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🔗 Video games 🔗 Computing

The ZX81 is a home computer that was produced by Sinclair Research and manufactured in Dundee, Scotland, by Timex Corporation. It was launched in the United Kingdom in March 1981 as the successor to Sinclair's ZX80 and designed to be a low-cost introduction to home computing for the general public. It was hugely successful; more than 1.5 million units were sold. In the United States it was initially sold as the ZX-81 under license by Timex. Timex later produced its own versions of the ZX81: the Timex Sinclair 1000 and Timex Sinclair 1500. Unauthorized ZX81 clones were produced in several countries.

The ZX81 was designed to be small, simple, and above all, inexpensive, with as few components as possible. Video output is to a television set rather than a dedicated monitor. Programs and data are loaded and saved onto compact audio cassettes. It uses only four silicon chips and a mere 1 KB of memory. There is no power switch or any moving parts with the exception of a VHF TV channel selector switch present in some models. It has a pressure-sensitive membrane keyboard. The ZX81's limitations prompted a market in third-party peripherals to improve its capabilities. Its distinctive case and keyboard brought designer Rick Dickinson a Design Council award.

The ZX81 could be bought by mail order preassembled or, for a lower price, in kit form. It was the first inexpensive mass-market home computer to be sold by high street stores, led by W. H. Smith and soon many other retailers. The ZX81 marked the point when computing in Britain became an activity for the general public rather than the preserve of businessmen and electronics hobbyists. It produced a huge community of enthusiasts, some of whom founded their own businesses producing software and hardware for the ZX81. Many went on to play major roles in the British computer industry. The ZX81's commercial success made Sinclair Research one of Britain's leading computer manufacturers and earned a fortune and an eventual knighthood for the company's founder Sir Clive Sinclair.

🔗 Lists 🔗 Buddhism 🔗 Project-independent assessment

The Buddhist games list is a list of games that Gautama Buddha is reputed to have said that he would not play and that his disciples should likewise not play, because he believed them to be a 'cause for negligence'. This list dates from the 6th or 5th century BCE and is the earliest known list of games.

There is some debate about the translation of some of the games mentioned, and the list given here is based on the translation by T. W. Rhys Davids of the Brahmajāla Sutta and is in the same order given in the original. The list is duplicated in a number of other early Buddhist texts, including the Vinaya Pitaka.

1. Games on boards with 8 or 10 rows. This is thought to refer to ashtapada and dasapada respectively, but later Sinhala commentaries refer to these boards also being used with games involving dice.
2. The same games played on imaginary boards. Akasam astapadam was an ashtapada variant played with no board, literally "astapadam played in the sky". A correspondent in the American Chess Bulletin identifies this as likely the earliest literary mention of a blindfold chess variant.
3. Games of marking diagrams on the floor such that the player can only walk on certain places. This is described in the Vinaya Pitaka as "having drawn a circle with various lines on the ground, there they play avoiding the line to be avoided". Rhys Davids suggests that it may refer to parihāra-patham, a form of hop-scotch.
4. Games where players either remove pieces from a pile or add pieces to it, with the loser being the one who causes the heap to shake (similar to the modern game pick-up sticks).
5. Games of throwing dice.
6. "Dipping the hand with the fingers stretched out in lac, or red dye, or flour-water, and striking the wet hand on the ground or on a wall, calling out 'What shall it be?' and showing the form required—elephants, horses, &c."
7. Ball games.
8. Blowing through a pat-kulal, a toy pipe made of leaves.
9. Ploughing with a toy plough.
10. Playing with toy windmills made from palm leaves.
11. Playing with toy measures made from palm leaves.
12. Playing with toy carts.
13. Playing with toy bows.
14. Guessing at letters traced with the finger in the air or on a friend's back.
15. Guessing a friend's thoughts.
16. Imitating deformities.

Although the modern game of chess had not been invented at the time the list was made, earlier chess-like games such as chaturaji may have existed. H.J.R. Murray refers to Rhys Davids' 1899 translation, noting that the 8×8 board game is most likely ashtapada while the 10×10 game is dasapada. He states that both are race games.

