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🔗 Mathematics

The Basel problem is a problem in mathematical analysis with relevance to number theory, first posed by Pietro Mengoli in 1650 and solved by Leonhard Euler in 1734, and read on 5 December 1735 in The Saint Petersburg Academy of Sciences. Since the problem had withstood the attacks of the leading mathematicians of the day, Euler's solution brought him immediate fame when he was twenty-eight. Euler generalised the problem considerably, and his ideas were taken up years later by Bernhard Riemann in his seminal 1859 paper "On the Number of Primes Less Than a Given Magnitude", in which he defined his zeta function and proved its basic properties. The problem is named after Basel, hometown of Euler as well as of the Bernoulli family who unsuccessfully attacked the problem.

The Basel problem asks for the precise summation of the reciprocals of the squares of the natural numbers, i.e. the precise sum of the infinite series:

${\displaystyle \sum _{n=1}^{\infty }{\frac {1}{n^{2}}}={\frac {1}{1^{2}}}+{\frac {1}{2^{2}}}+{\frac {1}{3^{2}}}+\cdots .}$

The sum of the series is approximately equal to 1.644934. The Basel problem asks for the exact sum of this series (in closed form), as well as a proof that this sum is correct. Euler found the exact sum to be π²/6 and announced this discovery in 1735. His arguments were based on manipulations that were not justified at the time, although he was later proven correct, and it was not until 1741 that he was able to produce a truly rigorous proof.

🔗 Law Enforcement 🔗 Crime and Criminal Biography

Nihilistic violent extremism (NVE), or nihilistic extremism, is a term used by law enforcement agencies to refer to extremism and violence lacking an ideological motivation, instead motivated by a misanthropic worldview and generalized hatred for society. It is closely associated with groups such as 764 and No Lives Matter. Despite nihilistic violent extremism's characterization as being unmotivated by genuine ideology, groups or individuals falling under this umbrella may adopt the aesthetics or tactics of, or have sympathies for, other extremist ideologies like neo-Nazism, the variant of Satanism associated with the Order of Nine Angles, and accelerationism. It is also closely associated with sexual misconduct, such as solicitation, production, or possession of child pornography, and sextortion, as well as general violence.

🔗 Video games 🔗 Role-playing games 🔗 Department of Fun

One theory that explains the addictive nature of Wikipedia and its tendency to produce Wikipediholics is that Wikipedia is a massively multiplayer online role-playing game (MMORPG). The following article explains how Wikipedia shares many characteristics with MMORPGs.

Wikipedia is a sequel to the game Nupedia, an encyclopedia-themed MMORPG in a hack and slash and "article roaming" style. It was released for the World Wide Web by the Wikimedia Foundation, and was developed by the community.

🔗 Psychology 🔗 History of Science 🔗 Sociology 🔗 Education 🔗 Science

The Matthew effect of accumulated advantage, Matthew principle, or Matthew effect for short, is sometimes summarized by the adage "the rich get richer and the poor get poorer". The concept is applicable to matters of fame or status, but may also be applied literally to cumulative advantage of economic capital. In the beginning, Matthew effects were primarily focused on the inequality in the way scientists were recognized for their work. However, Norman Storer, of Columbia University, led a new wave of research. He believed he discovered that the inequality that existed in the social sciences also existed in other institutions.

The term was coined by sociologist Robert K. Merton in 1968 and takes its name from the Parable of the talents or minas in the biblical Gospel of Matthew. Merton credited his collaborator and wife, sociologist Harriet Zuckerman, as co-author of the concept of the Matthew effect.

🔗 Computing 🔗 Computing/Computer hardware 🔗 Computing/Software

In computing, a Parallel Sysplex is a cluster of IBM mainframes acting together as a single system image with z/OS. Used for disaster recovery, Parallel Sysplex combines data sharing and parallel computing to allow a cluster of up to 32 systems to share a workload for high performance and high availability.

🔗 Mathematics

Toom–Cook, sometimes known as Toom-3, named after Andrei Toom, who introduced the new algorithm with its low complexity, and Stephen Cook, who cleaned the description of it, is a multiplication algorithm for large integers.

Given two large integers, a and b, Toom–Cook splits up a and b into k smaller parts each of length l, and performs operations on the parts. As k grows, one may combine many of the multiplication sub-operations, thus reducing the overall complexity of the algorithm. The multiplication sub-operations can then be computed recursively using Toom–Cook multiplication again, and so on. Although the terms "Toom-3" and "Toom–Cook" are sometimes incorrectly used interchangeably, Toom-3 is only a single instance of the Toom–Cook algorithm, where k = 3.

