Turtles all the way down

The most widely known version today appears in Stephen Hawking's 1988 book A Brief History of Time, which begins with an anecdote about an encounter between a scientist and an old lady: A well-known scientist (some say it was Bertrand Russell) once gave a public lecture on astronomy. He described how the Earth orbits around the sun and how the sun, in turn, orbits around the centre of a vast collection of stars called our galaxy. At the end of the lecture, a little old lady at the back of the room got up and said: ...

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Turtles all the way down, Turtles all the way down - Overview, Turtles all the way down - Interpretations, Turtles all the way down - Veracity, Turtles all the way down - Related Concepts, Turtles all the way down - Links

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Ad infinitum is a Latin phrase meaning "to infinity." In context, it usually means "continue forever," and thus can be used to describe a non-terminating process, a non-terminating repeating process, or a set of instructions to be repeated "forever," among other uses. It may also be used in a manner similar to the Latin phrase "et cetera" to denote written words or a concept that continues for a lengthy period beyond what is shown. Examples include: "The series 2, 4, 6, 8, 10 ... ...

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Directions within the Discworld are not given as North, South, East and West, but rather as directions relating to the disc itself: Hubward (towards the centre), Rimward (away from the centre) and to a lesser extent, turnwise and widdershins (relation to the direction of the disc's spin). There are five main continents on the Discworld. The one on which most of the books is set is unnamed, it is essentially the equivalent of Eurasia, and contains the Sto Plains and Ramtops, as well as the more Eastern European lands around Überwald.

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Discworld world, Discworld world - Great A'Tuin the star turtle, Discworld world - Geography, Discworld world - The unnamed continent, Discworld world - Other continents, Discworld world - Magic, Discworld world - Populace, Discworld world - Calendar, Discworld world - Communication and travel, Discworld world - Other Discworlds

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Other discworlds known to exist in the Discworld universe include Bathys, a water world which is home to sea trolls, and an unnamed world ringed by a giant serpent. ...

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Discworld world, Discworld world - Great A'Tuin the star turtle, Discworld world - Geography, Discworld world - The unnamed continent, Discworld world - Other continents, Discworld world - Magic, Discworld world - Populace, Discworld world - Calendar, Discworld world - Communication and travel, Discworld world - Other Discworlds

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Since their development around the time of The Fifth Elephant clacks towers have been one of the principal means of communication around the Disc. This massive network of semaphore towers stretches out across the Unnamed Continent and allows a message to be sent from Ankh-Morpork to Genua in a few hours where it would take a few days by coach. The Post Office, detailed alongside the clacks towers in Going Postal, went through a time of disrepair before Moist von Lipwig turned it into a successful enterprise. The use of m ...

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Discworld world, Discworld world - Great A'Tuin the star turtle, Discworld world - Geography, Discworld world - The unnamed continent, Discworld world - Other continents, Discworld world - Magic, Discworld world - Populace, Discworld world - Calendar, Discworld world - Communication and travel, Discworld world - Other Discworlds

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Main article: Discworld calendar Eight is a significant number on the Discworld. There are eight colours in the visible spectrum (the eighth being Octarine, the "colour of magic"), and eight days in a week (the eighth being Octeday). There are also, due to the peculiar astronomical arrangements, eight seasons (and 800 days) in a year, although most Discworlders consider four seasons make a year, whatever astronomer ...

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Discworld world, Discworld world - Great A'Tuin the star turtle, Discworld world - Geography, Discworld world - The unnamed continent, Discworld world - Other continents, Discworld world - Magic, Discworld world - Populace, Discworld world - Calendar, Discworld world - Communication and travel, Discworld world - Other Discworlds

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Main article: Magic (Discworld) Magic is the principal force on the Discworld, and operates in a similar vein to elemental forces such as gravity and electromagnetism on our own world. The Disc's "standing magical field" is basically the local breakdown of reality that allows a flat planet on the back of a turtle to even exist. The other varieties of magic are usually methods of shaping this force. It warps reality in much the same way as gravity warps space-time. Areas with larger than normal quantities of background magic ten ...

