Have a deep view into what people are curious about.

The angel problem is a question in combinatorial game theory proposed by John Horton Conway. The game is commonly referred to as the Angels and Devils game. The game is played by two players called the angel and the devil. It is played on an infinite chessboard (or equivalently the points of a 2D lattice). The angel has a power k (a natural number 1 or higher), specified before the game starts. The board starts empty with the angel at the origin. On each turn, the angel jumps to a different empty square which could be reached by at most k moves of a chess king, i.e. the distance from the starting square is at most k in the infinity norm. The devil, on its turn, may add a block on any single square not containing the angel. The angel may leap over blocked squares, but cannot land on them. The devil wins if the angel is unable to move. The angel wins by surviving indefinitely.

The angel problem is: can an angel with high enough power win?

There must exist a winning strategy for one of the players. If the devil can force a win then it can do so in a finite number of moves. If the devil cannot force a win then there is always an action that the angel can take to avoid losing and a winning strategy for it is always to pick such a move. More abstractly, the "pay-off set" (i.e., the set of all plays in which the angel wins) is a closed set (in the natural topology on the set of all plays), and it is known that such games are determined. Of course, for any infinite game, if player 2 doesn't have a winning strategy, player 1 can always pick a move that leads to a position where player 2 doesn't have a winning strategy, but in some games, simply playing forever doesn't confer a win to player 1, and that's why undetermined games may exist.

Conway offered a reward for a general solution to this problem ($100 for a winning strategy for an angel of sufficiently high power, and $1000 for a proof that the devil can win irrespective of the angel's power). Progress was made first in higher dimensions. In late 2006, the original problem was solved when independent proofs appeared, showing that an angel can win. Bowditch proved that a 4-angel (that is, an angel with power k=4) can win and Máthé and Kloster gave proofs that a 2-angel can win. At this stage, it has not been confirmed by Conway who is to be the recipient of his prize offer, or whether each published and subsequent solution will also earn $100 US.

🔗 Fencing

Dueling scars (German: Schmisse) have been seen as a "badge of honour" since as early as 1825. Known variously as "Mensur scars", "the bragging scar", "smite", "Schmitte" or "Renommierschmiss", dueling scars were popular amongst upper-class Austrians and Germans involved in academic fencing at the start of the 20th century. Being a practice amongst university students, it was seen as a mark of their class and honour, due to the status of dueling societies at German and Austrian universities at the time, and is an early example of scarification in European society. The practice of dueling and the associated scars was also present to some extent in the German military.

Foreign tourists visiting Germany in the late 19th century were shocked to see the students, generally with their Studentcorps, at major German universities such as Heidelberg, Bonn, or Jena with facial scars – some older, some more recent, and some still wrapped in bandages.

The sport of academic fencing at the time was very different from modern fencing using specially developed swords. The so-called Mensurschläger (or simply Schläger, "hitter") existed in two versions. The most common weapon is the Korbschläger with a basket-type guard. In some universities in the eastern part of Germany, the so-called Glockenschläger is in use which is equipped with a bell-shaped guard. The individual duels between students, known as Mensuren, were somewhat ritualised. In some cases, protective clothing was worn, including padding on the arm and an eye guard.

The culture of dueling scars was mainly common to Germany and Austria, to a lesser extent some central European countries and briefly at places such as Oxford and some other elite universities. German military laws permitted men to wage duels of honor until World War I. During the Third Reich the Mensur was prohibited at all Universities following the partyline.

Within the duel, it was seen as ideal and a way of showing courage to be able to stand and take the blow, as opposed to inflicting the wound. It was important to show one's dueling prowess, but also that one was capable of taking the wound that was inflicted.

🔗 Military history 🔗 Military history/Military science, technology, and theory 🔗 Ukraine 🔗 Military history/Medieval warfare

The Siege of Caffa was a 14th-century military encounter when Jani Beg of the Golden Horde sieged the city of Caffa, (today Feodosia) between two periods in the 1340s. The city of Caffa, a Genoese colony, was a vital trading hub located in Crimea. The city was then part of Gazaria, a group of seven ports located in Crimea and belonging to the maritime empire of the Republic of Genoa. The event is historically significant primarily because it is believed to be one of the earliest instances of biological warfare.

The siege of Caffa was characterized by intense military tactics from both sides. After several years of siege, the armies of the Horde were forced to withdraw. The siege is famous for a story recounted by Italian notary Gabriel de Mussis, which attributed the subsequent spread of the Black Death to plague-infested corpses having been launched over the walls at the end of the siege.

🔗 Typography

A fleuron (;), also known as printers' flower, is a typographic element, or glyph, used either as a punctuation mark or as an ornament for typographic compositions. Fleurons are stylized forms of flowers or leaves; the term derives from the Old French: floron ("flower"). Robert Bringhurst in The Elements of Typographic Style calls the forms "horticultural dingbats". A commonly-encountered fleuron is the ❦, the floral heart or hedera (ivy leaf). It is also known as an aldus leaf (after Italian Renaissance printer Aldus Manutius).

