Background.

The Wittgensteins.

According to a family tree prepared in Jerusalem after World War II, Wittgenstein's paternal great-great-grandfather was Moses Meier, a Jewish land agent who lived with his wife, Brendel Simon, in Bad Laasphe in the Principality of Wittgenstein, Westphalia. In July 1808, Napoleon issued a decree that everyone, including Jews, must adopt an inheritable family surname, so Meier's son, also Moses, took the name of his employers, the Sayn-Wittgensteins, and became Moses Meier Wittgenstein. His son, Hermann Christian Wittgenstein—who took the middle name "Christian" to distance himself from his Jewish background—married Fanny Figdor, also Jewish, who converted to Protestantism just before they married, and the couple founded a successful business trading in wool

Early life.

Wittgenstein's mother was Leopoldine Maria Josefa Kalmus, known among friends as Poldi. Her father was a Bohemian Jew and her mother was Austrian-Slovene Catholic—she was Wittgenstein's only non-Jewish grandparent. She was an aunt of the Nobel Prize laureate Friedrich Hayek on her maternal side. Wittgenstein was born at 8:30 pm on 26 April 1889 in the so-called "Wittgenstein Palace" at Alleegasse 16, now the Argentinierstrasse, near the Karlskirche. Karl and Poldi had nine children in all—four girls: Hermine, Margaret (Gretl), Helene, and a fourth daughter Dora who died as a baby; and five boys: Johannes (Hans), Kurt, Rudolf (Rudi), Paul—who became a concert pianist despite losing an arm in World War I—and Ludwig, who was the youngest of the family.  The children were baptized as Catholics, received formal Catholic instruction, and were raised in an

Family temperament and the brothers' suicides.

Ray Monk writes that Karl's aim was to turn his sons into captains of industry; they were not sent to school lest they acquire bad habits, but were educated at home to prepare them for work in Karl's industrial empire. Three of the five brothers would later commit suicide. Psychiatrist Michael Fitzgerald argues that Karl was a harsh perfectionist who lacked empathy, and that Wittgenstein's mother was anxious and insecure, unable to stand up to her husband. Johannes Brahms said of the family, whom he visited regularly: "They seemed to act towards one another as if they were at court." The family appeared to have a strong streak of depression running through it. Anthony Gottlieb tells a story about Paul practicing on one of the pianos in the Wittgensteins' main family mansion, when he suddenly shouted at Ludwig in the next room: "I cannot play when you are in the house, as I feel your scepticism seeping towards me from under the door!"  The family palace housed seven grand pianos and each of the siblings pursued music "with an enthusiasm that, at times, bordered on the pathological." The eldest

1903–1906: Realschule in Linz.

Realschule in Linz.

Wittgenstein was taught by private tutors at home until he was 14 years old. Subsequently, for three years, he attended a school. After the deaths of Hans and Rudi, Karl relented, and allowed Paul and Ludwig to be sent to school. Waugh writes that it was too late for Wittgenstein to pass his exams for the more academic "Gymnasium" in Wiener Neustadt; having had no formal schooling, he failed his entrance exam and only barely managed after extra tutoring to pass the exam for the more technically oriented k.u.k. "Realschule" in Linz, a small state school with 300 pupils. In 1903, when he was 14, he began his three years of formal schooling there, lodging nearby in term

Faith.

Wittgenstein was baptized as an infant by a Catholic priest and received formal instruction in Catholic doctrine as a child, as was common at the time. In an interview, his sister Gretl Stonborough-Wittgenstein says that their grandfather's "strong, severe, partly ascetic Christianity" was a strong influence on all the Wittgenstein children. While he was at the "Realschule", he decided he had lost his faith in God and became an atheist. He nevertheless believed in the importance of the idea of confession. He

Influence of Otto Weininger.

While a student at the "Realschule", Wittgenstein was influenced by Austrian philosopher Otto Weininger's 1903 book "Geschlecht und Charakter" ("Sex and Character"). Weininger (1880–1903), who was also Jewish, argued that the concepts male and female exist only as Platonic forms, and that Jews tend to embody the platonic femininity. Whereas men are basically rational, women operate only at the level of their emotions and sexual organs. Jews, Weininger argued, are similar, saturated with femininity, with no sense of right and wrong, and no soul. Weininger argues that man must choose between his masculine and feminine sides, consciousness and unconsciousness, Platonic love and sexuality. Love and sexual desire stand in contradiction, and love between a woman and a man is therefore doomed to misery or immorality. The only life worth living is the spiritual one—to live as a woman or a Jew means one has

Jewish background and Hitler.

There is much debate about the extent to which Wittgenstein and his siblings, who were of 3/4 Jewish descent, saw themselves as Jews. The issue has arisen in particular regarding Wittgenstein's schooldays, because Adolf Hitler was, for a while, at the same school at the same time. Laurence Goldstein argues it is "overwhelmingly probable" the boys met each other: that Hitler would have disliked Wittgenstein, a "stammering, precocious, precious, aristocratic upstart..." Other commentators have dismissed as irresponsible and uninformed any suggestion that Wittgenstein's wealth and unusual personality may have fed Hitler's antisemitism, in part because there is no indication that Hitler would have seen Wittgenstein as Jewish.  Wittgenstein and Hitler were born just six days apart, though Hitler had to re-sit his mathematics exam before being allowed into a higher class, while Wittgenstein was moved forward by

1906–1913: University.

Engineering at Berlin and Manchester.

He began his studies in mechanical engineering at the Technische Hochschule Berlin in Charlottenburg, Berlin, on 23 October 1906, lodging with the family of professor Dr. Jolles. He attended for three semesters, and was awarded a diploma ("Abgangzeugnis") on 5 May 1908.  During his time at the Institute, Wittgenstein developed an interest in aeronautics. He arrived at the Victoria University of Manchester in the spring of 1908 to study for a doctorate, full of plans for aeronautical projects, including designing and flying his own plane. He conducted research into the behavior of

Arrival at Cambridge.

Wittgenstein wanted to study with Frege, but Frege suggested he attend the University of Cambridge to study under Russell, so on 18 October 1911 Wittgenstein arrived unannounced at Russell's rooms in Trinity College. Russell was having tea with C. K. Ogden, when, according to Russell, "an unknown German appeared, speaking very little English but refusing to speak German. He turned out to be a man who had learned engineering at Charlottenburg, but during this course had acquired, by himself, a passion for the philosophy of mathematics & has now come to Cambridge on purpose to hear me." He was soon not only attending Russell's lectures, but dominating them. The lectures were poorly attended and Russell often found himself lecturing only to C. D. Broad, E. H. Neville, and H. T. J. Norton. Wittgenstein started following him after lectures back to his rooms to discuss more philosophy, until it was time for the evening meal in Hall. Russell grew irritated; he wrote to his lover Lady Ottoline Morrell: "My German friend threatens to be an

Cambridge Moral Sciences Club and Apostles.

In 1912 Wittgenstein joined the Cambridge Moral Sciences Club, an influential discussion group for philosophy dons and students, delivering his first paper there on 29 November that year, a four-minute talk defining philosophy as "all those primitive propositions which are assumed as true without proof by the various sciences." He dominated the society and for a time would stop attending in the early 1930s after complaints that he gave no one else a chance to speak.  The club became infamous within popular philosophy because of a meeting on 25 October 1946 at Richard Braithwaite's rooms in King's College, Cambridge, where

Cambridge Apostles.

The famous economist John Maynard Keynes also invited him to join the Cambridge Apostles, an elite secret society formed in 1820, which both Bertrand Russell and G. E. Moore had joined as students, but Wittgenstein did not greatly enjoy it and attended only infrequently. Russell had been worried that Wittgenstein would not

Frustrations at Cambridge.

Wittgenstein was quite vocal about his depression in his years at Cambridge, and before he went to war; on many an occasion, he told Russell of his woes. His mental anguish seemed to stem from two sources: his work, and his personal life. Wittgenstein made numerous remarks to Russell about logic driving him mad. Wittgenstein also stated to Russell that he "felt the curse of those who have half a talent". He later expresses this same worry, and tells of being in mediocre spirits due to his lack of progress in his logical work. Monk writes that Wittgenstein lived and breathed logic, and a

Sexual orientation and relationship with David Pinsent.

Wittgenstein had romantic relations with both men and women. He is generally believed to have fallen in love with at least three men, and had a relationship with the latter two: David Hume Pinsent in 1912, Francis Skinner in 1930, and Ben Richards in the late 1940s. He later revealed that, as a teenager in Vienna, he had had an affair with a woman. Additionally, in the 1920s Wittgenstein fell in love with a young Swiss woman, Marguerite Respinger, modelling a sculpture of her and proposing marriage, albeit on condition

1913–1920: World War I and the "Tractatus".

Work on "Logik".

Karl Wittgenstein died on 20 January 1913, and after receiving his inheritance Wittgenstein became one of the wealthiest men in Europe. He donated some of his money, at first anonymously, to Austrian artists and writers, including Rainer Maria Rilke and Georg Trakl. Trakl requested to meet his benefactor but in 1914 when Wittgenstein went to visit, Trakl had killed himself. Wittgenstein came to feel that he could not get to the heart of his most fundamental questions while surrounded by other academics, and so in 1913 he retreated to the village of Skjolden in Norway, where he rented the second floor of a

Military service.

On the outbreak of World War I, Wittgenstein immediately volunteered for the Austro-Hungarian Army, despite being eligible for a medical exemption. He served first on a ship and then in an artillery workshop'several miles from the action'. He was wounded in an accidental explosion, and hospitalised to Kraków. In March 1916, he was posted to a fighting unit on the front line of the Russian front, as part of the Austrian 7th Army, where his unit was involved in some of the heaviest fighting, defending against the Brusilov Offensive. Wittgenstein directed the fire of his own artillery from an observation post in no-man's land against Allied troops – one of the most dangerous jobs there was, since he was targeted by enemy fire. In action against British (?) troops, he was decorated with the Military Merit with Swords on the Ribbon, and was commended by the army for "His exceptionally courageous behaviour, calmness, sang-froid, and heroism," that "won the total admiration of the troops." In January 1917, he was sent as a member of a howitzer regiment to the Russian front,

Completion of the "Tractatus".

