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🔗 Computer science

The Schönhage–Strassen algorithm is an asymptotically fast multiplication algorithm for large integers. It was developed by Arnold Schönhage and Volker Strassen in 1971. The run-time bit complexity is, in Big O notation, ${\displaystyle O(n\cdot \log n\cdot \log \log n)}$ for two n-digit numbers. The algorithm uses recursive fast Fourier transforms in rings with 2ⁿ+1 elements, a specific type of number theoretic transform.

The Schönhage–Strassen algorithm was the asymptotically fastest multiplication method known from 1971 until 2007, when a new method, Fürer's algorithm, was announced with lower asymptotic complexity; however, Fürer's algorithm currently only achieves an advantage for astronomically large values and is used only in Basic Polynomial Algebra Subprograms (BPAS) (see Galactic algorithms).

In practice the Schönhage–Strassen algorithm starts to outperform older methods such as Karatsuba and Toom–Cook multiplication for numbers beyond 2²¹⁵ to 2²¹⁷ (10,000 to 40,000 decimal digits). The GNU Multi-Precision Library uses it for values of at least 1728 to 7808 64-bit words (33,000 to 150,000 decimal digits), depending on architecture. There is a Java implementation of Schönhage–Strassen which uses it above 74,000 decimal digits.

Applications of the Schönhage–Strassen algorithm include mathematical empiricism, such as the Great Internet Mersenne Prime Search and computing approximations of π, as well as practical applications such as Kronecker substitution, in which multiplication of polynomials with integer coefficients can be efficiently reduced to large integer multiplication; this is used in practice by GMP-ECM for Lenstra elliptic curve factorization.

🔗 New Zealand

Taumatawhakatangi­hangakoauauotamatea­turipukakapikimaunga­horonukupokaiwhen­uakitanatahu is a hill near Porangahau, south of Waipukurau in southern Hawke's Bay, New Zealand. The height of the hill is 305 metres (1,001 ft). The hill is notable primarily for its unusually long name, which is of Māori origin; it is often shortened to Taumata for brevity. It has gained a measure of fame as it is the longest place name found in any English-speaking country, and possibly the longest place name in the world; according to World Atlas. The name of the hill (with 85 characters) has also been listed in the Guinness World Records as the longest place name. Other versions of the name, including longer ones, are also sometimes used.

🔗 Statistics

In mathematics, Buffon's needle problem is a question first posed in the 18th century by Georges-Louis Leclerc, Comte de Buffon:

Suppose we have a floor made of parallel strips of wood, each the same width, and we drop a needle onto the floor. What is the probability that the needle will lie across a line between two strips?

Buffon's needle was the earliest problem in geometric probability to be solved; it can be solved using integral geometry. The solution for the sought probability p, in the case where the needle length l is not greater than the width t of the strips, is

${\displaystyle p={\frac {2}{\pi }}{\frac {l}{t}}.}$

This can be used to design a Monte Carlo method for approximating the number π, although that was not the original motivation for de Buffon's question.

🔗 Climate change 🔗 Environment 🔗 Meteorology 🔗 Urban studies and planning

An urban heat island (UHI) is an urban area or metropolitan area that is significantly warmer than its surrounding rural areas due to human activities. The temperature difference is usually larger at night than during the day, and is most apparent when winds are weak. UHI is most noticeable during the summer and winter. The main cause of the urban heat island effect is from the modification of land surfaces. Waste heat generated by energy usage is a secondary contributor. As a population center grows, it tends to expand its area and increase its average temperature. The term heat island is also used; the term can be used to refer to any area that is relatively hotter than the surrounding, but generally refers to human-disturbed areas.

Monthly rainfall is greater downwind of cities, partially due to the UHI. Increases in heat within urban centers increases the length of growing seasons, and decreases the occurrence of weak tornadoes. The UHI decreases air quality by increasing the production of pollutants such as ozone, and decreases water quality as warmer waters flow into area streams and put stress on their ecosystems.

Not all cities have a distinct urban heat island, and the heat island characteristics depend strongly on the background climate of the area in which the city is located. Mitigation of the urban heat island effect can be accomplished through the use of green roofs and the use of lighter-colored surfaces in urban areas, which reflect more sunlight and absorb less heat.

Concerns have been raised about possible contribution from urban heat islands to global warming. While some lines of research did not detect a significant impact, other studies have concluded that heat islands can have measurable effects on climate phenomena at the global scale.

🔗 Computing 🔗 Computer science 🔗 C/C++ 🔗 C/C++/C

In the C programming language, Duff's device is a way of manually implementing loop unrolling by interleaving two syntactic constructs of C: the do-while loop and a switch statement. Its discovery is credited to Tom Duff in November 1983, when Duff was working for Lucasfilm and used it to speed up a real-time animation program.

