it could be detonated by the explosion of a small charge of gunpowder, which in turn was ignited by a fuse. Within a year, he was adding mercury fulminate to the gunpowder charges of his detonators, and by 1867 he was using small copper capsules of mercury fulminate, triggered by a fuse, to detonate nitroglycerin.


title: Detonator

text: In 1868, Henry Julius Smith of Boston introduced a cap that combined a spark gap ignitor and mercury fulminate, the first electric cap able to detonate dynamite.


title: Detonator

text: In 1875, Smith—and then in 1887, Perry G. Gardner of North Adams, Massachusetts—developed electric detonators that combined a hot wire detonator with mercury fulminate explosive. These were the first generally modern type blasting caps. Modern caps use different explosives and separate primary and secondary explosive charges, but are generally very similar to the Gardner and Smith caps.


title: Detonator

text: Smith also invented the first satisfactory portable power supply for igniting blasting caps: a high-voltage magneto that was driven by a rack and pinion, which in turn was driven by a T-handle that was pushed downwards.


title: Detonator

text: Electric match caps were developed in the early 1900s in Germany, and spread to the US in the 1950s when ICI International purchased Atlas Powder Co. These match caps have become the predominant world standard cap type.


title: High tech

text: High technology (high tech), also known as advanced technology (advanced tech) or exotechnology, is technology that is at the cutting edge: the highest form of technology available. It can be defined as either the most complex or the newest technology on the market. The opposite of high tech is "low technology", referring to simple, often traditional or mechanical technology; for example, a slide rule is a low-tech calculating device. When high tech becomes old, it becomes low tech, for example vacuum tube electronics.


title: High tech

text: The phrase was used in a 1958 "The New York Times" story advocating "atomic energy" for Europe: "... Western Europe, with its dense population and its high technology ..." Robert Metz used the term in a financial column in 1969, saying Arthur H. Collins of Collins Radio "controls a score of high technology patents in a variety of fields." and in a 1971 article used the abbreviated form, "high tech."


title: High tech

text: A widely used classification of high-technological manufacturing industries was provided by the OECD in 2006. It is based on the intensity of research and development activities used in these industries within OECD countries, resulting in four distinct categories.


title: High tech

text: Startups working on high technologies (or developing new high technologies) are sometimes referred to as deep tech; the term may also refer to disruptive innovations or those based on scientific discoveries.


title: High tech

text: High-tech, as opposed to high-touch, may refer to self-service experiences that do not require human interaction.


title: Amyloid

text: Amyloids are aggregates of proteins characterised by a fibrillar morphology of 7–13 nm in diameter, a beta sheet (β-sheet) secondary structure (known as cross-β) and ability to be stained by particular dyes, such as Congo red. In the human body, amyloids have been linked to the development of various diseases. Pathogenic amyloids form when previously healthy proteins lose their normal structure and physiological functions (misfolding) and form fibrous deposits in amyloid plaques around cells which can disrupt the healthy function of tissues and organs.


title: Amyloid

text: Such amyloids have been associated with (but not necessarily as the cause of) more than 50 human diseases, known as amyloidosis, and may play a role in some neurodegenerative diseases. Some of these diseases are mainly sporadic and only a few cases are familial. Others are only familial. Some are iatrogenic as they result from medical treatment. Prions are an infectious form of amyloids that can act as a template to convert other non-infectious forms. Amyloids may also have normal biological functions; for example, in the formation of fimbriae in some genera of bacteria, transmission of epigenetic traits in fungi, as well as pigment deposition and hormone release in humans.


title: Amyloid

text: Amyloids have been known to arise from many different proteins. These polypeptide chains generally form β-sheet structures that aggregate into long fibers; however, identical polypeptides can fold into multiple distinct amyloid conformations. The diversity of the conformations may have led to different forms of the prion diseases.


title: Amyloid

text: An unusual secondary structure named alpha sheet has been proposed as the toxic constituent of amyloid precursor proteins. This idea is not widely accepted at present, but a fair amount of evidence has accumulated, especially recently, in its favor.


title: Amyloid

text: The name "amyloid" comes from the early mistaken identification by Rudolf Virchow of the substance as starch ( in Latin, from ), based on crude iodine-staining techniques. For a period, the scientific community debated whether or not amyloid deposits are fatty deposits or carbohydrate deposits until it was finally found (in 1859) that they are, in fact, deposits of albumoid proteinaceous material.


title: Amyloid

text: To date, 37 human proteins have been found to form amyloid in pathology and be associated with well-defined diseases. The International Society of Amyloidosis classifies amyloid fibrils and their associated diseases based upon associated proteins (for example ATTR is the group of diseases and associated fibrils formed by TTR). A table is included below.