In the summer of 1918 Wittgenstein took military leave and went to stay in one of his family's Vienna summer houses, Neuwaldegg. It was there in August 1918 that he completed the "Tractatus", which he submitted with the title "Der Satz" (German: proposition, sentence, phrase, set, but also "leap") to the publishers Jahoda and Siegel.  A series of events around this time left him deeply upset. On 13 August, his uncle Paul died. On 25 October, he learned that Jahoda and Siegel had decided not to publish the "Tractatus", and on 27 October, his brother Kurt killed himself, the third of his brothers to commit suicide. It was around this time he received a letter from David Pinsent's mother to say that

1920–1928: Teaching, the "Tractatus", Haus Wittgenstein.

Teacher training in Vienna.

In September 1919 he enrolled in the "Lehrerbildungsanstalt" (teacher training college) in the "Kundmanngasse" in Vienna. His sister Hermine said that Wittgenstein working as an elementary

Teaching posts in Austria.

In the summer of 1920, Wittgenstein worked as a gardener for a monastery. At first he applied, under a false name, for a teaching post at Reichenau, was awarded the job, but he declined it when his identity was discovered. As a teacher, he wished to no longer be recognized as a member of the famous Wittgenstein family. In response, his brother Paul wrote: "It is out of the question, really completely out of the question, that anybody bearing our name and whose elegant and gentle upbringing can be seen a thousand paces off, would not be identified as a member of our family... That one can neither simulate nor dissimulate anything including a refined education I need hardly tell you."  In 1920, Wittgenstein was given his first job as a primary school teacher in Trattenbach, under his real name, in a remote village of a few hundred people. His first letters describe it as beautiful, but in October 1921, he wrote to Russell: "I am still at Trattenbach, surrounded, as

Publication of the "Tractatus".

While Wittgenstein was living in isolation in rural Austria, the "Tractatus" was published to considerable interest, first in German in 1921 as "Logisch-Philosophische Abhandlung", part of Wilhelm Ostwald's journal "Annalen der Naturphilosophie", though Wittgenstein was not happy with the result and called it a pirate edition. Russell had agreed to write an introduction to explain why it was important, because it was otherwise unlikely to have been published: it was difficult if not impossible to understand, and Wittgenstein was unknown in philosophy.

Visit from Frank Ramsey, Puchberg.

In September 1922 he moved to a secondary school in a nearby village, Hassbach, but considered the people there just as bad—"These people are not human "at all" but loathsome worms," he wrote to a friend—and he left after a month. In November he began work at another primary school, this time in Puchberg in the Schneeberg mountains. There, he told Russell, the villagers were "one-quarter animal and three-quarters human."  Frank P. Ramsey visited him on 17 September 1923 to discuss the "Tractatus"; he had agreed to write a review of it for "Mind". He reported in a letter home that Wittgenstein was living frugally in

Haidbauer incident, Otterthal.

He moved schools again in September 1924, this time to Otterthal, near Trattenbach; the socialist headmaster, Josef Putre, was someone Wittgenstein had become friends with while at Trattenbach. While he was there, he wrote a 42-page pronunciation and spelling dictionary for the children, "Wörterbuch für Volksschulen", published in Vienna in 1926 by Hölder-Pichler-Tempsky, the only book of his apart from the "Tractatus" that was published in his lifetime. A first edition sold in 2005 for £75,000.  An incident occurred in April 1926 and became known as "Der Vorfall Haidbauer" (the Haidbauer incident). Josef Haidbauer was an 11-year-old pupil whose father had died and whose mother worked as a local maid. He was a slow learner, and one day Wittgenstein hit him two or three times on the head, causing him to collapse. Wittgenstein carried him to the headmaster's office, then quickly left the school, bumping into a parent, Herr Piribauer, on the way out. Piribauer had been sent for by the children when they saw Haidbauer collapse; Wittgenstein had previously pulled Piribauer's daughter, Hermine, so hard by the ears that her ears had bled. Piribauer said that when he met Wittgenstein in the hall that

The Vienna Circle.

The "Tractatus" was now the subject of much debate amongst philosophers, and Wittgenstein was a figure of increasing international fame. In particular, a discussion group of philosophers, scientists and mathematicians, known as the Vienna Circle, had built up purportedly as a result of the inspiration they had been given by reading the "Tractatus". While it is commonly assumed that Wittgenstein was a part of the Vienna Circle, in reality, this was not actually the case. German philosopher Oswald Hanfling writes bluntly: "Wittgenstein was never a member of the Circle, though he was in Vienna during much of the time. Yet his influence on the Circle's thought was at least as important as that of any of its members." However, the philosopher A. C. Grayling contends that while certain superficial similarities between Wittgenstein's early philosophy and logical positivism led its members to study the "Tractatus" in detail and to

Haus Wittgenstein.

In 1926 Wittgenstein was again working as a gardener for a number of months, this time at the monastery of Hütteldorf, where he had also inquired about becoming a monk. His sister, Margaret, invited him to help with the design of her new townhouse in Vienna's "Kundmanngasse". Wittgenstein, his friend Paul Engelmann, and a team of architects developed a spare modernist house. In particular, Wittgenstein focused on the windows, doors, and radiators, demanding that every detail be exactly as he specified. When the house was nearly finished Wittgenstein had an entire ceiling raised 30mm so that the room had the exact proportions he wanted. Monk writes that "This is not so marginal as it may at first appear, for it is precisely these details that lend what is otherwise a rather plain, even ugly house its

1929–1941: Fellowship at Cambridge.

PhD and fellowship.

According to Feigl (as reported by Monk), upon attending a conference in Vienna by mathematician L. E. J. Brouwer, Wittgenstein remained quite impressed, taking into consideration the possibility of a "return to Philosophy". At the urging of Ramsey and others, Wittgenstein returned to Cambridge in 1929. Keynes wrote in a letter to his wife: "Well, God has arrived. I met him on the 5.15 train." Despite this fame, he could not initially work at Cambridge as he did not have a

Anschluss.

From 1936 to 1937, Wittgenstein lived again in Norway, where he worked on the "Philosophical Investigations". In the winter of 1936/7, he delivered a series of "confessions" to close friends, most of them about minor infractions like white lies, in an effort to cleanse himself. In 1938, he travelled to Ireland to visit Maurice O'Connor Drury, a friend who became a psychiatrist, and considered such training himself, with the intention of abandoning philosophy for it. The visit to Ireland was at the

Professor of philosophy.

After G. E. Moore resigned the chair in philosophy in 1939, Wittgenstein was elected, and acquired British citizenship soon afterwards. In July 1939 he travelled to Vienna to assist Gretl and his other sisters, visiting Berlin for one day to meet an official of the Reichsbank. After this, he travelled to New York to persuade Paul, whose agreement was required, to back the scheme. The required Befreiung was granted in August 1939. The unknown amount signed over to the Nazis by the Wittgenstein family, a week or so before the outbreak of war, included amongst many other assets, 1,700 kg of gold. There is a report Wittgenstein visited Moscow a second time in 1939, travelling from Berlin, and again met the philosopher

1941–1947: World War II and Guy's Hospital.

Monk writes that Wittgenstein found it intolerable that a war was going on and he was teaching philosophy. He grew angry when any of his students wanted to become professional philosophers.  In September 1941, he asked John Ryle, the brother of the philosopher Gilbert Ryle, if he could get a manual job at Guy's Hospital in London. John Ryle was professor of medicine at Cambridge and had been involved in helping Guy's prepare for the Blitz. Wittgenstein told Ryle he would die slowly if left at Cambridge, and he would rather die quickly. He started working at Guy's shortly afterwards as a dispensary porter, delivering drugs from the pharmacy to the wards where he apparently advised the patients not to take them.  In the new year of 1942, Ryle took Wittgenstein to his home in Sussex to meet his wife who had been adamant to meet him. Ryle's son recorded the weekend in his diary;Wink is awful strange – not a very good english [sic] speaker, keeps on saying ‘I mean’ and ‘its “tolerable”’ meaning intolerable. The hospital staff were not told he was one of the world's most famous philosophers, though some of the medical staff did recognize him—at least one had attended Moral Sciences Club meetings—but they were discreet. "Good God, don't tell anybody who I am!" Wittgenstein begged one of them. Some of them nevertheless called him Professor Wittgenstein, and he was allowed to dine with the doctors. He wrote on 1 April 1942: "I no longer feel any hope for the future of my life. It is as though I had before me nothing more than a long stretch of living death. I cannot imagine any future for me other than a ghastly one. Friendless and joyless." It was at this time that Wittgenstein had an operation at Guy's to remove a gall-stone that had troubled him for some years.  He had developed a friendship

1947–1951: Final years.

Wittgenstein resigned the professorship at Cambridge in 1947 to concentrate on his writing, and in 1947 and 1948 travelled to Ireland, staying at Ross's Hotel in Dublin and at a farmhouse in Redcross, County Wicklow, where he began the manuscript volume MS 137, Band R. Seeking solitude he moved to "Rosro", a holiday cottage in Connemara owned by Maurice O'Connor-Drury.  He also accepted an invitation from Norman Malcolm, then professor at Cornell University, to stay with him and his wife for several months at Ithaca, New York. He made the trip in April 1949, although he told Malcolm he was too unwell to do philosophical work: "I haven't done any work since the beginning of March & I haven't had the strength of even trying to do any." A doctor in Dublin had diagnosed anaemia and prescribed iron and liver pills. The details of Wittgenstein's stay in America are recounted in Norman Malcolm's "Ludwig Wittgenstein: A Memoir". During his summer in America, Wittgenstein began his epistemological discussions, in particular his engagement with philosophical scepticism, that would eventually become the final fragments "On Certainty".  He returned to London, where he was diagnosed with an inoperable prostate cancer, which had spread to his bone marrow. He spent the next two months in Vienna, where his sister Hermine died on 11 February 1950; he went to see her every day, but she was hardly able to speak or recognize him. "Great loss for me and all of us," he wrote. "Greater than I would have thought." He moved around a lot after Hermine's death staying with various friends: to Cambridge in April 1950, where he stayed with G. H. von Wright; to London to stay with Rush Rhees; then to Oxford to see Elizabeth Anscombe, writing to Norman Malcolm that he was hardly doing any philosophy. He went to Norway in August with Ben Richards, then returned to Cambridge, where on 27 November he moved into "Storey's End" at 76 Storey's Way, the home of his doctor, Edward Bevan, and his wife Joan; he had told them he did not want to die in a hospital, so they said he could spend his last days in their home instead. Joan at first was afraid of Wittgenstein, but they soon became good friends.  By the beginning of 1951, it was clear that he had little time left. He wrote a new will in Oxford on 29 January, naming Rhees as his executor, and Anscombe and von Wright his literary administrators, and wrote to Norman Malcolm that month to say, "My mind's completely dead. This isn't a complaint, for I don't really suffer from it. I know that life must have an end once and that mental life can cease before the rest does." In February he returned to the Bevans' home to work on MS 175 and MS 176. These and other manuscripts were later published as "Remarks on Colour" and "On Certainty". He wrote to Malcolm on 16 April 13 days before his death: "An extraordinary thing happened to me. About a month ago I suddenly found myself in the right frame of mind for doing philosophy. I had been "absolutely" certain that I'd never again be able to do it. It's the first time after more than 2 years that the curtain in my brain has gone up.—Of course, so far I've only worked for about 5 weeks & it may be all over by tomorrow; but it bucks me up a lot now."