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Discworld world, Discworld world - Great A'Tuin the star turtle, Discworld world - Geography, Discworld world - The unnamed continent, Discworld world - Other continents, Discworld world - Magic, Discworld world - Populace, Discworld world - Calendar, Discworld world - Communication and travel, Discworld world - Other Discworlds

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See the Discworld characters and minor Discworld characters articles for a list of characters from the novels, including the gods. The Discworld is populated by numerous classic fantasy and mythological races as well as humans. While humans are typically the main inhabitants of the major cities there are many other races that have left their traditional domain and integrated with other, sometimes hostile, species. Pratchett has different characteristics for some of these races when compared to other noted authors. Dwarfs ...

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Discworld world, Discworld world - Great A'Tuin the star turtle, Discworld world - Geography, Discworld world - The unnamed continent, Discworld world - Other continents, Discworld world - Magic, Discworld world - Populace, Discworld world - Calendar, Discworld world - Communication and travel, Discworld world - Other Discworlds

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Main article: Great A'Tuin Great A'Tuin is the giant star turtle who travels through space, carrying the four giant elephants (named Berilia, Tubul, Great T'Phon, and Jerakeen) who in turn carry the Discworld. A member of the species Chelys galactica, A'Tuin is the only turtle ever to feature on the Hertzsprung-Russell diagram. Its shell is frosted with frozen methane, pitted with meteor craters, and scoured by asteroidal dust. Great A'Tuin's sex is unknown, but is the subject of much speculation by some of ...

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Discworld world, Discworld world - Great A'Tuin the star turtle, Discworld world - Geography, Discworld world - The unnamed continent, Discworld world - Other continents, Discworld world - Magic, Discworld world - Populace, Discworld world - Calendar, Discworld world - Communication and travel, Discworld world - Other Discworlds

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Recursion in computer programming defines a function in terms of itself. One example application of recursion is in parsers for programming languages. The great advantage of recursion is that an infinite set of possible sentences, designs or other data can be defined, parsed or produced by a finite computer program. One basic form of recursive computer program is to define one or a few base cases, and then define rules to break down other cases into the base case. This is analytic, and is the mo ...

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Recursion, Recursion - Recursion in mathematics, Recursion - Functional Recursion, Recursion - Recursive Proofs, Recursion - Recursion in computing, Recursion - Recursion in language, Recursion - Recurrence relations or algorithms, Recursion - Recursively defined sets, Recursion - Example: the natural numbers, Recursion - Example: The set of true reachable propositions, Recursion - Recursively defined functions, Recursion - Recursive algorithms, Recursion - The recursion theorem, Recursion - Proof of uniqueness, Recursion - Proof of existence, Recursion - Recursion in plain English, Recursion - Recursive humour

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A common geeky joke (for example [1]) is the following "definition" of recursion. Recursion See "Recursion". This is a parody on references in dictionaries, which in some careless cases may lead to circular definitions; in fact the above is the shortest possible one. Every joke has an element of wisdom, and also an element of misunderstanding. This one is also the second-shortest possible example of an erroneous recursive definition of an object, the error being the absence of the termin ...

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Recursion, Recursion - Recursion in mathematics, Recursion - Functional Recursion, Recursion - Recursive Proofs, Recursion - Recursion in computing, Recursion - Recursion in language, Recursion - Recurrence relations or algorithms, Recursion - Recursively defined sets, Recursion - Example: the natural numbers, Recursion - Example: The set of true reachable propositions, Recursion - Recursively defined functions, Recursion - Recursive algorithms, Recursion - The recursion theorem, Recursion - Proof of uniqueness, Recursion - Proof of existence, Recursion - Recursion in plain English, Recursion - Recursive humour

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A common geeky joke (for example [1]) is the following "definition" of recursion. Recursion See "Recursion". This is a parody on references in dictionaries, which in some careless cases may lead to circular definitions. Every joke has an element of wisdom, and also an element of misunderstanding. This one is also the second-shortest possible example of an erroneous recursive definition of an object, the error being the absence of the termination condition (or lack of the initial state, i ...

