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Maricha

In the Hindu epic Ramayana, Maricha, or Mareecha (Sanskrit: मारीच, IAST: Mārīca) is a rakshasha, who was killed by Rama, the hero of the epic and an avatar of Vishnu. He is mentioned as an ally of Ravana, the antagonist of the epic. His most notable exploit is his role in the kidnapping of Sita, Rama's wife. His son Kalanemi was killed by Hanuman.

Cursed to be a rakshasa along with his mother Tataka and brother Subahu, Maricha initially led his life terrorizing sages. He was defeated by Rama at the behest of the sage Vishvamitra. He tried again to kill Rama, but had to run for his life again. Ultimately, Maricha assumed the form of a golden deer and helped Ravana kidnap Sita.

Early life
Maricha was the son of the demon Sunda (son of Jamba or Jharjha) and a Yakshini named Tataka, also known as Taraka, Tadaka or Thataka. Tataka was the daughter of the yaksha king Suketu, who had gained her as a blessing from the god Brahma. Maricha also had a younger brother called Subahu. The siblings were very handsome and noble in character. They became skilled in sorcery. Once, Sunda attacked the ashram (hermitage) of the sage Agastya in an intoxicated state. The angry Agastya burnt him by his meditative powers. When Tataka learned of Sunda's death, she and her sons attacked Agastya to wreak vengeance on the sage. The sage cursed Tataka, Maricha and Subahu, transforming them into wicked, hideous, demonic Rakshasas.

Tataka and her sons then went to Patala (the underworld) to seek aid from Sumali, the patriarch of the Rakshasas. Sumali took them to his grandson, Ravana, the Rakshasa king of Lanka. Ravana helped the trio capture the states of Malada and Karusha, situated on the banks of the river Sarayu near its confluence with the Ganges. The trio destroyed the states and turned them into a dense forest, which became known as the forest of Tataka. They terrorized the people, devouring anyone who dared venture into that forest. The gods, demons and men, as well as even the sun and the clouds did not dare to enter the territory of Tataka and her sons. Maricha and Subahu liked to harass the sages (rishis) in the region and destroy their yajna sacrifices. The brothers threw blood, flesh, and bones on the sacrificial altars and destroyed the sanctity of the sacrifices of the sages.

Facing Rama at Vishvamitra's yajna
The great sage Vishvamitra was living in the area near the forest of Tadaka and was doing penance and yajna with his disciples, and being tormented by Tadaka and her sons. Unable to tolerate the menace any longer, Vishvamitra approached Dasharatha, the King of Ayodhya for help. He requested Dasharatha to send his eldest son, Rama to protect his yajna. Though Dasharatha was initially reluctant to send his 16-year-old boy, he finally sent Rama and his younger brother Lakshmana with Vishvamitra on the advice of the royal guru Vashishtha. Vishvamitra trained them in warfare and taught them various mantras.

When Vishvamitra and the princes were passing through the forest of Tadaka, Tadaka attacked them. Rama, aided by Lakshamana, slew her with his arrow. Vishvamitra blessed Rama, as the gods rejoiced in the end of Tadaka. The sage gave him divine weapons as a reward. Vishvamitra then began his six-day yajna, with the princes standing on guard.

While the first five days passed without incident, on the sixth day the sacrificial fire suddenly faltered, indicating trouble. Maricha and his brother Subahu, with a horde of rakshasas, appeared from the treetops like black clouds, roaring and making a thunderous noise. They tried to destroy the yajna fire by showering it with blood and flesh. Rama fired his Astra (weapon) Manavastra (which could hit a target miles away) from his bow. The arrow struck Maricha's chest and threw him a hundred leagues away, into the ocean. In another version, Maricha fled to the ocean just by hearing the sound of Rama's bow. Subahu and the other demons were killed by Rama, using various other weapons. The sacrifice was completed successfully. Later on, under the guidance of Vishvamitra, Rama weds Sita, the adopted daughter of Janaka and the princess of Mithila.

Encounter with Rama in Dandakaranya
Rama, Lakshmana and Sita were exiled for a period of fourteen years from the kingdom by Dasharatha at the behest of Rama's stepmother Kaikeyi. The trio traveled south from Ayodhya and passed through the Dandakaranya (Dandaka forest) to the banks of the Godavari River where they built a hermitage at Panchavati.

