title: Georg Cantor

text: The harsh criticism has been matched by later accolades. In 1904, the Royal Society awarded Cantor its Sylvester Medal, the highest honor it can confer for work in mathematics. David Hilbert defended it from its critics by declaring, "No one shall expel us from the paradise that Cantor has created."


title: Georg Cantor

text: Georg Cantor, born in 1845 in the western merchant colony of Saint Petersburg, Russia, was brought up in that city until the age of eleven. The oldest of six children, he was regarded as an outstanding violinist. His grandfather Franz Böhm (1788–1846) (the violinist Joseph Böhm's brother) was a well-known musician and soloist in a Russian imperial orchestra. Cantor's father had been a member of the Saint Petersburg stock exchange; when he became ill, the family moved to Germany in 1856, first to Wiesbaden, then to Frankfurt, seeking milder winters than those of Saint Petersburg. In 1860, Cantor graduated with distinction from the Realschule in Darmstadt; his exceptional skills in mathematics, trigonometry in particular, were noted. In August 1862, he then graduated from the "Höhere Gewerbeschule Darmstadt", now the Technische Universität Darmstadt. In 1862 Cantor entered the Swiss Federal Polytechnic in Zurich. After receiving a substantial inheritance upon his father's death in June 1863, Cantor transferred to the University of Berlin, attending lectures by Leopold Kronecker, Karl Weierstrass and Ernst Kummer. He spent the summer of 1866 at the University of Göttingen, then and later a center for mathematical research. Cantor was a good student, and he received his doctoral degree in 1867.


title: Georg Cantor

text: Cantor submitted his dissertation on number theory at the University of Berlin in 1867. After teaching briefly in a Berlin girls' school, he took up a position at the University of Halle, where he spent his entire career. He was awarded the requisite habilitation for his thesis, also on number theory, which he presented in 1869 upon his appointment at Halle University.


title: Georg Cantor

text: In 1874, Cantor married Vally Guttmann. They had six children, the last (Rudolph) born in 1886. Cantor was able to support a family despite his modest academic pay, thanks to his inheritance from his father. During his honeymoon in the Harz mountains, Cantor spent much time in mathematical discussions with Richard Dedekind, whom he had met at Interlaken in Switzerland


title: Georg Cantor

text: Cantor was promoted to extraordinary professor in 1872 and made full professor in 1879. To attain the latter rank at the age of 34 was a notable accomplishment, but Cantor desired a chair at a more prestigious university, in particular at Berlin, at that time the leading German university. However, his work encountered too much opposition for that to be possible. Kronecker, who headed mathematics at Berlin until his death in 1891, became increasingly uncomfortable with the prospect of having Cantor as a colleague, perceiving him as a "corrupter of youth" for teaching his ideas to a younger generation of mathematicians. Worse yet, Kronecker, a well-established figure within the mathematical community and Cantor's former professor, disagreed fundamentally with the thrust of Cantor's work ever since he had intentionally delayed the publication of Cantor's first major publication in 1874. Kronecker, now seen as one of the founders of the constructive viewpoint in mathematics, disliked much of Cantor's set theory because it asserted the existence of sets satisfying certain properties, without giving specific examples of sets whose members did indeed satisfy those properties. Whenever Cantor applied for a post in Berlin, he was declined, and the process usually involved Kronecker, so Cantor came to believe that Kronecker's stance would make it impossible for him ever to leave Halle.


title: Georg Cantor

text: In 1881, Cantor's Halle colleague Eduard Heine died. Halle accepted Cantor's suggestion that Heine's vacant chair be offered to Dedekind, Heinrich M. Weber and Franz Mertens, in that order, but each declined the chair after being offered it. Friedrich Wangerin was eventually appointed, but he was never close to Cantor.


title: Georg Cantor

text: In 1882, the mathematical correspondence between Cantor and Dedekind came to an end, apparently as a result of Dedekind's declining the chair at Halle. Cantor also began another important correspondence, with Gösta Mittag-Leffler in Sweden, and soon began to publish in Mittag-Leffler's journal "Acta Mathematica". But in 1885, Mittag-Leffler was concerned about the philosophical nature and new terminology in a paper Cantor had submitted to "Acta". He asked Cantor to withdraw the paper from "Acta" while it was in proof, writing that it was "... about one hundred years too soon." Cantor complied, but then curtailed his relationship and correspondence with Mittag-Leffler, writing to a third party, "Had Mittag-Leffler had his way, I should have to wait until the year 1984, which to me seemed too great a demand! ... But of course I never want to know anything again about "Acta Mathematica"."


title: Georg Cantor

text: Cantor suffered his first known bout of depression in May 1884. Criticism of his work weighed on his mind: every one of the fifty-two letters he wrote to Mittag-Leffler in 1884 mentioned Kronecker. A passage from one of these letters is revealing of the damage to Cantor's self-confidence:


title: Georg Cantor

text: This crisis led him to apply to lecture on philosophy rather than on mathematics. He also began an intense study of Elizabethan literature, thinking there might be evidence that Francis Bacon wrote the plays attributed to William Shakespeare (see Shakespearean authorship question); this ultimately resulted in two pamphlets, published in 1896 and 1897.


title: Georg Cantor

text: Cantor recovered soon thereafter, and subsequently made further important contributions, including his diagonal argument and theorem. However, he never again attained the high level of his remarkable papers of 1874–84, even after Kronecker's death on December 29, 1891. He eventually sought, and achieved, a reconciliation with Kronecker. Nevertheless, the philosophical disagreements and difficulties dividing them persisted.


title: Georg Cantor

text: In 1889, Cantor was instrumental in founding the German Mathematical Society, and he chaired its first meeting in Halle in 1891, where he first introduced his diagonal argument; his reputation was strong enough, despite Kronecker's opposition to his work, to ensure he was elected as the first president of this society. Setting aside the animosity Kronecker had displayed towards him, Cantor invited him to address the meeting, but Kronecker was unable to do so because his wife was dying from injuries sustained in a skiing accident at the time. Georg Cantor was also instrumental in the establishment of the first International Congress of Mathematicians, which took place in Zürich, Switzerland, in 1897.


title: Georg Cantor

text: After Cantor's 1884 hospitalization there is no record that he was in any sanatorium again until 1899. Soon after that second hospitalization, Cantor's youngest son Rudolph died suddenly on December 16 (Cantor was delivering a lecture on his views on Baconian theory and William Shakespeare), and this tragedy drained Cantor of much of his passion for mathematics. Cantor was again hospitalized in 1903. One year later, he was outraged and agitated by a paper presented by Julius König at the Third International Congress of Mathematicians. The paper attempted to prove that the basic tenets of transfinite set theory were false. Since the paper had been read in front of his daughters and colleagues, Cantor perceived himself as having been publicly humiliated. Although Ernst Zermelo demonstrated less than a day later that König's proof had failed, Cantor remained shaken, and momentarily questioning God. Cantor suffered from chronic depression for the rest of his life, for which he was excused from teaching on several occasions and repeatedly confined to various sanatoria. The events of 1904 preceded a series of hospitalizations at intervals of two or three years. He did not abandon mathematics completely, however, lecturing on the paradoxes of set theory (Burali-Forti paradox, Cantor's paradox, and Russell's paradox) to a meeting of the "Deutsche Mathematiker-Vereinigung" in 1903, and attending the International Congress of Mathematicians at Heidelberg in 1904.


title: Georg Cantor

text: In 1911, Cantor was one of the distinguished foreign scholars invited to the 500th anniversary of the founding of the University of St. Andrews in Scotland. Cantor attended, hoping to meet Bertrand Russell, whose newly-published "Principia Mathematica" repeatedly cited Cantor's work, but the encounter did not come about. The following year, St. Andrews awarded Cantor an honorary doctorate, but illness precluded his receiving the degree in person.


title: Georg Cantor

text: Cantor retired in 1913, and lived in poverty and suffering from malnourishment during World War I. The public celebration of his 70th birthday was canceled because of the war. In June 1917, he entered a sanatorium for the last time and continually wrote to his wife asking to be allowed to go home. Georg Cantor had a fatal heart attack on January 6, 1918, in the sanatorium where he had spent the last year of his life.


title: Georg Cantor

text: Cantor's work between 1874 and 1884 is the origin of set theory. Prior to this work, the concept of a set was a rather elementary one that had been used implicitly since the beginning of mathematics, dating back to the ideas of Aristotle. No one had realized that set theory had any nontrivial content. Before Cantor, there were only finite sets (which are easy to understand) and "the infinite" (which was considered a topic for philosophical, rather than mathematical, discussion). By proving that there are (infinitely) many possible sizes for infinite sets, Cantor established that set theory was not trivial, and it needed to be studied. Set theory has come to play the role of a foundational theory in modern mathematics, in the sense that it interprets propositions about mathematical objects (for example, numbers and functions) from all the traditional areas of mathematics (such as algebra, analysis, and topology) in a single theory, and provides a standard set of axioms to prove or disprove them. The basic concepts of set theory are now used throughout mathematics.


title: Georg Cantor

text: In one of his earliest papers, Cantor proved that the set of real numbers is "more numerous" than the set of natural numbers; this showed, for the first time, that there exist infinite sets of different sizes. He was also the first to appreciate the importance of one-to-one correspondences (hereinafter denoted "1-to-1 correspondence") in set theory. He used this concept to define finite and infinite sets, subdividing the latter into denumerable (or countably infinite) sets and nondenumerable sets (uncountably infinite sets).


title: Georg Cantor

text: Cantor developed important concepts in topology and their relation to cardinality. For example, he showed that the Cantor set, discovered by Henry John Stephen Smith in 1875, is nowhere dense, but has the same cardinality as the set of all real numbers, whereas the rationals are everywhere dense, but countable. He also showed that all countable dense linear orders without end points are order-isomorphic to the rational numbers.


title: Georg Cantor

text: Cantor introduced fundamental constructions in set theory, such as the power set of a set "A", which is the set of all possible subsets of "A". He later proved that the size of the power set of "A" is strictly larger than the size of "A", even when "A" is an infinite set; this result soon became known as Cantor's theorem. Cantor developed an entire theory and arithmetic of infinite sets, called cardinals and ordinals, which extended the arithmetic of the natural numbers. His notation for the cardinal numbers was the Hebrew letter formula_1 (aleph) with a natural number subscript; for the ordinals he employed the Greek letter ω (omega). This notation is still in use today.


