Have a deep view into what people are curious about.

🔗 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 significant 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. There is a generalization of the law to numbers expressed in other bases (for example, base 16), and also a generalization from leading 1 digit to leading n digits.

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, 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).

It 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.

🔗 Science 🔗 Academic Journals

FUTON bias (acronym for "full text on the Net") is a tendency of scholars to cite academic journals with open access—that is, journals that make their full text available on the Internet without charge—in preference to toll-access publications. Scholars in some fields can more easily discover and access articles whose full text is available online, which increases authors' likelihood of reading and citing these articles, an issue that was first raised and has been mainly studied in connection with medical research. In the context of evidence-based medicine, articles in expensive journals that do not provide open access (OA) may be "priced out of evidence", giving a greater weight to FUTON publications. FUTON bias may increase the impact factor of open-access journals relative to journals without open access.

One study concluded that authors in medical fields "concentrate on research published in journals that are available as full text on the internet, and ignore relevant studies that are not available in full text, thus introducing an element of bias into their search result". Authors of another study conclude that "the OA advantage is a quality advantage, rather than a quality bias", that authors make a "self-selection toward using and citing the more citable articles—once OA self-archiving has made them accessible", and that open access "itself will not make an unusable (hence uncitable) paper more used and cited".

The related no abstract available bias is a scholar's tendency to cite journal articles that have an abstract available online more readily than articles that do not—this affects articles' citation count similarly to FUTON bias.

🔗 Mathematics 🔗 Percussion

To hear the shape of a drum is to infer information about the shape of the drumhead from the sound it makes, i.e., from the list of overtones, via the use of mathematical theory.

"Can One Hear the Shape of a Drum?" is the title of a 1966 article by Mark Kac in the American Mathematical Monthly which made the question famous, though this particular phrasing originates with Lipman Bers. Similar questions can be traced back all the way to Hermann Weyl . For his paper, Kac was given the Lester R. Ford Award in 1967 and the Chauvenet Prize in 1968.

The frequencies at which a drumhead can vibrate depend on its shape. The Helmholtz equation calculates the frequencies if the shape is known. These frequencies are the eigenvalues of the Laplacian in the space. A central question is whether the shape can be predicted if the frequencies are known; for example, whether a circle-shaped triangle can be recognized in this way. Kac admitted he did not know if it was possible for two different shapes to yield the same set of frequencies. The question of whether the frequencies determine the shape was finally answered in the negative in the early 1990s by Gordon, Webb and Wolpert.

🔗 Philosophy 🔗 Skepticism 🔗 Psychology 🔗 Philosophy/Contemporary philosophy 🔗 Philosophy/Philosophy of mind 🔗 Alternative Views 🔗 Neuroscience

Bicameral mentality is a hypothesis introduced by Julian Jaynes who argued human ancestors as late as the ancient Greeks did not consider emotions and desires as stemming from their own minds but as the consequences of actions of gods external to themselves. The theory posits that the human mind once operated in a state in which cognitive functions were divided between one part of the brain which appears to be "speaking", and a second part which listens and obeys—a bicameral mind, and that the breakdown of this division gave rise to consciousness in humans. The term was coined by Jaynes who presented the idea in his 1976 book The Origin of Consciousness in the Breakdown of the Bicameral Mind, wherein he made the case that a bicameral mentality was the normal and ubiquitous state of the human mind as recently as 3,000 years ago, near the end of the Mediterranean bronze age.

🔗 Archaeology 🔗 Indigenous peoples of North America

The Solutrean hypothesis on the peopling of the Americas claims that the earliest human migration to the Americas took place from Europe, with Solutreans traveling along pack ice in the Atlantic Ocean. This hypothesis contrasts with the mainstream academic narrative that the Americas were first populated by people crossing the Bering Strait to Alaska by foot on what was land during the Last Glacial Period or by following the Pacific coastline from Asia to America by boat.

