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🔗 Physics

In quantum mechanics, the Kochen–Specker (KS) theorem, also known as the Bell–Kochen–Specker theorem, is a "no-go" theorem proved by John S. Bell in 1966 and by Simon B. Kochen and Ernst Specker in 1967. It places certain constraints on the permissible types of hidden-variable theories, which try to explain the predictions of quantum mechanics in a context-independent way. The version of the theorem proved by Kochen and Specker also gave an explicit example for this constraint in terms of a finite number of state vectors.

The theorem is a complement to Bell's theorem (to be distinguished from the (Bell–)Kochen–Specker theorem of this article). While Bell's theorem established nonlocality to be a feature of any hidden variable theory that recovers the predictions of quantum mechanics, the KS theorem established contextuality to be an inevitable feature of such theories.

The theorem proves that there is a contradiction between two basic assumptions of the hidden-variable theories intended to reproduce the results of quantum mechanics: that all hidden variables corresponding to quantum-mechanical observables have definite values at any given time, and that the values of those variables are intrinsic and independent of the device used to measure them. The contradiction is caused by the fact that quantum-mechanical observables need not be commutative. It turns out to be impossible to simultaneously embed all the commuting subalgebras of the algebra of these observables in one commutative algebra, assumed to represent the classical structure of the hidden-variables theory, if the Hilbert space dimension is at least three.

The Kochen–Specker theorem excludes hidden-variable theories that assume that elements of physical reality can all be consistently represented simultaneously by the quantum mechanical Hilbert space formalism disregarding the context of a particular framework (technically a projective decomposition of the identity operator) related to the experiment or analytical viewpoint under consideration. As succinctly worded by Isham and Butterfield, (under the assumption of a universal probabilistic sample space as in non-contextual hidden variable theories) the Kochen–Specker theorem "asserts the impossibility of assigning values to all physical quantities whilst, at the same time, preserving the functional relations between them".

🔗 Military history 🔗 Military history/Military aviation 🔗 Military history/North American military history 🔗 Military history/United States military history 🔗 Military history/Cold War

The Battle of Palmdale was the attempted shoot-down of a runaway drone by United States Air Force interceptors in the skies over Southern California in mid-August 1956. The drone was launched from Point Mugu Naval Air Station and soon went out of control. Interceptor aircraft took off from Oxnard Air Force Base and caught up with the drone, but were ultimately unable to bring it down, in spite of expending all of their rockets. After it ran out of fuel, the unmanned aircraft crashed in a sparsely populated tract of desert.

During the incident over 1000 acres were scorched and a substantial amount of property was damaged or destroyed.

🔗 Books 🔗 Maps

An Atlas of Fantasy, compiled by Jeremiah Benjamin Post, was originally published in 1973 by Mirage Press and revised for a 1979 edition by Ballantine Books. The 1979 edition dropped twelve maps from the first edition and added fourteen new ones. It also included an introduction by Lester del Rey.

To remain of manageable size, the Atlas excludes advertising maps, cartograms, most disproportionate maps, and alternate history ("might have been") maps, focusing instead on imaginary lands derived from literary sources. It purposefully omits "one-to-one" maps such as Thomas Hardy's Wessex (which merely renames places in southwest England), but includes Barsetshire and Yoknapatawpha County, which are evidently considered to be sufficiently fictionalized. The emphasis is on science fiction and fantasy, though Post suggests there exist enough mystery fiction maps to someday create The Detectives' Handy Pocket Atlas. Other maps were omitted due to permission costs or reproduction quality.

The maps are reproduced from many sources, and an Index of Artists is included.

🔗 Heraldry and vexillology 🔗 Visual arts

In Western art history, Mise en abyme (French pronunciation: ​[miz ɑ̃n‿abim]; also mise en abîme) is a formal technique of placing a copy of an image within itself, often in a way that suggests an infinitely recurring sequence. In film theory and literary theory, it refers to the technique of inserting a story within a story. The term is derived from heraldry and literally means "placed into abyss". It was first appropriated for modern criticism by the French author André Gide.

A common sense of the phrase is the visual experience of standing between two mirrors, seeing as a result an infinite reproduction of one's image. Another is the Droste effect, in which a picture appears within itself, in a place where a similar picture would realistically be expected to appear. That is named after the 1904 Droste cocoa package, which depicts a woman holding a tray bearing a Droste cocoa package, which bears a smaller version of her image.