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Recursion, Recursion - Recursion in mathematics, Recursion - Functional Recursion, Recursion - Recursive Proofs, Recursion - Recursion in computing, Recursion - Recursion in language, Recursion - Recurrence relations or algorithms, Recursion - Recursively defined sets, Recursion - Example: the natural numbers, Recursion - Example: The set of true reachable propositions, Recursion - Recursively defined functions, Recursion - Recursive algorithms, Recursion - The recursion theorem, Recursion - Proof of uniqueness, Recursion - Proof of existence, Recursion - Recursion in plain English, Recursion - Recursive humour

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Recursion - Functional Recursion. Mathematical recursion involves a function calling on itself over and over until reaching an end state. Each iteration increases the depth of the call. Once the end state is achieved, the function then backs all the way out, step by step. The key points of this kind of recursion are two fold: You have to have a function that calls itself with a smaller subset of the values with which it began. The function must be aware that an end state exists which terminates the recursive process. ...

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Recursion, Recursion - Recursion in mathematics, Recursion - Functional Recursion, Recursion - Recursive Proofs, Recursion - Recursion in computing, Recursion - Recursion in language, Recursion - Recurrence relations or algorithms, Recursion - Recursively defined sets, Recursion - Example: the natural numbers, Recursion - Example: The set of true reachable propositions, Recursion - Recursively defined functions, Recursion - Recursive algorithms, Recursion - The recursion theorem, Recursion - Proof of uniqueness, Recursion - Proof of existence, Recursion - Recursion in plain English, Recursion - Recursive humour

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Recursion is the process a procedure goes through when one of the steps of the procedure involves rerunning the entire same procedure. A procedure that goes through recursion is said to be recursive. Something is also said to be recursive when it is the result of a recursive procedure. To understand recursion, one must recognize the distinction between a procedure and the running of a procedure. A procedure is a set of steps that are to be taken based on a set of rules. The running of a procedure involves actually ...

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Recursion, Recursion - Recursion in mathematics, Recursion - Functional Recursion, Recursion - Recursive Proofs, Recursion - Recursion in computing, Recursion - Recursion in language, Recursion - Recurrence relations or algorithms, Recursion - Recursively defined sets, Recursion - Example: the natural numbers, Recursion - Example: The set of true reachable propositions, Recursion - Recursively defined functions, Recursion - Recursive algorithms, Recursion - The recursion theorem, Recursion - Proof of uniqueness, Recursion - Proof of existence, Recursion - Recursion in plain English, Recursion - Recursive humour

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In set theory, this is a theorem guaranteeing that recursively defined functions exist. Given a set X, an element a of X and a function , the theorem states that there is a unique function (where N denotes the set of natural numbers) such that F(0) = a F(n + 1) = f(F(n)) for any natural number n.

Recursion, Recursion - Recursion in mathematics, Recursion - Functional Recursion, Recursion - Recursive Proofs, Recursion - Recursion in computing, Recursion - Recursion in language, Recursion - Recurrence relations or algorithms, Recursion - Recursively defined sets, Recursion - Example: the natural numbers, Recursion - Example: The set of true reachable propositions, Recursion - Recursively defined functions, Recursion - Recursive algorithms, Recursion - The recursion theorem, Recursion - Proof of uniqueness, Recursion - Proof of existence, Recursion - Recursion in plain English, Recursion - Recursive humour

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Recursion - Example: the natural numbers. The canonical example of a recursively defined set is given by the natural numbers: 0 is in N if n is in N, then n + 1 is in N The set of natural numbers is the smallest set satisfying the previous two properties. Here's an alternative recursive definition of N: 0, 1 are in N; if n and n + 1 are in N, then n + 2 is in N; N is the small ...

