To stay up to date you can also follow on Mastodon.

🔗 Mathematics

In combinatorial mathematics, a superpermutation on n symbols is a string that contains each permutation of n symbols as a substring. While trivial superpermutations can simply be made up of every permutation concatenated together, superpermutations can also be shorter (except for the trivial case of n = 1) because overlap is allowed. For instance, in the case of n = 2, the superpermutation 1221 contains all possible permutations (12 and 21), but the shorter string 121 also contains both permutations.

It has been shown that for 1 ≤ n ≤ 5, the smallest superpermutation on n symbols has length 1! + 2! + … + n! (sequence A180632 in the OEIS). The first four smallest superpermutations have respective lengths 1, 3, 9, and 33, forming the strings 1, 121, 123121321, and 123412314231243121342132413214321. However, for n = 5, there are several smallest superpermutations having the length 153. One such superpermutation is shown below, while another of the same length can be obtained by switching all of the fours and fives in the second half of the string (after the bold 2):

12345123­41523412­53412354­12314523­14253142­35142315­42312453­12435124­31524312­54312134­52134251­34215342­13542132­45132415­32413524­13254132­14532143­52143251­432154321

For the cases of n > 5, a smallest superpermutation has not yet been proved nor a pattern to find them, but lower and upper bounds for them have been found.

🔗 United States 🔗 Law 🔗 Marketing & Advertising

Leonard v. Pepsico, Inc., 88 F. Supp. 2d 116, (S.D.N.Y. 1999), aff'd 210 F.3d 88 (2d Cir. 2000), more widely known as the Pepsi Points case, is an American contract law case regarding offer and acceptance. The case was brought in the United States District Court for the Southern District of New York in 1999; its judgment was written by Kimba Wood.

In 1996, PepsiCo began a promotional loyalty program, in which customers could earn Pepsi Points; these points could, in turn, be traded for physical items. A television commercial for the loyalty program displayed the commercial's protagonist flying a McDonnell Douglas AV-8B Harrier II vertical take off jet aircraft to school, valued at $37.4 million at the time, which could be redeemed for 7,000,000 Pepsi Points. The plaintiff, John Leonard, discovered a loophole in the promotion, allowing him to purchase Pepsi Points at 10¢ per point. Leonard promptly delivered a check for $700,008.50 to PepsiCo, attempting to purchase the jet. PepsiCo initially refuted Leonard's offer, citing the humorous nature of the offer in the advertisement. Leonard then sued PepsiCo, Inc. in an effort to enforce the offer and acceptance perceived by Leonard to be made in the advertisement. In her judgment, Wood sided with PepsiCo, noting the frivolous and improbable nature of landing a fighter jet in a school zone that was portrayed by the protagonist. PepsiCo would re-release the advertisement, valuing the jet at 700,000,000 Pepsi Points.

🔗 Paranormal

The Eltanin Antenna is an object photographed on the sea floor by the Antarctic oceanographic research ship USNS Eltanin in 1964, while photographing the sea bottom west of Cape Horn.

Due to its regular antenna-like structure and upright position on the seafloor at a depth of 3,904 metres (12,808 ft), some proponents of fringe and UFO-related theories including Bruce Cathie have suggested that it might be an extraterrestrial artifact. Other authorities have suggested that the object photographed by the Eltanin was an unusual carnivorous sponge, Chondrocladia concrescens (formerly Cladorhiza concrescens).

🔗 Typography

In typography, an asterism, ⁂, is a typographic symbol consisting of three asterisks placed in a triangle, which is used for a variety of purposes. The name originates from the astronomical term for a group of stars.

The asterism was originally used as a type of dinkus in typography, though increasingly rarely. It can also be used to mean "untitled" or author or title withheld – as seen, for example, in some editions of Album for the Young by composer Robert Schumann (№ 21, 26, and 30). In meteorology, an asterism in a station model indicates moderate snowfall.

🔗 Skepticism 🔗 History of Science 🔗 Sociology

The Sokal affair, also called the Sokal hoax, was a scholarly publishing sting perpetrated by Alan Sokal, a physics professor at New York University and University College London. In 1996, Sokal submitted an article to Social Text, an academic journal of postmodern cultural studies. The submission was an experiment to test the journal's intellectual rigor and, specifically, to investigate whether "a leading North American journal of cultural studies—whose editorial collective includes such luminaries as Fredric Jameson and Andrew Ross—[would] publish an article liberally salted with nonsense if (a) it sounded good and (b) it flattered the editors' ideological preconceptions".

The article, "Transgressing the Boundaries: Towards a Transformative Hermeneutics of Quantum Gravity", was published in the Social Text spring/summer 1996 "Science Wars" issue. It proposed that quantum gravity is a social and linguistic construct. At that time, the journal did not practice academic peer review and it did not submit the article for outside expert review by a physicist. Three weeks after its publication in May 1996, Sokal revealed in Lingua Franca that the article was a hoax.

The hoax sparked a debate about the scholarly merit of commentary on the physical sciences by those in the humanities; the influence of postmodern philosophy on social disciplines in general; academic ethics, including whether Sokal was wrong to deceive the editors and readers of Social Text; and whether Social Text had exercised appropriate intellectual rigor.

🔗 Psychology

Sad clown paradox is the contradictory association between comedy and mental disorders such as depression and anxiety. These comedic performers are characterised by feelings of deprivation and isolation in their early lives, where comedy evolves as a release for tension, removing feelings of suppressed physical rage through a verbal outlet.

