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Russell's paradox

In the foundations of mathematics, Russell's paradox, discovered by Bertrand Russell in 1901, showed that some attempted formalizations of the naïve set theory created by Georg Cantor led to a contradiction. The same paradox had been discovered in 1899 by Ernst Zermelo but he did not publish the idea, which remained known only to David Hilbert, Edmund Husserl, other members of the University of Göttingen. At the end of the 1890s Cantor himself had realized that his definition would lead to a contradiction, which he told Hilbert and Richard Dedekind by letter. According to naive set theory, any definable collection is a set. Let R be the set of all sets that are not members of themselves. If R is not a member of itself its definition dictates that it must contain itself, if it contains itself it contradicts its own definition as the set of all sets that are not members of themselves; this contradiction is Russell's paradox. Symbolically: Let R = R ∈ R ⟺ R ∉ R In 1908, two ways of avoiding the paradox were proposed, Russell's type theory and the Zermelo set theory.

Zermelo's axioms went well beyond Gottlob Frege's axioms of extensionality and unlimited set abstraction. The essential difference between Russell's and Zermelo's solution to the paradox is that Zermelo altered the axioms of set theory while preserving the logical language in which they are expressed, while Russell altered the logical language itself; the language of ZFC, with the help of Thoralf Skolem, turned out to be first-order logic. Most sets encountered aren't members of themselves. For example, the set of all squares in the plane; this set is not itself a square in the plane, thus it is not a member of itself. Let us call a set "normal" if it is not a member of itself, "abnormal" if it is a member of itself; the set of squares in the plane is normal. On the other hand, the complementary set that contains everything, not a square in the plane is itself not a square in the plane, so should be one of its own members and is therefore abnormal. Now we consider the set of all normal sets, R, try to determine whether R is normal or abnormal.

If R were normal, it would be contained in the set of all normal sets, therefore be abnormal. This leads to the conclusion that R is neither abnormal: Russell's paradox. Define Naive Set Theory as the theory of predicate logic with a binary predicate ∈ and the following axiom schema of unrestricted comprehension: ∃ y ∀ x for any formula φ with only the variable x free. Substitute x ∉ x for φ. By existential instantiation and universal instantiation we have y ∈ y ⟺ y ∉ y a contradiction. Therefore, NST is inconsistent. From the principle of explosion in logic, any proposition can be proved from a contradiction; therefore the presence of contradictions like Russell's paradox in an axiomatic set theory is disastrous. Further, since set theory was seen as the basis for an axiomatic development of all other branches of mathematics, Russell's paradox threatened the foundations of mathematics; this motivated a great deal of research around the turn of the 20th century to develop a consistent set theory.

In 1908, Ernst Zermelo proposed an axiomatization of set theory that avoided the paradoxes of naive set theory by replacing arbitrary set comprehension with weaker existence axioms, such as his axiom of separation. Modifications to this axiomatic theory proposed in the 1920s by Abraham Fraenkel, Thoralf Skolem, by Zermelo himself resulted in the axiomatic set theory called ZFC; this theory became accepted once Zermelo's axiom of choice ceased to be controversial, ZFC has remained the canonical axiomatic set theory down to the present day. ZFC does not assume. Rather, it asserts that given any set any subset of X definable using first-order logic exists; the object R discussed above cannot be constructed in this fashion, is therefore not a ZFC set. In some extensions of ZFC, objects like R are called proper classes. ZFC is silent about types, although the cumulative hierarchy has a notion of layers that resemble types. Zermelo himself never accepted Skolem's formulation of ZFC using the language of first-order logic.

As José Ferreirós notes, Zermelo insisted instead that "propositional functions used for separating off subsets, as well as the replacement functions, can be'entirely arbitrary'.

Peng Loh

Yoke Peng Loh is an American biochemist and molecular biologist acting as Senior Investigator and Head at the Section on Cellular Neurobiology, Laboratory of Developmental Neurobiology, Eunice Kennedy Shriver National Institute of Child Health and Human Development, National Institutes of Health. She earned a B. S. in biochemistry at University College Dublin in 1969 and a Ph. D. from the University of Pennsylvania in 1973. She did her postdoctoral work with Harold Gainer at NIH and at the Max Planck Institute in Germany. Dr Loh is recognized for her work in regulated secretory protein sorting in endocrine cells, protein processing and trafficking, mechanisms underlying the intracellular sorting of peptide hormones and neurotransmitters to the regulated secretory pathway, key proteolytic events and enzymes involved in the processing of prohormones to biologically active peptides in the endocrine and nervous systems. Dr Loh has served as an academic advisor or editorial member for several journals: Molecular and Cellular Neurosciences.