1953: Publication of the "Philosophical Investigations".

The "Blue Book", a set of notes dictated to his class at Cambridge in 1933–1934, contains the seeds of Wittgenstein's later thoughts on language and is widely read as a turning-point in his philosophy of language.  "Philosophical Investigations" was published in two parts in 1953. Most of Part I was ready for printing in 1946, but Wittgenstein withdrew the manuscript from his publisher. The shorter Part II was added by his editors, Elizabeth Anscombe and Rush Rhees. Wittgenstein asks the reader to think of language as a multiplicity of language-games within which parts of language develop and function. He argues the bewitchments of philosophical problems arise from philosophers' misguided attempts to consider

Other posthumous publications.

Wittgenstein left a voluminous archive of unpublished papers, including 83 manuscripts, 46 typescripts and 11 dictations, amounting to an estimated 20,000 pages. Choosing among repeated drafts, revisions, corrections and loose notes editorial work has found nearly one third of the total suitable for print. An Internet facility hosted by the University of Bergen allows access to images of almost all the material and to search the available transcriptions. In 2011 two new boxes of

Legacy.

Assessment.

In 1999 a survey among American university and college teachers ranked the "Investigations" as the most important book of 20th-century philosophy, standing out as "the one crossover masterpiece in twentieth-century philosophy, appealing across diverse specializations and philosophical orientations." The "Investigations" also ranked 54th on a list of most influential twentieth-century works in cognitive science prepared by the University of Minnesota's Center for Cognitive Sciences.  Peter Hacker argues that Wittgenstein's influence on

Scholarly interpretation.

There are diverging interpretations of Wittgenstein's thought. In the words of his friend and colleague Georg Henrik von Wright: He was of the opinion... that his ideas were generally misunderstood and distorted even by those who professed to be his disciples. He doubted he would be better understood in the future. He once said he felt as though he was writing for people who would think in a different way, breathe a different air of life, from that of present-day men.  Since Wittgenstein's death, scholarly interpretations of his philosophy have differed. Scholars have differed on the continuity between "early" and "late" Wittgenstein (that is, the difference between his views expressed in the "Tractatus" and those in "Philosophical Investigations"), with some seeing the two as starkly disparate and others stressing the gradual transition between

Bertrand Russell.

In October 1944, Wittgenstein returned to Cambridge around the same time as did Russell who had been living in America for several years. Russell returned to Cambridge after a backlash in America to his writings on morals and religion. Wittgenstein said of Russell's works to Drury;Russell’s books should be bound in two colours...those dealing with mathematical logic in red – and all students of philosophy should read them; those dealing with ethics and politics in blue – and no one should be allowed to read them.Russell made similar disparaging comments about Wittgenstein's later work;I have not found

Saul Kripke.

Saul Kripke's 1982 book "Wittgenstein on Rules and Private Language" contends that the central argument of Wittgenstein's "Philosophical Investigations" is a devastating rule-following paradox that undermines the possibility of our ever following rules in our use of language. Kripke writes that this paradox is "the most radical and original skeptical problem that philosophy has seen to date."  Kripke's book generated a large secondary literature, divided between those who find his sceptical problem interesting and perceptive, and others, such as Gordon Baker and Peter Hacker, who argue that his scepticism of meaning is a pseudo-problem that stems from a confused, selective reading of Wittgenstein. Kripke's position has, however recently been defended against these and other attacks by the Cambridge philosopher Martin Kusch (2006). Wittgenstein scholar David G. Stern considers the book to be "the most influential and widely discussed" work on Wittgenstein since the 1980s.

Works.

A collection of Ludwig Wittgenstein's manuscripts is held by Trinity College, Cambridge.

Ludwig Josef Johann Wittgenstein (; ; 26 April 1889 – 29 April 1951) was an Austrian-British philosopher who worked primarily in logic, the philosophy of mathematics, the philosophy of mind, and the philosophy of language.

Ludwig Josef Johann Wittgenstein (* 26. April 1889 in Wien; † 29. April 1951 in Cambridge) war einer der bedeutendsten Philosophen des 20. Jahrhunderts.


Early life.

Hamilton was born in Salisbury, Maryland. Hamilton's father, Carroll Stanford Hamilton, a physician, died when she was five, and her mother later married a police chief. Hamilton has an identical twin sister (Leslie Hamilton Gearren), one older sister and one younger brother. She has said that she was raised in a very 'boring' family, and "voraciously read books" during her spare time. Hamilton went to Wicomico Junior High (now Wicomico Middle School) and Wicomico High School in Salisbury, with Leslie, her twin. She studied for two years at Washington College in Chestertown, Maryland, before moving on to acting studies in New York City. Hamilton has said that her acting professor at Washington College told her she had no hope of earning a living as an actress. In New York, she attended acting workshops given by Lee Strasberg.

Career.

Hamilton's professional acting debut was on television and was followed by a major role as Lisa Rogers in the prime-time soap opera "Secrets of Midland Heights" (December 1980/January 1981). Her big-screen debut was in the thriller "" (1982) and as a result, she was listed as one of twelve "Promising New Actors of 1982" in John Willis' Screen World, Vol. 34. She also starred in the CBS made-for-TV movie "Country Gold" alongside Loni Anderson and Earl Holliman.  Hamilton played the lead role in "Children of the Corn" (1984), based on the horror short story by Stephen King. The movie, which made $14 million at the box office, was panned by critics. Hamilton's next role was in "The Terminator" (1984), opposite Michael Biehn. The movie was an unexpectedly huge commercial and critical success. Following "The Terminator", Hamilton starred in "Black Moon Rising", an action thriller with Tommy Lee Jones. She then returned to television as a guest-star in the mystery series "Murder, She Wrote", scoring favorable reviews. Hamilton next starred opposite Ron Perlman in the television series "Beauty and the Beast". The series was critically acclaimed, and she received Emmy Award and Golden Globe Award nominations. Hamilton left the series in 1989 and it ended in 1990.  Hamilton returned to the big screen with Michael Caine in "Mr. Destiny" (1990) and with "" (1991), the sequel to "The Terminator". The latter was a smash at the box office, grossing over $500 million, more than any other film of that year. Hamilton underwent intense physical training to emphasize the character's transformation from the first film. Her identical twin sister, Leslie Hamilton Gearren, was Linda's double in "Terminator 2". Hamilton received two MTV Movie Awards for her role in the film, one for Best Female Performance and the other for Most Desirable Female. She reprised the character, Sarah Connor, for the theme park attraction "". In 1990, Hamilton was chosen by "People Magazine" as one of the 50 Most Beautiful People in the world. Following the success of the "Terminator" series, she hosted "Saturday Night Live".  She returned to television in "A Mother's Prayer" (1995) playing a mother who lost her husband and is diagnosed with AIDS. For her performance in the film, which co-starred Kate Nelligan and Bruce Dern, Hamilton was awarded a CableACE Award for best dramatic performance and nominated for another Golden Globe Award in 1996. That same year, Hamilton filmed two motion pictures that were released one week apart in 1997: "Shadow Conspiracy" with Charlie Sheen and "Dante's Peak" with Pierce Brosnan. "Shadow Conspiracy" flopped at the box office, but "Dante's Peak" grossed $180 million and was one of the biggest commercial hits of the year. She received a Blockbuster Entertainment Award for female performance in "Dante's Peak".  Hamilton has since appeared on the television series "Frasier" (season 4 episode "Odd Man Out" as Laura) and "According to Jim" and has done more TV movies, including "On the Line", "Robots Rising", "Rescuers: Stories of Courage: Two Couples", "Point Last Seen" and "The Color of Courage". Hamilton and her "Beauty and the Beast" co-star Ron Perlman reunited in the post-Vietnam war drama "Missing in America" (2005).  In 2009, she returned as Sarah Connor in "Terminator Salvation", in voice-overs only. In 2010, she joined the cast of "Chuck" in the recurring guest role of Mary Elizabeth Bartowski, a CIA agent and long-missing mother of Chuck and Ellie. She also appeared as a guest star in the Showtime cable television series "Weeds" as the marijuana supplier for the series' main character (Mary-Louise Parker). In November 2011, she narrated the Chiller "The Future of Fear" horror documentary.  In 2013, Hamilton appeared as Acacia, a Valkyrie, in "Delinquents", a third-season episode of the TV series "Lost Girl", a role she would reprise in two subsequent episodes, "End of a Line" in the fourth season, and "Sweet Valkyrie High" in the fifth. She subsequently appeared in a recurring role on the Syfy series "Defiance", beginning in that show's second season. In 2019, she reprised her role as Sarah Connor in "", her first starring role as the character since 1991, and also voiced the character in the video game "Gears 5".

Personal life.

Hamilton has been married and divorced twice. Her first marriage, from 1982 to 1989, was to Bruce Abbott, who left her when she was pregnant with their son, Dalton, born 1989). In 1991, she moved in with film director James Cameron. They had a daughter, Josephine Archer Cameron, in 1993. She and Cameron married in 1997, ending in a $50 million divorce settlement in 1999.  Hamilton has described herself politically as a Democrat, but she voted for Republican candidate Arnold Schwarzenegger, her "Terminator" co-star, in the 2003 California gubernatorial election after his campaign convinced her he was suitable for the job.  In an October 2005 appearance on "Larry King Live", Hamilton discussed her depression and bipolar disorder, which led to violent mood swings and suicidal thoughts during her marriage to Abbott, and, in her view, caused the failure of both of her marriages. She also discussed how she eventually received therapy and medication to manage the condition.  While filming "Terminator 2: Judgment Day", Hamilton suffered permanent hearing damage in one ear when she fired a gun inside an elevator without using her ear plugs.

