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🔗 Religion 🔗 Christianity 🔗 Christianity/theology 🔗 Christianity/Catholicism

The Council of Trent (Latin: Concilium Tridentinum), held between 1545 and 1563 in Trent (or Trento), now in northern Italy, was the 19th ecumenical council of the Catholic Church. Prompted by the Protestant Reformation at the time, it has been described as the embodiment of the Counter-Reformation.

The Council issued condemnations of what it defined to be heresies committed by proponents of Protestantism, and also issued key statements and clarifications of the Church's doctrine and teachings, including scripture, the biblical canon, sacred tradition, original sin, justification, salvation, the sacraments, the Mass, and the veneration of saints. The Council met for twenty-five sessions between 13 December 1545 and 4 December 1563. Pope Paul III, who convoked the Council, oversaw the first eight sessions (1545–47), while the twelfth to sixteenth sessions (1551–52) were overseen by Pope Julius III and the seventeenth to twenty-fifth sessions (1562–63) by Pope Pius IV.

The consequences of the Council were also significant with regard to the Church's liturgy and practices. In its decrees, the Council made the Latin Vulgate the official biblical text of the Roman Church (without prejudice to the original texts in Hebrew and Greek, nor to other traditional translations of the Church, but favoring the Latin language over vernacular translations, such as the controversial English-language Tyndale Bible). In doing so, they commissioned the creation of a revised and standardized Vulgate in light of textual criticism, although this was not achieved until the 1590s. The Council also officially affirmed (for the second time at an ecumenical council) the traditional Catholic Canon of biblical books in response to the increasing Protestant exclusion of the deuterocanonical books. The former dogmatic affirmation of the Canonical books was at the Council of Florence in the 1441 bull Cantate Domino, as affirmed by Pope Leo XIII in his 1893 encyclical Providentissimus Deus (#20). In 1565, a year after the Council finished its work, Pius IV issued the Tridentine Creed (after Tridentum, Trent's Latin name) and his successor Pius V then issued the Roman Catechism and revisions of the Breviary and Missal in, respectively, 1566, 1568 and 1570. These, in turn, led to the codification of the Tridentine Mass, which remained the Church's primary form of the Mass for the next four hundred years.

More than three hundred years passed until the next ecumenical council, the First Vatican Council, was convened in 1869.

🔗 Mathematics

In number theory, specifically the study of Diophantine approximation, the lonely runner conjecture is a conjecture about the long-term behavior of runners on a circular track. It states that ${\displaystyle n}$ runners on a track of unit length, with constant speeds all distinct from one another, will each be lonely at some time—at least ${\displaystyle 1/n}$ units away from all others.

The conjecture was first posed in 1967 by German mathematician Jörg M. Wills, in purely number-theoretic terms, and independently in 1974 by T. W. Cusick; its illustrative and now-popular formulation dates to 1998. The conjecture is known to be true for 7 runners or less, but the general case remains unsolved. Implications of the conjecture include solutions to view-obstruction problems and bounds on properties, related to chromatic numbers, of certain graphs.

🔗 Statistics

A set of dice is nontransitive if it contains three dice, A, B, and C, with the property that A rolls higher than B more than half the time, and B rolls higher than C more than half the time, but it is not true that A rolls higher than C more than half the time. In other words, a set of dice is nontransitive if the binary relation – X rolls a higher number than Y more than half the time – on its elements is not transitive.

It is possible to find sets of dice with the even stronger property that, for each die in the set, there is another die that rolls a higher number than it more than half the time. Using such a set of dice, one can invent games which are biased in ways that people unused to nontransitive dice might not expect (see Example).

🔗 Military history 🔗 Military history/Military aviation 🔗 Military history/World War II 🔗 Military history/German military history 🔗 Military history/European military history 🔗 Military history/British military history

The Charlie Brown and Franz Stigler incident occurred on 20 December 1943, when, after a successful bomb run on Bremen, 2nd Lt Charles "Charlie" Brown's B-17 Flying Fortress (named "Ye Olde Pub") was severely damaged by German fighters. Luftwaffe pilot Franz Stigler had the opportunity to shoot down the crippled bomber but did not do so. After an extensive search by Brown, the two pilots met each other 50 years later and developed a friendship that lasted until Stigler's death in March 2008.

🔗 Computer science

In computer science, a succinct data structure is a data structure which uses an amount of space that is "close" to the information-theoretic lower bound, but (unlike other compressed representations) still allows for efficient query operations. The concept was originally introduced by Jacobson to encode bit vectors, (unlabeled) trees, and planar graphs. Unlike general lossless data compression algorithms, succinct data structures retain the ability to use them in-place, without decompressing them first. A related notion is that of a compressed data structure, in which the size of the data structure depends upon the particular data being represented.

Suppose that ${\displaystyle Z}$ is the information-theoretical optimal number of bits needed to store some data. A representation of this data is called:

• implicit if it takes ${\displaystyle Z+O(1)}$ bits of space,
• succinct if it takes ${\displaystyle Z+o(Z)}$ bits of space, and
• compact if it takes ${\displaystyle O(Z)}$ bits of space.