title: Georg Cantor

text: The "Continuum hypothesis", introduced by Cantor, was presented by David Hilbert as the first of his twenty-three open problems in his address at the 1900 International Congress of Mathematicians in Paris. Cantor's work also attracted favorable notice beyond Hilbert's celebrated encomium. The US philosopher Charles Sanders Peirce praised Cantor's set theory and, following public lectures delivered by Cantor at the first International Congress of Mathematicians, held in Zürich in 1897, Adolf Hurwitz and Jacques Hadamard also both expressed their admiration. At that Congress, Cantor renewed his friendship and correspondence with Dedekind. From 1905, Cantor corresponded with his British admirer and translator Philip Jourdain on the history of set theory and on Cantor's religious ideas. This was later published, as were several of his expository works.


title: Georg Cantor

text: Cantor's first ten papers were on number theory, his thesis topic. At the suggestion of Eduard Heine, the Professor at Halle, Cantor turned to analysis. Heine proposed that Cantor solve an open problem that had eluded Peter Gustav Lejeune Dirichlet, Rudolf Lipschitz, Bernhard Riemann, and Heine himself: the uniqueness of the representation of a function by trigonometric series. Cantor solved this problem in 1869. It was while working on this problem that he discovered transfinite ordinals, which occurred as indices "n" in the "n"th derived set "S" of a set "S" of zeros of a trigonometric series. Given a trigonometric series f(x) with "S" as its set of zeros, Cantor had discovered a procedure that produced another trigonometric series that had "S" as its set of zeros, where "S" is the set of limit points of "S". If "S" is the set of limit points of "S", then he could construct a trigonometric series whose zeros are "S". Because the sets "S" were closed, they contained their limit points, and the intersection of the infinite decreasing sequence of sets "S", "S", "S", "S"... formed a limit set, which we would now call "S", and then he noticed that "S" would also have to have a set of limit points "S", and so on. He had examples that went on forever, and so here was a naturally occurring infinite sequence of infinite numbers "ω", "ω" + 1, "ω" + 2, ...


title: Georg Cantor

text: Between 1870 and 1872, Cantor published more papers on trigonometric series, and also a paper defining irrational numbers as convergent sequences of rational numbers. Dedekind, whom Cantor befriended in 1872, cited this paper later that year, in the paper where he first set out his celebrated definition of real numbers by Dedekind cuts. While extending the notion of number by means of his revolutionary concept of infinite cardinality, Cantor was paradoxically opposed to theories of infinitesimals of his contemporaries Otto Stolz and Paul du Bois-Reymond, describing them as both "an abomination" and "a cholera bacillus of mathematics". Cantor also published an erroneous "proof" of the inconsistency of infinitesimals.


title: Georg Cantor

text: The beginning of set theory as a branch of mathematics is often marked by the publication of Cantor's 1874 paper, "Ueber eine Eigenschaft des Inbegriffes aller reellen algebraischen Zahlen" ("On a Property of the Collection of All Real Algebraic Numbers"). This paper was the first to provide a rigorous proof that there was more than one kind of infinity. Previously, all infinite collections had been implicitly assumed to be equinumerous (that is, of "the same size" or having the same number of elements). Cantor proved that the collection of real numbers and the collection of positive integers are not equinumerous. In other words, the real numbers are not countable. His proof differs from the diagonal argument that he gave in 1891. Cantor's article also contains a new method of constructing transcendental numbers. Transcendental numbers were first constructed by Joseph Liouville in 1844.


title: Georg Cantor

text: Cantor established these results using two constructions. His first construction shows how to write the real algebraic numbers as a sequence "a", "a", "a", ... In other words, the real algebraic numbers are countable. Cantor starts his second construction with any sequence of real numbers. Using this sequence, he constructs nested intervals whose intersection contains a real number not in the sequence. Since every sequence of real numbers can be used to construct a real not in the sequence, the real numbers cannot be written as a sequence – that is, the real numbers are not countable. By applying his construction to the sequence of real algebraic numbers, Cantor produces a transcendental number. Cantor points out that his constructions prove more – namely, they provide a new proof of Liouville's theorem: Every interval contains infinitely many transcendental numbers. Cantor's next article contains a construction that proves the set of transcendental numbers has the same "power" (see below) as the set of real numbers.


title: Georg Cantor

text: Between 1879 and 1884, Cantor published a series of six articles in "Mathematische Annalen" that together formed an introduction to his set theory. At the same time, there was growing opposition to Cantor's ideas, led by Leopold Kronecker, who admitted mathematical concepts only if they could be constructed in a finite number of steps from the natural numbers, which he took as intuitively given. For Kronecker, Cantor's hierarchy of infinities was inadmissible, since accepting the concept of actual infinity would open the door to paradoxes which would challenge the validity of mathematics as a whole. Cantor also introduced the Cantor set during this period.


title: Georg Cantor

text: The fifth paper in this series, "Grundlagen einer allgemeinen Mannigfaltigkeitslehre" (""Foundations of a General Theory of Aggregates""), published in 1883, was the most important of the six and was also published as a separate monograph. It contained Cantor's reply to his critics and showed how the transfinite numbers were a systematic extension of the natural numbers. It begins by defining well-ordered sets. Ordinal numbers are then introduced as the order types of well-ordered sets. Cantor then defines the addition and multiplication of the cardinal and ordinal numbers. In 1885, Cantor extended his theory of order types so that the ordinal numbers simply became a special case of order types.


title: Georg Cantor

text: In 1891, he published a paper containing his elegant "diagonal argument" for the existence of an uncountable set. He applied the same idea to prove Cantor's theorem: the cardinality of the power set of a set "A" is strictly larger than the cardinality of "A". This established the richness of the hierarchy of infinite sets, and of the cardinal and ordinal arithmetic that Cantor had defined. His argument is fundamental in the solution of the Halting problem and the proof of Gödel's first incompleteness theorem. Cantor wrote on the Goldbach conjecture in 1894.


title: Georg Cantor

text: In 1895 and 1897, Cantor published a two-part paper in "Mathematische Annalen" under Felix Klein's editorship; these were his last significant papers on set theory. The first paper begins by defining set, subset, etc., in ways that would be largely acceptable now. The cardinal and ordinal arithmetic are reviewed. Cantor wanted the second paper to include a proof of the continuum hypothesis, but had to settle for expositing his theory of well-ordered sets and ordinal numbers. Cantor attempts to prove that if "A" and "B" are sets with "A" equivalent to a subset of "B" and "B" equivalent to a subset of "A", then "A" and "B" are equivalent. Ernst Schröder had stated this theorem a bit earlier, but his proof, as well as Cantor's, was flawed. Felix Bernstein supplied a correct proof in his 1898 PhD thesis; hence the name Cantor–Bernstein–Schröder theorem.


title: Georg Cantor

text: Cantor's 1874 Crelle paper was the first to invoke the notion of a 1-to-1 correspondence, though he did not use that phrase. He then began looking for a 1-to-1 correspondence between the points of the unit square and the points of a unit line segment. In an 1877 letter to Richard Dedekind, Cantor proved a far stronger result: for any positive integer "n", there exists a 1-to-1 correspondence between the points on the unit line segment and all of the points in an "n"-dimensional space. About this discovery Cantor wrote to Dedekind: "" ("I see it, but I don't believe it!") The result that he found so astonishing has implications for geometry and the notion of dimension.


title: Georg Cantor

text: In 1878, Cantor submitted another paper to Crelle's Journal, in which he defined precisely the concept of a 1-to-1 correspondence and introduced the notion of "power" (a term he took from Jakob Steiner) or "equivalence" of sets: two sets are equivalent (have the same power) if there exists a 1-to-1 correspondence between them. Cantor defined countable sets (or denumerable sets) as sets which can be put into a 1-to-1 correspondence with the natural numbers, and proved that the rational numbers are denumerable. He also proved that "n"-dimensional Euclidean space R has the same power as the real numbers R, as does a countably infinite product of copies of R. While he made free use of countability as a concept, he did not write the word "countable" until 1883. Cantor also discussed his thinking about dimension, stressing that his mapping between the unit interval and the unit square was not a continuous one.


title: Georg Cantor

text: This paper displeased Kronecker and Cantor wanted to withdraw it; however, Dedekind persuaded him not to do so and Karl Weierstrass supported its publication. Nevertheless, Cantor never again submitted anything to Crelle.


title: Georg Cantor

text: Cantor was the first to formulate what later came to be known as the continuum hypothesis or CH: there exists no set whose power is greater than that of the naturals and less than that of the reals (or equivalently, the cardinality of the reals is "exactly" aleph-one, rather than just "at least" aleph-one). Cantor believed the continuum hypothesis to be true and tried for many years to prove it, in vain. His inability to prove the continuum hypothesis caused him considerable anxiety.


title: Georg Cantor

text: The difficulty Cantor had in proving the continuum hypothesis has been underscored by later developments in the field of mathematics: a 1940 result by Kurt Gödel and a 1963 one by Paul Cohen together imply that the continuum hypothesis can be neither proved nor disproved using standard Zermelo–Fraenkel set theory plus the axiom of choice (the combination referred to as "ZFC").


title: Georg Cantor

text: The transfinite is increasable in magnitude, while the absolute is unincreasable. For example, an ordinal α is transfinite because it can be increased to α + 1. On the other hand, the ordinals form an absolutely infinite sequence that cannot be increased in magnitude because there are no larger ordinals to add to it. In 1883, Cantor also introduced the well-ordering principle "every set can be well-ordered" and stated that it is a "law of thought".


title: Georg Cantor

text: Cantor extended his work on the absolute infinite by using it in a proof. Around 1895, he began to regard his well-ordering principle as a theorem and attempted to prove it. In 1899, he sent Dedekind a proof of the equivalent aleph theorem: the cardinality of every infinite set is an aleph. First, he defined two types of multiplicities: consistent multiplicities (sets) and inconsistent multiplicities (absolutely infinite multiplicities). Next he assumed that the ordinals form a set, proved that this leads to a contradiction, and concluded that the ordinals form an inconsistent multiplicity. He used this inconsistent multiplicity to prove the aleph theorem. In 1932, Zermelo criticized the construction in Cantor's proof.


title: Georg Cantor

text: Cantor avoided paradoxes by recognizing that there are two types of multiplicities. In his set theory, when it is assumed that the ordinals form a set, the resulting contradiction implies only that the ordinals form an inconsistent multiplicity. In contrast, Bertrand Russell treated all collections as sets, which leads to paradoxes. In Russell's set theory, the ordinals form a set, so the resulting contradiction implies that the theory is inconsistent. From 1901 to 1903, Russell discovered three paradoxes implying that his set theory is inconsistent: the Burali-Forti paradox (which was just mentioned), Cantor's paradox, and Russell's paradox. Russell named paradoxes after Cesare Burali-Forti and Cantor even though neither of them believed that they had found paradoxes.