title: Amyloid

text: Many examples of non-pathological amyloid with a well-defined physiological role have been identified in various organisms, including human. These may be termed as functional or physiological or native amyloid.


title: Amyloid

text: Amyloids are formed of long unbranched fibers that are characterized by an extended beta-sheet secondary structure in which individual beta strands (β-strands) (coloured arrows in the adjacent figure) are arranged in an orientation perpendicular to the long axis of the fiber. Such a structure is known as cross-β structure. Each individual fiber may be 7–13 nanometres in width and a few micrometres in length. The main hallmarks recognised by different disciplines to classify protein aggregates as amyloid is the presence of a fibrillar morphology with the expected diameter, detected using transmission electron microscopy (TEM) or atomic force microscopy (AFM), the presence of a cross-β secondary structure, determined with circular dichroism, FTIR, solid-state nuclear magnetic resonance (ssNMR), X-ray crystallography, or X-ray fiber diffraction (often considered the "gold-standard" test to see whether a structure contains cross-β fibres), and an ability to stain with specific dyes, such as Congo red, thioflavin T or thioflavin S.


title: Amyloid

text: The term "cross-β" was based on the observation of two sets of diffraction lines, one longitudinal and one transverse, that form a characteristic "cross" pattern. There are two characteristic scattering diffraction signals produced at 4.7 and 10 Ångstroms (0.47 nm and 1.0 nm), corresponding to the interstrand and stacking distances in beta sheets. The "stacks" of beta sheet are short and traverse the breadth of the amyloid fibril; the length of the amyloid fibril is built by aligned β-strands. The cross-β pattern is considered a diagnostic hallmark of amyloid structure.


title: Amyloid

text: Amyloid fibrils are generally composed of 1–8 protofilaments (one protofilament also corresponding to a fibril is shown in the figure), each 2–7 nm in diameter, that interact laterally as flat ribbons that maintain the height of 2–7 nm (that of a single protofilament) and are up to 30 nm wide; more often protofilaments twist around each other to form the typically 7–13 nm wide fibrils. Each protofilament possesses the typical cross-β structure and may be formed by 1–6 β-sheets (six are shown in the figure) stacked on each other. Each individual protein molecule can contribute one to several β-strands in each protofilament and the strands can be arranged in antiparallel β-sheets, but more often in parallel β-sheets. Only a fraction of the polypeptide chain is in a β-strand conformation in the fibrils, the remainder forms structured or unstructured loops or tails.


title: Amyloid

text: For a long time our knowledge of the atomic-level structure of amyloid fibrils was limited by the fact that they are unsuitable for the most traditional methods for studying protein structures. Recent years have seen progress in experimental methods, including solid-state NMR spectroscopy and Cryo-Electron Microscopy. Combined, these methods have provided 3D atomic structures of amyloid fibrils formed by amyloid β peptides, α-synuclein, tau, and the FUS protein, associated with various neurodegenerative diseases.


title: Amyloid

text: X-ray diffraction studies of microcrystals revealed atomistic details of core region of amyloid, although only for simplified peptides having a length remarkably shorter than that of peptides or proteins involved in disease. The crystallographic structures show that short stretches from amyloid-prone regions of amyloidogenic proteins run perpendicular to the filament axis, consistent with the "cross-β" feature of amyloid structure. They also reveal a number of characteristics of amyloid structures – neighboring β-sheets are tightly packed together via an interface devoid of water (therefore referred to as dry interface), with the opposing β-strands slightly offset from each other such that their side-chains interdigitate. This compact dehydrated interface created was termed a steric-zipper interface. There are eight theoretical classes of steric-zipper interfaces, dictated by the directionality of the β-sheets (parallel and anti-parallel) and symmetry between adjacent β-sheets. A limitation of X-ray crystallography for solving amyloid structure is represented by the need to form microcrystals, which can be achieved only with peptides shorter than those associated with disease.


title: Amyloid

text: Although bona fide amyloid structures always are based on intermolecular β-sheets, different types of "higher order" tertiary folds have been observed or proposed. The β-sheets may form a β-sandwich, or a β-solenoid which may be either β-helix or β-roll. Native-like amyloid fibrils in which native β-sheet containing proteins maintain their native-like structure in the fibrils have also been proposed.


title: Amyloid

text: One complicating factor in studies of amyloidogenic polypeptides is that identical polypeptides can fold into multiple distinct amyloid conformations. This phenomenon is typically described as "amyloid polymorphism".


