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🔗 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:

🔗 Systems 🔗 Systems/Control theory

A proportional–integral–derivative (PID) controller, or three-term controller, is a feedback-based control loop mechanism commonly used to manage machines and processes that require continuous control and automatic adjustment. It is typically used in industrial control systems and various other applications where constant control through modulation is necessary without human intervention. The PID controller automatically compares the desired target value (setpoint or SP) with the actual value of the system (process variable or PV). The difference between these two values is called the error value, denoted as ${\displaystyle e(t)}$.

It then applies corrective actions automatically to bring the PV to the same value as the SP using three methods: The proportional (P) component responds to the current error value by producing an output that is directly proportional to the magnitude of the error. This provides immediate correction based on how far the system is from the desired setpoint. The integral (I) component, in turn, considers the cumulative sum of past errors to address any residual steady-state errors that persist over time, eliminating lingering discrepancies. Lastly, the derivative (D) component predicts future error by assessing the rate of change of the error, which helps to mitigate overshoot and enhance system stability, particularly when the system undergoes rapid changes. The PID output signal can directly control actuators through voltage, current, or other modulation methods, depending on the application. The PID controller reduces the likelihood of human error and improves automation.

A common example is a vehicle’s cruise control system. For instance, when a vehicle encounters a hill, its speed will decrease if the engine power output is kept constant. The PID controller adjusts the engine's power output to restore the vehicle to its desired speed, doing so efficiently with minimal delay and overshoot.

The theoretical foundation of PID controllers dates back to the early 1920s with the development of automatic steering systems for ships. This concept was later adopted for automatic process control in manufacturing, first appearing in pneumatic actuators and evolving into electronic controllers. PID controllers are widely used in numerous applications requiring accurate, stable, and optimized automatic control, such as temperature regulation, motor speed control, and industrial process management.

🔗 United States 🔗 International relations 🔗 Military history 🔗 Military history/North American military history 🔗 Military history/United States military history 🔗 United States/Military history - U.S. military history 🔗 Iran 🔗 Israel 🔗 Western Asia 🔗 Military history/Middle Eastern military history 🔗 Military history/Post-Cold War

Numerous reasons have been given by different people for the 2026 Iran war, which began when the United States and Israel launched surprise airstrikes on Iran on 28 February 2026. The reasons are described as diverse, changing, and at times contradictory.

US and Israeli officials have framed it as a preemptive war of self-defense. They argue that diplomacy had failed to contain the unacceptable and potentially existential threats of Iran's nuclear program and ballistic missiles. They also argued the strikes were justified as a response to Iran's regional activities (support for proxy groups, attacks on shipping, etc.) and its violent suppression of domestic protests in January 2026. Critics have described it as a war of choice. Some analysts describe the war as a classic "security dilemma", where both sides saw the other's military buildup as threatening, making conflict increasingly likely even if neither side necessarily wanted full-scale war. Regional actors, like Saudi Arabia and the United Arab Emirates, share many of the US and Israel's war aims though differing on whether to pursue war or diplomacy.

🔗 Women's History 🔗 Gender Studies 🔗 Albania 🔗 LGBTQ+ studies

A sworn virgin is a traditional gender variant or third gender social role in certain Balkan cultures, consisting of people who are assigned female at birth but take a vow of chastity and live the rest of their lives socially recognized as men. The practice is most common in patriarchal northern Albania, Kosovo and Montenegro, where burrnesha are recognized under the tribal Kanun law, but also exists, or has existed, to a lesser extent in other parts of the western Balkans, including Bosnia, Dalmatia (Croatia), Serbia and North Macedonia.

In times when women had a prescribed role, burrnesha gave up their preexisting sexual, reproductive and social identities to acquire the same freedoms as men. They could dress as men, be head of the household, move freely in social situations, and take work traditionally open only to men. National Geographic's Taboo estimated in 2002 that there were fewer than 102 Albanian sworn virgins left. As of 2022, while there were no exact figures, twelve burrnesha were estimated to remain in Northern Albania and Kosovo.

🔗 Folklore 🔗 Saudi Arabia

Abu Fanous (Arabic: أبو فانوس) is a mysterious light phenomenon observed by travellers in the Arabian desert, mainly the Eastern Province, Riyadh, Najd, Rub' al-Khali and the Gulf. It appears at dawn or during the night as an orb or headlight that moves unpredictably and lures people into the desert, then vanishes without a trace.

🔗 Sports

Naismith's rule helps with the planning of a walking or hiking expedition by calculating how long it will take to travel the intended route, including any extra time taken when walking uphill. This rule of thumb was devised by William W. Naismith, a Scottish mountaineer, in 1892. A modern version can be formulated as follows:

Allow one hour for every 3 miles (5 km) forward, plus an additional hour for every 2,000 feet (600 m) of ascent.

🔗 United States 🔗 Mathematics 🔗 Law 🔗 History of Science 🔗 United States/Indiana

The Indiana Pi Bill is the popular name for bill #246 of the 1897 sitting of the Indiana General Assembly, one of the most notorious attempts to establish mathematical truth by legislative fiat. Despite its name, the main result claimed by the bill is a method to square the circle, rather than to establish a certain value for the mathematical constant π, the ratio of the circumference of a circle to its diameter. The bill, written by the crank Edward J. Goodwin, does imply various incorrect values of π, such as 3.2. The bill never became law, due to the intervention of Professor C. A. Waldo of Purdue University, who happened to be present in the legislature on the day it went up for a vote.

The impossibility of squaring the circle using only compass and straightedge constructions, suspected since ancient times, was rigorously proven in 1882 by Ferdinand von Lindemann. Better approximations of π than those implied by the bill have been known since ancient times.

🔗 United States 🔗 Novels 🔗 Novels/Science fiction 🔗 Science Fiction 🔗 Novels/Short story

"I Have No Mouth, and I Must Scream" is a post-apocalyptic science fiction short story by American writer Harlan Ellison. It was first published in the March 1967 issue of IF: Worlds of Science Fiction.

It won a Hugo Award in 1968. The name was also used for a short story collection of Ellison's work, featuring this story. It was reprinted by the Library of America, collected in volume two (Terror and the Uncanny, from the 1940s to Now) of American Fantastic Tales.

🔗 Human rights 🔗 Canada 🔗 LGBT studies 🔗 Law Enforcement 🔗 Discrimination 🔗 LGBTQ+ studies

"Fruit machine" is a term for a device developed in Canada by Frank Robert Wake that was supposed to be able to identify gay men (derogatorily referred to as "fruits"). The subjects were made to view pornography; the device then measured the diameter of the pupils of the eyes (pupillary response test), perspiration, and pulse for a supposed erotic response.

The "fruit machine" was employed in Canada in the 1950s and 1960s during a campaign to eliminate all gay men from the civil service, the Royal Canadian Mounted Police (RCMP), and the military. A substantial number of workers did lose their jobs. Although funding for the "fruit machine" project was cut off in the late 1960s, the investigations continued, and the RCMP collected files on over 9,000 "suspected" gay people.

The chair employed resembled that used by dentists. It had a pulley with a camera going towards the pupils, with a black box located in front of it that displayed pictures. The pictures ranged from the mundane to sexually explicit photos of men and women. It had previously been determined that the pupils would dilate in relation to the amount of interest in the picture per the technique termed 'the pupillary response test'.

People were first led to believe that the machine's purpose was to rate stress. After knowledge of its real purpose became widespread, few people volunteered for it.