title: Georg Cantor

text: In 1908, Zermelo published his axiom system for set theory. He had two motivations for developing the axiom system: eliminating the paradoxes and securing his proof of the well-ordering theorem. Zermelo had proved this theorem in 1904 using the axiom of choice, but his proof was criticized for a variety of reasons. His response to the criticism included his axiom system and a new proof of the well-ordering theorem. His axioms support this new proof, and they eliminate the paradoxes by restricting the formation of sets.


title: Georg Cantor

text: In 1923, John von Neumann developed an axiom system that eliminates the paradoxes by using an approach similar to Cantor's—namely, by identifying collections that are not sets and treating them differently. Von Neumann stated that a class is too big to be a set if it can be put into one-to-one correspondence with the class of all sets. He defined a set as a class that is a member of some class and stated the axiom: A class is not a set if and only if there is a one-to-one correspondence between it and the class of all sets. This axiom implies that these big classes are not sets, which eliminates the paradoxes since they cannot be members of any class. Von Neumann also used his axiom to prove the well-ordering theorem: Like Cantor, he assumed that the ordinals form a set. The resulting contradiction implies that the class of all ordinals is not a set. Then his axiom provides a one-to-one correspondence between this class and the class of all sets. This correspondence well-orders the class of all sets, which implies the well-ordering theorem. In 1930, Zermelo defined models of set theory that satisfy von Neumann's axiom.


title: Georg Cantor

text: The concept of the existence of an actual infinity was an important shared concern within the realms of mathematics, philosophy and religion. Preserving the orthodoxy of the relationship between God and mathematics, although not in the same form as held by his critics, was long a concern of Cantor's. He directly addressed this intersection between these disciplines in the introduction to his "Grundlagen einer allgemeinen Mannigfaltigkeitslehre", where he stressed the connection between his view of the infinite and the philosophical one. To Cantor, his mathematical views were intrinsically linked to their philosophical and theological implications – he identified the Absolute Infinite with God, and he considered his work on transfinite numbers to have been directly communicated to him by God, who had chosen Cantor to reveal them to the world. He was a devout Lutheran whose explicit Christian beliefs shaped his philosophy of science. Joseph Dauben has traced the effect Cantor's Christian convictions had on the development of transfinite set theory.


title: Georg Cantor

text: Debate among mathematicians grew out of opposing views in the philosophy of mathematics regarding the nature of actual infinity. Some held to the view that infinity was an abstraction which was not mathematically legitimate, and denied its existence. Mathematicians from three major schools of thought (constructivism and its two offshoots, intuitionism and finitism) opposed Cantor's theories in this matter. For constructivists such as Kronecker, this rejection of actual infinity stems from fundamental disagreement with the idea that nonconstructive proofs such as Cantor's diagonal argument are sufficient proof that something exists, holding instead that constructive proofs are required. Intuitionism also rejects the idea that actual infinity is an expression of any sort of reality, but arrive at the decision via a different route than constructivism. Firstly, Cantor's argument rests on logic to prove the existence of transfinite numbers as an actual mathematical entity, whereas intuitionists hold that mathematical entities cannot be reduced to logical propositions, originating instead in the intuitions of the mind. Secondly, the notion of infinity as an expression of reality is itself disallowed in intuitionism, since the human mind cannot intuitively construct an infinite set. Mathematicians such as L. E. J. Brouwer and especially Henri Poincaré adopted an intuitionist stance against Cantor's work. Finally, Wittgenstein's attacks were finitist: he believed that Cantor's diagonal argument conflated the intension of a set of cardinal or real numbers with its extension, thus conflating the concept of rules for generating a set with an actual set.


title: Georg Cantor

text: Some Christian theologians saw Cantor's work as a challenge to the uniqueness of the absolute infinity in the nature of God. In particular, neo-Thomist thinkers saw the existence of an actual infinity that consisted of something other than God as jeopardizing "God's exclusive claim to supreme infinity". Cantor strongly believed that this view was a misinterpretation of infinity, and was convinced that set theory could help correct this mistake: "... the transfinite species are just as much at the disposal of the intentions of the Creator and His absolute boundless will as are the finite numbers.". It is to note that prominent neo-scholastic german philosopher Constantin Gutberlet was in favor of such theory, holding that it didn't oppose the nature of God.


title: Georg Cantor

text: Cantor also believed that his theory of transfinite numbers ran counter to both materialism and determinism – and was shocked when he realized that he was the only faculty member at Halle who did "not" hold to deterministic philosophical beliefs.


title: Georg Cantor

text: It was important to Cantor that his philosophy provided an "organic explanation" of nature, and in his 1883 "Grundlagen", he said that such an explanation could only come about by drawing on the resources of the philosophy of Spinoza and Leibniz. In making these claims, Cantor may have been influenced by FA Trendelenburg, whose lecture courses he attended at Berlin, and in turn Cantor produced a Latin commentary on Book 1 of Spinoza's "Ethica". FA Trendelenburg was also the examiner of Cantor's "Habilitationsschrift".


title: Georg Cantor

text: In 1888, Cantor published his correspondence with several philosophers on the philosophical implications of his set theory. In an extensive attempt to persuade other Christian thinkers and authorities to adopt his views, Cantor had corresponded with Christian philosophers such as Tilman Pesch and Joseph Hontheim, as well as theologians such as Cardinal Johann Baptist Franzelin, who once replied by equating the theory of transfinite numbers with pantheism. Although later this Cardinal accepted the theory as valid, due to some clarifications from Cantor's. Cantor even sent one letter directly to Pope Leo XIII himself, and addressed several pamphlets to him.


title: Georg Cantor

text: Cantor's philosophy on the nature of numbers led him to affirm a belief in the freedom of mathematics to posit and prove concepts apart from the realm of physical phenomena, as expressions within an internal reality. The only restrictions on this metaphysical system are that all mathematical concepts must be devoid of internal contradiction, and that they follow from existing definitions, axioms, and theorems. This belief is summarized in his assertion that "the essence of mathematics is its freedom." These ideas parallel those of Edmund Husserl, whom Cantor had met in Halle.


title: Georg Cantor

text: Meanwhile, Cantor himself was fiercely opposed to infinitesimals, describing them as both an "abomination" and "the cholera bacillus of mathematics".


title: Georg Cantor

text: Cantor's 1883 paper reveals that he was well aware of the opposition his ideas were encountering: "... I realize that in this undertaking I place myself in a certain opposition to views widely held concerning the mathematical infinite and to opinions frequently defended on the nature of numbers."


title: Georg Cantor

text: Hence he devotes much space to justifying his earlier work, asserting that mathematical concepts may be freely introduced as long as they are free of contradiction and defined in terms of previously accepted concepts. He also cites Aristotle, René Descartes, George Berkeley, Gottfried Leibniz, and Bernard Bolzano on infinity. Instead, he always strongly rejected Kant's philosophy, in the realms of both the philosophy of mathematics and metaphysics. He shared B. Russell's motto "Kant or Cantor", and defined Kant "yonder sophistical Philistine who knew so little mathematics."


title: Georg Cantor

text: Cantor's paternal grandparents were from Copenhagen and fled to Russia from the disruption of the Napoleonic Wars. There is very little direct information on them. Cantor's father, Georg Waldemar Cantor, was educated in the Lutheran mission in Saint Petersburg, and his correspondence with his son shows both of them as devout Lutherans. Very little is known for sure about Georg Waldemar's origin or education. Cantor's mother, Maria Anna Böhm, was an Austro-Hungarian born in Saint Petersburg and baptized Roman Catholic; she converted to Protestantism upon marriage. However, there is a letter from Cantor's brother Louis to their mother, stating:


title: Georg Cantor

text: ("Even if we were descended from Jews ten times over, and even though I may be, in principle, completely in favour of equal rights for Hebrews, in social life I prefer Christians...") which could be read to imply that she was of Jewish ancestry.


title: Georg Cantor

text: According to biographers Eric Temple Bell, Cantor was of Jewish descent, although both parents were baptized. In a 1971 article entitled "Towards a Biography of Georg Cantor", the British historian of mathematics Ivor Grattan-Guinness mentions (Annals of Science 27, pp. 345–391, 1971) that he was unable to find evidence of Jewish ancestry. (He also states that Cantor's wife, Vally Guttmann, was Jewish).


title: Georg Cantor

text: In a letter written to Paul Tannery in 1896 (Paul Tannery, Memoires Scientifique 13 Correspondence, Gauthier-Villars, Paris, 1934, p. 306), Cantor states that his paternal grandparents were members of the Sephardic Jewish community of Copenhagen. Specifically, Cantor states in describing his father: "Er ist aber in Kopenhagen geboren, von israelitischen Eltern, die der dortigen portugisischen Judengemeinde..." ("He was born in Copenhagen of Jewish (lit: 'Israelite') parents from the local Portuguese-Jewish community.")


title: Georg Cantor

text: In addition, Cantor's maternal great uncle, a Hungarian violinist Josef Böhm, has been described as Jewish, which may imply that Cantor's mother was at least partly descended from the Hungarian Jewish community.


title: Georg Cantor

text: Until the 1970s, the chief academic publications on Cantor were two short monographs by Arthur Moritz Schönflies (1927) – largely the correspondence with Mittag-Leffler – and Fraenkel (1930). Both were at second and third hand; neither had much on his personal life. The gap was largely filled by Eric Temple Bell's "Men of Mathematics" (1937), which one of Cantor's modern biographers describes as "perhaps the most widely read modern book on the history of mathematics"; and as "one of the worst". Bell presents Cantor's relationship with his father as Oedipal, Cantor's differences with Kronecker as a quarrel between two Jews, and Cantor's madness as Romantic despair over his failure to win acceptance for his mathematics. Grattan-Guinness (1971) found that none of these claims were true, but they may be found in many books of the intervening period, owing to the absence of any other narrative. There are other legends, independent of Bell – including one that labels Cantor's father a foundling, shipped to Saint Petersburg by unknown parents. A critique of Bell's book is contained in Joseph Dauben's biography. Writes Dauben:


title: Anemometer

text: In meteorology, an anemometer () is a device that measures wind speed and direction. It is a common instrument used in weather stations. The earliest known description of an anemometer was by Italian architect and author Leon Battista Alberti (1404–1472) in 1450.


title: Anemometer

text: The anemometer has changed little since its development in the 15th century. Alberti is said to have invented it around 1450. In the ensuing centuries numerous others, including Robert Hooke


title: Anemometer

text: (1635–1703), developed their own versions, with some mistakenly credited as its inventor. In 1846, John Thomas Romney Robinson (1792–1882) improved the design by using four hemispherical cups and mechanical wheels. In 1926, Canadian meteorologist John Patterson (1872–1956) developed a three-cup anemometer, which was improved by Brevoort and Joiner in 1935. In 1991, Derek Weston added the ability to measure wind direction. In 1994, Andreas Pflitsch developed the sonic anemometer.


