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π Bellman's lost in a forest problem
Bellman's lost-in-a-forest problem is an unsolved minimization problem in geometry, originating in 1955 by the American applied mathematician Richard E. Bellman. The problem is often stated as follows: "A hiker is lost in a forest whose shape and dimensions are precisely known to him. What is the best path for him to follow to escape from the forest?" It is usually assumed that the hiker does not know the starting point or direction he is facing. The best path is taken to be the one that minimizes the worst-case distance to travel before reaching the edge of the forest. Other variations of the problem have been studied.
A proven solution is only known for a few shapes or classes of shape. A general solution would be in the form of a geometric algorithm which takes the shape of the forest as input and returns the optimal escape path as the output. Although real world applications are not apparent, the problem falls into a class of geometric optimization problems including search strategies that are of practical importance. A bigger motivation for study has been the connection to Moser's worm problem. It was included in a list of 12 problems described by the mathematician Scott W. Williams as "million buck problems" because he believed that the techniques involved in their resolution will be worth at least a million dollars to mathematics.
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- "Bellman's lost in a forest problem" | 2018-09-16 | 139 Upvotes 78 Comments
π Corecursion
In computer science, corecursion is a type of operation that is dual to recursion. Whereas recursion works analytically, starting on data further from a base case and breaking it down into smaller data and repeating until one reaches a base case, corecursion works synthetically, starting from a base case and building it up, iteratively producing data further removed from a base case. Put simply, corecursive algorithms use the data that they themselves produce, bit by bit, as they become available, and needed, to produce further bits of data. A similar but distinct concept is generative recursion which may lack a definite "direction" inherent in corecursion and recursion.
Where recursion allows programs to operate on arbitrarily complex data, so long as they can be reduced to simple data (base cases), corecursion allows programs to produce arbitrarily complex and potentially infinite data structures, such as streams, so long as it can be produced from simple data (base cases) in a sequence of finite steps. Where recursion may not terminate, never reaching a base state, corecursion starts from a base state, and thus produces subsequent steps deterministically, though it may proceed indefinitely (and thus not terminate under strict evaluation), or it may consume more than it produces and thus become non-productive. Many functions that are traditionally analyzed as recursive can alternatively, and arguably more naturally, be interpreted as corecursive functions that are terminated at a given stage, for example recurrence relations such as the factorial.
Corecursion can produce both finite and infinite data structures as results, and may employ self-referential data structures. Corecursion is often used in conjunction with lazy evaluation, to produce only a finite subset of a potentially infinite structure (rather than trying to produce an entire infinite structure at once). Corecursion is a particularly important concept in functional programming, where corecursion and codata allow total languages to work with infinite data structures.
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- "Corecursion" | 2014-05-08 | 167 Upvotes 62 Comments
π SNAP-10A was an experimental nuclear reactor launched into space in 1965
SNAP-10A (Systems for Nuclear, Auxiliary Power, aka Snapshot for Space Nuclear Auxiliary Power Shot, also known as OPS 4682, COSPAR 1965-027A) was a US experimental nuclear powered satellite launched into space in 1965 as part of the SNAPSHOT program. The test marked the world's first operation of a nuclear reactor in orbit, and also the first operation of an ion thruster system in orbit. It is the only fission reactor power system launched into space by the United States. The reactor stopped working after just 43 days due to a non-nuclear electrical component failure. The Systems Nuclear Auxiliary Power Program (SNAP) reactor was specifically developed for satellite use in the 1950s and early 1960s under the supervision of the U.S. Atomic Energy Commission.
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- "SNAP-10A was an experimental nuclear reactor launched into space in 1965" | 2015-12-27 | 30 Upvotes 11 Comments
π Gate Tower Building
Gate Tower Building (γ²γΌγγΏγ―γΌγγ«, gΔto tawΔ biru) is a 16 floor office building in Fukushima-ku, Osaka, Japan. It is notable for the highway offramp at Umeda Exit that passes through the building.
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- "Gate Tower Building" | 2014-01-02 | 196 Upvotes 50 Comments
π The Great Debate
The Great Debate, also called the ShapleyβCurtis Debate, was held on 26 April 1920 at the Smithsonian Museum of Natural History, between the astronomers Harlow Shapley and Heber Curtis. It concerned the nature of so-called spiral nebulae and the size of the universe; Shapley believed that distant nebulae were relatively small and lay within the outskirts of Earth's home galaxy, while Curtis held that they were in fact independent galaxies, implying that they were exceedingly large and distant.
The two scientists first presented independent technical papers about "The Scale of the Universe" during the day and then took part in a joint discussion that evening. Much of the lore of the Great Debate grew out of two papers published by Shapley and by Curtis in the May 1921 issue of the Bulletin of the National Research Council. The published papers each included counter arguments to the position advocated by the other scientist at the 1920 meeting.
In the aftermath of the public debate, scientists have been able to verify individual pieces of evidence from both astronomers, but on the main point of the existence of other galaxies, Curtis has been proven correct.
