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🔗 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.

🔗 Graphic design

A visiting card, also known as a calling card, is a small card used for social purposes. Before the 18th century, visitors making social calls left handwritten notes at the home of friends who were not at home. By the 1760s, the upper classes in France and Italy were leaving printed visiting cards decorated with images on one side and a blank space for hand-writing a note on the other. The style quickly spread across Europe and to the United States. As printing technology improved, elaborate color designs became increasingly popular. However, by the late 1800s, simpler styles became more common.

By the 19th century, men and women needed personalized calling or visiting cards to maintain their social status or to move up in society. These small cards, about the size of a modern-day business card, usually featured the name of the owner, and sometimes an address. Calling cards were left at homes, sent to individuals, or exchanged in person for various social purposes. Knowing and following calling card “rules” signaled one’s status and intentions.

🔗 Psychology 🔗 History of Science 🔗 Occult

Physiognomy (from the Greek φύσις, 'physis', meaning "nature", and 'gnomon', meaning "judge" or "interpreter") is the practice of assessing a person's character or personality from their outer appearance—especially the face. The term can also refer to the general appearance of a person, object, or terrain without reference to its implied characteristics—as in the physiognomy of an individual plant (see plant life-form) or of a plant community (see vegetation).

Physiognomy as a practice meets the contemporary definition of pseudoscience and it is so regarded among academic circles because of its unsupported claims; popular belief in the practice of physiognomy is nonetheless still widespread and modern advances in artificial intelligence have sparked renewed interest in the field of study. The practice was well-accepted by ancient Greek philosophers, but fell into disrepute in the Middle Ages while practised by vagabonds and mountebanks. It revived and was popularised by Johann Kaspar Lavater, before falling from favor in the late 19th century. Physiognomy in the 19th century is particularly noted as a basis for scientific racism. Physiognomy as it is understood today is a subject of renewed scientific interest, especially as it relates to machine learning and facial recognition technologyThe main interest for scientists today are the risks, including privacy concerns, of physiognomy in the context of facial recognition algorithms.

Physiognomy is sometimes referred to as 'anthroposcopy', a term originating in the 19th century.

🔗 Computing 🔗 Classical Greece and Rome 🔗 Greece 🔗 Astronomy 🔗 History of Science 🔗 Alternative Views 🔗 Time

The Antikythera mechanism (, ) is an ancient hand powered Greek analogue computer which has also been described as the first example of such device used to predict astronomical positions and eclipses for calendar and astrological purposes decades in advance. It could also be used to track the four-year cycle of athletic games which was similar to an Olympiad, the cycle of the ancient Olympic Games.

This artefact was retrieved from the sea in 1901, and identified on 17 May 1902 as containing a gear by archaeologist Valerios Stais, among wreckage retrieved from a shipwreck off the coast of the Greek island Antikythera. The instrument is believed to have been designed and constructed by Greek scientists and has been variously dated to about 87 BC, or between 150 and 100 BC, or to 205 BC, or to within a generation before the shipwreck, which has been dated to approximately 70–60 BC.

The device, housed in the remains of a 34 cm × 18 cm × 9 cm (13.4 in × 7.1 in × 3.5 in) wooden box, was found as one lump, later separated into three main fragments which are now divided into 82 separate fragments after conservation efforts. Four of these fragments contain gears, while inscriptions are found on many others. The largest gear is approximately 14 centimetres (5.5 in) in diameter and originally had 223 teeth.

It is a complex clockwork mechanism composed of at least 30 meshing bronze gears. A team led by Mike Edmunds and Tony Freeth at Cardiff University used modern computer x-ray tomography and high resolution surface scanning to image inside fragments of the crust-encased mechanism and read the faintest inscriptions that once covered the outer casing of the machine.

Detailed imaging of the mechanism suggests that it had 37 gear wheels enabling it to follow the movements of the Moon and the Sun through the zodiac, to predict eclipses and even to model the irregular orbit of the Moon, where the Moon's velocity is higher in its perigee than in its apogee. This motion was studied in the 2nd century BC by astronomer Hipparchus of Rhodes, and it is speculated that he may have been consulted in the machine's construction.