For example, a data structure that uses ${\displaystyle 2Z}$ bits of storage is compact, ${\displaystyle Z+{\sqrt {Z}}}$ bits is succinct, ${\displaystyle Z+\lg Z}$ bits is also succinct, and ${\displaystyle Z+3}$ bits is implicit.

Implicit structures are thus usually reduced to storing information using some permutation of the input data; the most well-known example of this is the heap.

🔗 Biography 🔗 Germany 🔗 Visual arts

The Master of the Playing Cards (German: Meister der Spielkarten) was the first major master in the history of printmaking. He was a German (or conceivably Swiss) engraver, and probably also a painter, active in southwestern Germany – probably in Alsace, from the 1430s to the 1450s, who has been called "the first personality in the history of engraving."

Various attempts to identify him have not been generally accepted, so he remains known only through his 106 engravings, which include the set of playing cards in five suits from which he takes his name. The majority of the set survives in unique impressions, most of which are in the Kupferstich-Kabinett in Dresden and the Bibliothèque nationale de France in Paris. A further 88 engravings are regarded as sufficiently close to his style to be by his pupils.

🔗 Video games

The Compact Disc-Interactive (CD-I, later CD-i) is a digital optical disc data storage format that was mostly developed and marketed by Dutch company Philips. It was created as an extension of CDDA and CD-ROM and specified in the Green Book, co-developed by Philips and Sony, to combine audio, text and graphics. The two companies initially expected to impact the education/training, point of sale, and home entertainment industries, but CD-i eventually became best known for its video games.

CD-i media physically have the same dimensions as CD, but with up to 744 MiB of digital data storage, including up to 72 minutes of full motion video. CD-i players were usually standalone boxes that connect to a standard television; some less common setups included integrated CD-i television sets and expansion modules for personal computers. Most players were created by Philips; the format was licensed by Philips and Microware for use by other manufacturers, notably Sony who released professional CD-i players under the "Intelligent Discman" brand. Unlike CD-ROM drives, CD-i players are complete computer systems centered around dedicated Motorola 68000-based microprocessors and its own operating system called CD-RTOS, which is an acronym for "Compact Disc – Real Time Operating System".

Media released on the format included video games and "edutainment" and multimedia reference titles, such as interactive encyclopedias and museum tours – which were popular before public Internet access was widespread – as well as business software. Philips's CD-i system also implemented Internet features, including subscriptions, web browsing, downloading, e-mail, and online play. Philips's aim with its players was to introduce interactive multimedia content for the general public by combining features of a CD player and game console, but at a lower price than a personal computer with a CD-ROM drive.

Authoring kits for the format were released first in 1988, and the first player aimed for home consumers, Philips's CDI 910/205, at the end of 1991, initially priced around US$1,000 (equivalent to $1,877 in 2019), and capable of playing interactive CD-i discs, Audio CDs, CD+G (CD+Graphics), Photo CDs and Video CDs (VCDs), though the latter required an optional "Digital Video Card" to provide MPEG-1 decoding. Initially marketed to consumers as "home entertainment systems", and in later years as a "gaming platform", CD-i did not manage to find enough success in the market, and was mostly abandoned by Philips in 1996. The format continued to be supported for licensees for a few more years after.

🔗 Computing 🔗 Economics 🔗 Systems 🔗 Systems/Cybernetics 🔗 Chile

Project Cybersyn was a Chilean project from 1971–1973 during the presidency of Salvador Allende aimed at constructing a distributed decision support system to aid in the management of the national economy. The project consisted of four modules: an economic simulator, custom software to check factory performance, an operations room, and a national network of telex machines that were linked to one mainframe computer.

Project Cybersyn was based on viable system model theory approach to organizational design, and featured innovative technology for its time: it included a network of telex machines (Cybernet) in state-run enterprises that would transmit and receive information with the government in Santiago. Information from the field would be fed into statistical modeling software (Cyberstride) that would monitor production indicators, such as raw material supplies or high rates of worker absenteeism, in "almost" real time, alerting the workers in the first case and, in abnormal situations, if those parameters fell outside acceptable ranges by a very large degree, also the central government. The information would also be input into economic simulation software (CHECO, for CHilean ECOnomic simulator) that the government could use to forecast the possible outcome of economic decisions. Finally, a sophisticated operations room (Opsroom) would provide a space where managers could see relevant economic data, formulate feasible responses to emergencies, and transmit advice and directives to enterprises and factories in alarm situations by using the telex network.

The principal architect of the system was British operations research scientist Stafford Beer, and the system embodied his notions of organisational cybernetics in industrial management. One of its main objectives was to devolve decision-making power within industrial enterprises to their workforce in order to develop self-regulation of factories.

🔗 Geology 🔗 Rocks and minerals 🔗 Iceland

Iceland spar, formerly called Iceland crystal (Icelandic: silfurberg [ˈsɪlvʏrˌpɛrk], lit. 'silver-rock') and also called optical calcite, is a transparent variety of calcite, or crystallized calcium carbonate, originally brought from Iceland, and used in demonstrating the polarization of light.