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🔗 Mathematics 🔗 Statistics

Benford's law, also called the Newcomb–Benford law, the law of anomalous numbers, or the first-digit law, is an observation about the frequency distribution of leading digits in many real-life sets of numerical data. The law states that in many naturally occurring collections of numbers, the leading significant digit is likely to be small. For example, in sets that obey the law, the number 1 appears as the leading significant digit about 30% of the time, while 9 appears as the leading significant digit less than 5% of the time. If the digits were distributed uniformly, they would each occur about 11.1% of the time. Benford's law also makes predictions about the distribution of second digits, third digits, digit combinations, and so on.

The graph to the right shows Benford's law for base 10. There is a generalization of the law to numbers expressed in other bases (for example, base 16), and also a generalization from leading 1 digit to leading n digits.

It has been shown that this result applies to a wide variety of data sets, including electricity bills, street addresses, stock prices, house prices, population numbers, death rates, lengths of rivers, physical and mathematical constants. Like other general principles about natural data—for example the fact that many data sets are well approximated by a normal distribution—there are illustrative examples and explanations that cover many of the cases where Benford's law applies, though there are many other cases where Benford's law applies that resist a simple explanation. It tends to be most accurate when values are distributed across multiple orders of magnitude, especially if the process generating the numbers is described by a power law (which are common in nature).

It is named after physicist Frank Benford, who stated it in 1938 in a paper titled "The Law of Anomalous Numbers", although it had been previously stated by Simon Newcomb in 1881.

🔗 Mathematics

In number theory, specifically the study of Diophantine approximation, the lonely runner conjecture is a conjecture about the long-term behavior of runners on a circular track. It states that ${\displaystyle n}$ runners on a track of unit length, with constant speeds all distinct from one another, will each be lonely at some time—at least ${\displaystyle 1/n}$ units away from all others.

The conjecture was first posed in 1967 by German mathematician Jörg M. Wills, in purely number-theoretic terms, and independently in 1974 by T. W. Cusick; its illustrative and now-popular formulation dates to 1998. The conjecture is known to be true for 7 runners or less, but the general case remains unsolved. Implications of the conjecture include solutions to view-obstruction problems and bounds on properties, related to chromatic numbers, of certain graphs.

🔗 Physiology 🔗 Molecular Biology 🔗 Physiology/cell 🔗 Molecular Biology/Molecular and Cell Biology

Peto's paradox is an observation that at the species level, the incidence of cancer does not appear to correlate with the number of cells in an organism. For example, the incidence of cancer in humans is much higher than the incidence of cancer in whales, despite whales having more cells than humans. If the probability of carcinogenesis were constant across cells, one would expect whales to have a higher incidence of cancer than humans. Peto's paradox is named after English statistician and epidemiologist Richard Peto, who first observed the connection.

🔗 Transport 🔗 Cycling

The Idaho stop is the common name for laws that allow cyclists to treat a stop sign as a yield sign, and a red light as a stop sign. It first became law in Idaho in 1982, but was not adopted elsewhere until Delaware adopted a limited stop-as-yield law, the "Delaware Yield", in 2017. Arkansas was the second state to legalize both stop-as-yield and red light-as-stop in April 2019. Studies in Delaware and Idaho have shown significant decreases in crashes at stop-controlled intersections.

🔗 Computing 🔗 Military history 🔗 Military history/Military science, technology, and theory 🔗 Cryptography 🔗 Cryptography/Computer science 🔗 Poland 🔗 Computing/Early computers

The bomba, or bomba kryptologiczna (Polish for "bomb" or "cryptologic bomb"), was a special-purpose machine designed around October 1938 by Polish Cipher Bureau cryptologist Marian Rejewski to break German Enigma-machine ciphers.

🔗 United Kingdom 🔗 Classical music 🔗 Classical music/Compositions

Edward Elgar composed his Variations on an Original Theme, Op. 36, popularly known as the Enigma Variations, between October 1898 and February 1899. It is an orchestral work comprising fourteen variations on an original theme.

Elgar dedicated the work "to my friends pictured within", each variation being a musical sketch of one of his circle of close acquaintances (see musical cryptogram). Those portrayed include Elgar's wife Alice, his friend and publisher Augustus J. Jaeger and Elgar himself. In a programme note for a performance in 1911 Elgar wrote:

This work, commenced in a spirit of humour & continued in deep seriousness, contains sketches of the composer's friends. It may be understood that these personages comment or reflect on the original theme & each one attempts a solution of the Enigma, for so the theme is called. The sketches are not 'portraits' but each variation contains a distinct idea founded on some particular personality or perhaps on some incident known only to two people. This is the basis of the composition, but the work may be listened to as a 'piece of music' apart from any extraneous consideration.