🔗 Medicine 🔗 Death 🔗 Health and fitness 🔗 Japan 🔗 Medicine/Society and Medicine 🔗 Japan/Culture 🔗 Japan/Science and technology

Karoshi (過労死, Karōshi), which can be translated literally as "overwork death" in Japanese, is occupational sudden mortality. The major medical causes of karoshi deaths are heart attack and stroke due to stress and a starvation diet. This phenomenon is also widespread in other parts of Asia.

🔗 Terrorism 🔗 Watches 🔗 Brands

The Casio F-91W is a digital watch manufactured by Japanese electronics company Casio. Introduced in 1989, it is popular for its low price and long battery life. Annual production is 3 million units per year.

🔗 Mathematics 🔗 Etymology

Zenzizenzizenzic is an obsolete form of mathematical notation representing the eighth power of a number (that is, the zenzizenzizenzic of x is x⁸), dating from a time when powers were written out in words rather than as superscript numbers. This term was suggested by Robert Recorde, a 16th-century Welsh writer of popular mathematics textbooks, in his 1557 work The Whetstone of Witte (although his spelling was zenzizenzizenzike); he wrote that it "doeth represent the square of squares squaredly".

At the time Recorde proposed this notation, there was no easy way of denoting the powers of numbers other than squares and cubes. The root word for Recorde's notation is zenzic, which is a German spelling of the medieval Italian word censo, meaning "squared". Since the square of a square of a number is its fourth power, Recorde used the word zenzizenzic (spelled by him as zenzizenzike) to express it. Some of the terms had prior use in Latin "zenzicubicus", "zensizensicus" and "zensizenzum". Similarly, as the sixth power of a number is equal to the square of its cube, Recorde used the word zenzicubike to express it; a more modern spelling, zenzicube, is found in Samuel Jeake's Logisticelogia. Finally, the word zenzizenzizenzic denotes the square of the square of a number's square, which is its eighth power: in modern notation,

${\displaystyle x^{8}=\left(\left(x^{2}\right)^{2}\right)^{2}.}$

Recorde proposed three mathematical terms by which any power (that is, index or exponent) greater than 1 could be expressed: zenzic, i.e. squared; cubic; and sursolid, i.e. raised to a prime number greater than three, the smallest of which is five. Sursolids were as follows: 5 was the first; 7, the second; 11, the third; 13, the fourth; etc.

Therefore, a number raised to the power of six would be zenzicubic, a number raised to the power of seven would be the second sursolid, hence bissursolid (not a multiple of two and three), a number raised to the twelfth power would be the "zenzizenzicubic" and a number raised to the power of ten would be the square of the (first) sursolid. The fourteenth power was the square of the second sursolid, and the twenty-second was the square of the third sursolid.

Curiously, Jeake's text appears to designate a written exponent of 0 as being equal to an "absolute number, as if it had no Mark", thus using the notation x⁰ to refer to x alone, while a written exponent of 1, in his text, denotes "the Root of any number", thus using the notation x¹ to refer to what is now known to be x^0.5.

The word, as well as the system, is obsolete except as a curiosity; the Oxford English Dictionary (OED) has only one citation for it. As well as being a mathematical oddity, it survives as a linguistic oddity: zenzizenzizenzic has more Zs than any other word in the OED.

Samuel Jeake the Younger gives zenzizenzizenzizenzike (the square of the square of the square of the square, or 16th power) in a table in A Compleat Body of Arithmetick:

🔗 Spaceflight 🔗 Meteorology 🔗 Meteorology/weather data, products and instrumentation

GOES-3, known as GOES-C before becoming operational, is an American geostationary weather and communications satellite. It was originally built for the National Oceanic and Atmospheric Administration as part of the Geostationary Operational Environmental Satellite system, and was launched in June 1978. It is positioned in geostationary orbit, from where it was initially used for weather forecasting in the United States. Since ceasing to function as a weather satellite in 1989, it has been used as a communications satellite, and has spent over thirty-eight years in operation. GOES-3 was decommissioned 29 June 2016 at the CSTARS facility in Miami, Florida.

GOES-3 was built by Ford Aerospace, and is based on the satellite bus developed for the SMS programme. At launch it had a mass of 627 kilograms (1,382 lb).