Linda Carroll Hamilton (born September 26, 1956) is an American actress. She is best known for her portrayal of Sarah Connor in the "Terminator" film series and Catherine Chandler in the television series "Beauty and the Beast" (1987-1990), for which she was nominated for two Golden Globe Awards and an Emmy Award. She also starred as Vicky Baxter in the horror film "Children of the Corn" (1984), Doctor Amy Franklin in the monster film "King Kong Lives" (1986), and Mayor Rachel Wando in the disaster thriller film "Dante's Peak" (1997). Hamilton had a recurring role as Mary Elizabeth Bartowski on NBC's "Chuck".

Linda Carroll Hamilton (* 26. September 1956 in Salisbury, Maryland) ist eine US-amerikanische Schauspielerin. Sie wurde vor allem durch die Rolle der "Sarah Connor" in den Filmen "Terminator" und "Terminator 2 – Tag der Abrechnung" bekannt.


Early life.

Martin Scorsese was born on November 17, 1942, in the Flushing area of New York City's Queens borough. His family moved to Little Italy in Manhattan before he started school. Both of Scorsese's parents, Charles Scorsese and Catherine Scorsese (born Cappa), worked in New York's Garment District. Charles was a clothes presser and an actor while Catherine was a seamstress and an actress. Both of them were of Italian descent: his paternal grandparents, Francesco Paolo and Teresa Scozzese, emigrated from Polizzi Generosa, while his maternal grandparents, Martino and Domenica Cappa, emigrated from Ciminna, both in the province of Palermo, Sicily. The original surname of the family was "Scozzese", later changed to Scorsese because of a transcription error. Scorsese was raised in a predominantly Catholic environment.  As a boy, he had asthma and could not play sports or take part in any activities with other children, so his parents and his older brother would often take him to movie theaters; it was at this stage in his life that he developed a passion for cinema. As a teenager in the Bronx, Scorsese frequently rented Powell and Pressburger's "The Tales of Hoffmann" (1951) from a store that had one copy of the reel. Scorsese was one of only two people who regularly rented it; the other was future film director George A.

Career.

Early career.

While attending the Tisch School of the Arts, Scorsese made the short films "What's a Nice Girl Like You Doing in a Place Like This?" (1963) and "It's Not Just You, Murray!" (1964). His most famous short of the period is the darkly comic "The Big Shave" (1967), which features Peter Bernuth. The film is an indictment of America's involvement in Vietnam, suggested by its alternative title "Viet '67". Scorsese has mentioned on several occasions that he was greatly inspired in his early days at New York University by film professor Haig P. Manoogian. In 1965, Scorsese married his first wife Laraine Marie Brennan, and they remained together for six years between

1970s.

Scorsese became friends with the influential "movie brats" of the 1970s: Brian De Palma, Francis Ford Coppola, George Lucas and Steven Spielberg. It was De Palma who introduced Scorsese to Robert De Niro. During this period, Scorsese worked as the assistant director and one of the editors on the documentary "Woodstock" (1970) and met actor–director John Cassavetes, who became a close friend and mentor. In 1972, Scorsese made the Depression-era exploiter "Boxcar Bertha" for B-movie producer Roger Corman, who also helped directors such as Francis Ford Coppola, James Cameron, and John Sayles launch their careers. It was Corman who taught Scorsese that entertaining films could be shot with very little money or time, preparing the young director well for the challenges to come with "Mean Streets". Following the film's release, Cassavetes encouraged Scorsese to make the films that he wanted to make, rather than someone

1980s.

By several accounts (Scorsese's included), Robert De Niro practically saved Scorsese's life when he persuaded him to kick his cocaine addiction to make his highly regarded film "Raging Bull". Writing for "The New Yorker" in March 2000, Mark Singer summarized Scorsese's condition stating: He (Scorsese) was more than mildly depressed. Drug abuse, and abuse of his body in general, culminated in a terrifying episode of internal bleeding. Robert De Niro came to see him in the hospital and asked, in so many words, whether he wanted to live or die. If you want to live, De Niro proposed, let's make this picture—referring to "Raging Bull," an as-told-to book by Jake La Motta, the former world middleweight boxing champion, that De Niro had given him to read years earlier. Convinced that he would never make another movie, he poured his energies into making this violent biopic of middleweight boxing champion Jake LaMotta, calling it a kamikaze method of film-making. The film is widely viewed as a masterpiece and was voted the greatest film of the 1980s by Britain's "Sight & Sound" magazine. It received eight

1990s.

After a decade of films considered by critics to be mixed results, some considered Scorsese's gangster epic "Goodfellas" (1990) his return to directorial form, and his most confident and fully realized film since "Raging Bull". De Niro and Joe Pesci offered a virtuoso display of Scorsese's bravura cinematic technique in the film and re-established, enhanced, and consolidated his reputation. After the film was released, Roger Ebert, a friend and supporter of Scorsese, named "Goodfellas" "the best mob movie ever". It is ranked No. 1 on Ebert's movie list for 1990, along with those of Gene Siskel and Peter Travers', and is widely considered one of the director's greatest achievements. The film was nominated for six Academy Awards, including Best Picture and Best Director, and Scorsese earned his third Best Director nomination but again lost to a first-time director, Kevin Costner ("Dances with Wolves"). Joe Pesci earned the Academy Award for Best Supporting Actor for his performance. Scorsese and the film also won a number of other awards, including five BAFTA Awards, a Silver Lion and more. The American Film Institute placed "Goodfellas" at No. 94 on the AFI's 100 Years... 100 Movies list. On the 2007 updated version, they moved "Goodfellas" up to No. 92 on the AFI's 100 Years... 100 Movies list (10th Anniversary Edition) and put "Goodfellas" at No. 2 on their list of the top 10 gangster films (after "The Godfather").  In 1990, he released his only short-form documentary: "Made in Milan" about fashion designer Giorgio Armani. The following year brought "Cape Fear", a remake of a cult 1962 movie

2000s.

In 1999, Scorsese produced a documentary on Italian filmmakers titled "Il Mio Viaggio in Italia", also known as "My Voyage to Italy". The documentary foreshadowed the director's next project, the epic "Gangs of New York" (2002), influenced by (amongst many others) major Italian directors such as Luchino Visconti and filmed in its entirety at Rome's famous Cinecittà film studios. With a production budget said to be in excess of $100 million, "Gangs of New York" was Scorsese's biggest and arguably most mainstream venture to date. Like "The Age of Innocence", it was set in 19th-century New York, although focusing on the other end of the social scale (and like that film, also starring Daniel Day-Lewis). The film marked the first collaboration between Scorsese and actor Leonardo DiCaprio, who became a fixture in later Scorsese films. The production was highly troubled, with many rumors referring to the director's conflict with Miramax boss Harvey Weinstein. Despite denials of artistic compromise, some felt that "Gangs of New York" was the director's most conventional film, featuring standard film tropes that the director had traditionally avoided, such as characters existing purely

2010s.

On October 22, 2007, "Daily Variety" reported that Scorsese would reunite with Leonardo DiCaprio on a fourth picture, "Shutter Island". Principal photography on the Laeta Kalogridis screenplay, based on the novel of the same name by Dennis Lehane, began in Massachusetts in March 2008. In December 2007, actors Mark Ruffalo, Max von Sydow, Ben Kingsley, and Michelle Williams joined the cast, marking the first time these actors had worked with Scorsese. The film was released on February 19, 2010. On May 20, 2010, the film became Scorsese's highest-grossing film. In 2010, "The Wall Street Journal" reported that Scorsese was supporting the David Lynch Foundation's initiative to help 10,000 military veterans overcome posttraumatic stress disorder through Transcendental Meditation; Scorsese has publicly discussed his own practice of TM.  Scorsese directed the series premiere for "Boardwalk Empire", an HBO drama series, starring Steve Buscemi and Michael Pitt, based on Nelson Johnson's book "Boardwalk Empire: The Birth, High Times and Corruption of Atlantic City". Terence Winter, who wrote for "The Sopranos", created the series. In addition to directing the pilot (for which he won the 2011 Primetime Emmy Award for Outstanding Directing), Scorsese also served as an executive producer on the series. The

2020s.

In July 2019, Scorsese started scouting locations in preparation for the 2020 filming of his next film "Killers of the Flower Moon", a film adaptation of the book of the same

Filmmaking style and technique.

Several recurring filmmaking techniques are identifiable in many of Scorsese's films. He has established a filmmaking history which involves repeat collaborations with actors, screenwriters, film editors, and cinematographers, sometimes extending over several decades, such as that with recurring cinematographers Michael Ballhaus, Robert Richardson, and Rodrigo Prieto.

Slow motion and freeze frame.

Scorsese is known for his frequent use of slow motion, for example, in "Who's That Knocking at My Door" (1967) and "Mean Streets" (1973). He is also known for using freeze frames, such as: in the opening credits of "The King of Comedy" (1983), throughout "Goodfellas" (1990), "Casino" (1995), "The Departed" (2006), and in "The Irishman" (2019). His blonde leading ladies are usually seen through the eyes of the protagonist as angelic and ethereal; they wear white in their first scene and are photographed in slow motion—Cybill Shepherd in "Taxi Driver"; Cathy Moriarty's white bikini in "Raging Bull"; Sharon Stone's white minidress in

Cameo appearances.

Scorsese usually has a quick cameo in his films ("Who's That Knocking at My Door", "Boxcar Bertha", "Mean Streets", "Alice Doesn't Live Here Anymore", "Taxi Driver", "The King of Comedy", "After Hours", "The Last Temptation of Christ" (albeit hidden under a hood), "The Age of Innocence", "Gangs of New York", "Hugo"), he is also known to contribute his voice to a film without appearing on screen

Religious guilt.

Guilt is a prominent theme in many of his films, as is the role of Catholicism in creating and dealing with guilt ("Who's That Knocking at My Door", "Mean Streets", "Raging Bull", "Bringing Out the Dead", "The Departed", "Shutter Island", and "The Irishman"). In a similar manner, Scorsese considered "Silence" a "passion project": it had been in development since 1990, two years after the release of his film "The Last Temptation of Christ", which also

Political corruption.