title: Anemometer

text: A simple type of anemometer was invented in 1845 by Rev Dr John Thomas Romney Robinson of Armagh Observatory. It consisted of four hemispherical cups on horizontal arms mounted on a vertical shaft. The air flow past the cups in any horizontal direction turned the shaft at a rate roughly proportional to the wind's speed. Therefore, counting the shaft's revolutions over a set time interval produced a value proportional to the average wind speed for a wide range of speeds. This type of instrument is also called a "rotational" anemometer.


title: Anemometer

text: With a four-cup anemometer, the wind always has the hollow of one cup presented to it, and is blowing on the back of the opposing cup. Since a hollow hemisphere has a drag coefficient of .38 on the spherical side and 1.42 on the hollow side, more force is generated on the cup that presenting its hollow side to the wind. Because of this asymmetrical force, torque is generated on the anemometer's axis, causing it to spin.


title: Anemometer

text: Theoretically, the anemometer's speed of rotation should be proportional to the wind speed because the force produced on an object is proportional to the speed of the gas or fluid flowing past it. However, in practice, other factors influence the rotational speed, including turbulence produced by the apparatus, increasing drag in opposition to the torque produced by the cups and support arms, and friction on the mount point. When Robinson first designed his anemometer, he asserted that the cups moved one-third of the speed of the wind, unaffected by cup size or arm length. This was apparently confirmed by some early independent experiments, but it was incorrect. Instead, the ratio of the speed of the wind and that of the cups, the "anemometer factor", depends on the dimensions of the cups and arms, and can have a value between two and a little over three. Once the error was discovered, all previous experiment involving anemometers had to be repeated.


title: Anemometer

text: The three-cup anemometer developed by Canadian John Patterson in 1926, and subsequent cup improvements by Brevoort & Joiner of the United States in 1935, led to a cupwheel design with a nearly linear response and an error of less than 3% up to . Patterson found that each cup produced maximum torque when it was at 45° to the wind flow. The three-cup anemometer also had a more constant torque and responded more quickly to gusts than the four-cup anemometer.


title: Anemometer

text: The three-cup anemometer was further modified by Australian Dr. Derek Weston in 1991 to also measure wind direction. He added a tag to one cup, causing the cupwheel speed to increase and decrease as the tag moved alternately with and against the wind. Wind direction is calculated from these cyclical changes in speed, while wind speed is determined from the average cupwheel speed.


title: Anemometer

text: Three-cup anemometers are currently the industry standard for wind resource assessment studies and practice.


title: Anemometer

text: One of the other forms of mechanical velocity anemometer is the "vane anemometer". It may be described as a windmill or a propeller anemometer. Unlike the Robinson anemometer, whose axis of rotation is vertical, the vane anemometer must have its axis parallel to the direction of the wind and is therefore horizontal. Furthermore, since the wind varies in direction and the axis has to follow its changes, a wind vane or some other contrivance to fulfill the same purpose must be employed.


title: Anemometer

text: A "vane anemometer" thus combines a propeller and a tail on the same axis to obtain accurate and precise wind speed and direction measurements from the same instrument. The speed of the fan is measured by a rev counter and converted to a windspeed by an electronic chip. Hence, volumetric flow rate may be calculated if the cross-sectional area is known.


title: Anemometer

text: In cases where the direction of the air motion is always the same, as in ventilating shafts of mines and buildings, wind vanes known as air meters are employed, and give satisfactory results.


title: Anemometer

text: Hot wire anemometers use a fine wire (on the order of several micrometres) electrically heated to some temperature above the ambient. Air flowing past the wire cools the wire. As the electrical resistance of most metals is dependent upon the temperature of the metal (tungsten is a popular choice for hot-wires), a relationship can be obtained between the resistance of the wire and the speed of the air. In most cases, they cannot be used to measure the direction of the airflow, unless coupled with a wind vane.


title: Anemometer

text: Several ways of implementing this exist, and hot-wire devices can be further classified as CCA (constant current anemometer), CVA (constant voltage anemometer) and CTA (constant-temperature anemometer). The voltage output from these anemometers is thus the result of some sort of circuit within the device trying to maintain the specific variable (current, voltage or temperature) constant, following Ohm's law.


title: Anemometer

text: Additionally, PWM (pulse-width modulation) anemometers are also used, wherein the velocity is inferred by the time length of a repeating pulse of current that brings the wire up to a specified resistance and then stops until a threshold "floor" is reached, at which time the pulse is sent again.


title: Anemometer

text: Hot-wire anemometers, while extremely delicate, have extremely high frequency-response and fine spatial resolution compared to other measurement methods, and as such are almost universally employed for the detailed study of turbulent flows, or any flow in which rapid velocity fluctuations are of interest.


title: Anemometer

text: An industrial version of the fine-wire anemometer is the thermal flow meter, which follows the same concept, but uses two pins or strings to monitor the variation in temperature. The strings contain fine wires, but encasing the wires makes them much more durable and capable of accurately measuring air, gas, and emissions flow in pipes, ducts, and stacks. Industrial applications often contain dirt that will damage the classic hot-wire anemometer.


title: Anemometer

text: In laser Doppler velocimetry, laser Doppler anemometers use a beam of light from a laser that is divided into two beams, with one propagated out of the anemometer. Particulates (or deliberately introduced seed material) flowing along with air molecules near where the beam exits reflect, or backscatter, the light back into a detector, where it is measured relative to the original laser beam. When the particles are in great motion, they produce a Doppler shift for measuring wind speed in the laser light, which is used to calculate the speed of the particles, and therefore the air around the anemometer.


title: Anemometer

text: Ultrasonic anemometers, first developed in the 1950s, use ultrasonic sound waves to measure wind velocity. They measure wind speed based on the time of flight of sonic pulses between pairs of transducers. Measurements from pairs of transducers can be combined to yield a measurement of velocity in 1-, 2-, or 3-dimensional flow. The spatial resolution is given by the path length between transducers, which is typically 10 to 20 cm. Ultrasonic anemometers can take measurements with very fine temporal resolution, 20 Hz or better, which makes them well suited for turbulence measurements. The lack of moving parts makes them appropriate for long-term use in exposed automated weather stations and weather buoys where the accuracy and reliability of traditional cup-and-vane anemometers are adversely affected by salty air or dust. Their main disadvantage is the distortion of the air flow by the structure supporting the transducers, which requires a correction based upon wind tunnel measurements to minimize the effect. An international standard for this process, ISO 16622 "Meteorology—Ultrasonic anemometers/thermometers—Acceptance test methods for mean wind measurements" is in general circulation. Another disadvantage is lower accuracy due to precipitation, where rain drops may vary the speed of sound.


title: Anemometer

text: Since the speed of sound varies with temperature, and is virtually stable with pressure change, ultrasonic anemometers are also used as thermometers.


title: Anemometer

text: Two-dimensional (wind speed and wind direction) sonic anemometers are used in applications such as weather stations, ship navigation, aviation, weather buoys and wind turbines. Monitoring wind turbines usually requires a refresh rate of wind speed measurements of 3 Hz, easily achieved by sonic anemometers. Three-dimensional sonic anemometers are widely used to measure gas emissions and ecosystem fluxes using the eddy covariance method when used with fast-response infrared gas analyzers or laser-based analyzers.


title: Anemometer

text: Acoustic resonance anemometers are a more recent variant of sonic anemometer. The technology was invented by Savvas Kapartis and patented in 1999. Whereas conventional sonic anemometers rely on time of flight measurement, acoustic resonance sensors use resonating acoustic (ultrasonic) waves within a small purpose-built cavity in order to perform their measurement.


title: Anemometer

text: Built into the cavity is an array of ultrasonic transducers, which are used to create the separate standing-wave patterns at ultrasonic frequencies. As wind passes through the cavity, a change in the wave's property occurs (phase shift). By measuring the amount of phase shift in the received signals by each transducer, and then by mathematically processing the data, the sensor is able to provide an accurate horizontal measurement of wind speed and direction.


title: Anemometer

text: Because acoustic resonance technology enables measurement within a small cavity, the sensors tend to be typically smaller in size than other ultrasonic sensors. The small size of acoustic resonance anemometers makes them physically strong and easy to heat, and therefore resistant to icing. This combination of features means that they achieve high levels of data availability and are well suited to wind turbine control and to other uses that require small robust sensors such as battlefield meteorology. One issue with this sensor type is measurement accuracy when compared to a calibrated mechanical sensor. For many end uses, this weakness is compensated for by the sensor's longevity and the fact that it does not require recalibration once installed.


title: Anemometer

text: A common anemometer for basic use is constructed from a ping-pong ball attached to a string. When the wind blows horizontally, it presses on and moves the ball; because ping-pong balls are very lightweight, they move easily in light winds. Measuring the angle between the string-ball apparatus and the vertical gives an estimate of the wind speed.


title: Anemometer

text: This type of anemometer is mostly used for middle-school level instruction, which most students make on their own, but a similar device was also flown on the Phoenix Mars Lander.


title: Anemometer

text: These are the first modern anemometers. They consist of a flat plate suspended from the top so that the wind deflects the plate. In 1450, the Italian art architect Leon Battista Alberti invented the first mechanical anemometer; in 1664 it was re-invented by Robert Hooke (who is often mistakenly considered the inventor of the first anemometer). Later versions of this form consisted of a flat plate, either square or circular, which is kept normal to the wind by a wind vane. The pressure of the wind on its face is balanced by a spring. The compression of the spring determines the actual force which the wind is exerting on the plate, and this is either read off on a suitable gauge, or on a recorder. Instruments of this kind do not respond to light winds, are inaccurate for high wind readings, and are slow at responding to variable winds. Plate anemometers have been used to trigger high wind alarms on bridges.


title: Anemometer

text: James Lind's anemometer of 1775 consisted of a vertically mounted glass U tube containing a liquid manometer (pressure gauge), with one end bent out in a horizontal direction to face the wind flow and the other vertical end capped. Though the Lind was not the first it was the most practical and best known anemometer of this type. If the wind blows into the mouth of a tube it causes an increase of pressure on one side of the manometer. The wind over the open end of a vertical tube causes little change in pressure on the other side of the manometer. The resulting elevation difference in the two legs of the U tube is an indication of the wind speed. However, an accurate measurement requires that the wind speed be directly into the open end of the tube; small departures from the true direction of the wind causes large variations in the reading.


