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🔗 Physics

The quantum Zeno effect (also known as the Turing paradox) is a feature of quantum-mechanical systems allowing a particle's time evolution to be slowed down by measuring it frequently enough with respect to some chosen measurement setting.

Sometimes this effect is interpreted as "a system cannot change while you are watching it". One can "freeze" the evolution of the system by measuring it frequently enough in its known initial state. The meaning of the term has since expanded, leading to a more technical definition, in which time evolution can be suppressed not only by measurement: the quantum Zeno effect is the suppression of unitary time evolution in quantum systems provided by a variety of sources: measurement, interactions with the environment, stochastic fields, among other factors. As an outgrowth of study of the quantum Zeno effect, it has become clear that applying a series of sufficiently strong and fast pulses with appropriate symmetry can also decouple a system from its decohering environment.

The name comes from Zeno's arrow paradox, which states that because an arrow in flight is not seen to move during any single instant, it cannot possibly be moving at all. The first rigorous and general derivation of the quantum Zeno effect was presented in 1974 by Degasperis, Fonda, and Ghirardi, although it had previously been described by Alan Turing. The comparison with Zeno's paradox is due to a 1977 article by George Sudarshan and Baidyanath Misra.

According to the reduction postulate, each measurement causes the wavefunction to collapse to an eigenstate of the measurement basis. In the context of this effect, an observation can simply be the absorption of a particle, without the need of an observer in any conventional sense. However, there is controversy over the interpretation of the effect, sometimes referred to as the "measurement problem" in traversing the interface between microscopic and macroscopic objects.

Another crucial problem related to the effect is strictly connected to the time–energy indeterminacy relation (part of the indeterminacy principle). If one wants to make the measurement process more and more frequent, one has to correspondingly decrease the time duration of the measurement itself. But the request that the measurement last only a very short time implies that the energy spread of the state in which reduction occurs becomes increasingly large. However, the deviations from the exponential decay law for small times is crucially related to the inverse of the energy spread, so that the region in which the deviations are appreciable shrinks when one makes the measurement process duration shorter and shorter. An explicit evaluation of these two competing requests shows that it is inappropriate, without taking into account this basic fact, to deal with the actual occurrence and emergence of Zeno's effect.

Closely related (and sometimes not distinguished from the quantum Zeno effect) is the watchdog effect, in which the time evolution of a system is affected by its continuous coupling to the environment.

🔗 Computing 🔗 Computing/Software 🔗 Microsoft 🔗 Reference works

Microsoft Encarta was a digital multimedia encyclopedia published by Microsoft Corporation from 1993 to 2009. Originally sold on CD-ROM or DVD, it was also later available on the World Wide Web via an annual subscription – although later many articles could also be viewed free online with advertisements. By 2008, the complete English version, Encarta Premium, consisted of more than 62,000 articles, numerous photos and illustrations, music clips, videos, interactive content, timelines, maps, atlases and homework tools.

Microsoft published similar encyclopedias under the Encarta trademark in various languages, including German, French, Spanish, Dutch, Italian, Portuguese and Japanese. Localized versions contained contents licensed from national sources and more or less content than the full English version. For example, the Dutch version had content from the Dutch Winkler Prins encyclopedia.

In March 2009, Microsoft announced it was discontinuing both the Encarta disc and online versions. The MSN Encarta site was closed on October 31, 2009, in all countries except Japan, where it was closed on December 31, 2009. Microsoft continued to operate the Encarta online dictionary until 2011.

🔗 Mathematics 🔗 Biology 🔗 Physics 🔗 Plants

Tendril perversion, often referred to in context as simply perversion, is a geometric phenomenon found in helical structures such as plant tendrils, in which a helical structure forms that is divided into two sections of opposite chirality, with a transition between the two in the middle. A similar phenomenon can often be observed in kinked helical cables such as telephone handset cords.

The phenomenon was known to Charles Darwin, who wrote in 1865,

A tendril ... invariably becomes twisted in one part in one direction, and in another part in the opposite direction... This curious and symmetrical structure has been noticed by several botanists, but has not been sufficiently explained.

The term "tendril perversion" was coined by Goriely and Tabor in 1998 based on the word perversion found in the 19th Century science literature. "Perversion" is a transition from one chirality to another and was known to James Clerk Maxwell, who attributed it to the topologist J. B. Listing.

Tendril perversion can be viewed as an example of spontaneous symmetry breaking, in which the strained structure of the tendril adopts a configuration of minimum energy while preserving zero overall twist.

Tendril perversion has been studied both experimentally and theoretically. Gerbode et al. have made experimental studies of the coiling of cucumber tendrils. A detailed study of a simple model of the physics of tendril perversion was made by MacMillen and Goriely in the early 2000s. Liu et al. showed in 2014 that "the transition from a helical to a hemihelical shape, as well as the number of perversions, depends on the height to width ratio of the strip's cross-section."