More recently, his films have featured corrupt authority figures, such as policemen in "The Departed" and politicians in "Gangs of New York" and "The Aviator". He is also known for his liberal usage of profanity, dark humor, and violence.  Scorsese's interest in political corruption as depicted in his films was expanded further in his 2019 film "The Irishman". Richard Brody writing for "The New Yorker" found the main interpretation of the film to be

Frequent collaborators.

Scorsese often casts the same actors in his films, particularly Robert De Niro, who has collaborated with Scorsese on nine feature films and one short film. Included are the three films ("Taxi Driver", "Raging Bull", and "Goodfellas") that made AFI's 100 Years... 100 Movies list. Scorsese has often said he thinks De Niro's best work under his direction was Rupert Pupkin in "The King of Comedy". After the turn of the century, Scorsese found a new muse with younger actor Leonardo DiCaprio, collaborating on five feature films and one short to date. Several critics have compared Scorsese's new partnership with DiCaprio with his previous one with De Niro. Frequent collaborators also include: Victor Argo (6), Harvey Keitel (6), Harry Northup (6), Murray Moston (5), Illeana Douglas (4), J.

Filmography.

, Scorsese has directed a total of 25 full-length films

Favorite films.

In 2012, Scorsese participated in the "Sight & Sound" film polls of that year. Held every ten years to

Film preservation.

The Film Foundation.

Scorsese had been at the forefront in film preservation and restoration ever since 1990, when he created The Film Foundation, a non-profit film organization which collaborates with film studios to restore prints of old or damaged films. Scorsese launched the organization with Woody Allen, Robert Altman, Francis Ford Coppola, Clint Eastwood, Stanley Kubrick, George Lucas, Sydney Pollack, Robert Redford, and Steven Spielberg, who all sat on

The World Cinema Project.

In 2007, Scorsese established the World Cinema Project with the mission, to preserve and present marginalized and infrequently screened films from regions generally ill equipped to preserve their own cinema history. Scorsese's organization has worked with the Criterion Collection to not only preserve the films but to allow them to be released on DVD and Blu-ray boxsets and on streaming services such

The African Film Heritage Project.

In 2017, Scorsese also introduced The African Film Heritage Project (AFHP), which is a joint initiative between Scorsese’s non-profit The Film Foundation, UNESCO, Cineteca di Bologna, and the Pan African Federation of Filmmakers (FEPACI). The project aims to locate and preserve 50 classic African films, some thought lost and others beyond repair, with hopes to make them available to audiences everywhere. In an interview with "Cinema Escapist" in 2018, Scorsese talked about the ambitious collaboration saying, "Our first goal is to launch and conduct a thorough investigation in film archives

Legacy.

Scorsese's films have been nominated for numerous awards both nationally and internationally, with an Academy Award win for "The Departed". In 1997, Scorsese received the AFI Life Achievement Award. In 1998, the American Film Institute placed three Scorsese films on their list of the greatest American movies: "Raging Bull" at #24, "Taxi Driver" at #47, and "Goodfellas" at #94. For the tenth-anniversary edition of their list, "Raging Bull" was moved to #4, "Taxi Driver" was moved to #52, and "Goodfellas" was moved to #92. In 2001, the American Film Institute placed two Scorsese films on their list of the most "heart-pounding movies" in American cinema: "Taxi Driver" at #22 and "Raging Bull" at #51. At a ceremony in Paris, France, on January 5, 2005, Martin Scorsese was awarded the French Legion of Honour in recognition of his contribution to cinema. On February 8, 2006, at the 48th Annual Grammy Awards, Scorsese was awarded the Grammy Award for Best Long Form Music Video for "No Direction Home".  In 2007, Scorsese was listed among "Time" magazine's 100 Most Influential People in The World. In August 2007, Scorsese was named the second-greatest director of all time in a poll by "Total Film" magazine, in front of Steven Spielberg and behind Alfred Hitchcock. In 2007, Scorsese was honored by the National Italian American Foundation (N.I.A.F.) at the nonprofit's thirty-second Anniversary Gala. During the ceremony, Scorsese helped launch N.I.A.F.'s Jack Valenti Institute in memory of former foundation board member and past president of the Motion Picture Association of America (M.P.A.A.) Jack Valenti. The Institute provides support to Italian film students in the U.S. Scorsese received his award from Mary Margaret Valenti, Valenti's widow. Certain pieces of Scorsese's film-related material and personal papers are contained in the Wesleyan University Cinema Archives, to which scholars and media experts from around the world may have full access. On September 11, 2007, the Kennedy Center Honors committee, which recognizes career excellence and cultural influence, named Scorsese as one of the honorees for the year. On June 17, 2008, the American Film Institute placed two of Scorsese's films on the AFI's 10 Top 10 list: "Raging Bull" at number one for the Sports genre and "Goodfellas" at number two for the Gangster genre. In 2013, the staff of "Entertainment Weekly" voted "Mean Streets" the seventh greatest film ever made. On January 17, 2010, at the 67th Golden Globe Awards, Scorsese was the recipient of the Golden Globe Cecil B. DeMille Award. On September 18, 2011, at the 63rd Primetime Emmy Awards, Scorsese won the Primetime Emmy Award for Outstanding Directing for a Drama Series for his work on the series premiere of "Boardwalk Empire". In 2011, Scorsese received an honorary doctorate from the National Film School in Lodz. At the awards ceremony he said, "I feel like I'm a part of this school and that I attended it," paying tribute to the films of Wajda, Munk, Has, Polanski and Skolimowski. King Missile wrote "Martin Scorsese" in his honor. On February 12, 2012, at the 65th British Academy Film Awards, Scorsese was the recipient of the BAFTA Academy Fellowship Award.  On September 16, 2012, Scorsese won two Emmy Awards for Outstanding Directing for Nonfiction Programming and Outstanding Nonfiction Special for his work on the documentary "George Harrison: Living in the Material World". In 2013, the National Endowment for the Humanities selected Scorsese for the Jefferson Lecture, the U.S. federal government's highest honor for achievement in the humanities. He was the first filmmaker chosen for the honor. His lecture, delivered on April 1, 2013, at the John F. Kennedy Center for the Performing Arts, was titled "Persistence of Vision: Reading the Language of Cinema". Scorsese was awarded the Polish Gold Medal for Merit to Culture – Gloria Artis on April 11, 2017, in recognition of his contribution to Polish cinema. Scorsese has also garnered favorable responses from numerous film giants including Ingmar Bergman, Frank Capra, Jean-Luc Godard, Werner Herzog, Elia Kazan, Akira Kurosawa, David Lean, Michael Powell, Satyajit Ray, and François Truffaut. He was awarded an Honorary Doctorate from the University of Oxford on June 20, 2018. As of 2019, five of Scorsese's film have been selected by the Library of Congress for preservation in the National Film Registry for being "culturally, historically, or aesthetically significant". In commenting on Scorsese's 2019 film "The Irishman", Guillermo del Toro cited Scorsese's ability as a director for the depiction of character development comparable to the films of "Renoir, Bresson, Bergman, Oliveira or Kurosawa". Sam Mendes, in his acceptance speech after winning the 2020 Golden Globe Award for Best Director for "1917", praised Scorsese's contribution to cinema, stating, "There's not one director in this room, not one director in the world, that is not in the shadow of Martin Scorsese... I just have to say that." Bong Joon-ho, in his acceptance speech for the 2020 Academy Award for Best Director for "Parasite", said, "When I was young and studying cinema, there was a saying that I carved deep into my heart, which is, the most personal is the most creative." He then said that this quote had come from Scorsese, which prompted the audience to give Scorsese a standing ovation.

Martin Charles Scorsese (, ; born November 17, 1942) is an American film director, producer, screenwriter, and actor. One of the major figures of the New Hollywood era, he is widely regarded as one of the most significant and influential directors in film history. Scorsese's body of work explores themes such as Italian-American identity, Catholic concepts of guilt and redemption, faith, machismo, crime and tribalism. Many of his films are known for their depiction of violence, and the liberal use of profanity and rock music. In 1990, he founded The Film Foundation, a nonprofit organization dedicated to film preservation, in 2007 he founded the World Cinema Foundation and in 2017, he introduced the African Film Heritage Project.

Martin Charles Scorsese [] (* 17. November 1942 in Queens, New York) ist ein US-amerikanischer Regisseur, Drehbuchautor, Filmproduzent und Schauspieler. Er gehört zu den einflussreichsten Regisseuren des zeitgenössischen amerikanischen Kinos. Zu seinen bekanntesten Filmen zählen "Taxi Driver" (1976)", Good Fellas" (1990), "Departed – Unter Feinden" (2006) sowie "The Wolf of Wall Street" (2013).


History.

The Mandelbrot set has its origin in complex dynamics, a field first investigated by the French mathematicians Pierre Fatou and Gaston Julia at the beginning of the 20th century. This fractal was first defined and drawn in 1978 by Robert W. Brooks and Peter Matelski as part of a study of Kleinian groups. On 1 March 1980, at IBM's Thomas J. Watson Research Center in Yorktown Heights, New York, Benoit Mandelbrot first saw a visualization of the set.  Mandelbrot studied the parameter space of quadratic polynomials in an article that appeared in 1980. The mathematical study of the Mandelbrot set really began with work by the mathematicians Adrien Douady and John H. Hubbard (1985), who established many of its fundamental properties and named the set in honor of Mandelbrot for his influential work in fractal geometry.  The mathematicians Heinz-Otto Peitgen and Peter Richter became well known for promoting the set with photographs, books (1986), and an internationally touring exhibit of the German Goethe-Institut (1985).  The cover article of the August 1985 "Scientific American" introduced a wide audience to the algorithm for computing the Mandelbrot set. The cover featured an image located at −0.909 + −0.275 "i" and was created by Peitgen et al. The Mandelbrot set became prominent in the mid-1980s as a computer graphics demo, when personal computers became powerful enough to plot and display the set in high resolution.  The work of Douady and Hubbard coincided with a huge increase in interest in complex dynamics and abstract mathematics, and the study of the Mandelbrot set has been a centerpiece of this field ever since. An exhaustive list of all who have contributed to the understanding of this set since then is long but would include Mikhail Lyubich, Curt McMullen, John Milnor, Mitsuhiro Shishikura and Jean-Christophe Yoccoz.

Formal definition.