Maricha recalls the following incident when talking with Ravana. However, it does not appear as a separate event in the chronological telling of the Ramayana. Maricha returned to Dandakaranya and disguised himself as a beast with a flaming tongue and two sharp horns. He was accompanied by two rakshasas in the form of animals. They feasted on human flesh and traveled to pilgrimage sites, terrorizing ascetics. They would kill ascetics and drink their blood. Once, Maricha saw Rama, Lakshmana and Sita. Remembering his last encounter, Maricha attacked them in his ferocious beast form to seek vengeance with his demonic companions. Rama shot three arrows at once, killing Maricha's allies, but the third arrow narrowly missed Maricha, who fled in fear.

The spared Maricha was transformed into a saintly person. He lived a life of an ascetic. He set up an ashram, grew matted hair and wore tree bark. He gave up his demonic qualities and started to realise his mistakes and became a devotee of Rama by then. At last he will die at the hands of Rama according to Ravana's strategy.

Role as the golden deer
One day, Surpanakha, the rakshasa sister of Ravana, disguised herself as a beautiful maiden and proposed marriage to Rama. Rama refused her proposal and directed her to Lakshmana in jest. Lakshmana joked that she should marry his master Rama. An angry Surpanakha returned to Rama and attacked Sita. But Lakshmana took out his sword and cut off Shurpanakha's ears and nose. The humiliated Surpanakha approached Khara, a man-eating rakshasha, to avenge her with a vendetta against Rama. However, Khara, his general Dushana and his army of 14,000 were killed by Rama when they attacked him. Surpanakha and her maternal uncle, Akampana, who escaped the carnage, reached Lanka with the news and proposed that Ravana steal Sita, Rama's beautiful wife.

Ravana started brooding and thinking of his next course of action. He then flew in his aerial chariot across the sea to meet his ally, Maricha. Maricha lived in a secluded hermitage on the ocean coast. Ravana informed Maricha of the death of Khara, Dushana and their army as well as of the insult of Surpanakha. He told Maricha to turn into a golden deer with silver spots and graze in the vicinity of Rama's ashram. On seeing the deer, Sita would surely tell Rama and Lakshamana to catch it. When the brothers left Sita alone, Ravana would abduct her. Rama, saddened by the grief of Sita's separation, would be easily killed by Ravana. Maricha, who had a first-hand experience of Rama's strength, was horrified by the idea. The wise Maricha attempted to dissuade Ravana by recalling the righteousness and valor of Rama and warned that this idea would only lead to the doom of Ravana, Lanka and the rakshasa race. He narrated his first encounter with Rama, when he underestimated Rama and dismissed him as a boy, how he was thrown hundreds of leagues away by Rama's single arrow. He followed that with the story of his second encounter with Rama in Dandakaranya.

However, Ravana ignored Maricha's words and asked how he dared praise Rama and question the prowess of Ravana, his king. Ravana announced that he would abduct Sita with or without Maricha's help to get revenge for the death of rakshasas. He reiterated his plan and told Maricha to be the golden deer. If successful, he and Maricha would return to Lanka and Ravana would grant half his kingdom to Maricha. Ravana threatened that while his plan might lead to Maricha's death by Rama, Maricha's refusal would mean an instant death at his, Ravana's, hand. Finally Maricha agreed, but not before prophesying his death as well as the end of Ravana, Lanka and rakshasas and warning Ravana that he would suffer the results of dismissing Maricha's words, which were for his own good. Another version states that Maricha felt that death by the divine Rama would be better than one by Ravana. Ravana was pleased by Maricha's consent and embraced him.

Maricha and Ravana then flew to Panchavati in Ravana's chariot and stopped close to the ashram of Rama. Maricha then assumed the form of a beautiful golden deer, which had silver spots and glowed with many gems like sapphire, moonstone, black jet and amethyst on its body. Maricha began grazing in the vicinity of Rama's ashram so that Sita would catch a glimpse of him. As soon as the animal-eating rakshasa Maricha entered the forest in the form of a deer, the other animals smelt something was wrong and ran away in fear. Maricha found Sita collecting flowers and ran in front of her. The golden luster of the deer which was gamboling around the hermitage lured Sita, who was awestruck and called Rama and Lakshmana to see the spectacular animal.

