Hint: You are looking at the most popular articles. If you are interested in popular topics instead, click here.

🔗 Mathematics

A tautochrone or isochrone curve (from Greek prefixes tauto- meaning same or iso- equal, and chrono time) is the curve for which the time taken by an object sliding without friction in uniform gravity to its lowest point is independent of its starting point on the curve. The curve is a cycloid, and the time is equal to π times the square root of the radius (of the circle which generates the cycloid) over the acceleration of gravity. The tautochrone curve is related to the brachistochrone curve, which is also a cycloid.

🔗 Computer science

TLA⁺ is a formal specification language developed by Leslie Lamport. It is used to design, model, document, and verify programs, especially concurrent systems and distributed systems. TLA⁺ has been described as exhaustively-testable pseudocode, and its use likened to drawing blueprints for software systems; TLA is an acronym for Temporal Logic of Actions.

For design and documentation, TLA⁺ fulfills the same purpose as informal technical specifications. However, TLA⁺ specifications are written in a formal language of logic and mathematics, and the precision of specifications written in this language is intended to uncover design flaws before system implementation is underway.

Since TLA⁺ specifications are written in a formal language, they are amenable to finite model checking. The model checker finds all possible system behaviours up to some number of execution steps, and examines them for violations of desired invariance properties such as safety and liveness. TLA⁺ specifications use basic set theory to define safety (bad things won't happen) and temporal logic to define liveness (good things eventually happen).

TLA⁺ is also used to write machine-checked proofs of correctness both for algorithms and mathematical theorems. The proofs are written in a declarative, hierarchical style independent of any single theorem prover backend. Both formal and informal structured mathematical proofs can be written in TLA⁺; the language is similar to LaTeX, and tools exist to translate TLA⁺ specifications to LaTeX documents.

TLA⁺ was introduced in 1999, following several decades of research into a verification method for concurrent systems. A toolchain has since developed, including an IDE and distributed model checker. The pseudocode-like language PlusCal was created in 2009; it transpiles to TLA⁺ and is useful for specifying sequential algorithms. TLA⁺² was announced in 2014, expanding language support for proof constructs. The current TLA⁺ reference is The TLA⁺ Hyperbook by Leslie Lamport.

🔗 Books 🔗 Socialism 🔗 Anarchism

Bullshit Jobs: A Theory is a 2018 book by anthropologist David Graeber that argues the existence and societal harm of meaningless jobs. He contends that over half of societal work is pointless, which becomes psychologically destructive when paired with a work ethic that associates work with self-worth. Graeber describes five types of meaningless jobs, in which workers pretend their role is not as pointless or harmful as they know it to be: flunkies, goons, duct tapers, box tickers, and taskmasters. He argues that the association of labor with virtuous suffering is recent in human history, and proposes universal basic income as a potential solution.

The book is an extension of a popular essay Graeber published in 2013, which was later translated into 12 languages and whose underlying premise became the subject of a YouGov poll. Graeber subsequently solicited hundreds of testimonials of meaningless jobs and revised his case into a book that was published by Simon & Schuster in May 2018.

🔗 Mathematics

In mathematics, 0.999... (also written as 0.9, among other ways) denotes the repeating decimal consisting of infinitely many 9s after the decimal point (and one 0 before it). This repeating decimal represents the smallest number no less than every decimal number in the sequence (0.9, 0.99, 0.999, ...). This number is equal to 1. In other words, "0.999..." and "1" represent the same number. There are many ways of showing this equality, from intuitive arguments to mathematically rigorous proofs. The technique used depends on the target audience, background assumptions, historical context, and preferred development of the real numbers, the system within which 0.999... is commonly defined. (In other systems, 0.999... can have the same meaning, a different definition, or be undefined.)

More generally, every nonzero terminating decimal has two equal representations (for example, 8.32 and 8.31999...), which is a property of all base representations. The utilitarian preference for the terminating decimal representation contributes to the misconception that it is the only representation. For this and other reasons—such as rigorous proofs relying on non-elementary techniques, properties, or disciplines—some people can find the equality sufficiently counterintuitive that they question or reject it. This has been the subject of several studies in mathematics education.

🔗 China 🔗 Maps

Due to national security concerns, the use of geographic information in the People's Republic of China is restricted to entities that obtain a special authorization from the administrative department for surveying and mapping under the State Council. Consequences of the restriction include fines for unauthorized surveys, lack of geotagging information on many cameras when the GPS chip detects a location within China, incorrect alignment of street maps with satellite maps in various applications, and seeming unlawfulness of crowdsourced mapping efforts such as OpenStreetMap.

🔗 Electronics 🔗 Guild of Copy Editors

The capacitor plague was a problem related to a higher-than-expected failure rate of non-solid aluminum electrolytic capacitors, between 1999 and 2007, especially those from some Taiwanese manufacturers, due to faulty electrolyte composition that caused corrosion accompanied by gas generation, often rupturing the case of the capacitor from the build-up of pressure.

High failure rates occurred in many well-known brands of electronics, and were particularly evident in motherboards, video cards, and power supplies of personal computers.

The Berlin key (also known as, German, Schließzwangschlüssel, or, in English, forced-locking key) is a key for a type of door lock. It was designed to force people to close and lock their doors, usually a main entrance door or gate leading into a common yard or tenement block. The key was a solution to the problem of access via communal doors of such blocks (Mietskaserne) as early as the 19th century.

🔗 Computing 🔗 Computing/Software 🔗 Computing/Computer science

Wirth's law is an adage on computer performance which states that software is getting slower more rapidly than hardware is becoming faster.

The adage is named after Niklaus Wirth, who discussed it in his 1995 article "A Plea for Lean Software".

🔗 Philosophy 🔗 Philosophy/Logic

The nirvana fallacy is the informal fallacy of comparing actual things with unrealistic, idealized alternatives. It can also refer to the tendency to assume there is a perfect solution to a particular problem. A closely related concept is the "perfect solution fallacy."

By creating a false dichotomy that presents one option which is obviously advantageous—while at the same time being completely implausible—a person using the nirvana fallacy can attack any opposing idea because it is imperfect. Under this fallacy, the choice is not between real world solutions; it is, rather, a choice between one realistic achievable possibility and another unrealistic solution that could in some way be "better".

🔗 Russia 🔗 Russia/demographics and ethnography of Russia 🔗 Ukraine 🔗 Visual arts 🔗 Russia/history of Russia 🔗 Russia/visual arts in Russia

Reply of the Zaporozhian Cossacks to Sultan Mehmed IV of the Ottoman Empire, also known as Cossacks of Saporog Are Drafting a Manifesto (Russian: Запорожцы пишут письмо турецкому султану), is a painting by Russian artist Ilya Repin. The 2.03 m (6 foot 7 inch) by 3.58 m (11 foot 9 inch) canvas was started in 1880 and finished in 1891. Repin recorded the years of work along the lower edge of the canvas. Alexander III bought the painting for 35,000 rubles, at the time the greatest sum ever paid for a Russian painting. Since then, the canvas has been exhibited in the State Russian Museum in Saint Petersburg.