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🔗 Physics 🔗 Energy

Thorium-based nuclear power generation is fueled primarily by the nuclear fission of the isotope uranium-233 produced from the fertile element thorium. According to proponents, a thorium fuel cycle offers several potential advantages over a uranium fuel cycle—including much greater abundance of thorium found on Earth, superior physical and nuclear fuel properties, and reduced nuclear waste production. However, development of thorium power has significant start-up costs. Proponents also cite the low weaponization potential as an advantage of thorium due to how difficult it is to weaponize the specific uranium-233/232 and plutonium-238 isotopes produced by thorium reactors, while critics say that development of breeder reactors in general (including thorium reactors, which are breeders by nature) increases proliferation concerns. As of 2020, there are no operational thorium reactors in the world.

A nuclear reactor consumes certain specific fissile isotopes to produce energy. Currently, the most common types of nuclear reactor fuel are:

• Uranium-235, purified (i.e. "enriched") by reducing the amount of uranium-238 in natural mined uranium. Most nuclear power has been generated using low-enriched uranium (LEU), whereas high-enriched uranium (HEU) is necessary for weapons.
• Plutonium-239, transmuted from uranium-238 obtained from natural mined uranium.

Some believe thorium is key to developing a new generation of cleaner, safer nuclear power. According to a 2011 opinion piece by a group of scientists at the Georgia Institute of Technology, considering its overall potential, thorium-based power "can mean a 1000+ year solution or a quality low-carbon bridge to truly sustainable energy sources solving a huge portion of mankind’s negative environmental impact."

After studying the feasibility of using thorium, nuclear scientists Ralph W. Moir and Edward Teller suggested that thorium nuclear research should be restarted after a three-decade shutdown and that a small prototype plant should be built.

🔗 Mathematics 🔗 Statistics

Benford's law, also called the Newcomb–Benford law, the law of anomalous numbers, or the first-digit law, is an observation about the frequency distribution of leading digits in many real-life sets of numerical data. The law states that in many naturally occurring collections of numbers, the leading digit is likely to be small. For example, in sets that obey the law, the number 1 appears as the leading significant digit about 30% of the time, while 9 appears as the leading significant digit less than 5% of the time. If the digits were distributed uniformly, they would each occur about 11.1% of the time. Benford's law also makes predictions about the distribution of second digits, third digits, digit combinations, and so on.

The graph to the right shows Benford's law for base 10, one of infinitely many cases of a generalized law regarding numbers expressed in arbitrary (integer) bases, which rules out the possibility that the phenomenon might be an artifact of the base 10 number system. Further generalizations were published by Hill in 1995 including analogous statements for both the nth leading digit as well as the joint distribution of the leading n digits, the latter of which leads to a corollary wherein the significant digits are shown to be a statistically dependent quantity. ).

It has been shown that this result applies to a wide variety of data sets, including electricity bills, street addresses, stock prices, house prices, population numbers, death rates, lengths of rivers, and physical and mathematical constants. Like other general principles about natural data—for example the fact that many data sets are well approximated by a normal distribution—there are illustrative examples and explanations that cover many of the cases where Benford's law applies, though there are many other cases where Benford's law applies that resist a simple explanation. It tends to be most accurate when values are distributed across multiple orders of magnitude, especially if the process generating the numbers is described by a power law (which are common in nature).

The law is named after physicist Frank Benford, who stated it in 1938 in a paper titled "The Law of Anomalous Numbers", although it had been previously stated by Simon Newcomb in 1881.

🔗 Geography

The First Law of Geography, according to Waldo Tobler, is "everything is related to everything else, but near things are more related than distant things." This first law is the foundation of the fundamental concepts of spatial dependence and spatial autocorrelation and is utilized specifically for the inverse distance weighting method for spatial interpolation and to support the regionalized variable theory for kriging. It is a modern formulation of David Hume's principle of contiguity.

Tobler first presented his seminal idea during a meeting of the International Geographical Union's Commission on Qualitative Methods held in 1969 and later published by him in 1970. Though simple in its presentation, this idea is profound. Without it, "the full range of conditions anywhere on the Earth's surface could in principle be found packed within any small area. There would be no regions of approximately homogeneous conditions to be described by giving attributes to area objects. Topographic surfaces would vary chaotically, with slopes that were everywhere infinite, and the contours of such surfaces would be infinitely dense and contorted. Spatial analysis, and indeed life itself, would be impossible."

Less well known is his second law, which complements the first: "The phenomenon external to an area of interest affects what goes on inside".