title: Amyloid

text: Amyloid is formed through the polymerization of hundreds to thousands of monomeric peptides or proteins into long fibers. Amyloid formation involves a "lag phase" (also called "nucleation phase"), an "exponential phase" (also called "growth phase") and a "plateau phase" (also called "saturation phase"), as shown in the figure. Indeed, when the quantity of fibrils is plotted versus time, a sigmoidal time course is observed reflecting the three distinct phases.


title: Amyloid

text: In the simplest model of 'nucleated polymerization' (marked by red arrows in the figure below), individual unfolded or partially unfolded polypeptide chains (monomers) convert into a nucleus (monomer or oligomer) via a thermodynamically unfavourable process that occurs early in the lag phase. Fibrils grow subsequently from these nuclei through the addition of monomers in the exponential phase.


title: Amyloid

text: A different model, called 'nucleated conformational conversion' and marked by blue arrows in the figure below, was introduced later on to fit some experimental observations: monomers have often been found to convert rapidly into misfolded and highly disorganized oligomers distinct from nuclei. Only later on, will these aggregates reorganise structurally into nuclei, on which other disorganised oligomers will add and reorganise through a templating or induced-fit mechanism (this 'nucleated conformational conversion' model), eventually forming fibrils.


title: Amyloid

text: Normally folded proteins have to unfold partially before aggregation can take place through one of these mechanisms. In some cases, however, folded proteins can aggregate without crossing the major energy barrier for unfolding, by populating native-like conformations as a consequence of thermal fluctuations, ligand release or local unfolding occurring in particular circumstances. In these native-like conformations, segments that are normally buried or structured in the fully folded and possessing a high propensity to aggregate become exposed to the solvent or flexible, allowing the formation of native-like aggregates, which convert subsequently into nuclei and fibrils. This process is called 'native-like aggregation' (green arrows in the figure) and is similar to the 'nucleated conformational conversion' model.


title: Amyloid

text: A more recent, modern and thorough model of amyloid fibril formation involves the intervention of secondary events, such as 'fragmentation', in which a fibril breaks into two or more shorter fibrils, and 'secondary nucleation', in which fibril surfaces (not fibril ends) catalyze the formation of new nuclei. Both secondary events increase the number of fibril ends able to recruit new monomers or oligomers, therefore accelerating fibril formation through a positive feedback mechanism. These events add to the well recognised steps of primary nucleation (formation of the nucleus from the monomers through one of models described above), fibril elongation (addition of monomers or oligomers to growing fibril ends) and dissociation (opposite process).


title: Amyloid

text: Such a new model is described in the figure on the right and involves the utilization of a master equation that includes all steps of amyloid fibril formation, i.e. primary nucleation, fibril elongation, secondary nucleation and fibril fragmentation. The rate constants of the various steps can be determined from a global fit of a number of time courses of aggregation (for example ThT fluorescence emission versus time) recorded at different protein concentrations. The general master equation approach to amyloid fibril formation with secondary pathways has been developed by Knowles, Vendruscolo, Cohen, Michaels and coworkers and considers the time evolution of the concentration formula_1 of fibrils of length formula_2 (here formula_2 represents the number of monomers in an aggregate). formula_4where formula_5 denotes the Kronecker delta. The physical interpretation of the various terms in the above master equation is straight forward: the terms on the first line describe the growth of fibrils via monomer addition with rate constant formula_6 (elongation). The terms on the second line describe monomer dissociation, i.e. the inverse process of elongation. formula_7 is the rate constant of monomer dissociation. The terms on the third line describe the effect of fragmentation, which is assumed to occur homogeneously along fibrils with rate constant formula_8. Finally, the terms on the last line describe primary and secondary nucleation respectively. Note that the rate of secondary nucleation is proportional to the mass of aggregates, defined as formula_9.


title: Amyloid

text: Following this analytical approach, it has become apparent that the lag phase does not correspond necessarily to only nucleus formation, but rather results from a combination of various steps. Similarly, the exponential phase is not only fibril elongation, but results from a combination of various steps, involving primary nucleation, fibril elongation, but also secondary events. A significant quantity of fibrils resulting from primary nucleation and fibril elongation may be formed during the lag phase and secondary steps, rather than only fibril elongation, can be the dominant processes contributing to fibril growth during the exponential phase. With this new model, any perturbing agents of amyloid fibril formation, such as putative drugs, metabolites, mutations, chaperones, etc., can be assigned to a specific step of fibril formation.


title: Amyloid

text: In general, amyloid polymerization (aggregation or non-covalent polymerization) is sequence-sensitive, that is mutations in the sequence can induce or prevent self-assembly. For example, humans produce amylin, an amyloidogenic peptide associated with type II diabetes, but in rats and mice prolines are substituted in critical locations and amyloidogenesis does not occur. Studies comparing synthetic to recombinant β amyloid peptide in assays measuring rate of fibrillation, fibril homogeneity, and cellular toxicity showed that recombinant β amyloid peptide has a faster fibrillation rate and greater toxicity than synthetic β amyloid peptide.