The Mandelbrot set is the set of values of "c" in the complex plane for which the orbit of 0 under iteration of the quadratic map  remains bounded. Thus, a complex number "c" is a member of the Mandelbrot set if, when starting with "z" = 0 and applying the iteration repeatedly, the absolute value of "z" remains bounded for all "n" > 0.  For example, for "c" = 1, the sequence is 0, 1, 2, 5, 26,..., which tends to infinity, so 1 is not an element of the Mandelbrot set. On the other hand, for "c" = −1, the sequence is 0, −1, 0, −1, 0,..., which is bounded, so −1 does belong to the set.  The Mandelbrot set can also be defined as the connectedness locus of a family of polynomials.

Basic properties.

The Mandelbrot set is a compact set, since it is closed and contained in the closed disk of radius 2 around the origin. More specifically, a point formula_1 belongs to the Mandelbrot set if and only if  In other words, if the absolute value of formula_19 ever becomes larger than 2, the sequence will escape to infinity.  The intersection of formula_20 with the real axis is precisely the interval [−2, 1/4]. The parameters along this interval can be put in one-to-one correspondence with those of the real logistic family, The correspondence is given by  In fact, this gives a correspondence between the entire parameter space of the logistic family and that of the Mandelbrot set.  Douady and Hubbard have shown that the Mandelbrot set is connected. In fact, they constructed an explicit conformal isomorphism between the complement of the Mandelbrot set and the complement of the closed unit disk. Mandelbrot had originally conjectured that the Mandelbrot set is disconnected. This conjecture was based on computer pictures generated by programs that are unable to detect the thin filaments connecting different parts of formula_20. Upon further experiments, he revised his conjecture, deciding that formula_20 should be connected. There also exists a topological proof to the connectedness that was discovered in 2001 by Jeremy Kahn.  The dynamical formula for the uniformisation of the complement of the Mandelbrot set, arising from Douady and Hubbard's proof of the connectedness of formula_20, gives rise to external rays of the Mandelbrot set. These rays can be used to study the Mandelbrot set in combinatorial terms and form the backbone of the Yoccoz parapuzzle.  The boundary of the Mandelbrot set is exactly the bifurcation locus of the quadratic family; that is, the set of parameters formula_1 for which the dynamics changes abruptly under small changes of formula_27 It can be constructed as the limit set of a sequence of plane algebraic curves, the "Mandelbrot curves", of the general type known as polynomial lemniscates. The Mandelbrot curves are defined by setting "p" = "z", "p" = "p" + "z", and then interpreting the set of points = 2 in the complex plane as a curve in the real Cartesian plane of degree 2 in "x" and "y". These algebraic curves appear in images of the Mandelbrot set computed using the "escape time algorithm" mentioned below.

Other properties.

Main cardioid and period bulbs.

Upon looking at a picture of the Mandelbrot set, one immediately notices the large cardioid-shaped region in the center. This "main cardioid" is the region of parameters formula_1 for which formula_29 has an attracting fixed point. It consists of all parameters of the form for some formula_31 in the open unit disk.  To the left of the main cardioid, attached to it at the point formula_32, a circular-shaped bulb is visible. This bulb consists of those parameters formula_1 for which formula_29 has an attracting cycle of period 2. This set of parameters is an actual circle, namely that of radius 1/4 around −1.  There are infinitely many other bulbs tangent to the main cardioid: for every rational number formula_35, with "p" and "q" coprime, there is such a bulb that is tangent at the parameter  This bulb is called the "formula_35-bulb" of the Mandelbrot set. It consists of parameters that have an attracting cycle of period formula_38 and combinatorial rotation number formula_35. More precisely, the formula_38 periodic Fatou components containing the attracting cycle all touch at a common point (commonly called the "formula_41-fixed point"). If we label these components formula_42 in counterclockwise orientation, then formula_29 maps the component formula_44 to the component formula_45.  The change of behavior occurring at formula_46 is known as a bifurcation: the attracting fixed point "collides" with a repelling period "q"-cycle. As we pass through the bifurcation parameter into the formula_35-bulb, the attracting fixed point turns into a repelling fixed point (the formula_41-fixed point), and the period "q"-cycle becomes attracting.

Hyperbolic components.

All the bulbs we encountered in the previous section were interior components of the Mandelbrot set in which the maps formula_29 have an attracting periodic cycle. Such components are called "hyperbolic components".  It is conjectured that these are the "only" interior regions of formula_20. This problem, known as "density of hyperbolicity", may be the most important open problem in the field of complex dynamics. Hypothetical non-hyperbolic components of the Mandelbrot set are often referred to as "queer" or ghost components. For "real" quadratic polynomials, this question was answered positively in the 1990s independently by Lyubich and by Graczyk and Świątek. (Note that hyperbolic components intersecting the real axis correspond exactly to periodic windows in the Feigenbaum diagram. So this result states that such windows exist near every parameter in the diagram.)  Not every hyperbolic component can be reached by a sequence of direct bifurcations from the main cardioid of the Mandelbrot set. However, such a component "can" be reached by a sequence of direct bifurcations from the main cardioid of a little Mandelbrot copy (see below).  Each of the hyperbolic components has a "center", which is a point "c" such that the inner Fatou domain for formula_51 has a super-attracting cycle – that is, that the attraction is infinite (see the image ). This means that the cycle contains the critical point 0, so that 0 is iterated back to itself after some iterations. We therefore have that formula_29formula_53 for some "n". If we call this polynomial formula_54 (letting it depend on "c" instead of "z"), we have that formula_55 and that the degree of formula_54 is formula_57. We can therefore construct the centers of the hyperbolic components by successively solving the equations formula_58. The number of new centers produced in each step is given by Sloane's.

Local connectivity.

It is conjectured that the Mandelbrot set is locally connected. This famous conjecture is known as "MLC" (for "Mandelbrot locally connected"). By the work of Adrien Douady and John H. Hubbard, this conjecture would result in a simple abstract "pinched disk" model of the Mandelbrot set. In particular, it would imply the important "hyperbolicity conjecture" mentioned above.  The work of Jean-Christophe Yoccoz established local connectivity of the Mandelbrot set at all finitely renormalizable parameters; that is, roughly speaking those contained only in finitely many small Mandelbrot copies. Since then, local connectivity has been proved at many other points of formula_20, but the full conjecture is still open.

Self-similarity.

The Mandelbrot set is self-similar under magnification in the neighborhoods of the Misiurewicz points. It is also conjectured to be self-similar around generalized Feigenbaum points (e.g., −1.401155 or −0.1528 + 1.0397"i"), in the sense of converging to a limit set. The Mandelbrot set in general is not strictly self-similar but it is quasi-self-similar, as small slightly different versions of itself can be found at arbitrarily small scales.  The little copies of the Mandelbrot set are all slightly different, mostly because of the thin threads connecting them to the main body of the set.

Further results.

The Hausdorff dimension of the boundary of the Mandelbrot set equals 2 as determined by a result of Mitsuhiro Shishikura. It is not known whether the boundary of the Mandelbrot set has positive planar Lebesgue measure.  In the Blum–Shub–Smale model of real computation, the Mandelbrot set is not computable, but its complement is computably enumerable. However, many simple objects ("e.g.", the graph of exponentiation) are also not computable in the BSS model. At present, it is unknown whether the Mandelbrot set is computable in models of real computation based on computable analysis, which correspond more closely to the intuitive notion of "plotting the set by a computer". Hertling has shown that the Mandelbrot set is computable in this model if the hyperbolicity conjecture is true.

Relationship with Julia sets.

As a consequence of the definition of the Mandelbrot set, there is a close correspondence between the geometry of the Mandelbrot set at a given point and the structure of the corresponding Julia set. For instance, a point is in the Mandelbrot set exactly when the corresponding Julia set is connected.  This principle is exploited in virtually all deep results on the Mandelbrot set. For example, Shishikura proved that, for a dense set of parameters in the boundary of the Mandelbrot set, the Julia set has Hausdorff dimension two, and then transfers this information to the parameter plane. Similarly, Yoccoz first proved the local connectivity of Julia sets, before establishing it for the Mandelbrot set at the corresponding parameters. Adrien Douady phrases this principle as:

Geometry.

For every rational number formula_35, where "p" and "q" are relatively prime, a hyperbolic component of period "q" bifurcates from the main cardioid. The part of the Mandelbrot set connected to the main cardioid at this bifurcation point is called the "p"/"q"-limb. Computer experiments suggest that the diameter of the limb tends to zero like formula_61. The best current estimate known is the "Yoccoz-inequality", which states that the size tends to zero like formula_62.  A period-"q" limb will have "q" − 1 "antennae" at the top of its limb. We can thus determine the period of a given bulb by counting these antennas.

Pi in the Mandelbrot set.

In an attempt to demonstrate that the thickness of the "p"/"q"-limb is zero, David Boll carried out a computer experiment in 1991, where he computed the number of iterations required for the series to diverge for "z" = − + "iε" (− being the location thereof). As the series doesn't diverge for the exact value of "z" = −, the number of iterations required increases with a small "ε". It turns out that multiplying the value of ε with the number of iterations required yields an approximation of π that becomes better for smaller "ε". For example, for "ε" = 0.0000001 the number of iterations is 31415928 and the product is 3.1415928.

Fibonacci sequence in the Mandelbrot set.

It can be shown that the Fibonacci sequence is located within the Mandelbrot Set and that a relation exists between the main cardioid and the Farey Diagram. Upon mapping the main cardioid to a disk, one can notice that the amount of antennae that extends from the next largest Hyperbolic component, and that is located between the two previously selected components, follows suit with the Fibonacci sequence. The amount of antennae also correlates with the Farey Diagram and the denominator amounts within the corresponding fractional values, of which relate to the distance around the disk. Both portions of these fractional values themselves can be summed together after formula_63to produce the location of the next Hyperbolic component within the sequence. Thus, the Fibonacci sequence of 1, 2, 3, 5, 8, 13, and 21 can be found within the Mandelbrot set.

Image gallery of a zoom sequence.