Toom-3 reduces 9 multiplications to 5, and runs in Θ(n^{log(5)/log(3)}) ≈ Θ(n^1.46). In general, Toom-k runs in Θ(c(k) n^e), where e = log(2k − 1) / log(k), n^e is the time spent on sub-multiplications, and c is the time spent on additions and multiplication by small constants. The Karatsuba algorithm is a special case of Toom–Cook, where the number is split into two smaller ones. It reduces 4 multiplications to 3 and so operates at Θ(n^{log(3)/log(2)}) ≈ Θ(n^1.58). Ordinary long multiplication is equivalent to Toom-1, with complexity Θ(n²).

Although the exponent e can be set arbitrarily close to 1 by increasing k, the function c unfortunately grows very rapidly. The growth rate for mixed-level Toom–Cook schemes was still an open research problem in 2005. An implementation described by Donald Knuth achieves the time complexity Θ(n 2^{√2 log n} log n).

Due to its overhead, Toom–Cook is slower than long multiplication with small numbers, and it is therefore typically used for intermediate-size multiplications, before the asymptotically faster Schönhage–Strassen algorithm (with complexity Θ(n log n log log n)) becomes practical.

Toom first described this algorithm in 1963, and Cook published an improved (asymptotically equivalent) algorithm in his PhD thesis in 1966.

🔗 Agriculture 🔗 Indigenous peoples of North America

The Three Sisters are the three main agricultural crops of various Indigenous peoples of North America: squash, maize ("corn"), and climbing beans (typically tepary beans or common beans). In a technique known as companion planting, the maize and beans are often planted together in mounds formed by hilling soil around the base of the plants each year; squash is typically planted between the mounds. The cornstalk serves as a trellis for climbing beans, the beans fix nitrogen in their root nodules and stabilize the maize in high winds, and the wide leaves of the squash plant shade the ground, keeping the soil moist and helping prevent the establishment of weeds.

Indigenous peoples throughout North America cultivated different varieties of the Three Sisters, adapted to varying local environments. The individual crops and their use in polyculture originated in Mesoamerica; where squash was domesticated first, followed by maize and then beans, over a period of 5,000–6,500 years. European records from the sixteenth century describe highly productive Indigenous agriculture based on cultivation of the Three Sisters throughout what are now the Eastern United States and Canada, where the crops were used for both food and trade. Geographer Carl O. Sauer described the Three Sisters as "a symbiotic plant complex of North and Central America without an equal elsewhere".

🔗 Geography 🔗 Mountains

A gravity hill, also known as a magnetic hill, mystery hill, mystery spot, gravity road, or anti-gravity hill, is a place where the layout of the surrounding land produces an optical illusion, making a slight downhill slope appear to be an uphill slope. Thus, a car left out of gear will appear to be rolling uphill against gravity. There are hundreds of recognized gravity hills around the world.

The slope of gravity hills is an optical illusion, although sites are often accompanied by claims that magnetic or supernatural forces are at work. The most important factor contributing to the illusion is a completely or mostly obstructed horizon. Without a horizon, it becomes difficult to judge the slope of a surface as a reliable reference is missing. Objects which one would normally assume to be more or less perpendicular to the ground, such as trees, may actually be leaning, offsetting the visual reference.

A 2003 study looked into how the absence of a horizon can skew the perspective on gravity hills by recreating a number of antigravity places in the lab to see how volunteers would react. As a conclusion, researchers from Universities of Padova and Pavia in Italy found that without a true horizon in sight, landmarks such as trees and signs actually played these tricks on the human brain.

The illusion is similar to the Ames room, in which objects can also appear to roll against gravity.

The opposite phenomenon—an uphill road that appears flat—is known in bicycle racing as a "false flat".

🔗 United States 🔗 China 🔗 Sociology

Satellite babies (also called Satellite Children) refer to immigrants’ children who are temporarily sent back to their home country by their parents to be reared by extended family. Typically, the satellite babies are born in the host country and sent back as infants, returning to their parents in time to start schooling or when their parents have established financial stability. Research and media articles on satellite babies have predominantly focused on the topic from a Chinese-American context. Satellite babies have become more prevalent in recent decades due to globalisation, prompting researchers and social workers to raise concerns about the psychological impacts of repeated attachment disruptions and acculturation associated with satellite babies.

🔗 Media

The Covox Speech Thing is an external audio device attached to the computer to output digital sound. It was composed of a primitive 8-bit DAC using a resistor ladder and an analogue signal output, and plugged into the printer port of the PC.

The Speech Thing was introduced on December 18, 1987 by Covox, Inc of Eugene, Oregon, for about US$70 (US$79.95 as of 1989), but as its parts were much cheaper than the complete plug, and as its design was fairly simple, people soon started to build their own variants. The plug was used long into the 1990s, as sound cards were still very expensive at that time. The plug was also quite popular in the demoscene.

An inherent problem of the design is that it requires very precise resistors. If normal parts are used, the values get shuffled, especially for quiet sounds, resulting in distortion. Nevertheless, the sound quality of the Covox plug is far superior compared to the PC speaker; even today, a self-built Covox plug is still an inexpensive way to give old computers sound capabilities.