On seeing the wondrous deer, Lakshmana sensed foul play and suggested that the deer was an illusory form of Maricha, who preyed on kings who came into the forest for hunting. Sita persuaded Rama to get her the deer, dead or alive. If caught, she said it could be bred as a pet and taken back to Ayodhya as remembrance of their 14 years exile. Rama said that this deer would die at his hands that day to comply with Sita's wish, or, if it was a magical rakshasa like Maricha – who killed kings and harmed sages – as Lakshmana had said, then too it was his duty to kill the beast. Rama decided to go after the deer and slay it and asked Lakshmana to take care of Sita in the meantime.

Maricha ran, followed by Rama. Maricha led Rama far away from the hermitage, which made Rama very angry. After a long chase, the tired deer stopped in a shady grassland. Rama seized the opportunity and shot it down with his golden arrow. When the dying Maricha was returning to his real form he cried out, "Oh Sita! Oh Lakshmana!", mimicking Rama's voice. Sita fell prey to the ruse and asked Lakshmana to go and search for Rama. When Lakshmana insisted that no one could harm Rama, Sita – still very much worried – implored, and then ordered Lakshmana to go. Lakshmana reluctantly left to look for Rama. With Lakshmana gone, Ravana appeared as a mendicant (Sadhu) and kidnapped Sita as she stepped forward to give him alms. The Ramayana then narrates the tale of how Rama defeats Ravana in Lanka and regains Sita.

title: Maricha


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Lakshmana rekha

Lakshmana Rekha (लक्ष्मण रेखा), in some later versions of the Hindu epic Ramayana, is a line in the soil drawn by Lakshmana. This line is drawn around the dwelling in the forest that he shared with his elder brother, Rama, and Rama's wife, Sita. The line is meant to protect Sita, while he was away searching for Rama. This line is not featured in the original epic by Valmiki.

In the story, Rama goes chasing a golden deer (which is actually the rakshasa Maricha in disguise), and does not return for a long time. When Sita beseeches Lakshmana to depart in search of his brother, the prince, who could not bear to see Sita cry in grief, reluctantly decides to go and search for Rama. However, this is subject to his condition that Sita not cross the protective line that he draws around the dwelling. According to this legend, anybody other than Rama, Sita, and himself who attempted to cross the line would be burnt. Once Lakshmana leaves in search of Rama, the rakshasa king, Ravana, arrives on the site in the form of a mendicant, and asks Sita for alms. Not suspecting the ploy, she unsuspectingly crosses the Lakshmana Rekha to provide alms to him. Ravana promptly kidnaps her and flies her to Lanka upon his Pushpaka Vimana.

The Ramacharitamanas, the popular north Indian rendering of the story of Rama, does not feature the Lakshmana Rekha story in the Aranya Kanda. However, in the Lanka Kanda of the Ramcharitmanas, (35.1) Ravana's wife Mandodari rebukes him on his boisterous claims of valour by hinting that his claims of strength and valour are shallow, for he could not even cross a small line drawn by Rama's younger brother, Lakshmana.

The Radhey Shyam Ramayana mentions that the crossing of Lakshamana Rekha by Sita was done absent-mindedly by an anxious Sita only to honour the Indian tradition of Atithi Devo Bhava : guests are to be accorded the respect of God himself. Sita crosses the boundary only to give alms to Ravana once he insists that the alms cannot be accepted across a barrier as crossing it was against the principle of the free will of the donor.

In local tradition, the line is believed to have been drawn at Panchavati, in the forest of Dandakaranya, which is now part of the city of Nashik in Maharashtra.

Modern use
Lakshmana Rekha, in modern Indian parlance, refers to a strict convention or a rule, never to be broken. See the American Bright-line rule. It often refers to the ethical limits of an action, traversing which may lead to undesirable consequences. Example of use:
 * Constitution is very clear on the roles of the Judiciary and the Legislature, Lok Sabha Speaker  Somnath Chatterjee said; both should not cross the Lakshman Rekha.

license: Creative Commons - Attribution Share-Alike - https://creativecommons.org/licenses/by-sa/4.0/

title: Lakshmana rekha


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Subahu

Subahu (सुबाहु) was a rakshasa featured in the Hindu epic Ramayana.