🔗 Statistics

In statistics, a Pólya urn model (also known as a Pólya urn scheme or simply as Pólya's urn), named after George Pólya, is a type of statistical model used as an idealized mental exercise framework, unifying many treatments.

In an urn model, objects of real interest (such as atoms, people, cars, etc.) are represented as colored balls in an urn or other container. In the basic Pólya urn model, the urn contains x white and y black balls; one ball is drawn randomly from the urn and its color observed; it is then returned in the urn, and an additional ball of the same color is added to the urn, and the selection process is repeated. Questions of interest are the evolution of the urn population and the sequence of colors of the balls drawn out.

This endows the urn with a self-reinforcing property sometimes expressed as the rich get richer.

Note that in some sense, the Pólya urn model is the "opposite" of the model of sampling without replacement, where every time a particular value is observed, it is less likely to be observed again, whereas in a Pólya urn model, an observed value is more likely to be observed again. In both of these models, the act of measurement has an effect on the outcome of future measurements. (For comparison, when sampling with replacement, observation of a particular value has no effect on how likely it is to observe that value again.) In a Pólya urn model, successive acts of measurement over time have less and less effect on future measurements, whereas in sampling without replacement, the opposite is true: After a certain number of measurements of a particular value, that value will never be seen again.

One of the reasons for interest in this particular rather elaborate urn model (i.e. with duplication and then replacement of each ball drawn) is that it provides an example in which the count (initially x black and y white) of balls in the urn is not concealed, which is able to approximate the correct updating of subjective probabilities appropriate to a different case in which the original urn content is concealed while ordinary sampling with replacement is conducted (without the Pólya ball-duplication). Because of the simple "sampling with replacement" scheme in this second case, the urn content is now static, but this greater simplicity is compensated for by the assumption that the urn content is now unknown to an observer. A Bayesian analysis of the observer's uncertainty about the urn's initial content can be made, using a particular choice of (conjugate) prior distribution. Specifically, suppose that an observer knows that the urn contains only identical balls, each coloured either black or white, but he does not know the absolute number of balls present, nor the proportion that are of each colour. Suppose that he holds prior beliefs about these unknowns: for him the probability distribution of the urn content is well approximated by some prior distribution for the total number of balls in the urn, and a beta prior distribution with parameters (x,y) for the initial proportion of these which are black, this proportion being (for him) considered approximately independent of the total number. Then the process of outcomes of a succession of draws from the urn (with replacement but without the duplication) has approximately the same probability law as does the above Pólya scheme in which the actual urn content was not hidden from him. The approximation error here relates to the fact that an urn containing a known finite number m of balls of course cannot have an exactly beta-distributed unknown proportion of black balls, since the domain of possible values for that proportion are confined to being multiples of ${\displaystyle 1/m}$, rather than having the full freedom to assume any value in the continuous unit interval, as would an exactly beta distributed proportion. This slightly informal account is provided for reason of motivation, and can be made more mathematically precise.

This basic Pólya urn model has been enriched and generalized in many ways.

🔗 Mathematics 🔗 Statistics

In probability theory, the birthday problem or birthday paradox concerns the probability that, in a set of n randomly chosen people, some pair of them will have the same birthday. By the pigeonhole principle, the probability reaches 100% when the number of people reaches 367 (since there are only 366 possible birthdays, including February 29). However, 99.9% probability is reached with just 70 people, and 50% probability with 23 people. These conclusions are based on the assumption that each day of the year (excluding February 29) is equally probable for a birthday.

Actual birth records show that different numbers of people are born on different days. In this case, it can be shown that the number of people required to reach the 50% threshold is 23 or fewer. For example, if half the people were born on one day and the other half on another day, then any two people would have a 50% chance of sharing a birthday.

It may well seem surprising that a group of just 23 individuals is required to reach a probability of 50% that at least two individuals in the group have the same birthday: this result is perhaps made more plausible by considering that the comparisons of birthday will actually be made between every possible pair of individuals = 23 × 22/2 = 253 comparisons, which is well over half the number of days in a year (183 at most), as opposed to fixing on one individual and comparing his or her birthday to everyone else's. The birthday problem is not a "paradox" in the literal logical sense of being self-contradictory, but is merely unintuitive at first glance.