1986 Pfizer Traveling Scientist 1989 Public Health Service "Superior Service Award". 1994 EEO Special Achievement Award for outstanding contributions to career development of Women Scientists. 1998 Asian Pacific American Organization Award for Outstanding Research. 1998 Women in Endocrinology Mentor's Award for Outstanding Research and Mentoring in promoting the careers of women scientists. 1999 NIH Director's Award. 2000 Excellence in Science Award from the Federation of American Societies of Experimental Biology: The Excellence in Science Award recognizes outstanding achievement by women in biological science. Nominations recognize a woman whose career achievements have contributed to further our understanding of a particular discipline by excellence in research." Dr Loh was awarded for Regulated Secretory Protein Sorting in Endocrine Cells: Unmasking Novel Signals and Lipid Rafts. 2001 NIH Director's Award for Mentoring. 2014 Anita B. Roberts Lecture, an honor for distinguished women scientists at the NIH.

Loh Lab: Section on Cellular Neurobiology

Achyra rantalis

Achyra rantalis, the garden webworm, is a moth of the family Crambidae described by Achille Guenée in 1854. It is found in North America, where it has been recorded from Maine to southern Quebec and Ontario, south to Florida and Mexico, it has been recorded from Iowa, Colorado and the West Indies. Its habitat consists of gardens; the wingspan is 17–23 millimetres. The forewings are brown or grayish brown; the hindwings are lighter. Adults are on wing from April to November in the south. There may be up to four generations per year in the south; the larvae feed on the leaves of various low-growing plants, including alfalfa, clover, cotton and strawberries. They have a yellowish, pale green or dark greenish body and a yellowish-brown head and reach a length of about 24 mm

Friedrich Wegener

Dr. Friedrich Wegener was a German pathologist, notable for his description of a rare disease referred to Wegener disease and now referred to as granulomatosis with polyangiitis. Although this disease was known before Wegener's description, from the 1950s onwards it was referred to as Wegener's granulomatosis. Friedrich Wegener was born on 7th April, 1907 in Varel, Germany, his father was his mother a Swedish gymnastic director. More detail about aspects of Wegener's biography during the Nazi regime first became available in 2006. Wegener joined the pre-Nazi Party in 1932, he was a member of the Sturmabteilung, a paramilitary branch of the Nazi party which participated in violent conflicts. As a high-ranking military physician, he spent some of World War II in a medical office three blocks from the Łódź Ghetto, a Jewish ghetto in Łódź, Poland, he conducted autopsies on Jewish concentration camp inmates and the facility he worked in performed experiments on prisoners. There is no direct evidence of active participation of Dr. Wegener in these human experiments, but it is he was aware of them.

The United Nations War Crimes Commission had a legal mandate against Friedrich Wegener and the Polish Institute for the Prosecution of German War Crimes confirmed that he had appeared on the central list of war criminal and security suspects. Dr. Wegener was released without a trial. In an editorial in 2006 the evidence was regarded as “thin but tangible”. In 1936, Friedrich Wegener described the disease that bears his name, Wegener disease, as systemic disorder characterized by aseptic vasculitis granulomatrous inflammation and vasculitis which affects the upper and lower respitory tracts and the kidneys. WG is a rare disorder; the American College of Chest Physicians awarded Wegener a “master clinician” prize in 1989. After his Nazi past was discovered in 2000, the ACCP rescinded the prize and campaigned to rename Wegener's granulomatosis to ANCA-associated granulomatous vasculitis. More several professional societies, including the American College of Rheumatology, the European League Against Rheumatism, the American Society of Nephrology, proposed the name'granulomatosis with polyangiitis' in a 2011 editorial.

The new name for the condition is now adopted in the scientific literature and by institutions and charities. List of medical eponyms with Nazi associations Woywodt A, Haubitz M, Haller H, Matteson EL. "Wegener's granulomatosis". Lancet. 367: 1362–6. Doi:10.1016/S0140-673668583-8. PMID 16631915. Woywodt A, Matteson EL. "Wegener's granulomatosis--probing the untold past of the man behind the eponym". Rheumatology. 45: 1303–6. Doi:10.1093/rheumatology/kel258. PMID 16887845

Faruk Kulenović

Faruk Kulenović is a Croatian-Bosnian professional basketball coach. When he coached KK Šibenik, Dražen Petrović were youngster at the club; as a player 1963-1973 HAKK Mladost as a coach 1973-1978 Medveščak 1979-1981 Borovo 1981-1982 Šibenik 1982-1985 Kvarner 1985-1987 Pula 1988 Hapoel Jerusalem 1989 KK Šibenik 1990-1993 Alba Berlin 1993-1994 Fenerbahçe 1994-1995 National team of Bosnia and Herzegovina 1995-1996 Zrinjevac 1996-1999 Slavonski Brod 1999-2000 Zrinjevac 2000-2001 Ohud Medina 2005-2006 Darüşşafaka Doğuş Youth Team 2008-2009 İstanbul Teknik Üniversitesi Youth Team