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Recursion, Recursion - Recursion in mathematics, Recursion - Functional Recursion, Recursion - Recursive Proofs, Recursion - Recursion in computing, Recursion - Recursion in language, Recursion - Recurrence relations or algorithms, Recursion - Recursively defined sets, Recursion - Example: the natural numbers, Recursion - Example: The set of true reachable propositions, Recursion - Recursively defined functions, Recursion - Recursive algorithms, Recursion - The recursion theorem, Recursion - Proof of uniqueness, Recursion - Proof of existence, Recursion - Recursion in plain English, Recursion - Recursive humour

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Linguist Noam Chomsky produced evidence that unlimited extension of a language such as English is possible only by the recursive device of embedding sentences in sentences. Thus, a talky little girl may say, "Dorothy, who met the wicked Witch of the West in Munchkin Land where her wicked Witch sister was killed, liquidated her with a pail of water." Clearly, two simple sentences — "Dorothy met the Wicked Witch of the West in Munchkin Land" and "Her sister was killed in Munchkin Land" — can be embedded in a third sentence, "Dorothy liquidated her with a p ...

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Recursion, Recursion - Recursion in mathematics, Recursion - Functional Recursion, Recursion - Recursive Proofs, Recursion - Recursion in computing, Recursion - Recursion in language, Recursion - Recurrence relations or algorithms, Recursion - Recursively defined sets, Recursion - Example: the natural numbers, Recursion - Example: The set of true reachable propositions, Recursion - Recursively defined functions, Recursion - Recursive algorithms, Recursion - The recursion theorem, Recursion - Proof of uniqueness, Recursion - Proof of existence, Recursion - Recursion in plain English, Recursion - Recursive humour

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Functions whose domains can be recursively defined can be given recursive definitions patterned after the recursive definition of their domain. The canonical example of a recursively defined function is the following definition of the factorial function f(n): f(0) = 1 f(n) = n * f(n − 1) for any natural number n > 0 Given this definition, also called a recurrence relation, we wo ...

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Recursion, Recursion - Recursion in mathematics, Recursion - Functional Recursion, Recursion - Recursive Proofs, Recursion - Recursion in computing, Recursion - Recursion in language, Recursion - Recurrence relations or algorithms, Recursion - Recursively defined sets, Recursion - Example: the natural numbers, Recursion - Example: The set of true reachable propositions, Recursion - Recursively defined functions, Recursion - Recursive algorithms, Recursion - The recursion theorem, Recursion - Proof of uniqueness, Recursion - Proof of existence, Recursion - Recursion in plain English, Recursion - Recursive humour

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A common method of simplification is to divide a problem into subproblems of the same type. As a computer programming technique, this is called divide and conquer and is key to the design of many important algorithms, as well as being a fundamental part of dynamic programming. Virtually all programming languages in use today allow the direct specification of recursive functions and procedures. When such a function is called, the computer (for most languages on most stack-based architectures) or the language implementation keeps track ...

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Recursion, Recursion - Recursion in mathematics, Recursion - Functional Recursion, Recursion - Recursive Proofs, Recursion - Recursion in computing, Recursion - Recursion in language, Recursion - Recurrence relations or algorithms, Recursion - Recursively defined sets, Recursion - Example: the natural numbers, Recursion - Example: The set of true reachable propositions, Recursion - Recursively defined functions, Recursion - Recursive algorithms, Recursion - The recursion theorem, Recursion - Proof of uniqueness, Recursion - Proof of existence, Recursion - Recursion in plain English, Recursion - Recursive humour

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The differences between the two forms of the anecdote point to the difference in its intended meaning. For Hawking, the turtle myth is one of two accounts of the nature of the universe; he asserts that the turtle theory is patently ridiculous, but admits that his own theories may be just as ridiculous. "Only time will tell," he concludes. For Geertz, however, the myth is patently wise, ...

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Turtles all the way down, Turtles all the way down - Overview, Turtles all the way down - Interpretations, Turtles all the way down - Veracity, Turtles all the way down - Related Concepts, Turtles all the way down - Links

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