🔗 Mathematics

Sexagesimal (also known as base 60 or sexagenary) is a numeral system with sixty as its base. It originated with the ancient Sumerians in the 3rd millennium BC, was passed down to the ancient Babylonians, and is still used—in a modified form—for measuring time, angles, and geographic coordinates.

The number 60, a superior highly composite number, has twelve factors, namely 1, 2, 3, 4, 5, 6, 10, 12, 15, 20, 30, and 60, of which 2, 3, and 5 are prime numbers. With so many factors, many fractions involving sexagesimal numbers are simplified. For example, one hour can be divided evenly into sections of 30 minutes, 20 minutes, 15 minutes, 12 minutes, 10 minutes, 6 minutes, 5 minutes, 4 minutes, 3 minutes, 2 minutes, and 1 minute. 60 is the smallest number that is divisible by every number from 1 to 6; that is, it is the lowest common multiple of 1, 2, 3, 4, 5, and 6.

In this article, all sexagesimal digits are represented as decimal numbers, except where otherwise noted. For example, 10 means the number ten and 60 means the number sixty.

🔗 Mexico 🔗 Spain 🔗 Folklore 🔗 Tambayan Philippines

A folk legend holds that in October 1593 a soldier of the Spanish Empire (named Gil Pérez in a 1908 version) was mysteriously transported from Manila in the Philippines to the Plaza Mayor (now the Zócalo) in Mexico City. The soldier's claim to have come from the Philippines was disbelieved by the Mexicans until his account of the assassination of Gómez Pérez Dasmariñas was corroborated months later by the passengers of a ship which had crossed the Pacific Ocean with the news. Folklorist Thomas Allibone Janvier in 1908 described the legend as "current among all classes of the population of the City of Mexico". Twentieth-century paranormal investigators giving credence to the story have offered teleportation and alien abduction as explanations.

🔗 Biography 🔗 Mathematics 🔗 France 🔗 Women scientists 🔗 Biography/science and academia 🔗 Women's History 🔗 Mathematics/Mathematicians

Marie-Sophie Germain (French: [maʁi sɔfi ʒɛʁmɛ̃]; 1 April 1776 – 27 June 1831) was a French mathematician, physicist, and philosopher. Despite initial opposition from her parents and difficulties presented by society, she gained education from books in her father's library, including ones by Leonhard Euler, and from correspondence with famous mathematicians such as Lagrange, Legendre, and Gauss (under the pseudonym of «Monsieur LeBlanc»). One of the pioneers of elasticity theory, she won the grand prize from the Paris Academy of Sciences for her essay on the subject. Her work on Fermat's Last Theorem provided a foundation for mathematicians exploring the subject for hundreds of years after. Because of prejudice against her sex, she was unable to make a career out of mathematics, but she worked independently throughout her life. Before her death, Gauss had recommended that she be awarded an honorary degree, but that never occurred. On 27 June 1831, she died from breast cancer. At the centenary of her life, a street and a girls’ school were named after her. The Academy of Sciences established the Sophie Germain Prize in her honor.

🔗 Chess 🔗 Japan

Taikyoku shōgi (Japanese: 大局将棋) lit. "ultimate chess" is the largest known variant of shogi (Japanese chess). The game was created around the mid-16th century (presumably by priests) and is based on earlier large board shogi games. Before the rediscovery of taikyoku shogi in 1997, tai shogi was believed to be the largest playable chess variant ever. It has not been shown that taikyoku shogi was ever widely played. There are only two sets of restored taikyoku shogi pieces and one of them is held at Osaka University of Commerce. One game may be played over several long sessions and require each player to make over a thousand moves.

Because the game was found only recently after centuries of obscurity, it is difficult to say exactly what all the rules were. Several documents describing the game have been found; however, there are differences between them. Many of the pieces appear in other shogi variants but their moves may be different. The board, and likewise the pieces, were made much smaller, making archeological finds difficult to decipher. Research into this game continues for historical and cultural reasons, but also to satisfy the curious and those who wish to play what could be the most challenging chess-like game ever made. More research must be done however. This article focuses on one likely set of rules that can make the game playable in modern times but is by no means canon. These rules may change as more discoveries are made and secrets of the game unlocked.