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- "Great Debate (Astronomy)" | 2020-04-25 | 62 Upvotes 9 Comments
- "The Great Debate" | 2019-08-21 | 14 Upvotes 2 Comments
π Tacit Programming
Tacit programming, also called point-free style, is a programming paradigm in which function definitions do not identify the arguments (or "points") on which they operate. Instead the definitions merely compose other functions, among which are combinators that manipulate the arguments. Tacit programming is of theoretical interest, because the strict use of composition results in programs that are well adapted for equational reasoning. It is also the natural style of certain programming languages, including APL and its derivatives, and concatenative languages such as Forth. The lack of argument naming gives point-free style a reputation of being unnecessarily obscure, hence the epithet "pointless style".
Unix scripting uses the paradigm with pipes.
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- "Tacit Programming" | 2024-02-23 | 134 Upvotes 92 Comments
π An Automat is a fast food restaurant where foods and drink are served by vending machines.
An automat is a fast food restaurant where simple foods and drink are served by vending machines. The world's first automat was named Quisisana, which opened in Berlin, Germany in 1895.
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- "An Automat is a fast food restaurant where foods and drink are served by vending machines." | 2008-09-27 | 7 Upvotes 14 Comments
π Network (1976 Film)
Network is a 1976 American satirical black comedy-drama film released by Metro-Goldwyn-Mayer, written by Paddy Chayefsky and directed by Sidney Lumet. It is about a fictional television network, UBS, and its struggle with poor ratings. The film stars Faye Dunaway, William Holden, Peter Finch (in his final film role), Robert Duvall, Wesley Addy, Ned Beatty, and Beatrice Straight.
Network received widespread critical acclaim, with particular praise for the performances. The film was a commercial success, with nine Oscar nominations at the 49th Academy Awards, including Best Picture, that led to four wins: Best Actor (Finch), Best Actress (Dunaway), Best Supporting Actress (Straight), and Best Original Screenplay.
In 2000, the film was selected for preservation in the United States National Film Registry by the Library of Congress as being "culturally, historically, or aesthetically significant". In 2002, it was inducted into the Producers Guild of America Hall of Fame as a film that has "set an enduring standard for American entertainment". In 2005, the two Writers Guilds of America voted Chayefsky's script one of the 10 greatest screenplays in the history of cinema. In 2007, the film was 64th among the 100 greatest American films as chosen by the American Film Institute, a ranking slightly higher than the one AFI had given it ten years earlier.
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- "Network (1976 Film)" | 2022-11-23 | 10 Upvotes 2 Comments
π List of Epidemics
This article is a list of deaths caused by an infectious disease. Widespread non-communicable diseases such as cardiovascular disease and cancer are not included.
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- "List of Epidemics" | 2020-01-26 | 78 Upvotes 38 Comments
π Tractatus Logico-Philosophicus
The Tractatus Logico-Philosophicus (widely abbreviated and cited as TLP) is the only book-length philosophical work by the Austrian philosopher Ludwig Wittgenstein that was published during his lifetime. The project had a broad goal: to identify the relationship between language and reality and to define the limits of science. Wittgenstein wrote the notes for the Tractatus while he was a soldier during World War I and completed it during a military leave in the summer of 1918. It was originally published in German in 1921 as Logisch-Philosophische Abhandlung (Logical-Philosophical Treatise). In 1922 it was published together with an English translation and a Latin title, which was suggested by G. E. Moore as homage to Baruch Spinoza's Tractatus Theologico-Politicus (1670).
The Tractatus is written in an austere and succinct literary style, containing almost no arguments as such, but consists of altogether 525 declarative statements, which are hierarchically numbered.
The Tractatus is recognized by philosophers as one of the most significant philosophical works of the twentieth century and was influential chiefly amongst the logical positivist philosophers of the Vienna Circle, such as Rudolf Carnap and Friedrich Waismann and Bertrand Russell's article "The Philosophy of Logical Atomism".
Wittgenstein's later works, notably the posthumously published Philosophical Investigations, criticised many of his ideas in the Tractatus. There are, however, elements to see a common thread in Wittgenstein's thinking, in spite of those criticisms of the Tractatus in later writings. Indeed, the legendary contrast between βearlyβ and βlateβ Wittgenstein has been countered by such scholars as Pears (1987) and Hilmy (1987). For example, a relevant, yet neglected aspect of continuity in Wittgensteinβs central issues concerns βmeaningβ as βuseβ. Connecting his early and later writings on βmeaning as useβ is his appeal to direct consequences of a term or phrase, reflected e.g. in his speaking of language as a βcalculusβ. These passages are rather crucial to Wittgensteinβs view of βmeaning as useβ, though they have been widely neglected in scholarly literature. The centrality and importance of these passages are corroborated and augmented by renewed examination of Wittgensteinβs NachlaΓ, as is done in "From Tractatus to Later Writings and Back - New Implications from the Nachlass" (de Queiroz 2023).
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- "Tractatus Logico-Philosophicus" | 2023-08-12 | 65 Upvotes 68 Comments