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🔗 Psychology

The surprisingly popular answer is a wisdom of the crowd technique that taps into the expert minority opinion within a crowd. For a given question, a group is asked both "What do you think the right answer is?" and "What do you think the popular answer will be?" The answer that maximizes the average difference between the "right" answer and the "popular" answer is the "surprisingly popular" answer.

🔗 Mathematics

In geometric topology, the Clifford torus is the simplest and most symmetric flat embedding of the cartesian product of two circles S¹_a and S¹_b (in the same sense that the surface of a cylinder is "flat"). It is named after William Kingdon Clifford. It resides in R⁴, as opposed to in R³. To see why R⁴ is necessary, note that if S¹_a and S¹_b each exist in their own independent embedding spaces R²_a and R²_b, the resulting product space will be R⁴ rather than R³. The historically popular view that the cartesian product of two circles is an R³ torus in contrast requires the highly asymmetric application of a rotation operator to the second circle, since that circle will only have one independent axis z available to it after the first circle consumes x and y.

Stated another way, a torus embedded in R³ is an asymmetric reduced-dimension projection of the maximally symmetric Clifford torus embedded in R⁴. The relationship is similar to that of projecting the edges of a cube onto a sheet of paper. Such a projection creates a lower-dimensional image that accurately captures the connectivity of the cube edges, but also requires the arbitrary selection and removal of one of the three fully symmetric and interchangeable axes of the cube.

If S¹_a and S¹_b each has a radius of ${\displaystyle \textstyle {\sqrt {1/2}}}$, their Clifford torus product will fit perfectly within the unit 3-sphere S³, which is a 3-dimensional submanifold of R⁴. When mathematically convenient, the Clifford torus can be viewed as residing inside the complex coordinate space C², since C² is topologically equivalent to R⁴.

The Clifford torus is an example of a square torus, because it is isometric to a square with opposite sides identified. It is further known as a Euclidean 2-torus (the "2" is its topological dimension); figures drawn on it obey Euclidean geometry as if it were flat, whereas the surface of a common "doughnut"-shaped torus is positively curved on the outer rim and negatively curved on the inner. Although having a different geometry than the standard embedding of a torus in three-dimensional Euclidean space, the square torus can also be embedded into three-dimensional space, by the Nash embedding theorem; one possible embedding modifies the standard torus by a fractal set of ripples running in two perpendicular directions along the surface.

🔗 Biography 🔗 Africa 🔗 Japan 🔗 Japan/History 🔗 Japan/Biography

Yasuke (variously rendered as 弥助 or 弥介, 彌助 or 彌介 in different sources) was a man of African origin who served as a retainer under the Japanese daimyō Oda Nobunaga. In 1579, Yasuke arrived in Japan in the service of Italian Jesuit missionary Alessandro Valignano, Visitor of Missions in the Indies, in India.

Yasuke is thought by some to have been the first African that Nobunaga had ever seen and he was one of the many Africans to have come with the Portuguese to Japan during the Nanban trade. He was also present during the Honnō-ji Incident, the forced suicide of Nobunaga at the hands of his samurai general Akechi Mitsuhide on 21 June 1582.

🔗 Novels

Lanark, subtitled A Life in Four Books, is the first novel of Scottish writer Alasdair Gray. Written over a period of almost thirty years, it combines realist and dystopian surrealist depictions of his home city of Glasgow.

Its publication in 1981 prompted Anthony Burgess to call Gray "the best Scottish novelist since Walter Scott". Lanark won the inaugural Saltire Society Book of the Year award in 1982, and was also named Scottish Arts Council Book of the Year. The book, still his best known, has since become a cult classic. In 2008, The Guardian heralded Lanark as "one of the landmarks of 20th-century fiction."

🔗 Physics 🔗 Philosophy 🔗 Time

The possibility that there might be more than one dimension of time has occasionally been discussed in physics and philosophy. Similar ideas appear in folklore and fantasy literature.

🔗 Human rights 🔗 Soviet Union 🔗 Russia 🔗 Military history 🔗 Crime 🔗 Death 🔗 Socialism 🔗 Poland 🔗 Military history/World War II 🔗 Military history/Russian, Soviet and CIS military history 🔗 Russia/history of Russia 🔗 Military history/Polish military history 🔗 Military history/European military history

The Katyn massacre (Polish: zbrodnia katyńska, "Katyń crime"; Russian: Катынская резня Katynskaya reznya, "Katyn massacre", or Russian: Катынский расстрел, "Katyn execution by shooting") was a series of mass executions of about 22,000 Polish military officers and intelligentsia carried out by the Soviet Union, specifically the NKVD ("People's Commissariat for Internal Affairs", the Soviet secret police) in April and May 1940. Though the killings also occurred in the Kalinin and Kharkiv prisons and elsewhere, the massacre is named after the Katyn Forest, where some of the mass graves were first discovered.