The Mandelbrot set shows more intricate detail the closer one looks or magnifies the image, usually called "zooming in". The following example of an image sequence zooming to a selected "c" value gives an impression of the infinite richness of different geometrical structures and explains some of their typical rules.  The magnification of the last image relative to the first one is about 10 to 1. Relating to an ordinary monitor, it represents a section of a Mandelbrot set with a diameter of 4 million kilometers. Its border would show an astronomical number of different fractal structures.  The seahorse "body" is composed by 25 "spokes" consisting of two groups of 12 "spokes" each and one "spoke" connecting to the main cardioid. These two groups can be attributed by some kind of metamorphosis to the two "fingers" of the "upper hand" of the Mandelbrot set; therefore, the number of "spokes" increases from one "seahorse" to the next by 2; the "hub" is a so-called Misiurewicz point. Between the "upper part of the body" and the "tail" a distorted small copy of the Mandelbrot set called satellite may be recognized. The islands in the third-to-last step seem to consist of infinitely many parts like Cantor sets, as is actually the case for the corresponding Julia set "J". However, they are connected by tiny structures, so that the whole represents a simply connected set. The tiny structures meet each other at a satellite in the center that is too small to be recognized at this magnification. The value of "c" for the corresponding "J" is not that of the image center but, relative to the main body of the Mandelbrot set, has the same position as the center of this image relative to the satellite shown in the 6th zoom step.

3D images of Mandelbrot and Julia sets.

In addition to creating two dimensional images of the Mandelbrot set, various techniques can be used to render Mandelbrot and Julia sets as 3D Heightmap images, where each pixel in a 2D image is given a height value, and the resulting image is rendered as a 3D graphic.  The simplest approach to 3D rendering uses the iteration value for each pixel as a height value. This produces images with distinct "steps" in the height value.  If instead you use the fractional iteration value (also known as the potential function) to calculate the height value for each point, you avoid steps in the resulting image. However, images rendered in 3D using fractional iteration data still look rather bumpy and visually noisy.  An alternative approach is to use Distance Estimate (DE) data for each point to calculate a height value. Non-linear mapping of distance estimate value using an exponential function can produce visually pleasing images. Images plotted using DE data are often visually striking, and more importantly, the 3D shape makes it easy to visualize the thin "tendrils" that connect points of the set. Color plates 29 and 30 on page 121 of "The Science of Fractal Images" show a 2D and 3D image plotted using External Distance Estimates.  Below is a 3D version of the "Image gallery of a zoom sequence" gallery above, rendered as height maps using Distance Estimate data, and using similar cropping and coloring.  The image below is similar to "zoom 5", above, but is an attempt to create a 3D version of the image "Map 44" from page 85 of the book "The Beauty of Fractals" using a visually similar color scheme that shows the details of the plot in 3D.

Generalizations.

Multibrot sets.

Multibrot sets are bounded sets found in the complex plane for members of the general monic univariate polynomial family of recursions  For an integer d, these sets are connectedness loci for the Julia sets built from the same formula. The full cubic connectedness locus has also been studied; here one considers the two-parameter recursion formula_65, whose two critical points are the complex square roots of the parameter "k". A parameter is in the cubic connectedness locus if both critical points are stable. For general families of holomorphic functions, the "boundary" of the Mandelbrot set generalizes to the bifurcation locus, which is a natural object to study even when the connectedness locus is not useful.  The Multibrot set is obtained by varying the value of the exponent "d". The article has a video that shows the development from "d" = 0 to 7, at which point there are 6 i.e. ("d" − 1) lobes around the perimeter. A similar development with negative exponents results in (1 − "d") clefts on the inside of a ring.

Higher dimensions.

There is no perfect extension of the Mandelbrot set into 3D. This is because there is no 3D analogue of the complex numbers for it to iterate on. However, there is an extension of the complex numbers into 4 dimensions, called the quaternions, that creates a perfect extension of the Mandelbrot set and the Julia sets into 4 dimensions. These can then be either cross-sectioned or projected into a 3D structure.

Other, non-analytic, mappings.

Of particular interest is the tricorn fractal, the connectedness locus of the anti-holomorphic family  The tricorn (also sometimes called the "Mandelbar") was encountered by Milnor in his study of parameter slices of real cubic polynomials. It is "not" locally connected. This property is inherited by the connectedness locus of real cubic polynomials.  Another non-analytic generalization is the Burning Ship fractal, which is obtained by iterating the following :

Computer drawings.

]  There exist a multitude of various algorithms for plotting the Mandelbrot set via a computing device. Here, the most widely used and simplest algorithm will be demonstrated, namely, the naïve "escape time algorithm". In the escape time algorithm, a repeating calculation is performed for each "x", "y" point in the plot area and based on the behavior of that calculation, a color is chosen for that pixel.  The "x" and "y" locations of each point are used as starting values in a repeating, or iterating calculation (described in detail below). The result of each iteration is used as the starting values for the next. The values are checked during each iteration to see whether they have reached a critical "escape" condition, or "bailout". If that condition is reached, the calculation is stopped, the pixel is drawn, and the next "x", "y" point is examined.  The color of each point represents how quickly the values reached the escape point. Often black is used to show values that fail to escape before the iteration limit, and gradually brighter colors are used for points that escape. This gives a visual representation of how many cycles were required before reaching the escape condition.  To render such an image, the region of the complex plane we are considering is subdivided into a certain number of pixels. To color any such pixel, let formula_1 be the midpoint of that pixel. We now iterate the critical point 0 under formula_29, checking at each step whether the orbit point has modulus larger than 2. When this is the case, we know that formula_1 does not belong to the Mandelbrot set, and we color our pixel according to the number of iterations used to find out. Otherwise, we keep iterating up to a fixed number of steps, after which we decide that our parameter is "probably" in the Mandelbrot set, or at least very close to it, and color the pixel black.  In pseudocode, this algorithm would look as follows. The algorithm does not use complex numbers and manually simulates complex-number operations using two real numbers, for those who do not have a complex data type. The program may be simplified if the programming language includes complex-data-type operations.  Here, relating the pseudocode to formula_1, formula_12 and formula_29: and so, as can be seen in the pseudocode in the computation of "x" and "y":  To get colorful images of the set, the assignment of a color to each value of the number of executed iterations can be made using one of a variety of functions (linear, exponential, etc.).

References in popular culture.

The Mandelbrot set is considered by many the most popular fractal, and has been referenced several times in popular culture.

The Mandelbrot set is the set of complex numbers formula_1 for which the function formula_2 does not diverge when iterated from formula_3, i.e., for which the sequence formula_4, formula_5, etc., remains bounded in absolute value. Its definition is credited to Adrien Douady who named it in tribute to the mathematician Benoit Mandelbrot. The set is connected to a Julia set, and related Julia sets produce similarly complex fractal shapes.

Die Mandelbrot-Menge, benannt nach Benoît Mandelbrot, ist die Menge der komplexen Zahlen formula_1, für welche die durch die Iteration definierte Folge formula_3 beschränkt ist.


Early life.

Ende was born 12 November 1929 in Garmisch-Partenkirchen, Bavaria, the only child of the surrealist painter Edgar Ende and Luise Bartholomä Ende, a physiotherapist (Coby). In 1935, when Michael was six, the Ende family moved to the "artists' quarter of Schwabing" in Munich (Haase). Growing up in this rich artistic and literary environment influenced Ende's later writing.  In 1936, his father's work was declared "degenerate" and banned by the Nazi party, so Edgar Ende was forced to work in secret. The horrors of World War II heavily influenced Ende's childhood. He was twelve years old when the first air raid took place above Munich. He reflected: Our street was consumed by flames. The fire didn't crackle; it roared. The flames were roaring. I remember singing and careering through the blaze like a drunkard. I was in the grip of a kind of euphoria. I still don't truly understand it, but I was almost tempted to cast myself into the fire like a moth into the light. He was horrified by the 1943 Hamburg bombing, which he experienced while visiting his paternal uncle. At the first available opportunity his uncle put him on a train back to Munich. There, Ende attended the Maximillians Gymnasium in Munich until schools were closed as the air raids intensified and pupils were evacuated. Ende returned to Garmisch-Partenkirchen, where he was billeted in a boarding-house, Haus Kramerhof and later in Haus Roseneck. It was there that his interest in poetry was awakened. As well as writing his own poetry, he began to study poetical movements and styles. A good deal of modern poetry was banned at the time, so he studied the Romantic poet Novalis, whose "Hymns to the Night" left a great impression on him.  In 1944, Edgar Ende's studio at no. 90 Kaulbachstraße, Munich went up in flames. Over two hundred and fifty paintings and sketches were destroyed, as well as all his prints and etchings., Director of Public Art for Bavaria, was still in possession of a number of Ende's paintings, and they survived the raids. After the bombing, Luise Ende was relocated to the Munich district of Solln. In 1945, Edgar Ende was taken prisoner by the Americans and released soon after the war.  In 1945, German youths as young as fourteen were drafted into the "Volkssturm" and sent to war against the advancing Allied armies. Three of Michael Ende's classmates were killed on their first day of action. Ende was also drafted, but he tore up his call-up papers and joined a Bavarian resistance movement founded to sabotage the SS's declared intention to defend Munich until the "bitter end". He served as a courier for the group for the remainder of the war.  In 1946, Michael Ende's grammar school re-opened, and he attended classes for a year, following which the financial support of family friends allowed him to complete his high-school education at a Waldorf School in Stuttgart. This seemingly charitable gesture was motivated by more self-interest: Ende had fallen in love with a girl three years his senior, and her parents funded his two-year stay in Stuttgart to keep the pair apart. It was at this time that he first began to write stories ("Michael," par. 3). He aspired to be a "dramatist," but wrote mostly short stories and poems (Haase).

Career.

Early career.