title: Amyloid

text: There are multiple classes of amyloid-forming polypeptide sequences. Glutamine-rich polypeptides are important in the amyloidogenesis of Yeast and mammalian prions, as well as trinucleotide repeat disorders including Huntington's disease. When glutamine-rich polypeptides are in a β-sheet conformation, glutamines can brace the structure by forming inter-strand hydrogen bonding between its amide carbonyls and nitrogens of both the backbone and side chains. The onset age for Huntington's disease shows an inverse correlation with the length of the polyglutamine sequence, with analogous findings in a "C. elegans" model system with engineered polyglutamine peptides.


title: Amyloid

text: Other polypeptides and proteins such as amylin and the β amyloid peptide do not have a simple consensus sequence and are thought to aggregate through the sequence segments enriched with hydrophobic residues, or residues with high propensity to form β-sheet structure. Among the hydrophobic residues, aromatic amino-acids are found to have the highest amyloidogenic propensity.


title: Amyloid

text: Cross-polymerization (fibrils of one polypeptide sequence causing other fibrils of another sequence to form) is observed in vitro and possibly in vivo. This phenomenon is important, since it would explain interspecies prion propagation and differential rates of prion propagation, as well as a statistical link between Alzheimer's and type 2 diabetes. In general, the more similar the peptide sequence the more efficient cross-polymerization is, though entirely dissimilar sequences can cross-polymerize and highly similar sequences can even be "blockers" that prevent polymerization.


title: Amyloid

text: The reasons why amyloid cause diseases are unclear. In some cases, the deposits physically disrupt tissue architecture, suggesting disruption of function by some bulk process. An emerging consensus implicates prefibrillar intermediates, rather than mature amyloid fibers, in causing cell death, particularly in neurodegenerative diseases. The fibrils are, however, far from innocuous, as they keep the protein homeostasis network engaged, release oligomers, cause the formation of toxic oligomers via secondary nucleation, grow indefinitely spreading from district to district and, in some cases, may be toxic themselves.


title: Amyloid

text: Calcium dysregulation has been observed to occur early in cells exposed to protein oligomers. These small aggregates can form ion channels through lipid bilayer membranes and activate NMDA and AMPA receptors. Channel formation has been hypothesized to account for calcium dysregulation and mitochondrial dysfunction by allowing indiscriminate leakage of ions across cell membranes. Studies have shown that amyloid deposition is associated with mitochondrial dysfunction and a resulting generation of reactive oxygen species (ROS), which can initiate a signalling pathway leading to apoptosis. There are reports that indicate amyloid polymers (such as those of huntingtin, associated with Huntington's disease) can induce the polymerization of essential amyloidogenic proteins, which should be deleterious to cells. Also, interaction partners of these essential proteins can also be sequestered.


title: Amyloid

text: All these mechanisms of toxicity are likely to play a role. In fact, the aggregation of a protein generates a variety of aggregates, all of which are likely to be toxic to some degree. A wide variety of biochemical, physiological and cytological perturbations has been identified following the exposure of cells and animals to such species, independently of their identity. The oligomers have also been reported to interact with a variety of molecular targets. Hence, it is unlikely that there is a unique mechanism of toxicity or a unique cascade of cellular events. The misfolded nature of protein aggregates causes a multitude of aberrant interactions with a multitude of cellular components, including membranes, protein receptors, soluble proteins, RNAs, small metabolites, etc.


title: Amyloid

text: In the clinical setting, amyloid diseases are typically identified by a change in the spectroscopic properties of planar aromatic dyes such as thioflavin T, congo red or NIAD-4. In general, this is attributed to the environmental change, as these dyes intercalate between beta-strands to confine their structure.


title: Amyloid

text: Congo Red positivity remains the gold standard for diagnosis of amyloidosis. In general, binding of Congo Red to amyloid plaques produces a typical apple-green birefringence when viewed under cross-polarized light. Recently, significant enhancement of fluorescence quantum yield of NIAD-4 was exploited to super-resolution fluorescence imaging of amyloid fibrils and oligomers. To avoid nonspecific staining, other histology stains, such as the hematoxylin and eosin stain, are used to quench the dyes' activity in other places such as the nucleus, where the dye might bind. Modern antibody technology and immunohistochemistry has made specific staining easier, but often this can cause trouble because epitopes can be concealed in the amyloid fold; in general, an amyloid protein structure is a different conformation from the one that the antibody recognizes.