Story
Subahu was the son of Shambara, a demon slayed by Indra. Subahu, Maricha and Maricha's mother, Tataka, took immense pleasure in harassing the munis of the jungle, especially Vishvamitra, by disrupting their yajnas with rains of flesh and blood.

Vishvamitra approached Dasharatha for help in getting rid of these pestilences. Dasharatha obliged by sending two of his sons, Rama and Lakshmana, to the forest with Vishvamitra, charging them to protect both the sage and his sacrificial fires.

When Subahu and Maricha again attempted to rain flesh and blood on the sage's yajna, Subahu was killed by Rama.

Maricha escaped to Lanka. In the fear of Rama, he lived as a sage but was then ordered by Ravana to trick Rama into hunting him down. Maricha refused and tried to persuade Ravana to not do such a dreadful task but Ravana insisted and threatened to kill him. Maricha eventually decided to be killed by Rama since it was honourable to die at the hands of God rather than Ravana. He was eventually killed by Rama when he took the form of a deer.

title: Subahu


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Equinumerosity

In mathematics, two sets or classes A and B are equinumerous if there exists a one-to-one correspondence (or bijection) between them, that is, if there exists a function from A to B such that for every element y of B, there is exactly one element x of A with f(x) = y. Equinumerous sets are said to have the same cardinality (number of elements). The study of cardinality is often called equinumerosity (equalness-of-number). The terms equipollence (equalness-of-strength) and equipotence (equalness-of-power) are sometimes used instead.

Equinumerosity has the characteristic properties of an equivalence relation. The statement that two sets A and B are equinumerous is usually denoted
 * $$A \approx B \,$$ or $$A \sim B$$, or $$|A|=|B|.$$

The definition of equinumerosity using bijections can be applied to both finite and infinite sets, and allows one to state whether two sets have the same size even if they are infinite. Georg Cantor, the inventor of set theory, showed in 1874 that there is more than one kind of infinity, specifically that the collection of all natural numbers and the collection of all real numbers, while both infinite, are not equinumerous (see Cantor's first uncountability proof). In his controversial 1878 paper, Cantor explicitly defined the notion of "power" of sets and used it to prove that the set of all natural numbers and the set of all rational numbers are equinumerous (an example where a proper subset of an infinite set is equinumerous to the original set), and that the Cartesian product of even a countably infinite number of copies of the real numbers is equinumerous to a single copy of the real numbers.

Cantor's theorem from 1891 implies that no set is equinumerous to its own power set (the set of all its subsets). This allows the definition of greater and greater infinite sets starting from a single infinite set.

If the axiom of choice holds, then the cardinal number of a set may be regarded as the least ordinal number of that cardinality (see initial ordinal). Otherwise, it may be regarded (by Scott's trick) as the set of sets of minimal rank having that cardinality.

The statement that any two sets are either equinumerous or one has a smaller cardinality than the other is equivalent to the axiom of choice.

Cardinality
Equinumerous sets have a one-to-one correspondence between them, and are said to have the same cardinality. The cardinality of a set X is essentially a measure of the number of elements of the set. Equinumerosity has the characteristic properties of an equivalence relation (reflexivity, symmetry, and transitivity):
 * Reflexivity: Given a set A, the identity function on A is a bijection from A to itself, showing that every set A is equinumerous to itself: A ~ A.
 * Symmetry: For every bijection between two sets A and B there exists an inverse function which is a bijection between B and A, implying that if a set A is equinumerous to a set B then B is also equinumerous to A: A ~ B implies B ~ A.
 * Transitivity: Given three sets A, B and C with two bijections f : A → B and g : B → C, the composition g ∘ f of these bijections is a bijection from A to C, so if A and B are equinumerous and B and C are equinumerous then A and C are equinumerous: A ~ B and B ~ C together imply A ~ C.

An attempt to define the cardinality of a set as the equivalence class of all sets equinumerous to it is problematic in Zermelo–Fraenkel set theory, the standard form of axiomatic set theory, because the equivalence class of any non-empty set would be too large to be a set: it would be a proper class. Within the framework of Zermelo–Fraenkel set theory, relations are by definition restricted to sets (a binary relation on a set A is a subset of the Cartesian product A × A), and there is no set of all sets in Zermelo–Fraenkel set theory. In Zermelo–Fraenkel set theory, instead of defining the cardinality of a set as the equivalence class of all sets equinumerous to it one tries to assign a representative set to each equivalence class (cardinal assignment). In some other systems of axiomatic set theory, for example in Von Neumann–Bernays–Gödel set theory and Morse–Kelley set theory, relations are extended to classes.