title: Anemometer

text: The successful metal pressure tube anemometer of William Henry Dines in 1892 utilized the same pressure difference between the open mouth of a straight tube facing the wind and a ring of small holes in a vertical tube which is closed at the upper end. Both are mounted at the same height. The pressure differences on which the action depends are very small, and special means are required to register them. The recorder consists of a float in a sealed chamber partially filled with water. The pipe from the straight tube is connected to the top of the sealed chamber and the pipe from the small tubes is directed into the bottom inside the float. Since the pressure difference determines the vertical position of the float this is a measure of the wind speed.


title: Anemometer

text: The great advantage of the tube anemometer lies in the fact that the exposed part can be mounted on a high pole, and requires no oiling or attention for years; and the registering part can be placed in any convenient position. Two connecting tubes are required. It might appear at first sight as though one connection would serve, but the differences in pressure on which these instruments depend are so minute, that the pressure of the air in the room where the recording part is placed has to be considered. Thus if the instrument depends on the pressure or suction effect alone, and this pressure or suction is measured against the air pressure in an ordinary room, in which the doors and windows are carefully closed and a newspaper is then burnt up the chimney, an effect may be produced equal to a wind of 10 mi/h (16 km/h); and the opening of a window in rough weather, or the opening of a door, may entirely alter the registration.


title: Anemometer

text: While the Dines anemometer had an error of only 1% at , it did not respond very well to low winds due to the poor response of the flat plate vane required to turn the head into the wind. In 1918 an aerodynamic vane with eight times the torque of the flat plate overcame this problem.


title: Anemometer

text: Modern tube anemometers use the same principle as in the Dines anemometer but using a different design. The implementation uses a pitot-static tube which is a pitot tube with two ports, pitot and static, that is normally used in measuring the airspeed of aircraft. The pitot port measures the dynamic pressure of the open mouth of a tube with pointed head facing wind, and the static port measures the static pressure from small holes along the side on that tube. The pitot tube is connected to a tail so that it always makes the tube's head to face the wind. Additionally, the tube is heated to prevent rime ice formation on the tube. There are two lines from the tube down to the devices to measure the difference in pressure of the two lines. The measurement devices can be manometers, pressure transducers, or analog chart recorders.


title: Anemometer

text: In the tube anemometer the dynamic pressure is actually being measured, although the scale is usually graduated as a velocity scale. If the actual air density differs from the calibration value, due to differing temperature, elevation or barometric pressure, a correction is required to obtain the actual wind speed. Approximately 1.5% (1.6% above 6,000 feet) should be added to the velocity recorded by a tube anemometer for each 1000 ft (5% for each kilometer) above sea-level.


title: Anemometer

text: At airports, it is essential to have accurate wind data under all conditions, including freezing precipitation. Anemometry is also required in monitoring and controlling the operation of wind turbines, which in cold environments are prone to in-cloud icing. Icing alters the aerodynamics of an anemometer and may entirely block it from operating. Therefore, anemometers used in these applications must be internally heated. Both cup anemometers and sonic anemometers are presently available with heated versions.


title: Anemometer

text: In order for wind speeds to be comparable from location to location, the effect of the terrain needs to be considered, especially in regard to height. Other considerations are the presence of trees, and both natural canyons and artificial canyons (urban buildings). The standard anemometer height in open rural terrain is 10 meters.


title: Taiwanese Hokkien

text: Taiwanese Hokkien () (; Tâi-lô: "Tâi-uân-uē"), also known as Taigi/Taigu (; Pe̍h-ōe-jī/Tâi-lô: "Tâi-gí / Tâi-gú"), Taiwanese, Taiwanese Minnan, Hoklo and Holo, is a variety of the Hokkien language spoken natively by about 70%+ of the population of Taiwan. It is spoken by a significant portion of Taiwanese people descended from immigrants of southern Fujian during the Qing dynasty. It is one of the national languages of Taiwan.


title: Taiwanese Hokkien

text: Taiwanese is generally similar to spoken Amoy Hokkien, Quanzhou Hokkien, and Zhangzhou Hokkien, as well as their dialectal forms used in Southeast Asia, such as Singaporean Hokkien, Penang Hokkien, Philippine Hokkien, Medan Hokkien, & Southern Peninsular Malaysian Hokkien. It is mutually intelligible with Amoy Hokkien and Zhangzhou Hokkien at the mouth of the Jiulong River (九龍) immediately to the west in mainland China and with Philippine Hokkien to the south, spoken altogether by about 3 million people. The mass popularity of Hokkien entertainment media from Taiwan has given prominence to the Taiwanese variety of Hokkien, especially since the 1980s.


title: Taiwanese Hokkien

text: Taiwanese Hokkien is a branched-off variety of standard Hokkien, a group of Southern Min language. Like many Min varieties, it has distinct literary and colloquial layers of vocabulary, often associated with formal and informal registers respectively. The literary layer can be traced to the late Tang dynasty and can thus be related to Middle Chinese. In contrast, the colloquial layers of Min varieties are believed to have branched from the mainstream of Chinese around the time of the Han dynasty.


title: Taiwanese Hokkien

text: Regional variations within the Taiwanese variant may be traced back to Hokkien variants spoken in Southern Fujian, specifically those from Quanzhou and Zhangzhou, then later Amoy. Taiwanese also contains loanwords from Japanese and the native Formosan languages. Recent work by scholars such as Ekki Lu, Toru Sakai (酒井亨 "Sakai Tōru"), and Lí Khîn-hoāⁿ (also known as Tavokan Khîn-hoāⁿ or Chin-An Li), based on former research by scholars such as Ông Io̍k-tek, has gone so far as to associate part of the basic vocabulary of the colloquial Taiwanese with the Austronesian and Tai language families; however, such claims are controversial.


title: Taiwanese Hokkien

text: The literary form of Hokkien once flourished in Fujian and was brought to Taiwan by early emigrants. "Tale of the Lychee Mirror", a manuscript for a series of plays published during the Ming dynasty in 1566, is one of the earliest known works. This form of the language is now largely extinct. However, literary readings of the numbers are used in certain contexts such as reciting telephone numbers (see Literary and colloquial readings of Chinese characters).


title: Taiwanese Hokkien

text: During the Yuan dynasty, Quanzhou became a major international port for trade with the outside world. From that period onwards, many people from the Hokkien-speaking regions (southern Fujian) started to emigrate overseas due to political and economic reasons. One of the destinations of the emigrants is the relatively undeveloped island of Formosa, starting around 1600. They brought with them their native language, Hokkien.


title: Taiwanese Hokkien

text: During the late Ming dynasty, the political chaos pushed more migrants from southern Fujian and eastern Guangdong to Taiwan. The earliest immigrants involved in Taiwan's development included pirate-merchants Pedro Yan Shiqi and Zheng Zhilong. In 1621, Chinese Peter and his forces, hailing from Zhangzhou, occupied "Ponkan" (modern-day Beigang, Yunlin) and started to develop "Tirosen" (modern-day Chiayi). After the death of Peter and another pirate, Li Dan of Quanzhou, Zheng sought to dominate the Strait of Taiwan. By 1628, he had grown so powerful that the Ming court bestowed him the official title, "Patrolling Admiral".


title: Taiwanese Hokkien

text: In 1624, the number of Chinese in the island was about 25,000. During the reign of Chongzhen Emperor (1627–1644), there were frequent droughts in the Fujian region. Zheng and a Chinese official suggested sending victims to Taiwan and provide "for each person three taels of silver and for each three people one ox". Although this plan was never carried out, the Zheng family maintained an interest in Taiwan that would have dire consequences for the Dutch, who ruled Taiwan as Dutch Formosa at the time.


title: Taiwanese Hokkien

text: In 1624 and 1626, the Dutch and Spanish forces occupied the Tainan and Keelung areas, respectively. During the 40 years of Dutch colonial rule of Taiwan, the Dutch recruited many Chinese from the Quanzhou, Zhangzhou area of southern Fujian to help develop Taiwan.


title: Taiwanese Hokkien

text: In the 1661 Siege of Fort Zeelandia, Chinese general Koxinga, marshalling a military force composed of fellow hometown hoklo soldiers of Southern Fujian, expelled the Dutch and established the Kingdom of Tungning. Koxinga originated from the Quanzhou region. Chen Yonghua, who was in charge of establishing the education system of Tungning, also originated from Tong'an county of Quanzhou Prefecture. Because most of the soldiers he brought to Taiwan came from Quanzhou, the prestige variant of Hokkien on the island at the time was the Quanzhou dialect.


title: Taiwanese Hokkien

text: In 1683, Chinese admiral Shi Lang, marshalling a military force again composed of fellow hometown hoklo soldiers of Southern Fujian, attacked Taiwan in the Battle of Penghu, ending the Tungning era and beginning Qing dynasty rule (until 1895).


title: Taiwanese Hokkien

text: In the first decades of the 18th century, the linguistic differences between the Qing imperial bureaucrats and the commoners were recorded by the Mandarin-speaking first Imperial High Commissioner to Taiwan (1722), Huang Shujing:


title: Taiwanese Hokkien

text: The tone of Huang's message foretold the uneasy relationships between different language communities and colonial establishments over the next few centuries.


title: Taiwanese Hokkien

text: During the 200 years of Qing dynasty rule, thousands of immigrants from Fujian arrived yearly; the population was over one million in the middle of the 18th century. Civil unrest and armed conflicts were frequent. In addition to resistance against governments (both Chinese and later Japanese), battles between ethnic groups were also significant: the belligerents usually grouped around the language they used. History has recorded battles between Hakka speakers and Hokkien speakers, between these and the aborigines, and even between those who spoke different variants of Hokkien.


title: Taiwanese Hokkien

text: In the early 20th century, the Hoklo people in Taiwan could be categorized as originating from modern day Xiamen, Quanzhou, Zhangzhou, and Zhangpu. People from the former two areas (Quanzhou-speaking) were dominant in the north of the island and along the west coast, whereas people from the latter two areas (Zhangzhou-speaking) were dominant in the south and perhaps the central plains as well.


title: Taiwanese Hokkien

text: Although there were conflicts between Quanzhou- and Zhangzhou-speakers in Taiwan historically, their gradual intermingling led to the mixture of the two accents. Apart from Lukang city and Yilan County, which have preserved their original Quanzhou and Zhangzhou accents respectively, almost every region of Taiwan now speaks a mixture of Quanzhou and Zhangzhou Hokkien. A similar phenomenon occurred in Xiamen (Amoy) after 1842, when the mixture of Quanzhou and Zhangzhou Hokkien displaced the Quanzhou dialect to yield the modern Amoy dialect.


title: Taiwanese Hokkien

text: During the Japanese colonial rule of Taiwan, Taiwan began to hold Amoy Hokkien as its standard pronunciation; the Japanese called this mixture .


