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🔗 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.

🔗 United States 🔗 Biography 🔗 Aviation 🔗 Aviation/Aviation accident 🔗 Oregon 🔗 Aviation/aerospace biography 🔗 United States/FBI 🔗 Crime and Criminal Biography

D. B. Cooper is a media epithet used to refer to an unidentified man who hijacked a Boeing 727 aircraft in United States airspace between Portland, Oregon, and Seattle, Washington, on the afternoon of November 24, 1971. He extorted $200,000 in ransom (equivalent to $1,278,000 in 2020) and parachuted to an uncertain fate over southwestern Washington. The man purchased his airline ticket using the alias Dan Cooper but, because of a news miscommunication, became known in popular lore as D. B. Cooper.

The FBI maintained an active investigation for 45 years after the hijacking. Despite a case file that grew to over 60 volumes over that period, no definitive conclusions were reached regarding Cooper's true identity or fate. The crime remains the only unsolved air piracy in commercial aviation history.

Numerous theories of widely varying plausibility have been proposed over the years by investigators, reporters, and amateur enthusiasts. $5,880 of the ransom was found along the banks of the Columbia River in 1980, which triggered renewed interest but ultimately only deepened the mystery. The great majority of the ransom remains unrecovered.

The FBI officially suspended active investigation of the case in July 2016, but the agency continues to request that any physical evidence that might emerge related to the parachutes or the ransom money be submitted for analysis.

🔗 Visual arts 🔗 Japan 🔗 Japan/Culture 🔗 Collections Care

Kintsugi (金継ぎ, "golden joinery"), also known as kintsukuroi (金繕い, "golden repair"), is the Japanese art of repairing broken pottery by mending the areas of breakage with lacquer dusted or mixed with powdered gold, silver, or platinum, a method similar to the maki-e technique. As a philosophy, it treats breakage and repair as part of the history of an object, rather than something to disguise.

🔗 United States/U.S. Government 🔗 United States 🔗 Philosophy 🔗 Politics 🔗 Philosophy/Social and political philosophy 🔗 Philosophy/Contemporary philosophy 🔗 United States Public Policy 🔗 United States/U.S. Public Policy

The Overton window is the range of policies politically acceptable to the mainstream population at a given time. It is also known as the window of discourse. The term is named after Joseph P. Overton, who stated that an idea's political viability depends mainly on whether it falls within this range, rather than on politicians' individual preferences. According to Overton, the window frames the range of policies that a politician can recommend without appearing too extreme to gain or keep public office given the climate of public opinion at that time.

🔗 Economics

The term exorbitant privilege (privilège exorbitant in French) refers to the benefits the United States has due to its own currency (the US dollar) being the international reserve currency. For example, the US would not face a balance of payments crisis, because their imports are purchased in their own currency. Exorbitant privilege as a concept cannot refer to currencies that have a regional reserve currency role, only to global reserve currencies.

Academically, the exorbitant privilege literature analyzes two empirical puzzles, the position puzzle and the income puzzle. The position puzzle refers to the difference between the (negative) U.S. net international investment position (NIIP) and the accumulated U.S. current account deficits, the former being much smaller than the latter. The income puzzle is that despite a deeply negative NIIP, the U.S. income balance is positive, i.e. despite having much more liabilities than assets, earned income is higher than interest expenses.

🔗 Typography 🔗 Industrial design

The IBM Selectric typewriter was a highly successful line of electric typewriters introduced by IBM on 31 July 1961.

Instead of the "basket" of individual typebars that swung up to strike the ribbon and page in a typical typewriter of the period, the Selectric had an "element" (frequently called a "typeball", or less formally, a "golf ball") that rotated and pivoted to the correct position before striking. The element could be easily changed so as to use different fonts in the same document typed on the same typewriter, resurrecting a capability that had been pioneered by typewriters such as the Hammond and Blickensderfer in the late 19th century. The Selectric also replaced the traditional typewriter's horizontally moving carriage with a roller (platen) that turned to advance the paper but did not move horizontally, while the typeball and ribbon mechanism did.

The Selectric mechanism was notable for using internal mechanical binary coding and two mechanical digital-to-analog converters, called whiffletree linkages, to select the character to be typed.

Selectrics and their descendants eventually captured 75 percent of the United States market for electric typewriters used in business. IBM replaced the Selectric line with the IBM Wheelwriter in 1984 and transferred its typewriter business to the newly formed Lexmark in 1991. By its 25th anniversary, in 1986, a total of more than 13 million machines were made and sold.

🔗 United States/U.S. Government 🔗 United States 🔗 Medicine 🔗 Medicine/Society and Medicine

Crimson Contagion was a simulation administered by the U.S. Department of Health and Human Services from January to August 2019 that tested the capacity of the U.S. federal government and twelve U.S. states to respond to a severe influenza pandemic originating in China. The exercise involves a scenario in which tourists returning from China spread a respiratory virus in the United States, beginning in Chicago. In less than two months the virus had infected 110 million Americans, killing more than half a million. The report issued at the conclusion of the exercise outlines the government's limited capacity to respond to a pandemic, with federal agencies lacking the funds, coordination, and resources to facilitate an effective response to the virus.

"Pierre Menard, Author of the Quixote" (original Spanish title: "Pierre Menard, autor del Quijote") is a short story by Argentine writer Jorge Luis Borges.

It originally appeared in Spanish in the Argentine journal Sur in May 1939. The Spanish-language original was first published in book form in Borges's 1941 collection El jardín de senderos que se bifurcan (The Garden of Forking Paths), which was included in his much-reprinted Ficciones (1944).

🔗 Volcanoes 🔗 Islands 🔗 Hawaii

Lanai (Hawaiian: Lānaʻi, Hawaiian: [laːˈnɐʔi, naːˈnɐʔi], lə-NY, lah-NAH-ee, also US: lah-NY, lə-NAH-ee,) is the sixth-largest of the Hawaiian Islands and the smallest publicly accessible inhabited island in the chain. It is colloquially known as the Pineapple Island because of its past as an island-wide pineapple plantation. The island's only settlement of note is the small town of Lanai City. As of 2012, the island is 98% owned by Larry Ellison, cofounder and chairman of Oracle Corporation; the remaining 2% is owned by the state of Hawaii or individual homeowners.

Lanai is a roughly apostrophe-shaped island with a width of 18 miles (29 km) in the longest direction. The land area is 140.5 square miles (364 km²), making it the 43rd largest island in the United States. It is separated from the island of Molokaʻi by the Kalohi Channel to the north, and from Maui by the Auʻau Channel to the east. The United States Census Bureau defines Lanai as Census Tract 316 of Maui County. Its total population rose to 3,367 as of the 2020 United States census, up from 3,193 as of the 2000 census and 3,131 as of the 2010 census. As visible via satellite imagery, many of the island's landmarks are accessible only by dirt roads that require a four-wheel drive vehicle due to the lack of paved roadways.

There is one school, Lanai High and Elementary School, serving the entire island from kindergarten through 12th grade. There is also one hospital, Lanai Community Hospital, with 24 beds, and a community health center providing primary care, dental, behavioral health and selected specialty services in Lanai City. There are no traffic lights on the island.

🔗 Russia 🔗 Archaeology

Onfim (Old Novgorodian: онѳиме, Onfime; also, Anthemius of Novgorod) was a boy who lived in Novgorod in the 13th century. He left his notes and homework exercises scratched in soft birch bark (beresta) which was preserved in the clay soil of Novgorod. Onfim, who was six or seven at the time, wrote in Old Novgorodian; besides letters and syllables, he drew "battle scenes and drawings of himself and his teacher".