Real-world applications for the birthday problem include a cryptographic attack called the birthday attack, which uses this probabilistic model to reduce the complexity of finding a collision for a hash function, as well as calculating the approximate risk of a hash collision existing within the hashes of a given size of population.

The history of the problem is obscure. W. W. Rouse Ball indicated (without citation) that it was first discussed by Harold Davenport. However, Richard von Mises proposed an earlier version of what is considered today to be the birthday problem.

🔗 Computing 🔗 Military history 🔗 Military history/Military science, technology, and theory 🔗 Cryptography 🔗 Cryptography/Computer science 🔗 Cold War 🔗 NATO

Link 16 is a military tactical data link network used by NATO and nations allowed by the MIDS International Program Office (IPO). Its specification is part of the family of Tactical Data Links.

With Link 16, military aircraft as well as ships and ground forces may exchange their tactical picture in near-real time. Link 16 also supports the exchange of text messages, imagery data and provides two channels of digital voice (2.4 kbit/s or 16 kbit/s in any combination). Link 16 is defined as one of the digital services of the JTIDS / MIDS in NATO's Standardization Agreement STANAG 5516. MIL-STD-6016 is the related United States Department of Defense Link 16 MIL-STD.

🔗 Computing 🔗 Perl

The WikiWikiWeb is the first-ever wiki, or user-editable website. It was launched on 25 March 1995 by its inventor, programmer Ward Cunningham, to accompany the Portland Pattern Repository website discussing software design patterns. The name WikiWikiWeb originally also applied to the wiki software that operated the website, written in the Perl programming language and later renamed to "WikiBase". The site is frequently referred to by its users as simply "Wiki", and a convention established among users of the early network of wiki sites that followed was that using the word with a capitalized W referred exclusively to the original site.

🔗 Environment 🔗 Economics 🔗 Law 🔗 Anthropology 🔗 Sociology 🔗 Game theory

The tragedy of the anticommons is a type of coordination breakdown, in which a commons does not emerge, even when general access to resources or infrastructure would be a social good. It is a mirror-image of the older concept of tragedy of the commons, in which numerous rights holders' combined use exceeds the capacity of a resource and depletes or destroys it. The "tragedy of the anticommons" covers a range of coordination failures, including patent thickets and submarine patents. Overcoming these breakdowns can be difficult, but there are assorted means, including eminent domain, laches, patent pools, or other licensing organizations.

The term originally appeared in Michael Heller's 1998 article of the same name and is the thesis of his 2008 book. The model was formalized by James M. Buchanan and Yong Yoon. In a 1998 Science article, Heller and Rebecca S. Eisenberg, while not disputing the role of patents in general in motivating invention and disclosure, argue that biomedical research was one of several key areas where competing patent rights could actually prevent useful and affordable products from reaching the marketplace.

🔗 Physics 🔗 Astronomy

The Oh-My-God particle was the highest-energy cosmic ray detected at the time (15 October 1991) by the Fly's Eye detector in Dugway Proving Ground, Utah, US. Its energy was estimated as (3.2±0.9)×10²⁰ eV, or 51 J. This is 20 million times more energetic than the highest energy measured in electromagnetic radiation emitted by an extragalactic object and 10²⁰ (100 quintillion) times the photon energy of visible light, equivalent to a 142-gram (5 oz) baseball travelling at about 26 m/s (94 km/h; 58 mph). Although higher energy cosmic rays have been detected since then, this particle's energy was unexpected, and called into question theories of that era about the origin and propagation of cosmic rays.

Assuming it was a proton, this particle traveled at 99.99999999999999999999951% of the speed of light, its Lorentz factor was 3.2×10¹¹ and its rapidity was 27.1. At this speed, if a photon were travelling with the particle, it would take over 215,000 years for the photon to gain a 1 cm lead as seen in Earth's reference frame.