title: Taiwanese Hokkien

text: Due to the influx of Japanese loanwords before 1945 and the political separation after 1949, Amoy Hokkien and Taiwanese Hokkien began to diverge slightly.


title: Taiwanese Hokkien

text: Later, in the 20th century, the conceptualization of Taiwanese is more controversial than most variations of Chinese because at one time it marked a clear division between the Mainlanders who arrived in 1949 and the pre-existing majority native Taiwanese. Although the political and linguistic divisions between the two groups have blurred considerably, the political issues surrounding Taiwanese have been more controversial and sensitive than for other varieties of Chinese.


title: Taiwanese Hokkien

text: After the First Sino-Japanese War, due to military defeat to the Japanese, the Qing dynasty ceded Taiwan to Japan, causing contact with the Hokkien-speaking regions of mainland China to stop. During Japanese rule, Japanese became an official language in Taiwan, and Taiwanese began to absorb large number of Japanese loanwords into its language. Examples of such loanwords (some which had in turn been borrowed from English) include "piān-só͘" from , "phêng" from (see also Taiwanese units of measurement), "ga-suh" from , "o͘-tó͘-bái" from . All of these caused Taiwanese to deviate from Hokkien used elsewhere.


title: Taiwanese Hokkien

text: During Kōminka of the late Japanese colonial period, the Japanese language appeared in every corner of Taiwan. The Second Sino-Japanese War beginning in 1937 brought stricter measures into force, and along with the outlawing of romanized Taiwanese, various publications were prohibited and Confucian-style private schools which taught Classical Chinese with literary Southern Min pronunciation – were closed down in 1939. Taiwanese thus was reduced to a common daily language. In 1937 the colonial government introduced a concept called "National Language Family" (, which meant that families that proved that they adopted Japanese as their daily language enjoyed benefits such as greater access to education.


title: Taiwanese Hokkien

text: After the handover of Taiwan to the Republic of China in 1945, there was brief cultural exchange with mainland China followed by further oppression. The Chinese Civil War resulted in another political separation when the Kuomintang (Chinese Nationalist Party) government retreated to Taiwan following their defeat by the communists in 1949. The influx of two million soldiers and civilians caused the population of Taiwan to increase from 6 million to 8 million. The government subsequently promoted Mandarin while suppressing, but short of banning, the use of written Taiwanese Hokkien (e.g. Pe̍h-ōe-jī, a phonetic rendering of spoken Hokkien using the Latin alphabet) as part of its general policy of political repression. In 1964 the use of spoken Taiwanese Hokkien or Hakka in schools or in official settings was forbidden; violations of the prohibition in schools often resulted in physical punishments, fines, or humiliation.


title: Taiwanese Hokkien

text: Only after the lifting of martial law in 1987 and the mother tongue movement in the 1990s did Taiwan finally see a true revival in Taiwanese Hokkien. Today, there are a large number of Taiwanese Hokkien scholars dedicated to researching the language. Despite this, however, according to census data the number of people speaking Taiwanese continued to drop.


title: Taiwanese Hokkien

text: The history of the Taiwanese variety of Hokkien and its interaction with Mandarin is complex and at times controversial, even regarding its name. The language has no official name in Taiwan. Some dislike the name "Taiwanese" as they feel that it belittles other languages spoken on the island such as Mandarin, Hakka, and the indigenous languages. Others prefer the names Southern Min, Minnan or Hokkien as this views Taiwanese as a form of the Chinese variety spoken in Fujian province in mainland China. Others dislike those names for precisely the same reason. In the American Community Survey run by the United States Census Bureau, Taiwanese was referred to as "Formosan" from 2012 to 2015 and as "Min Nan Chinese" since 2016.


title: Taiwanese Hokkien

text: Phonologically, Hokkien is a tonal language with extensive tone sandhi rules. Syllables consist maximally of an initial consonant, a vowel, a final consonant, and a tone.


title: Taiwanese Hokkien

text: Unlike many other varieties of Chinese such as Mandarin and Cantonese, there are no native labiodental phonemes (i.e., ).


title: Taiwanese Hokkien

text: The vowel is akin to a schwa; in contrast, (with dot) is a more open vowel. In addition, there are several diphthongs and triphthongs (for example, ). The consonants and can function as a syllabic nucleus and are therefore included here as vowels. The vowels may be either plain or nasal: is non-nasal, and is the same vowel with concurrent nasal articulation. This is similar to French, Portuguese, Polish, and many other languages.


title: Taiwanese Hokkien

text: There are two pronunciations of vowel . In the south (e.g., Tainan and Kaohsiung) it is ; in the north (e.g., Taipei) it is . Due to development of transportation and communication, both pronunciations are common and acceptable throughout the country.


title: Taiwanese Hokkien

text: In the traditional analysis, there are eight "tones", numbered from 1 to 8. Strictly speaking, there are only five tonal contours. But as in other Sinitic languages, the two kinds of stopped syllables are considered also to be tones and assigned numbers 4 and 8. In Taiwanese tone 6 has merged into tone 7, and thus duplicated in the count. Here the eight tones are shown, following the traditional tone class categorization, named after the tones of Middle Chinese:


title: Taiwanese Hokkien

text: For tones 4 and 8, a final consonant , , or may appear. When this happens, it is impossible for the syllable to be nasal. Indeed, these are the counterpart to the nasal final consonants , , and , respectively, in other tones. However, it is possible to have a nasal 4th or 8th tone syllable such as , as long as there is no final consonant other than .


title: Taiwanese Hokkien

text: In the dialect spoken near the northern coast of Taiwan, there is no distinction between tones number 8 and number 4 – both are pronounced as if they follow the tone sandhi rules of tone number 4.


title: Taiwanese Hokkien

text: Tone number 0, typically written with two consecutive hyphens (--a) or a point (·a) before the syllable with this tone, is used to mark enclitics denoting the extent of a verb action, the end of a noun phrase, etc. A frequent use of this tone is to denote a question, such as in "Chia̍h-pá--bōe?", literally meaning 'Have you eaten yet?’. This is realized by speaking the syllable with either a low-falling tone (3) or a low stop (4). The syllable prior to the maintains its original tone.


title: Taiwanese Hokkien

text: A syllable requires a vowel (or diphthong or triphthong) to appear in the middle. All consonants can appear at the initial position. The consonants and (and some consider ) may appear at the end of a syllable. Therefore, it is possible to have syllables such as ("(to) tickle") and ("soup").


title: Taiwanese Hokkien

text: Taiwanese has extremely extensive tone sandhi (tone-changing) rules: in an utterance, only the last syllable pronounced is not affected by the rules. What an ‘utterance’ (or ‘intonational phrase’) is, in the context of this language, is an ongoing topic for linguistic research, but some general rules apply:


title: Taiwanese Hokkien

text: The following rules, listed in the traditional pedagogical mnemonic order, govern the pronunciation of tone on each of the syllables affected (that is, all but those described according to the rules listed above):


title: Taiwanese Hokkien

text: There are a number of a single syllable words that undergo double tone sandhi, that is, they follow the tone change rule twice and are pronounced according to the second tone change. These syllables are almost always a 4th tone ending in -h, and include the words 欲 (beh), 佮 (kah), 閣 (koh), 才 (chiah), as well as the 3rd tone verb 去 khì. As a result of following the tone change rule twice, these syllables are all pronounced as tone number 1.


title: Taiwanese Hokkien

text: Apart from the normal tone sandhi rules described above, there are two special cases where a different set of tone sandhi apply. In a noun with the noun suffix " (), the penultimate syllable is governed by the following rules:


title: Taiwanese Hokkien

text: Finally, in the case of single-syllable adjective triplication (for added emphasis), the first syllable is governed by the following rules (the second syllable follows the normal tone sandhi rules above):


title: Taiwanese Hokkien

text: See , and the work of Robert L. Cheng (鄭良偉; Tēⁿ Liông-úi) for modern linguistic approaches to tones and tone sandhi in Taiwanese.


title: Taiwanese Hokkien

text: Watch this video by 阿勇台語 (Aiong Taigi) for a more in depth look at the triplicated tone sandhi with examples.


title: Taiwanese Hokkien

text: Modern linguistic studies (by Robert L. Cheng and Chin-An Li, for example) estimate that most (75% to 90%) Taiwanese words have cognates in other Sinitic languages. False friends do exist; for example, "cháu" () means "to run" in Taiwanese, whereas the Mandarin cognate, "zǒu", means "to walk". Moreover, cognates may have different lexical categories; for example, the morpheme "phīⁿ" () means not only "nose" (a noun, as in Mandarin "bí") but also "to smell" (a verb, unlike Mandarin).


title: Taiwanese Hokkien

text: Among the apparently cognate-less words are many basic words with properties that contrast with similar-meaning words of pan-Chinese derivation. Often the former group lacks a standard Han character, and the words are variously considered colloquial, intimate, vulgar, uncultured, or more concrete in meaning than the pan-Chinese synonym. Some examples: "lâng" ( or , person, concrete) vs. "jîn" (人, person, abstract); "" (, woman) vs. "lú-jîn" (女人, woman, literary). Unlike the English Germanic/Latin contrast, however, the two groups of Taiwanese words cannot be as strongly attributed to the influences of two disparate linguistic sources.


title: Taiwanese Hokkien

text: Extensive contact with the Japanese language has left a legacy of Japanese loanwords, with 172 recorded in the Ministry of Education's "Dictionary of Frequently-Used Taiwan Minnan". Although a very small percentage of the vocabulary, their usage tends to be high-frequency because of their relevance to modern society and popular culture. Examples are: "o͘-tó͘-bái" from and "pháng" from . Grammatical particles borrowed from Japanese, notably "te̍k" from and "ka" from , show up in the Taiwanese of older speakers.


title: Taiwanese Hokkien

text: Whereas Mandarin attaches a syllabic suffix to the singular pronoun to make a collective form, Taiwanese pronouns are collectivized through nasalization. For example, "i" (he/she/it) and "goá" (I) become "in" (they) and "goán" (we), respectively. The "-n" thus represents a subsyllabic morpheme. Like all other varieties of Chinese, Taiwanese does not have true grammatical plurals.


title: Taiwanese Hokkien

text: Unlike English, Taiwanese has two first-person plural pronouns. This distinction is called inclusive, which includes the addressee, and exclusive, which excludes the addressee. Thus, "goán" means "we excluding you", while "lán" means "we including you" (similar to pluralis auctoris). The inclusive "lán" may be used to express politeness or solidarity, as in the example of a speaker asking a stranger "Where do we live?" while implicitly asking "Where do "you" live?".