Further, because of the terse and often incomplete wording of the historical sources for the large shogi variants, except for chu shogi and to a lesser extent dai shogi (which were at some points of time the most prestigious forms of shogi being played), the historical rules of taikyoku shogi are not clear. Different sources often differ significantly in the moves attributed to the pieces, and the degree of contradiction (summarised below with the listing of most known alternative moves) is such that it is likely impossible to reconstruct the "true historical rules" with any degree of certainty, if there ever was such a thing. It is not clear if the game was ever played much historically, as there is no record of any sets having been made.

🔗 Italy 🔗 Musical Instruments 🔗 Classical music

Intonarumori are experimental musical instruments invented and built by the Italian futurist Luigi Russolo between roughly 1910 and 1930. There were 27 varieties of intonarumori in total with different names.

🔗 London

Lloyd's Coffee House was a significant meeting place in London in the 17th and 18th centuries.

It was opened by Edward Lloyd (c. 1648–15 February 1713) on Tower Street in 1686. The establishment was a popular place for sailors, merchants and shipowners, and Lloyd catered to them by providing reliable shipping news. The shipping industry community frequented the place to discuss maritime insurance, shipbroking and foreign trade. The dealings that took place led to the establishment of the insurance market Lloyd's of London, Lloyd's Register and several related shipping and insurance businesses.

The coffee shop relocated to Lombard Street in December 1691. Lloyd had a pulpit installed in the new premises, from which maritime auction prices and shipping news were announced. Candle auctions were held in the establishment, with lots frequently involving ships and shipping. From 1696–1697 Lloyd also experimented with publishing a newspaper, Lloyd's News, reporting on shipping schedules and insurance agreements reached in the coffee house. In 1713, the year of Edward Lloyd's death, he modified his will to assign the lease of the coffee house to his head waiter, William Newton, who then married one of Lloyd's daughters, Handy. Newton died the following year and Handy subsequently married Samuel Sheppard. She died in 1720 and Sheppard died in 1727, leaving the coffee house to his sister Elizabeth and her husband, Thomas Jemson. Jemson founded the Lloyd's List newspaper in 1734, similar to the previous Lloyd's News. Merchants continued to discuss insurance matters here until 1774, when the participating members of the insurance arrangement formed a committee and moved to the Royal Exchange on Cornhill as the Society of Lloyd's.

🔗 United States 🔗 Politics 🔗 Politics/American politics 🔗 Elections and Referendums 🔗 United States/U.S. presidential elections

The 1876 United States presidential election was the 23rd quadrennial presidential election, held on Tuesday, November 7, 1876, in which Republican nominee Rutherford B. Hayes faced Democrat Samuel J. Tilden. It was one of the most contentious and controversial presidential elections in American history, and gave rise to the Compromise of 1877 by which the Democrats conceded the election to Hayes in return for an end to Reconstruction and the withdrawal of federal troops from the South. After a controversial post-election process, Hayes was declared the winner.

After President Ulysses S. Grant declined to seek a third term despite previously being expected to do so, Congressman James G. Blaine emerged as the front-runner for the Republican nomination. However, Blaine was unable to win a majority at the 1876 Republican National Convention, which settled on Governor Hayes of Ohio as a compromise candidate. The 1876 Democratic National Convention nominated Governor Tilden of New York on the second ballot.

The results of the election remain among the most disputed ever. Although it is not disputed that Tilden outpolled Hayes in the popular vote, after a first count of votes, Tilden had won 184 electoral votes to Hayes's 165, with 20 votes from four states unresolved: in Florida, Louisiana, and South Carolina, each party reported its candidate had won the state, while in Oregon, one elector was replaced after being declared illegal for being an "elected or appointed official". The question of who should have been awarded these electoral votes is the source of the continued controversy.

An informal deal was struck to resolve the dispute: the Compromise of 1877, which awarded all 20 electoral votes to Hayes; in return for the Democrats' acquiescence to Hayes' election, the Republicans agreed to withdraw federal troops from the South, ending Reconstruction. The Compromise in effect ceded power in the Southern states to the Democratic Redeemers, who proceeded to disenfranchise black voters thereafter.

The 1876 election is the second of five presidential elections in which the person who won the most popular votes did not win the election, but the only such election in which the popular vote winner received a majority (rather than a plurality) of the popular vote. To date, it remains the election that recorded the smallest electoral vote victory (185–184), and the election that yielded the highest voter turnout of the eligible voting age population in American history, at 81.8%. Despite not becoming president, Tilden was the first Democratic presidential nominee since James Buchanan in 1856 to win the popular vote and the first since Franklin Pierce in 1852 to do so in an outright majority (In fact, Tilden received a slightly higher percentage than Pierce in 1852, despite the fact that Pierce won in a landslide).