🔗 Yugoslavia 🔗 Economics

Despite common origins, the economy of the Socialist Federal Republic of Yugoslavia (SFRY) was significantly different from the economies of the Soviet Union and other Eastern European socialist states, especially after the Yugoslav-Soviet break-up in 1948. The occupation and liberation struggle in World War II left Yugoslavia's infrastructure devastated. Even the most developed parts of the country were largely rural and the little industry of the country was largely damaged or destroyed.

🔗 Military history 🔗 Military history/Military science, technology, and theory 🔗 Military history/Weaponry 🔗 Military history/French military history 🔗 Military history/Cold War 🔗 Rocketry 🔗 Military history/European military history

The S3 was a French land-based Intermediate Range Ballistic Missile, equipped with a single 1.2-megatonne thermonuclear warhead. In France it is called an SSBS, for Sol-Sol Balistique Stratégique, or Ground-Ground Strategic Ballistic Missile.

🔗 Biography 🔗 Aviation 🔗 France 🔗 France/Paris 🔗 Iran 🔗 Aviation/airport

Mehran Karimi Nasseri (Persian: مهران کریمی ناصری‎ pronounced [mehˈrɒn kæriˈmi nɒseˈri]; born 1946), also known as Sir Alfred Mehran, is an Iranian refugee who lived in the departure lounge of Terminal One in Charles de Gaulle Airport from 26 August 1988 until July 2006, when he was hospitalized. His autobiography was published as a book, The Terminal Man, in 2004. His story was the inspiration for the 2004 Steven Spielberg film The Terminal.

🔗 Business

Topgrading is a corporate hiring and interviewing methodology that is intended to identify preferred candidates for a particular position. In the methodology, prospective employees undergo a 12-step process that includes extensive interviews, the creation of detailed job scorecards, research into job history, coaching, and more. After being interviewed and reference-checked, job candidates are grouped into one of three categories: A Players, B Players, or C Players. A Players have the most potential for high performance in their role while B and C Players may require more work to be successful. The methodology has been used by major corporations and organizations like General Electric, Lincoln Financial, Honeywell, Barclays, and the American Heart Association.

🔗 Mathematics 🔗 Statistics

In statistics, the 68–95–99.7 rule, also known as the empirical rule, is a shorthand used to remember the percentage of values that lie within an interval estimate in a normal distribution: 68%, 95%, and 99.7% of the values lie within one, two, and three standard deviations of the mean, respectively.

In mathematical notation, these facts can be expressed as follows, where Pr() is the probability function, Χ is an observation from a normally distributed random variable, μ (mu) is the mean of the distribution, and σ (sigma) is its standard deviation:

${\displaystyle {\begin{aligned}\Pr(\mu -1\sigma \leq X\leq \mu +1\sigma )&\approx 68.27\%\\\Pr(\mu -2\sigma \leq X\leq \mu +2\sigma )&\approx 95.45\%\\\Pr(\mu -3\sigma \leq X\leq \mu +3\sigma )&\approx 99.73\%\end{aligned}}}$

The usefulness of this heuristic especially depends on the question under consideration.

In the empirical sciences, the so-called three-sigma rule of thumb (or 3σ rule) expresses a conventional heuristic that nearly all values are taken to lie within three standard deviations of the mean, and thus it is empirically useful to treat 99.7% probability as near certainty.

In the social sciences, a result may be considered "significant" if its confidence level is of the order of a two-sigma effect (95%), while in particle physics, there is a convention of a five-sigma effect (99.99994% confidence) being required to qualify as a discovery.

A weaker three-sigma rule can be derived from Chebyshev's inequality, stating that even for non-normally distributed variables, at least 88.8% of cases should fall within properly calculated three-sigma intervals. For unimodal distributions, the probability of being within the interval is at least 95% by the Vysochanskij–Petunin inequality. There may be certain assumptions for a distribution that force this probability to be at least 98%.

🔗 Computing 🔗 Project-independent assessment

JOVE (Jonathan's Own Version of Emacs) is an open-source, Emacs-like text editor, primarily intended for Unix-like operating systems. It also supports MS-DOS and Microsoft Windows. JOVE was inspired by Gosling Emacs but is much smaller and simpler, lacking Mocklisp. It was originally created in 1983 by Jonathan Payne while at Lincoln-Sudbury Regional High School in Massachusetts, United States on a PDP-11 minicomputer. JOVE was distributed with several releases of BSD Unix, including 2.9BSD, 4.3BSD-Reno and 4.4BSD-Lite2.

As of 2022, the latest development release of JOVE is version 4.17.4.4; the stable version is 4.16. Unlike GNU Emacs, JOVE does not support UTF-8.