The knowledge of this technology was lost at some point in antiquity. Similar technological works later appeared in the medieval Byzantine and Islamic worlds, but works with similar complexity did not appear again until the development of mechanical astronomical clocks in Europe in the fourteenth century. All known fragments of the Antikythera mechanism are now kept at the National Archaeological Museum in Athens, along with a number of artistic reconstructions and replicas of the mechanism to demonstrate how it may have looked and worked.

🔗 U.S. Congress

The candy desk has been a tradition of the United States Senate since 1968, whereby a senator who sits at a particular desk near a busy entrance keeps a drawer full of candy for members of the body. The current occupant of the candy desk is Pennsylvania Senator Pat Toomey.

In 1965, California's George Murphy joined the Senate, and kept candy in his desk to offer his colleagues, and for himself, though eating is not allowed on the Senate floor. When he left the Senate after a six-year term, other Republican senators maintained the custom. The nascent tradition did not become publicly known until the mid-1980s, when Washington Senator Slade Gorton disclosed it in announcing that he would be sitting at the candy desk.

Senators who have maintained the candy desk tradition include John McCain, Harrison Schmitt, and Rick Santorum, who stocked it with confectionery from his home state of Pennsylvania, including from the Hershey Chocolate Company. After Santorum left the Senate in 2007, the candy desk was maintained by a number of senators for a short time each, before Pennsylvania Senator Toomey began his stay in 2015.

🔗 Russia 🔗 Russia/mass media in Russia 🔗 Politics 🔗 Media 🔗 Russia/politics and law of Russia

The firehose of falsehood, or firehosing, is a propaganda technique in which a large number of messages are broadcast rapidly, repetitively, and continuously over multiple channels (such as news and social media) without regard for truth or consistency. Since 2014, when it was successfully used by Russia during its annexation of Crimea, this model has been adopted by other governments and political movements around the world.

🔗 Apple Inc. 🔗 Computing 🔗 Computing/Software 🔗 Computing/Free and open-source software 🔗 Linux 🔗 Perl

Vim (; a contraction of Vi IMproved) is a clone, with additions, of Bill Joy's vi text editor program for Unix. Vim's author, Bram Moolenaar, based it upon the source code for a port of the Stevie editor to the Amiga and released a version to the public in 1991. Vim is designed for use both from a command-line interface and as a standalone application in a graphical user interface. Vim is free and open-source software and is released under a license that includes some charityware clauses, encouraging users who enjoy the software to consider donating to children in Uganda. The license is compatible with the GNU General Public License through a special clause allowing distribution of modified copies "under the GNU GPL version 2 or any later version".

Since its release for the Amiga, cross-platform development has made it available on many other systems. In 2006, it was voted the most popular editor amongst Linux Journal readers; in 2015 the Stack Overflow developer survey found it to be the third most popular text editor, and the fifth most popular development environment in 2019.

🔗 Lists

This is a list of countries and territories by home ownership rate, which is the ratio of owner-occupied units to total residential units in a specified area.

🔗 Mathematics

Curry's paradox is a paradox in which an arbitrary claim F is proved from the mere existence of a sentence C that says of itself "If C, then F", requiring only a few apparently innocuous logical deduction rules. Since F is arbitrary, any logic having these rules proves everything. The paradox may be expressed in natural language and in various logics, including certain forms of set theory, lambda calculus, and combinatory logic.

The paradox is named after the logician Haskell Curry. It has also been called Löb's paradox after Martin Hugo Löb, due to its relationship to Löb's theorem.

🔗 Technology 🔗 Physics 🔗 Ancient Near East 🔗 Ancient Egypt 🔗 Archaeology 🔗 Spectroscopy 🔗 Blades

Tutankhamun's meteoric iron dagger, also known as Tutankhamun's iron dagger and King Tut's dagger, is an iron-bladed dagger from the tomb of the ancient Egyptian Pharaoh Tutankhamun (reigned c. 1334–1325 BC). As the blade composition and homogeneity closely correlate with meteorite composition and homogeneity, the material for the blade is determined to have originated by way of a meteoritic landing. The dagger is currently displayed at the Egyptian Museum in Cairo.