A set A is said to have cardinality smaller than or equal to the cardinality of a set B, if there exists a one-to-one function (an injection) from A into B. This is denoted |A| ≤ |B|. If A and B are not equinumerous, then the cardinality of A is said to be strictly smaller than the cardinality of B. This is denoted |A| < |B|. If the axiom of choice holds, then the law of trichotomy holds for cardinal numbers, so that any two sets are either equinumerous, or one has a strictly smaller cardinality than the other. The law of trichotomy for cardinal numbers also implies the axiom of choice.

The Schröder–Bernstein theorem states that any two sets A and B for which there exist two one-to-one functions f : A → B and g : B → A are equinumerous: if |A| ≤ |B| and |B| ≤ |A|, then |A| = |B|. This theorem does not rely on the axiom of choice.

Cantor's theorem
Cantor's theorem implies that no set is equinumerous to its power set (the set of all its subsets). This holds even for infinite sets. Specifically, the power set of a countably infinite set is an uncountable set.

Assuming the existence of an infinite set N consisting of all natural numbers and assuming the existence of the power set of any given set allows the definition of a sequence N, P(N), P(P(N)), P(P(P(N))), … of infinite sets where each set is the power set of the set preceding it. By Cantor's theorem, the cardinality of each set in this sequence strictly exceeds the cardinality of the set preceding it, leading to greater and greater infinite sets.

Cantor's work was harshly criticized by some of his contemporaries, for example by Leopold Kronecker, who strongly adhered to a finitist philosophy of mathematics and rejected the idea that numbers can form an actual, completed totality (an actual infinity). However, Cantor's ideas were defended by others, for example by Richard Dedekind, and ultimately were largely accepted, strongly supported by David Hilbert. See Controversy over Cantor's theory for more.

Within the framework of Zermelo–Fraenkel set theory, the axiom of power set guarantees the existence of the power set of any given set. Furthermore, the axiom of infinity guarantees the existence of at least one infinite set, namely a set containing the natural numbers. There are alternative set theories, e.g. "general set theory" (GST), Kripke–Platek set theory, and pocket set theory (PST), that deliberately omit the axiom of power set and the axiom of infinity and do not allow the definition of the infinite hierarchy of infinites proposed by Cantor.

The cardinalities corresponding to the sets N, P(N), P(P(N)), P(P(P(N))), … are the beth numbers $$\beth_0$$, $$\beth_1$$, $$\beth_2$$, $\beth_3$, …, with the first beth number $$\beth_0$$ being equal to $$\aleph_0$$ (aleph naught), the cardinality of any countably infinite set, and the second beth number $$\beth_1$$ being equal to $$\mathfrak c$$, the cardinality of the continuum.

Dedekind-infinite sets
In some occasions, it is possible for a set S and its proper subset to be equinumerous. For example, the set of even natural numbers is equinumerous to the set of all natural numbers. A set that is equinumerous to a proper subset of itself is called Dedekind-infinite.

The axiom of countable choice (ACω), a weak variant of the axiom of choice (AC), is needed to show that a set that is not Dedekind-infinite is actually finite. The axioms of Zermelo–Fraenkel set theory without the axiom of choice (ZF) are not strong enough to prove that every infinite set is Dedekind-infinite, but the axioms of Zermelo–Fraenkel set theory with the axiom of countable choice (ZF + ACω) are strong enough. Other definitions of finiteness and infiniteness of sets than that given by Dedekind do not require the axiom of choice for this, see.

Compatibility with set operations
Equinumerosity is compatible with the basic set operations in a way that allows the definition of cardinal arithmetic. Specifically, equinumerosity is compatible with disjoint unions: Given four sets A, B, C and D with A and C on the one hand and B and D on the other hand pairwise disjoint and with A ~ B and C ~ D then A ∪ C ~ B ∪ D. This is used to justify the definition of cardinal addition.