During his time in Stuttgart, Ende first encountered Expressionist and Dadaist writing and began schooling himself in literature. He studied Theodor Däubler, Yvan Goll, Else Lasker-Schüler and Alfred Mombert, but his real love was the poetry of Rainer Maria Rilke, Stefan George and Georg Trakl. He also made his first attempts at acting, performing with friends in Stuttgart's America House. He was involved in productions of Chekhov's one-act comedy "The Bear", in which he played the principal role, and in the German premiere of Jean Cocteau's "Orpheus". Ende's first play "Denn die Stunde drängt (As Time is Running Out)" dates to this period. It was dedicated to Hiroshima, and was never performed.  Ende decided that he wanted to be a playwright, but financial considerations ruled out a university degree, so in 1948 he auditioned for the Otto Falckenberg School of the Performing Arts in Munich and was granted a two-year scholarship (Haase). On leaving drama school, his first job as an actor took him to a provincial theatre company in Schleswig-Holstein. The troupe travelled from town to town by bus, usually performing on makeshift stages, surrounded by beer, smoke and the clatter of skittles from nearby bowling alleys. The acting was a disappointment, he usually had to play old men and malicious schemers, and had barely enough time to memorize his lines. Despite the frustrations and disappointments of his early acting career, Ende came to value his time in the provinces as a valuable learning experience that endowed him with a practical, down-to-earth approach to his work: "It was a good experience, a healthy experience. Anyone interested in writing should be made to do that sort of thing. It doesn't have to be restricted to acting. It could be any kind of practical activity like cabinet making—learning how to construct a cabinet in which the doors fit properly." In Ende's view, practical training had the potential to be more useful than a literary degree.  Thanks to the numerous contacts of his girlfriend Ingeborg Hoffmann, Michael Ende was introduced to a variety of cabaret groups. In 1955,, head of (the 'Little Fish' cabaret), commissioned Ende to write a piece in commemoration of the 150th anniversary of Friedrich Schiller's death. Ende produced a sketch in which a statue of Schiller was interviewed about newsworthy issues, and replied with quotes from Schiller's work. "There was rapturous applause, and commissions arrived from other cabarets too." Michael Ende began to compose sketches, chansons and monologues. He also worked as a film critic during the 1950s.

Commercial success: writing "Jim Knopf".

In the late 1950s, Ende wrote his first novel "Jim Button".  Michael Ende always said that ideas only came to him when the logic of the story required them. On some occasions he waited a long time for inspiration to arrive. At one point during the writing of "Jim Button" the plot reached a dead end. Jim and Luke were stuck among black rocks and their tank engine couldn't go any further. Ende was at a loss to think of a way out of the adventure, but cutting the episode struck him as disingenuous. Three weeks later he was about to shelve the novel when suddenly he had an idea—the steam from the tank engine could freeze and cover the rocks in snow, thus saving his characters from their scrape. "In my case, writing is primarily a question of patience," he once commented.  After nearly a year the five hundred pages of manuscript were complete. Over the next eighteen months he sent the manuscript to ten different publishers, but they all responded that it was "Unsuitable for our list" or "Too long for children". In the end he began to lose hope and toyed with the idea of throwing away the script. He eventually tried it at a small family publishing-house, K. in Stuttgart. Michael Ende's manuscript was accepted by company director Lotte Weitbrecht who liked the story. Her only stipulation was that the manuscript had to be published as two separate books.  The first of the "Jim Button" novels was published in 1960. About a year later, on the morning of the announcement that his novel, "Jim Button and Luke the Engine Driver", had won the German Prize for Children's Fiction, Ende was being sued by his landlady for seven months' rent backpayment. With the prize money of five thousand marks, Michael Ende's financial situation improved substantially and his writing career began in earnest. After the awards ceremony, he embarked on his first reading tour, and within a year, the first "Jim Knopf" book was also nominated for the Hans Christian Andersen Award and received the Berlin Literary Prize for Youth Fiction. The second "Jim Knopf" novel, "Jim Button and the Wild Thirteen", was published in 1962. Both books were serialized on radio and TV, and the Augsburger Puppenkiste famously adapted the novels in a version filmed by Hesse's broadcasting corporation. The print-runs sold out so rapidly that K. Thienemanns could barely keep up. Translations into numerous foreign languages soon followed.

Writing style and themes.

Ende claimed, "It is for this child in me, and in all of us, that I tell my stories", and that "[my books are] for any child between 80 and 8 years" (qtd. Senick 95, 97). He often expressed frustration over being perceived as a children's writer exclusively, considering that his purpose was to speak of cultural problems and spiritual wisdom to people of all ages. Especially in Germany, Ende was accused by some critics of escapism. He wrote in 1985:  One may enter the literary parlor via just about any door, be it the prison door, the madhouse door, or the brothel door. There is but one door one may not enter it through, which is the nursery door. The critics will never forgive you such. The great Rudyard Kipling is one to have suffered this. I keep wondering to myself what this peculiar contempt towards anything related to childhood is all about.  Ende's writing could be described as a surreal mixture of reality and fantasy. The reader is often invited to take a more interactive role in the story, and the worlds in his books often mirror our reality, using fantasy to bring light to the problems of an increasingly technological modern society. His writings were influenced by Rudolf Steiner and his anthroposophy. Ende was also known as a proponent of economic reform, and claimed to have had the concept of aging money, or demurrage, in mind when writing "Momo". A theme of his work was the loss of fantasy and magic in the modern world.

Japan.

Michael Ende had been fascinated by Japan since his childhood. He loved Lafcadio Hearn's Japanese legends and ghost stories, and in 1959 he wrote a play inspired by Hearn's material. "Die Päonienlaterne" (The Peony Lantern) was written for radio, but never broadcast. Ende was primarily interested in Japan because of its radical otherness. The Japanese language and script were so different from Ende's native German that it seemed they were grounded in a different kind of consciousness—an alternative way of seeing the world. He was particularly intrigued by the way in which everyday circumstances were shaped into intricate rituals, such as the tea ceremony. There was, he realized, a sharp contrast between the traditions of ancient Japan and its industry-oriented modern-day society.  Ende won a devoted following in Japan, and by 1993 over two million copies of "Momo" and "The Neverending Story" had been sold in Japan.  In 1986 Michael Ende was invited to attend the annual congress of the JBBY (Japanese Committee for International Children's Literature) in Tokyo. He gave a lecture on "Eternal Child-likeness"—the first detailed explanation of his artistic vision. 1989 marked the opening of the exhibition "Michael and Edgar Ende" in Tokyo. The exhibition was subsequently shown in Otsu, Miyazaki, Nagasaki, Osaka, Nagoya and Fukuyama. At the invitation of "Shimbun", a Japanese newspaper, Michael Ende attended the opening and spent two months touring Japan. It was his third trip accompanied by the Japanese-born Mariko Sato, whom he married in September 1989. The following year an archive devoted to Michael Ende was established at Kurohime Dowakan, a museum in the Japanese city of Shinano-machi. Ende donated letters and other personal items to the collection. On 23 October 1992 Michael Ende made his final trip to Japan. In the course of their three-week visit Michael Ende and Mariko Sato-Ende visited the Dowakan museum, joined Ende's Japanese publishers, Iwanami, in celebrating the millionth sale of Momo, and travelled to Kanazawa and Hamamatsu and a number of other cities that were new to Ende.

Personal life.

On New Year's Eve 1952, Michael Ende met the actress Ingeborg Hoffmann during a party with friends. According to Ende, he was standing at an ivy-covered counter serving as barman, when Hoffmann strode towards him, looking "flame-haired, fiery and chic". She declaimed: "Leaning up against the ivy-covered wall / Of this old terrace"; "Mörike", Ende said instantly, recognizing the quote. Hoffmann, eight years his senior, made a big impression on Ende. She in turn was intrigued by his literary cultivation and artistic inclinations. They began a relationship that led to their marriage in 1964 in Rome, Italy, and ended with Ingeborg Hoffmann's sudden and unexpected death in 1985 from a pulmonary embolism; she was 63 years old.  Hoffmann influenced Ende profoundly. In addition to assisting with getting his first major manuscript published, Hoffmann worked with him on his others, reading them and discussing them with him. Hoffman also influenced Ende's life in other ways. She encouraged Ende to join the Humanistic Union, an organization committed to furthering humanist values. Together they campaigned for human rights, protested against rearmament, and worked towards peace. Thanks to Ingeborg Hoffmann's numerous contacts, Michael Ende was introduced to a variety of cabaret groups. In 1955, Therese Angeloff, head of Die kleinen Fische (the 'Little Fish' cabaret), commissioned Ende to write a piece in commemoration of the 150th anniversary of Friedrich Schiller's death. Ende produced a sketch in which a statue of Schiller was interviewed about newsworthy issues, and replied with quotes from Schiller's work. "There was rapturous applause, and commissions arrived from other cabarets too." Michael Ende began to compose sketches, chansons and monologues.  For fourteen years, Ende and Hoffmann, who greatly admired Italian culture, lived just outside Rome in Genzano, Italy, in a house they called Casa Liocorno ("The Unicorn"). It was there that Ende wrote most of the novel "Momo". Following the death of his wife, Ende sold the home in Genzano and returned to Munich.  He married a second time in 1989, the Japanese woman Mariko Sato, and they remained married until his death. He first met Mariko Sato in 1976. Sato had moved from Japan to Germany in 1974 and was working for the International Youth Library in Munich. After their meeting at the Bologna Children's Book Fair, Sato translated some of Ende's books into Japanese and helped answer some of his questions about Japanese culture. From 1977 to 1980 Michael Ende and Mariko Sato worked together to produce a German translation of ten fairy tales by Japanese writer Kenji Miyazawa. The German text was never published, but the working partnership turned into a friendship. Mariko Sato accompanied him on a number of trips to Japan. The first trip took place in 1977 and included visits to Tokyo and Kyoto. For the first time Ende was able to experience Kabuki and Noh theatre, and was greatly impressed by traditional Japanese drama. Michael Ende had no children.

Death.

In June 1994, Ende was diagnosed with stomach cancer. Over the next few months he underwent various treatments, but the disease progressed. He ultimately succumbed to the disease in Filderstadt, Germany, on 28 August 1995.

Selected works.

Michael Ende's works include:

Michael Andreas Helmuth Ende (12 November 1929 – 28 August 1995) was a German writer of fantasy and children's fiction. He is best known for his epic fantasy "The Neverending Story"; other famous works include "Momo" and "Jim Button and Luke the Engine Driver". His works have been translated into more than 40 languages, sold more than 35 million copies, and adapted as motion pictures, stage plays, operas and audio books. Ende is one of the most popular and famous German authors of the 20th century, mostly due to the enormous success of his children's fiction. He was not strictly a children's writer, however, as he wrote books for adults too. Ende's writing could be described as a surreal mixture of reality and fantasy.

Michael Andreas Helmuth Ende (* 12. November 1929 in Garmisch; † 28. August 1995 in Filderstadt) war ein deutscher Schriftsteller. Er zählt zu den erfolgreichsten deutschen Jugendbuchautoren. Bücher wie "Die unendliche Geschichte", "Momo" und "Jim Knopf und Lukas der Lokomotivführer" waren internationale Erfolge und wurden vielfach für Film, Fernsehen und Theater adaptiert. Endes Werke verkauften sich über 30 Millionen Mal und wurden in über 40 Sprachen übersetzt.