Generalized tendril perversions were put forward by Silva et al., to include perversions that can be intrinsically produced in elastic filaments, leading to a multiplicity of geometries and dynamical properties.

🔗 Philosophy 🔗 Philosophy/Philosophical literature 🔗 Books 🔗 Philosophy/Logic

Gödel, Escher, Bach: An Eternal Golden Braid, also known as GEB, is a 1979 book by Douglas Hofstadter. By exploring common themes in the lives and works of logician Kurt Gödel, artist M. C. Escher, and composer Johann Sebastian Bach, the book expounds concepts fundamental to mathematics, symmetry, and intelligence. Through illustration and analysis, the book discusses how, through self-reference and formal rules, systems can acquire meaning despite being made of "meaningless" elements. It also discusses what it means to communicate, how knowledge can be represented and stored, the methods and limitations of symbolic representation, and even the fundamental notion of "meaning" itself.

In response to confusion over the book's theme, Hofstadter emphasized that Gödel, Escher, Bach is not about the relationships of mathematics, art, and music—but rather about how cognition emerges from hidden neurological mechanisms. One point in the book presents an analogy about how individual neurons in the brain coordinate to create a unified sense of a coherent mind by comparing it to the social organization displayed in a colony of ants.

The tagline "a metaphorical fugue on minds and machines in the spirit of Lewis Carroll" was used by the publisher to describe the book.

🔗 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.

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🔗 Mathematics

In combinatorial mathematics, the ménage problem or problème des ménages asks for the number of different ways in which it is possible to seat a set of male-female couples at a round dining table so that men and women alternate and nobody sits next to his or her partner. This problem was formulated in 1891 by Édouard Lucas and independently, a few years earlier, by Peter Guthrie Tait in connection with knot theory. For a number of couples equal to 3, 4, 5, ... the number of seating arrangements is

12, 96, 3120, 115200, 5836320, 382072320, 31488549120, ... (sequence A059375 in the OEIS).

Mathematicians have developed formulas and recurrence equations for computing these numbers and related sequences of numbers. Along with their applications to etiquette and knot theory, these numbers also have a graph theoretic interpretation: they count the numbers of matchings and Hamiltonian cycles in certain families of graphs.

🔗 United States/U.S. Government 🔗 United States 🔗 Appalachia 🔗 National Archives 🔗 Tennessee 🔗 Energy 🔗 Alabama

The Tennessee Valley Authority (TVA) is a federally owned electric utility corporation in the United States. TVA's service area covers all of Tennessee, portions of Alabama, Mississippi, and Kentucky, and small areas of Georgia, North Carolina, and Virginia. While owned by the federal government, TVA receives no taxpayer funding and operates similarly to a private for-profit company. It is headquartered in Knoxville, Tennessee, and is the sixth-largest power supplier and largest public utility in the country.

The TVA was created by Congress in 1933 as part of President Franklin D. Roosevelt's New Deal. Its initial purpose was to provide navigation, flood control, electricity generation, fertilizer manufacturing, regional planning, and economic development to the Tennessee Valley, a region that had suffered from lack of infrastructure and even more extensive poverty during the Great Depression than other regions of the nation. TVA was envisioned both as a power supplier and a regional economic development agency that would work to help modernize the region's economy and society. It later evolved primarily into an electric utility. It was the first large regional planning agency of the U.S. federal government, and remains the largest.

Under the leadership of David E. Lilienthal, the TVA also became the global model for the United States' later efforts to help modernize agrarian societies in the developing world. The TVA historically has been documented as a success in its efforts to modernize the Tennessee Valley and helping to recruit new employment opportunities to the region. Historians have criticized its use of eminent domain and the displacement of over 125,000 Tennessee Valley residents to build the agency's infrastructure projects.

🔗 United States 🔗 Politics 🔗 Cold War 🔗 Vietnam

The madman theory is a political theory commonly associated with the foreign policy of U.S. president Richard Nixon and his administration, who tried to make the leaders of hostile communist bloc countries think Nixon was irrational and volatile so that they would avoid provoking the U.S. in fear of an unpredictable response.

The premise of madman theory is that it makes seemingly incredible threats seem credible. For instance, in an era of mutually assured destruction, threats by a rational leader to escalate a dispute may seem suicidal and thus easily dismissible by adversaries. However, a leader's suicidal threats may seem credible if the leader is believed to be irrational.

International relations scholars have been skeptical of madman theory as a strategy for success in coercive bargaining. Prominent "madmen", such as Nixon, Nikita Khrushchev, Saddam Hussein, and Muammar Gaddafi failed to win coercive disputes. One difficulty is making others believe you are genuinely a madman. Another difficulty is the inability of a madman to assure others that they will not be punished even if they yield to a particular demand. One study found that madman theory is frequently counterproductive, but that it can be effective under certain conditions. Another study found that there are both bargaining advantages and disadvantages to perceived madness.