Loop unrolling attempts to reduce the overhead of conditional branching needed to check whether a loop is done, by executing a batch of loop bodies per iteration. To handle cases where the number of iterations is not divisible by the unrolled-loop increments, a common technique among assembly language programmers is to jump directly into the middle of the unrolled loop body to handle the remainder. Duff implemented this technique in C by using C's case label fall-through feature to jump into the unrolled body.

🔗 Death 🔗 Economics 🔗 Philosophy 🔗 Business 🔗 Philosophy/Ethics

The value of life is an economic value used to quantify the benefit of avoiding a fatality. It is also referred to as the cost of life, value of preventing a fatality (VPF), implied cost of averting a fatality (ICAF), and value of a statistical life (VSL). In social and political sciences, it is the marginal cost of death prevention in a certain class of circumstances. In many studies the value also includes the quality of life, the expected life time remaining, as well as the earning potential of a given person especially for an after-the-fact payment in a wrongful death claim lawsuit.

As such, it is a statistical term, the cost of reducing the average number of deaths by one. It is an important issue in a wide range of disciplines including economics, health care, adoption, political economy, insurance, worker safety, environmental impact assessment, globalization, and process safety.

The motivation for placing a monetary value on life is to enable policy and regulatory analysts to allocate the limited supply of resources, infrastructure, labor, and tax revenue. Estimates for the value of a life are used to compare the life-saving and risk-reduction benefits of new policies, regulations, and projects against a variety of other factors, often using a cost-benefit analysis.

Estimates for the statistical value of life are published and used in practice by various government agencies. In Western countries and other liberal democracies, estimates for the value of a statistical life typically range from US$1 million—US$10 million; for example, the United States FEMA estimated the value of a statistical life at US$7.5 million in 2020.

🔗 Judaism 🔗 Writing systems 🔗 Kabbalah

Gematria (; Hebrew: גמטריא or gimatria גימטריה, plural גמטראות or גימטריאות, gimatriot) is the practice of assigning a numerical value to a name, word or phrase by reading it as a number, or sometimes by using an alphanumerical cipher. The letters of the alphabets involved have standard numerical values, but a word can yield several values if a cipher is used.

According to Aristotle (384–322 BCE), isopsephy, based on the Milesian numbering of the Greek alphabet developed in the Greek city of Miletus, was part of the Pythagorean tradition, which originated in the 6th century BCE. The first evidence of use of Hebrew letters as numbers dates to 78 BCE; gematria is still used in Jewish culture. Similar systems have been used in other languages and cultures, derived from or inspired by either Greek isopsephy or Hebrew gematria, and include Arabic abjad numerals and English gematria.

The most common form of Hebrew gematria is used in the Talmud and Midrash, and elaborately by many post-Talmudic commentators. It involves reading words and sentences as numbers, assigning numerical instead of phonetic value to each letter of the Hebrew alphabet. When read as numbers, they can be compared and contrasted with other words or phrases – cf. the Hebrew proverb נכנס יין יצא סוד (nichnas yayin yatza sod, lit. 'wine entered, secret went out', i.e. "in vino veritas"). The gematric value of יין ('wine') is 70 (י=10; י=10; ן=50) and this is also the gematric value of סוד ('secret', ס=60; ו=6; ד=4)‎.

Although a type of gematria system ('Aru') was employed by the ancient Babylonian culture, their writing script was logographic, and the numerical assignments they made were to whole words. Aru was very different from the Milesian systems used by Greek and Hebrew cultures, which used alphabetic writing scripts. The value of words with Aru were assigned in an entirely arbitrary manner and correspondences were made through tables, and so cannot be considered a true form of gematria.

Gematria sums can involve single words, or a string of lengthy calculations. A short example of Hebrew numerology that uses gematria is the word חי (chai, lit. 'alive'), which is composed of two letters that (using the assignments in the mispar gadol table shown below) add up to 18. This has made 18 a "lucky number" among the Jewish people. Donations of money in multiples of 18 are very popular.

In early Jewish sources, the term can also refer to other forms of calculation or letter manipulation, for example atbash.

🔗 Books 🔗 Sociology

The Power Elite is a 1956 book by sociologist C. Wright Mills, in which Mills calls attention to the interwoven interests of the leaders of the military, corporate, and political elements of society and suggests that the ordinary citizen in modern times is a relatively powerless subject of manipulation by those three entities.

🔗 Philosophy

The Tinkerbell effect is an American English expression describing things that are thought to exist only because people believe in them. The effect is named after Tinker Bell, the fairy in the play Peter Pan, who is revived from near death by the belief of the audience.

Another form is called the Reverse Tinkerbell effect, a term coined by David Post in 2003. It stipulates that the more you believe in something the more likely it is to vanish. For example, as more people believe that driving is safe, more people will drive carelessly, in turn making driving less safe.

🔗 Law 🔗 Sexology and sexuality 🔗 Pornography

The Miller test, also called the three-prong obscenity test, is the United States Supreme Court's test for determining whether speech or expression can be labeled obscene, in which case it is not protected by the First Amendment to the United States Constitution and can be prohibited.