In naming his theme "Enigma", Elgar posed a challenge which has generated much speculation but has never been conclusively answered. The Enigma is widely believed to involve a hidden melody.

After its 1899 London premiere the Variations achieved immediate popularity and established Elgar's international reputation.

🔗 Lists 🔗 Comedy 🔗 Measurement

Many people have made use of, or invented, units of measurement intended primarily for their humor value. This is a list of such units invented by sources that are notable for reasons other than having made the unit itself, and that are widely known in the anglophone world for their humor value.

🔗 Soviet Union 🔗 Russia 🔗 Russia/technology and engineering in Russia 🔗 Spaceflight 🔗 Dogs 🔗 Russia/science and education in Russia 🔗 Russia/history of Russia

Laika (Russian: Лайка; c. 1954 – 3 November 1957) was a Soviet space dog who was one of the first animals in space and the first to orbit the Earth. A stray mongrel from the streets of Moscow, she flew aboard the Sputnik 2 spacecraft, launched into low orbit on 3 November 1957. As the technology to de-orbit had not yet been developed, Laika's survival was never expected. She died of overheating hours into the flight, on the craft's fourth orbit.

Little was known about the impact of spaceflight on living creatures at the time of Laika's mission, and animal flights were viewed by engineers as a necessary precursor to human missions. The experiment, which monitored Laika's vital signs, aimed to prove that a living organism could survive being launched into orbit and continue to function under conditions of weakened gravity and increased radiation, providing scientists with some of the first data on the biological effects of spaceflight.

Laika died within hours from overheating, possibly caused by a failure of the central R‑7 sustainer to separate from the payload. The true cause and time of her death were not made public until 2002; instead, it was widely reported that she died when her oxygen ran out on day six or, as the Soviet government initially claimed, she was euthanised prior to oxygen depletion. In 2008, a small monument to Laika depicting her standing atop a rocket was unveiled near the military research facility in Moscow that prepared her flight. She also appears on the Monument to the Conquerors of Space in Moscow.

🔗 Internet culture 🔗 Medicine 🔗 Psychology 🔗 Electronic music 🔗 Neuroscience 🔗 Medicine/Neurology 🔗 Medicine/Society and Medicine 🔗 Albums

Everywhere at the End of Time is the eleventh recording by the Caretaker, an alias of English electronic musician Leyland Kirby. Released between 2016 and 2019, its six studio albums use degrading loops of sampled ballroom music to portray the progression of Alzheimer's disease. Inspired by the success of An Empty Bliss Beyond This World (2011), Kirby produced Everywhere as his final major work under the alias. The albums were produced in Krakow and released over six-month periods to "give a sense of time passing". The album covers are abstract paintings by his friend Ivan Seal. The series drew comparisons to the works of composer William Basinski and electronic musician Burial; later stages were influenced by avant-gardist composer John Cage.

The series comprises six hours of music, portraying a range of emotions and characterised by noise throughout. Although the first three stages are similar to An Empty Bliss, the last three stages depart from Kirby's earlier ambient works. The albums reflect the patient's disorder and death, their feelings, and the phenomenon of terminal lucidity. To promote the series, Kirby partnered with anonymous visual artist Weirdcore to make music videos. At first, concerned about whether the series would seem pretentious, Kirby thought of not creating Everywhere at all; he spent more time producing it than any of his other releases. The album covers received attention from a French art exhibition named after the Caretaker's Everywhere, an Empty Bliss (2019), a compilation of archived songs.

As each stage was released, the series received increasingly positive reviews from critics; its length and dementia-driven concept led many reviewers to feel emotional about the complete edition. Considered to be Kirby's magnum opus, Everywhere was one of the most praised music releases of the 2010s. Caregivers of people with dementia also praised the albums for increasing empathy for patients among younger listeners, although some medics felt the series was too linear. It became an Internet phenomenon in the early 2020s, emerging in TikTok videos as a listening challenge, being transformed into a mod for the video game Friday Night Funkin' (2020), and appearing in internet memes.

🔗 Economics

A Minsky moment is a sudden, major collapse of asset values which marks the end of the growth phase of a cycle in credit markets or business activity.