The massacre was initiated in NKVD chief Lavrentiy Beria's proposal of 5 March 1940 to execute all captive members of the Polish officer corps, approved by the Soviet Politburo led by Joseph Stalin. Of the total killed, about 8,000 were officers imprisoned during the 1939 Soviet invasion of Poland, another 6,000 were police officers, and the remaining 8,000 were Polish intelligentsia the Soviets deemed to be "intelligence agents, gendarmes, landowners, saboteurs, factory owners, lawyers, officials, and priests". The Polish Army officer class was representative of the multi-ethnic Polish state; the murdered included ethnic Poles, Polish Ukrainians, Belarusians, and Polish Jews including the Chief Rabbi of the Polish Army, Baruch Steinberg.

The government of Nazi Germany announced the discovery of mass graves in the Katyn Forest in April 1943. Stalin severed diplomatic relations with the London-based Polish government-in-exile when it asked for an investigation by the International Committee of the Red Cross. The USSR claimed the Nazis had killed the victims, and it continued to deny responsibility for the massacres until 1990, when it officially acknowledged and condemned the killings by the NKVD, as well as the subsequent cover-up by the Soviet government.

An investigation conducted by the office of the Prosecutors General of the Soviet Union (1990–1991) and the Russian Federation (1991–2004) confirmed Soviet responsibility for the massacres, but refused to classify this action as a war crime or as an act of mass murder. The investigation was closed on the grounds the perpetrators were dead, and since the Russian government would not classify the dead as victims of the Great Purge, formal posthumous rehabilitation was deemed inapplicable.

In November 2010, the Russian State Duma approved a declaration blaming Stalin and other Soviet officials for ordering the massacre.

🔗 Sociology 🔗 Urban studies and planning

In sociology, the third place refers to the social surroundings that are separate from the two usual social environments of home ("first place") and the workplace ("second place"). Examples of third places include churches, cafes, clubs, public libraries, gyms, bookstores, stoops and parks. In his book The Great Good Place (1989), Ray Oldenburg argues that third places are important for civil society, democracy, civic engagement, and establishing feelings of a sense of place.

Robert Putnam addressed issues related to third place, but without using the term, in Bowling Alone: America's Declining Social Capital (1995, 2000).

🔗 Yugoslavia 🔗 Economics

Despite common origins, the economy of the Socialist Federal Republic of Yugoslavia (SFRY) was significantly different from the economies of the Soviet Union and other Eastern European socialist states, especially after the Yugoslav-Soviet break-up in 1948. The occupation and liberation struggle in World War II left Yugoslavia's infrastructure devastated. Even the most developed parts of the country were largely rural and the little industry of the country was largely damaged or destroyed.

🔗 Astronomy 🔗 Astronomy/Astronomical objects

Hoag's Object is a non-typical galaxy of the type known as a ring galaxy. The galaxy is named after Arthur Hoag who discovered it in 1950 and identified it as either a planetary nebula or a peculiar galaxy with eight billion stars, spanning roughly 100,000 light years.

🔗 Novels 🔗 Novels/Science fiction

Last and First Men: A Story of the Near and Far Future is a "future history" science fiction novel written in 1930 by the British author Olaf Stapledon. A work of unprecedented scale in the genre, it describes the history of humanity from the present onwards across two billion years and eighteen distinct human species, of which our own is the first. The book employs a narrative conceit that, under subtle inspiration, the novelist has unknowingly been dictated a channelled text from the last human species.

Stapledon's conception of history is based on the Hegelian Dialectic, following a repetitive cycle with many varied civilisations rising from and descending back into savagery over millions of years, but it is also one of progress, as the later civilisations rise to far greater heights than the first. The book anticipates the science of genetic engineering, and is an early example of the fictional supermind; a consciousness composed of many telepathically linked individuals.

In 1932, Stapledon followed Last and First Men with the far less acclaimed Last Men in London. Another Stapledon novel, Star Maker (1937), could also be considered a sequel to Last and First Men (mentioning briefly man's evolution on Neptune), but is even more ambitious in scope, being a history of the entire universe.

It is the 11th title in the SF Masterworks series.