A series of psychological experiments first published in 1981 by psychologist Seymour Fisher indicated certain behavioural traits exclusive to comedians and not matched in regular actors. Later work conducted by Kaufman and Kozbelt re-interpreted these results, drawing the understanding that whilst comedy serves as a coping mechanism to hide trauma, it may also motivate a comedian to use humour as a way of forming relations and gaining acceptance.

Humour has been shown to develop from a young age, fostered by parental behaviour. A parent's immature nature can lead to additional responsibilities forced onto children, which can evoke issues of self-worth and a need for acceptance. The constant search for approval may cause mental health issues such as anxiety or depression and when untreated can lead to suicide in extreme situations. Laughter can evolve as a medium for self-preservation, detaching the individual from any adversity faced allowing for perceived control over uncomfortable situations.

Sad clown paradox is characterised by a cyclothymic temperament, which encourages the creation of light-hearted humour in a professional setting, despite inner turmoil. The use of humour as a form of self-medication provides short periods of satisfaction, repeatedly needing to deal with inner turmoil. There is an ever present anxiety amongst comedians that their popularity may disappear tomorrow and hence are driven to exhaustion in their work.

🔗 Computing 🔗 Military history 🔗 Military history/Military science, technology, and theory

Fifth-generation warfare (5GW) is warfare that is conducted primarily through non-kinetic military action, such as social engineering, misinformation, cyberattacks, along with emerging technologies such as artificial intelligence and fully autonomous systems. Fifth generation warfare has been described by Daniel Abbot as a war of "information and perception". There is no widely agreed upon definition of fifth-generation warfare, and it has been rejected by some scholars, including William S. Lind, who was one of the original theorists of fourth-generation warfare.

🔗 California 🔗 California/San Francisco Bay Area 🔗 Philosophy 🔗 Psychology 🔗 Philosophy/Social and political philosophy 🔗 Sociology

The Third Wave was an experimental social movement created by California high school history teacher Ron Jones in 1967 to explain how the German population could accept the actions of the Nazi regime during the Second World War. While he taught his students about Nazi Germany during his "Contemporary World History" class, Jones found it difficult to explain how the German people could accept the actions of the Nazis, and decided to create a social movement as a demonstration of the appeal of fascism. Over the course of five days, Jones – a member of the SDS, Cubberley United Student Movement sponsor and Black Panthers supporter – conducted a series of exercises in his classroom emphasizing discipline and community, intended to model certain characteristics of the Nazi movement. As the movement grew outside his class and began to number in the hundreds, Jones began to feel that the movement had spiraled out of control. He convinced the students to attend a rally where he claimed that the classroom project was part of a nationwide movement, and that the announcement of a Third Wave presidential candidate would be televised. Upon their arrival, the students were presented with a blank channel. Jones told his students of the true nature of the movement as an experiment in fascism, and presented to them a short film discussing the actions of Nazi Germany.

🔗 History 🔗 Ancient Near East 🔗 Malta 🔗 Phoenicia

The Cippi of Melqart are a pair of Phoenician marble cippi that were unearthed in Malta under undocumented circumstances and dated to the 2nd century BC. These are votive offerings to the god Melqart, and are inscribed in two languages, Ancient Greek and Phoenician, and in the two corresponding scripts, the Greek and the Phoenician alphabet. They were discovered in the late 17th century, and the identification of their inscription in a letter dated 1694 made them the first Phoenician writing to be identified and published in modern times. Because they present essentially the same text (with some minor differences), the cippi provided the key to the modern understanding of the Phoenician language. In 1758, the French scholar Jean-Jacques Barthélémy relied on their inscription, which used 17 of the 22 letters of the Phoenician alphabet, to decipher the unknown language.

The tradition that the cippi were found in Marsaxlokk was only inferred by their dedication to Heracles, whose temple in Malta had long been identified with the remains at Tas-Silġ. The Grand Master of the Order of the Knights Hospitaller, Fra Emmanuel de Rohan-Polduc, presented one of the cippi to the Académie des Inscriptions et Belles-Lettres in 1782. This cippus is currently in the Louvre Museum in Paris, while the other rests in the National Museum of Archaeology in Valletta, Malta. The inscription is known as KAI 47.

🔗 Technology 🔗 Writing systems 🔗 Visual arts 🔗 Writing

A pencil ( ) is a writing or drawing implement with a solid pigment core in a protective casing that reduces the risk of core breakage, and keeps it from marking the user's hand.

Pencils create marks by physical abrasion, leaving a trail of solid core material that adheres to a sheet of paper or other surface. They are distinct from pens, which dispense liquid or gel ink onto the marked surface.

Most pencil cores are made of graphite powder mixed with a clay binder. Graphite pencils (traditionally known as "lead pencils") produce grey or black marks that are easily erased, but otherwise resistant to moisture, most chemicals, ultraviolet radiation and natural aging. Other types of pencil cores, such as those of charcoal, are mainly used for drawing and sketching. Coloured pencils are sometimes used by teachers or editors to correct submitted texts, but are typically regarded as art supplies, especially those with cores made from wax-based binders that tend to smear when erasers are applied to them. Grease pencils have a softer, oily core that can leave marks on smooth surfaces such as glass or porcelain.

The most common pencil casing is thin wood, usually hexagonal in section but sometimes cylindrical or triangular, permanently bonded to the core. Casings may be of other materials, such as plastic or paper. To use the pencil, the casing must be carved or peeled off to expose the working end of the core as a sharp point. Mechanical pencils have more elaborate casings which are not bonded to the core; instead, they support separate, mobile pigment cores that can be extended or retracted (usually through the casing's tip) as needed. These casings can be reloaded with new cores (usually graphite) as the previous ones are exhausted.