Furthermore, equinumerosity is compatible with cartesian products: These properties are used to justify cardinal multiplication.
 * If A ~ B and C ~ D then A × C ~ B × D.
 * A × B ~ B × A
 * (A × B) × C ~ A × (B × C)

Given two sets X and Y, the set of all functions from Y to X is denoted by XY. Then the following statements hold: These properties are used to justify cardinal exponentiation.
 * If A ~ B and C ~ D then AC ~ BD.
 * AB ∪ C ~ AB × AC for disjoint B and C.
 * (A × B)C ~ AC × BC
 * (AB)C ~ AB×C

Furthermore, the power set of a given set A (the set of all subsets of A) is equinumerous to the set 2A, the set of all functions from the set A to a set containing exactly two elements.

Categorial definition
In category theory, the category of sets, denoted Set, is the category consisting of the collection of all sets as objects and the collection of all functions between sets as morphisms, with the composition of functions as the composition of the morphisms. In Set, an isomorphism between two sets is precisely a bijection, and two sets are equinumerous precisely if they are isomorphic as objects in Set.

title: Equinumerosity


text:
Talk:Polish notation

Query
This stub is confusing. The notation for existential quantifier ($x)Gx does not seem to match the notation used in the artical.

Also, postfix notation redirects to Reverse Polish Notation

but  Polish notation redirects to prefix notation.

I am tempted to fix this but the stub does not seem to say much on the general concept of prefix notation, and I don't think my maths is up to it. -- Chris Q 09:39, 20 Nov 2003 (UTC)

I've just added the "Query" title here. --Ludvikus 00:10, 13 October 2007 (UTC)

Merits
The following part of the article removed, for clarifications.

This was a piece from article:
 * Polish notation is slightly easier to implement for computers, since the operation is encountered first, then the data to perform the operation comes later. However, people are much more familiar with infix notation.

This is a recent commment added by an anon into the article body:

 * The "easier" part is simply not true, and the argumentation is arbitrary.

 * Reverse Polish notation is, indeed, easier to implement, mainly because we are spared of the need for speculating about the order of operations. "Straight" Polish notation, however, is even a step-back from Infix notation with that respect, if we have to process it in natural (left-to-right) order.

 * The ordering of operands with respect to the operation is of imaginary significance and is completely irrelevant to the ease of implementation "for computers." Note that what comes after the operation is not necessarily "data," but may be another prefix expression.

The remarks are of merit IMO. So, what are real advantages of this notation? See Reverse Polish Notation how they are presented. Mikkalai 19:59, 18 Mar 2005 (UTC)

 * The point was that the original text was misleading, and was most probably due to confusion with RPN. PN is essentially isomorphic to RPN, and can be processed as such from right to left, thus leveraging the benefits of, but offering no advantages over, RPN.

 * --AoS 14:51, 21 Mar 2005 (UTC)

Polish notation is also used for Symbolic Logic, in fact it was invented for this purpose. This fact is ignored in the article. I intend to correct this latter when I can get to my own computer.

Tcl
The note about this being used in Tcl is rather misleading. math in Tcl is in infix notation, but the language syntax is polish notation. Being this is a math article and when I first read the line, I became rather confused at what it meant. Could someone re-word this to read more clearly? I'm unsure how to word it myself. — Striker 22:48, 5 December 2005 (UTC)

Question about sentence

 * The "conventional" notation did not become so until the 1970s and 80s.

Does this mean to say that "The (common OR currently used) notation did not become conventional until the 1970s and 80s." or somesuch? - Centrx 22:59, 21 May 2006 (UTC)

Tone
This page is written in a strange tone. I don't think it's good form to use the word "we" in an article (just as an example). Mo-Al 06:19, 25 June 2006 (UTC)

Polish notation for logic maybe wrong?
I believe that the D operator is not the "nand" (sheffer stroke) operator but the "dubious" operator, which is a unary operator:

Dx = ExNx

That is, when x is equivalent to not-x. This makes sense for the many-valued logics. (See C.I.Lewis and C.H. Langford's Symbolic Logic, (Dover Press, 1959), where they write about Łukasiewicz's 3-valued logic, Ł3.

-RR

Reference to Łukasiewicz Articles
A reference to an article by Łukasiewicz which introduces this system is needed. The notation is used in his works written in the 1920s, though I think that the standard is Elements of Mathematical Logic written 1929.