title: Taiwanese Hokkien

text: The syntax of Taiwanese is similar to southern sinitic languages such as Hakka and Yue. The subject–verb–object sequence is typical as in, for example, Mandarin, but subject–object–verb or the passive voice (with the sequence object–subject–verb) is possible with particles. Take a simple sentence for example: 'I hold you.' The words involved are: "goá" ('I' or 'me'), "phō" ('to hold'), "lí" ('you').


title: Taiwanese Hokkien

text: With this, more complicated sentences can be constructed: "Goá kā chúi hō͘ lí lim" ('I give water for you to drink': "chúi" means 'water'; "lim" is 'to drink').


title: Taiwanese Hokkien

text: This article can only give a few very simple examples on the syntax, for flavour. Linguistic work on the syntax of Taiwanese is still a (quite nascent) scholarly topic being explored.


title: Taiwanese Hokkien

text: Until the late 19th century, Taiwanese speakers wrote mostly in Classical Chinese, although songbooks using Han characters are attested from the 1820s. Among many systems of writing Taiwanese using Latin characters, the most used is called Pe̍h-ōe-jī (POJ) and was developed in the 19th century, while the Taiwanese Romanization System (Tâi-lô) has been officially promoted since 2006 by Taiwan's Ministry of Education. (For additional romanized systems, see references in "Orthography in Latin characters", below.) Nonetheless, Taiwanese speakers nowadays most commonly write in Mandarin, though many of the same characters are also used to write Taiwanese.


title: Taiwanese Hokkien

text: In most cases, Taiwanese speakers write using the script called Han characters as in Mandarin, although there are a number of special characters which are unique to Taiwanese and which are sometimes used in informal writing. Where Han characters are used, they are not always etymological or genetic; the borrowing of similar-sounding or similar-meaning characters is a common practice. Bilingual speakers of both Mandarin and Taiwanese sometimes attempt to represent the sounds by adopting similar-sounding Mandarin Han characters. For example, the Han characters of the vulgar slang 'khoàⁿ sáⁿ-siâu' (, substituted for the etymologically correct , meaning 'What the hell are you looking at?’) has very little meaning in Mandarin and may not be readily understood by a Taiwanese monolingual, as knowledge of Mandarin character readings is required to fully decipher it.


title: Taiwanese Hokkien

text: In 2007, the Ministry of Education in Taiwan published the first list of Taiwanese Southern Min Recommended Characters, a list of 300 Han characters standardized for the use of writing Taiwanese and implemented the teaching of them in schools. In 2008, the ministry published a second list of 100 characters, and in 2009 added 300 more, giving a total of 700 standardized characters used to write uniquely Taiwanese words. With increasing literacy in Taiwanese, there are currently more Taiwanese online bloggers who write Taiwanese online using these standardized Chinese characters. Han characters are also used by Taiwan's Hokkien literary circle for Hokkien poets and writers to write literature or poetry in Taiwanese.


title: Taiwanese Hokkien

text: There are several Latin-based orthographies, the oldest being Pe̍h-ōe-jī (POJ, meaning "vernacular writing"), developed in the 19th century. Taiwanese Romanization System (Tâi-ôan lô-má-jī, Tâi-lô) and Taiwanese Language Phonetic Alphabet (TLPA) are two later adaptations of POJ. Other 20th-century innovations include Daighi tongiong pingim (DT), Ganvsig daiuuan bhanlam ghiw tongiong pingimv (GDT), Modern Literal Taiwanese (MLT), Simplified MLT (SMLT), Phofsit Daibuun (PSDB). The last four employ tonal spelling to indicate tone without use of diacritic symbols, but letters instead.


title: Taiwanese Hokkien

text: Twenty-four in all, including the obsolete , which was used to represent the modern at some places. The additional necessities are the nasal symbol   (superscript ; the uppercase form is sometimes used in all caps texts, such as book titles or section headings), and the tonal diacritics.


title: Taiwanese Hokkien

text: POJ was developed first by Presbyterian missionaries and later by the indigenous Presbyterian Church in Taiwan; they have been active in promoting the language since the late 19th century. Recently there has been an increase in texts using a mixed orthography of Han characters and romanization, although these texts remain uncommon.


title: Taiwanese Hokkien

text: In 2006, the National Languages Committee (Ministry of Education, Republic of China) proposed Taiwanese Romanization System (Tâi-ôan Lô-má-jī pheng-im, Tâi-Lô). This alphabet reconciles two orthographies, TLPA and POJ. The changes for the consonants involved using for POJ's (reverting to the orthography in the 19th century), and for . For the vowels, could optionally represented as . The nasal mark could also be represented optionally as . The rest of the alphabet, most notably the use of diacritics to mark the tones, appeared to keep to the POJ tradition. One of the aims of this compromise was to curb any increase of 'market share' for Daighi tongiong pingim/Tongyong Pinyin. It is unclear whether the community will adopt this new agreement.


title: Taiwanese Hokkien

text: There was an orthography of Taiwanese based on the Japanese kana during Japanese rule. The Kuomintang government also tried to introduce an orthography in bopomofo.


title: Taiwanese Hokkien

text: Many keyboard layouts and input methods for entering either Latin or Han characters in Taiwanese are available. Some of them are free-of-charge, some commercial.


title: Taiwanese Hokkien

text: The Min Nan dialect group is registered per as zh-min-nan. Taiwanese Min Nan can be represented as 'zh-min-nan-TW'.


title: Taiwanese Hokkien

text: When writing Taiwanese in Han characters, some writers create 'new' characters when they consider it is impossible to use directly or borrow existing ones; this corresponds to similar practices in character usage in Cantonese, Vietnamese chữ nôm, Korean hanja and Japanese kanji. These are usually not encoded in Unicode (or the corresponding ISO/IEC 10646: Universal Character Set), thus creating problems in computer processing.


title: Taiwanese Hokkien

text: All Latin characters required by Pe̍h-ōe-jī can be represented using Unicode (or the corresponding ISO/IEC 10646: Universal character set), using precomposed or combining (diacritics) characters.


title: Taiwanese Hokkien

text: Prior to June 2004, the vowel akin to but more open than ⟨o⟩, written with a 'dot above right', was not encoded. The usual workaround was to use the (stand-alone; spacing) character ‘middle dot’ (U+00B7, ⟨·⟩) or less commonly the combining character 'dot above' (U+0307). As these are far from ideal, since 1997 proposals have been submitted to the ISO/IEC working group in charge of ISO/IEC 10646 – namely, ISO/IEC JTC1/SC2/WG2 – to encode a new combining character 'dot above right'. This is now officially assigned to U+0358 (see documents N1593, N2507, N2628,


title: Taiwanese Hokkien

text: The prestige variant of Taiwanese Hokkien is the southern speech found in Tainan and Kaohsiung. Other major variants are the northern speech, the central speech (near Taichung and the port town of Lukang), and the northern (northeastern) coastal speech (dominant in Yilan).


title: Taiwanese Hokkien

text: The distinguishing feature of the coastal speech is the use of the vowel in place of . The northern speech is distinguished by the absence of the 8th tone, and some vowel exchanges (for example, and , and ). The central speech has an additional vowel or between and , which may be represented as . There are also a number of other pronunciation and lexical differences between the Taiwanese variants; the online Ministry of Education dictionary specifies these to a resolution of eight regions on Taiwan proper, in addition to Kinmen and Penghu.


title: Taiwanese Hokkien

text: Concerning the fifth (rising) tone in normal sandhi patterns, the Quanzhou/Coastal/Northern dialects change to seventh (mid level) tone, whereas the Zhangzhou/"Mixed"/Southern dialects change to third (low falling) tone.


title: Taiwanese Hokkien

text: Certain new north–south distinctions have appeared in recent decades. The fourth and eighth tones tend to be reversed in the north and south.


title: Taiwanese Hokkien

text: Hokkien immigrants to Taiwan originated from Quanzhou prefecture (44.8%) and Zhangzhou prefecture (35.2%). The original phonology from these regions was spread around Taiwan during the immigration process. With the advanced development of transportation and greater mobility of the Taiwanese population, Taiwanese speech has steered itself towards a mixture of Quanzhou and Zhangzhou speech, known as "Chiang–Chôan-lām" (漳泉濫, in Mandarin "Zhāng–Quán làn"). Due to different proportion of mixture, some regions are inclined more towards Quanzhou accent, while others are inclined more towards Zhangzhou accent.


title: Taiwanese Hokkien

text: In general, Quanzhou accent is more common along the coastal region and is known as the "hái-kháu" accent; Zhangzhou accent is more common within the mountainous region of Taiwan and is known as the "lāi-po͘" accent. The regional variation within Taiwanese may be attributed to variations in the mixture of Quanzhou and Zhangzhou accents and/or lexicons. It ranges from Lukang accent (based on Quanzhou accent) on one end, to the northern coastal Yilan accent (based on Zhangzhou accent) on another end. Tainan, Kaohsiung and Taitung accents, on the other hand, are closest to the prestige accent.


title: Taiwanese Hokkien

text: Recent research has found a need for new terminology of Taiwanese dialects, mainly because the Quanzhou and Zhangzhou dialects in Taiwan developed independently from those in Fujian. Thus, some scholars (i.e., Klöter, following ) have divided Taiwanese into five subdialects, based on geographic region:


title: Taiwanese Hokkien

text: Both "phian-hái" and "phian-lāi" are intermediate dialects between "hái-kháu" and "lāi-po͘", these also known as "thong-hêng" () or "". In some ways this mixed dialect is similar to the Amoy dialect, which itself is a blend of Quanzhou and Zhangzhou speech. The common dialect refers to that which can be heard on radio, television, official announcements, etc.


title: Taiwanese Hokkien

text: A great majority of people in Taiwan can speak both Mandarin and Hokkien, the degree of fluency varies widely. There are however small but significant numbers of people in Taiwan, mainly but not exclusively Hakka and Mainlanders, who cannot speak Taiwanese fluently. A shrinking percentage of the population, mainly people born before the 1950s, cannot speak Mandarin at all, or learned to speak Mandarin later in life, though some of these speak Japanese fluently. Urban, working-class Hakkas as well as younger, southern-Taiwan Mainlanders tend to have better, even native-like fluency. Approximately half of the Hakka in Taiwan do speak Taiwanese. There are many families of mixed Hakka, Hoklo, and Aboriginal bloodlines. There is, however, a large percentage of people in Taiwan, regardless of their background, whose ability to understand and read written Taiwanese is greater than their ability to speak it. This is the case with some singers who can sing Taiwanese songs with native-like proficiency, but can neither speak nor understand the language.