The Solutrean hypothesis posits that around 21,000 years ago a group of people from the Solutré region of France, who are historically characterized by their unique lithic technique, migrated to North America along pack ice in the Atlantic Ocean. Once they made it to North America, their lithic technique dispersed around the continent (c. 13,000 years ago) to provide the basis for the later popularization of Clovis lithic technology. The premise behind the Solutrean Hypothesis is that the similarities between Clovis and Solutrean lithic technologies are evidence that the Solutreans were the first people to migrate to the Americas, dating far before mainstream scientific theories of the peopling of the Americas.

Originally proposed in the 1970s, the theory has received some support in the 2010s, notably by Dennis Stanford of the Smithsonian Institution and Bruce Bradley of the University of Exeter. However, according to David Meltzer, "[f]ew if any archaeologists—or, for that matter, geneticists, linguists, or physical anthropologists—take seriously the idea of a Solutrean colonization of America." The evidence for the hypothesis is considered more consistent with other scenarios. In addition to an interval of thousands of years between the Clovis and Solutrean eras, the two technologies show only incidental similarities. There is no evidence for any Solutrean seafaring, far less for any technology that could take humans across the Atlantic in an ice age. Genetic evidence supports the theory of Asian, not European, origins for the peopling of the Americas.

🔗 Physics

The Bohr–van Leeuwen theorem states that when statistical mechanics and classical mechanics are applied consistently, the thermal average of the magnetization is always zero. This makes magnetism in solids solely a quantum mechanical effect and means that classical physics cannot account for diamagnetism.

🔗 Systems 🔗 Robotics 🔗 Systems/Cybernetics

The Johns Hopkins Beast was a mobile automaton, an early pre-robot, built in the 1960s at the Johns Hopkins University Applied Physics Laboratory. The machine had a rudimentary intelligence and the ability to survive on its own. As it wandered through the white halls of the laboratory, it would seek black wall outlets. When it found one it would plug in and recharge.

The robot was cybernetic. It did not use a computer. Its control circuitry consisted of dozens of transistors controlling analog voltages. It used photocell optics and sonar to navigate. The 2N404 transistors were used to create NOR logic gates that implemented the Boolean logic to tell it what to do when a specific sensor was activated. The 2N404 transistors were also used to create timing gates to tell it how long to do something. 2N1040 Power transistors were used to control the power to the motion treads, the boom, and the charging mechanism.

The original sensors in Mod I were physical touch only. The wall socket was detected by physical switches on the arm that followed the wall. Once detected, two electrical prongs were extended until they entered the wall socket and made the electrical connection to charge the vehicle. The stairway, doors, and pipes on the hall wall were also detected by physical switches and recognized by appropriate logic.

The sonar guidance system was developed for Mod I and improved for Mod II. It used two ultrasonic transducers to determine distance, location within the halls, and obstructions in its path. This provided "The Beast" with bat-like guidance. At this point, it could detect obstructions in the hallway, such as people in the hallway. Once an obstruction was detected, the Beast would slow down and then decide whether to stop or divert around the obstruction. It could also ultrasonically recognize the stairway and doorways to take appropriate action.

An optical guidance system was added to Mod II. This provided, among other capabilities, the ability to optically identify the black wall sockets that contrasted with the white wall.

The Hopkins Beast Autonomous Robot Mod II link below was written by Dr. Ronald McConnell, at that time a co-op student and one of the designers for Mod II.

🔗 LGBTQ+ studies

“Ur-Fascism” or “Eternal Fascism: Fourteen Ways of Looking at a Blackshirt” (in Italian: Il fascismo eterno, or Ur-Fascismo) is a renowned essay authored by the Italian philosopher, novelist, and semiotician Umberto Eco. First published in 1995, this influential essay provides an analysis of fascism, a definition of fascism, and discusses the fundamental characteristics and traits of fascism. Drawing on Eco's personal experiences growing up in Mussolini's Italy and his extensive research on fascist movements, the essay offers his insights into the nature of fascism and its manifestations.