Linie 1

Linie 1 is the second-most successful German musical after Bertolt Brecht’s Threepenny Opera. The title refers to Berlin's subway line U1; the musical was first performed by the ensemble of the GRIPS-Theater on 30 April 1986. In October 2017, the troupe put on its 1,800th performance; the music was written by Birger Heymann, the text written by Volker Ludwig, the set designed by Mathias Fischer-Dieskau, the musical directed by Wolfgang Kolneder. In 1988, a film version was made, in 2008, GRIPS released a live recording on DVD; the story follows a young woman who runs away from her provincial hometown and ends up at Berlin’s notorious Zoo station, searching for a rock musician who got her pregnant on a one-night stand. She gets stuck in underground line 1 and encounters a kaleidoscope of urban characters and their fates. According to the GRIPS, “it’s a show, a drama, a musical about living and surviving in a large city and adaptation, courage and self-deceit, to laugh and cry at, to dream, to think about oneself.”

As its other plays, Linie 1 includes sociocritical elements, but it serves as an amusing portrait of Berlin's society before the fall of the Berlin Wall. In 1985, Volker Ludwig wrote the musical Line 1; the title refers to Berlin's subway line U1. The music was written by German musician and composer Birger Heymann, a longtime friend of Ludwig, the rock band No Ticket; the musical became the biggest success of the GRIPS-Theatre. The success of Linie 1 had its drawbacks. Due to the production's considerable costs, ticket sales no longer covered the theatre's expenses. However, after Volker Ludwig mentioned on a talk show that the theatre would have to close without additional support, the government increased its subsidies. Germany's main stages ignored Linie 1, but when the Stuttgart State Theatre ran the musical, other theatres followed suit. Linie 1 became known nationwide after several of its songs were performed on satirical TV show Scheibenwischer; the show's creator, German satirist and author Dieter Hildebrandt had a cameo appearance in the 1988 film version film version of the musical.

For years, Linie 1 was the most-played German production and it remains the second-most successful musical after Bertolt Brecht’s Threepenny Opera. In 1987, the musical’s author Volker Ludwig was awarded the Mülheimer Dramatikerpreis, considered Germany’s leading theatre award. To this day, the musical has been performed at over 150 German-language theatres and adapted by theatres in 15 countries, including Brazil, Denmark, Greece, India, Namibia, the Netherlands, South Korea, Spain and Yemen. In Barcelona, Hong Kong, Seoul, Vilnius and Aden, the original play was adapted to the respective cities and retained the original music. In Seoul Line 1, a young Chinese Korean woman from Yanbian comes to Seoul, traveling back and forth between the Seoul Station and the Cheongnyangni 588 red light district; the Nazi widows of the original play become widows of former military big shots. This Korean version, adapted by Kim Min-ki, became more successful than the original in Berlin. While the GRIPS put on its 1,800th performance of Linie 1 in October 2017, Seoul Line 1 was performed over 4,000 times during the 13 years the musical belonged to the Hakchon Theatre's repertoire.

Since September 8, 2018, Hakchon Theatre is staging a new version of the musical. In the Namibian version, a German girl arrives in Windhoek searching for a Namibian musician she met while he was playing in Germany, she travels all over Namibia with various typical means of transport, such as minibus taxis and a donkey cart. The Wilmersdorf widows in this version are widows of former Boers still dreaming of white supremacy in Africa. 6 Uhr 14 Bahnhof Zoo Tag ich hasse dich Warten Du sitzt mir gegenüber Komm, komm Wenn die Liebe erwacht Marias Lied / Kontroletti-Tango Der Anmacher Berlin Es ist herrlich zu leben Linie 1 Fahr mal wieder U-Bahn Wilmersdorfer Witwen In jeder Großstadt bin ich zu Haus Unbekanntes Wesen Nachruf Mut zum Träumen Only You Bitte halt mich fest In 2002, German punk rock band Beatsteaks released a cover version of Marias Lied, titled Hey Du, on their EP Wohnzimmer. The song was included on the band's 2008 live album Kanonen auf Spatzen and released as single; the accompanying video was nominated in the category "Best National Video" at the Echo Music Prize.

In 2009, Berlin rapper Sido released a single with the title Hey du!, which included the first verse of Marias Lied. Official English Summary Select scenes from theatre production on YouTube Linie 1 on IMDb