The energy of this particle is some 40 million times that of the highest energy protons that have been produced in any terrestrial particle accelerator. However, only a small fraction of this energy would be available for an interaction with a proton or neutron on Earth, with most of the energy remaining in the form of kinetic energy of the products of the interaction. The effective energy available for such a collision is √2Emc², where E is the particle's energy and mc² is the mass energy of the proton. For the Oh-My-God particle, this gives 7.5×10¹⁴ eV, roughly 60 times the collision energy of the Large Hadron Collider.

While the particle's energy was higher than anything achieved in terrestrial accelerators, it was still about 40 million times lower than the Planck energy. Particles of such energy would be required in order to explore the Planck scale. A proton with that much energy would travel 1.665×10¹⁵ times closer to the speed of light than the Oh-My-God particle. As viewed from Earth it would take about 3.579×10²⁰ years, or 2.59×10¹⁰ times the current age of the universe, for a photon to gain a 1 cm lead over a Planck energy proton as observed in Earth's reference frame.

Since the first observation, at least 72 similar (energy > 5.7×10¹⁹ eV) events have been recorded, confirming the phenomenon. These ultra-high-energy cosmic ray particles are very rare; the energy of most cosmic ray particles is between 10 MeV and 10 GeV. More recent studies using the Telescope Array have suggested a source for the particles within a 20-degree radius "warm spot" in the direction of the constellation Ursa Major.

🔗 Mathematics

In geometry, the problem of dividing a circle into areas by means of an inscribed polygon with n sides in such a way as to maximise the number of areas created by the edges and diagonals, sometimes called Moser's circle problem, has a solution by an inductive method. The greatest possible number of regions, r_G = ( ⁿ
₄ ) + ( ⁿ
₂ ) + 1, giving the sequence 1, 2, 4, 8, 16, 31, 57, 99, 163, 256, ... (OEIS: A000127). Though the first five terms match the geometric progression 2^{n − 1}, it diverges at n = 6, showing the risk of generalising from only a few observations.

🔗 Biography 🔗 Mathematics 🔗 Environment 🔗 Iran 🔗 Biography/science and academia 🔗 Astronomy 🔗 Geography 🔗 History of Science 🔗 Astrology 🔗 Middle Ages 🔗 Islam 🔗 Middle Ages/History 🔗 Central Asia 🔗 Maps 🔗 Iraq 🔗 Biography/Core biographies 🔗 Islam/Muslim scholars

Muḥammad ibn Mūsā al-Khwārizmī (Persian: Muḥammad Khwārizmī محمد بن موسی خوارزمی‎; c. 780 – c. 850), Arabized as al-Khwarizmi with al- and formerly Latinized as Algorithmi, was a Persian polymath who produced works in mathematics, astronomy, and geography. Around 820 CE he was appointed as the astronomer and head of the library of the House of Wisdom in Baghdad.

Al-Khwarizmi's popularizing treatise on algebra (The Compendious Book on Calculation by Completion and Balancing, c. 813–833 CE) presented the first systematic solution of linear and quadratic equations. One of his principal achievements in algebra was his demonstration of how to solve quadratic equations by completing the square, for which he provided geometric justifications. Because he was the first to treat algebra as an independent discipline and introduced the methods of "reduction" and "balancing" (the transposition of subtracted terms to the other side of an equation, that is, the cancellation of like terms on opposite sides of the equation), he has been described as the father or founder of algebra. The term algebra itself comes from the title of his book (specifically the word al-jabr meaning "completion" or "rejoining"). His name gave rise to the terms algorism and algorithm. His name is also the origin of (Spanish) guarismo and of (Portuguese) algarismo, both meaning digit.

In the 12th century, Latin translations of his textbook on arithmetic (Algorithmo de Numero Indorum) which codified the various Indian numerals, introduced the decimal positional number system to the Western world. The Compendious Book on Calculation by Completion and Balancing, translated into Latin by Robert of Chester in 1145, was used until the sixteenth century as the principal mathematical text-book of European universities.

In addition to his best-known works, he revised Ptolemy's Geography, listing the longitudes and latitudes of various cities and localities. He further produced a set of astronomical tables and wrote about calendaric works, as well as the astrolabe and the sundial. He also made important contributions to trigonometry, producing accurate sine and cosine tables, and the first table of tangents.