title: Taiwanese Hokkien

text: Which variant is used depends strongly on the context, and in general people will use Mandarin in more formal situations and Taiwanese in more informal situations. Taiwanese tends to get used more in rural areas, while Mandarin is used more in urban settings. Older people tend to use Taiwanese, while younger people tend to use Mandarin. In the broadcast media where Mandarin is used in many genres, soap opera, variety shows, and even some news programs can also be found in Taiwanese.


title: Taiwanese Hokkien

text: Taiwanese is also perceived by some to have a slight masculine leaning, making it more popular among the males of the younger population. It is sometimes perceived as "unladylike" when spoken by the females of the younger population.


title: Taiwanese Hokkien

text: "Chhit-jī-á" (literally, "that which has seven syllables") is a poetic meter where each verse has 7 syllables.


title: Taiwanese Hokkien

text: There is a special form of musical/dramatic performance "koa-á-hì": the Taiwanese opera; the subject matter is usually a historical event. A similar form "pò͘-tē-hì" (glove puppetry) is also unique and has been elaborated in the past two decades into impressive televised spectacles.


title: Taiwanese Hokkien

text: As with many other languages, the translations of the Bible in Taiwanese marked milestones in the standardization attempts of the language and its orthography.


title: Taiwanese Hokkien

text: The first translation of the Bible in Amoy or Taiwanese in the Pe̍h-ōe-jī orthography was by the first missionary to Taiwan, James Laidlaw Maxwell, with the New Testament "Lán ê Kiù-chú Iâ-so͘ Ki-tok ê Sin-iok" published in 1873 and the Old Testament "Kū-iok ê Sèng Keng" in 1884.


title: Taiwanese Hokkien

text: The next translation of the Bible in Taiwanese or Amoy was by the missionary to Taiwan, Thomas Barclay, carried out in Fujian and Taiwan. A New Testament translation was completed and published in 1916. The resulting work containing the Old and the New Testaments, in the Pe̍h-ōe-jī orthography, was completed in 1930 and published in 1933 as the Amoy Romanized Bible () . 2000 copies of the Amoy Romanized Bible were confiscated by the Taiwan Garrison from the Bible Society of Taiwan in 1975. This edition was later transliterated into Han characters and published as in 1996.


title: Taiwanese Hokkien

text: The Ko-Tân (Kerygma) Colloquial Taiwanese Version of the New Testament ("Sin-iok") in Pe̍h-ōe-jī, also known as the (), was published in 1973 as an ecumenical effort between the Protestant Presbyterian Church in Taiwan and the Roman Catholic mission Maryknoll. This translation used a more modern vocabulary (somewhat influenced by Mandarin), and reflected the central Taiwan dialect, as the Maryknoll mission was based near Tâi-tiong. It was soon confiscated by the Kuomintang government (which objected to the use of Latin orthography) in 1975. The copies of the ecumenical NT are now available on the online stores.


title: Taiwanese Hokkien

text: A translation using the principle of functional equivalence, "Today's Taiwanese Romanized Version" () , containing only the New Testament, again in Pe̍h-ōe-jī, was published in 2008 as a collaboration between the Presbyterian Church in Taiwan and the Bible Society in Taiwan. A translation of the Old Testament, following the same principle, is being prepared.


title: Taiwanese Hokkien

text: Another translation using the principle of functional equivalence, "Common Taiwanese Bible" (), with versions of Pe̍h-ōe-jī, Han characters and Ruby version (both Han characters and Pe̍h-ōe-jī) was published in 2015, available in printed and online.


title: Taiwanese Hokkien

text: Until the 1980s, the use of Taiwanese Hokkien, along with all varieties other than Mandarin, was discouraged by the Kuomintang through measures such as banning its use in schools and limiting the amount of Taiwanese broadcast on electronic media. These measures were removed by the 1990s, and Taiwanese became an emblem of localization. Mandarin remains the predominant language of education, although there is a "mother tongue" language requirement in Taiwanese schools which can be satisfied with student's choice of mother tongue: Taiwanese, Hakka, or aboriginal languages.


title: Taiwanese Hokkien

text: Although the use of Taiwanese Hokkien over Mandarin was historically part of the Taiwan independence movement, the linkage between politics and language is not as strong as it once was. Some fluency in Taiwanese Hokkien is desirable for political office in Taiwan for both independence and unificationist politicians. At the same time even some supporters of Taiwan independence have played down its connection with Taiwanese in order to gain the support of the Mainlanders and Hakka people.


title: Taiwanese Hokkien

text: James Soong restricted the use of Taiwanese Hokkien and other local tongues in broadcasting while serving as Director of the Government Information Office earlier in his career, but later became one of the first politicians of Mainlander origin to use it in semi-formal occasions. Since then, politicians opposed to Taiwanese independence have used it frequently in rallies, even when they are not native speakers. Conversely, politicians who have traditionally been identified with Taiwan independence have used Mandarin on formal occasions and semi-formal occasions such as press conferences. An example of the latter is former President Chen Shui-bian who uses Mandarin in all official state speeches, but uses mainly Taiwanese in political rallies and some informal state occasions such as New Year greetings. The current President of Taiwan and of the (DPP), Tsai Ing-wen has been criticized by her supporters for not using Taiwanese in speeches. Former President Ma Ying-jeou spoke in Taiwanese during his 2008 Double Ten Day speech when he was talking about the state of the economy in Taiwan.


title: Taiwanese Hokkien

text: In the early 21st century, there are few differences in language usage between the pro-unification leaning Pan-Blue Coalition and the independence leaning Pan-Green Coalition. Both tend to use Taiwanese at political rallies and sometimes in informal interviews, and both tend to use Mandarin at formal press conferences and official state functions. Both also tend to use more Mandarin in Northern Taiwan and more Taiwanese in Southern Taiwan. However, at official party gatherings (as opposed to both Mandarin-leaning state functions and Taiwanese-leaning party rallies), the DPP tends to use Taiwanese while KMT and PFP tend to use Mandarin. The Taiwan Solidarity Union, which advocates a strong line on Taiwan independence, tends to use Taiwanese even in formal press conferences. In speaking, politicians will frequently code switch. In writing, almost everyone uses vernacular Mandarin which is further from Taiwanese, and the use of semi-alphabetic writing or even colloquial Taiwanese characters is rare.


title: Taiwanese Hokkien

text: In 2002, the Taiwan Solidarity Union, a party with about 10% of the Legislative Yuan seats at the time, suggested making Taiwanese Hokkien a second official language. This proposal encountered strong opposition not only from Mainlander groups but also from Hakka and aboriginal groups who felt that it would slight their home languages, as well as others including Hoklo who objected to the proposal on logistical grounds and on the grounds that it would increase ethnic tensions. Because of these objections, support for this measure is lukewarm among moderate Taiwan independence supporters, and the proposal did not pass.


title: Taiwanese Hokkien

text: In 2003, there was a controversy when parts of the civil service examination for judges were written in characters used only in Taiwanese Hokkien. After strong objections, these questions were not used in scoring. As with the official-language controversy, objections to the use of Taiwanese came not only from Mainlander groups, but also Hoklo, Hakka and aborigines. The Control Yuan later created a rule that only allowed Standard Mandarin characters on civil service exams. According to public opinion surveys in 2008, more people supported making English a second official language than Taiwanese.


title: Taiwanese Hokkien

text: In 2017, indigenous languages were given official status in Taiwan, as was the Hakka language. , English was planned to become an official language in Taiwan, although this has not happened ever since. Taiwanese Hokkien is required for some activities but not others. For further information, see Languages of Taiwan.


title: Taiwanese Hokkien

text: Taiwanization developed in the 1990s into a ‘mother tongue revival movement' aiming to save, preserve, and develop the local ethnic culture and language of Holo (Taiwanese), Hakka, and aborigines. The effort to save declining languages has since allowed them to revive and flourish. In 1993, Taiwan became the first country in the world to implement the teaching of Taiwanese Hokkien in schools. By 2001, Taiwanese languages such as Taiwanese Hokkien, Hakka, and indigenous languages were taught in all Taiwanese schools. Since the 2000s, elementary school students are required to take a class in either Taiwanese, Hakka or aboriginal languages. In junior high this is usually an available elective. Taiwan also has its own literary circle whereby Hokkien poets and writers compose poetry and literature in Taiwanese on a regular basis.


title: Taiwanese Hokkien

text: As a result of the mother tongue movement, Taiwan has emerged as a significant cultural hub for Hokkien in the world in the 21st century. It also plans to be the major export center for Hokkien culture worldwide in the 21st century.


title: Taiwanese Hokkien

text: Klöter's "Written Taiwanese" (cited below) has been described as "the most comprehensive English-language study of written Taiwanese".


title: 1999 (Prince album)

text: 1999 is the fifth studio album by American recording artist Prince, released on October 27, 1982, by Warner Bros. Records. It became his first album to be recorded with his band the Revolution. "1999" critical and commercial success propelled Prince to a place in the public psyche and marked the beginning of two years of heightened fame via his following releases.


title: 1999 (Prince album)

text: "1999" was Prince's first top 10 album on the " Billboard" 200, peaking at number nine, and was fifth in the " Billboard" Year-End Albums of 1983. "1999", a protest against nuclear proliferation, was a "Billboard" Hot 100 top 20 hit, peaking at number 12. It has since become one of Prince's most recognizable compositions. "Delirious" reached number eight on the "Billboard" Hot 100, while "Little Red Corvette" peaked at number six, becoming Prince's highest charting US single at the time. "International Lover" was also nominated for Best Male R&B Vocal Performance at the 26th Grammy Awards, which was Prince's first Grammy Award nomination.


title: 1999 (Prince album)

text: "1999" received widespread acclaim from critics, and was seen as Prince's breakthrough album. On March 24, 1999, "1999" was certified quadruple platinum by the Recording Industry Association of America (RIAA). Following Prince's death in 2016, the album re-entered the "Billboard" 200 and peaked at number seven, besting its original performance on the chart thirty-three years earlier. A re-release and remaster of the album, including 35 previously unreleased recordings, was released in November 2019.


title: 1999 (Prince album)

text: "1999" has been ranked as one of the greatest albums of all time by several publications and organizations. The music videos for both "1999" and "Little Red Corvette" received heavy rotation on MTV, making Prince one of the first black artists to be in heavy rotation on the television channel. According to the "Rolling Stone Album Guide" (2004), ""1999" may be Prince's most influential album: Its synth-and-drum machine-heavy arrangements codified the Minneapolis sound that loomed over mid-'80s R&B and pop, not to mention the next two decades' worth of electro, house, and techno." It is also included on Rolling Stone's 500 Greatest Albums of All Time. In 2008, the album was inducted into the Grammy Hall of Fame.