Is this a mistake?
The article reads : "Although obvious, it is important to note that the number of operands in an expression must equal the number of operators plus one, otherwise the statement makes no sense (assuming only binary operators are used in the expression). This can be easy to overlook when dealing with longer, more complicated expressions with several operators, so care must be taken to double check that an expression makes sense when using Polish notation."

I'm not sure I understand it, can someone please add an explanation or confirm if it's a mistake?

 * It means that the number of things getting operated on is the number of operators + 1. For example, in "+ 1 2", "+" is the operator, and "1" and "2" are the operands. Mo-Al 02:40, 12 August 2006 (UTC)

In a more technically polish way
I'm reading this article, and towards the end it gives examples of association and distribution. For each it offers a more polish way of writing the statement of equivalence, using "=" as a binary operator.

I'm not sure that this use is appropriate, because it renders the equivalence confusing (and I have never seen this usage before... which does not mean it is incorrect, of course). Slightly Drunk 19:58, 4 January 2007 (UTC)

Polish notation vs. Prefix notation
Furthermore, Google shows us the former is far more common.
 * As a formal student of Philosophy and Logic in the United States, I have always known this subject by its former name.
 * Accordingly, I'm recommending that the Title of this Article be changed to the former. Yours truly, --Ludvikus 00:08, 13 October 2007 (UTC)
 * 76,900 Google hits for "Prefix notation": . --Ludvikus 00:14, 13 October 2007 (UTC)
 * 155,000 Google hits for "Polish notation": --Ludvikus 00:17, 13 October 2007 (UTC)
 * Should we also change all occurences of "prefix notation" (but not necessarily "prefix expression") to "Polish notation" in the article? I think we should either do that, or change the "or less frequently known as 'Prefix notation'" in the first sentence to "also known as 'Prefix notation'" (although the former is true, the article doesn't call it that "less frequently" than the alternative). --Spug (talk) 01:04, 12 December 2007 (UTC)
 * I think the article should be called Prefix notation since it is country neutral. Accordingly, Reverse Polish Notation should be Postfix notation. 68.239.247.134 (talk) 05:24, 27 December 2009 (UTC)

Sections "Computer programming" and "Order of operations"
We should probably rewrite these sections; they overlap, and the former describes RPN as used in many stack-based programming languages, while the former says that PN is especially popular with those languages. --Spug (talk) 01:01, 12 December 2007 (UTC)

example is incorrect?
The statement "In the previous example, the parentheses in the infix version were required, since moving them (5 − 6) + 7 or simply removing them 5 − 6 + 7 would change the meaning and result of the overall expression."

This is not true. Addition is associative - the parentheses don't matter! This would be true if addition and multiplication were mixed: 5 - (6 * 7) <> (5 - 6) * 7 Jesse1919 (talk) 03:37, 24 February 2008 (UTC)

Yes, I also think that the example fails to illustrate the point. I will change it to one that mixes addition and multiplication. Borromean-ring (talk) 16:21, 4 May 2008 (UTC)

Polish logic
Polish notation? ==

Is Polish notation also referred to as "Polish logic," or does/can that term have a different meaning? The article Polish Logic, about an anthology, has a hatnote pointing to this article. -- ℜob C. alias ᴀʟᴀʀoʙ 18:39, 7 September 2008 (UTC)

Conversion of Infix to Prefix notation
is there an algorithm to convert infix to prefix? —Preceding unsigned comment added by 72.68.199.83 (talk) 05:04, 3 March 2009 (UTC)
 * Certainly. For example, construct the parse tree of the infix formula, and traverse it in preorder.—Emil J. 15:45, 18 October 2010 (UTC)
 * See Shunting-yard algorithm. —Bkell (talk) 16:19, 18 October 2010 (UTC)

Infix equivalent needlessly complex
The example ((15 / (7 - (1 + 1))) * 3) - (2 + (1 + 1)) uses an unnecessary number of parentheses, (15 / (7 - (1 + 1))) * 3 - (2 + 1 + 1) is, as far as I can tell, the normal equivalent example. If parentheses are used to avoid talking about precedence rules, perhaps this should be noted. Exaggerating the verbosity of infix notation makes the article look biased. Polish notation, especially reverse, is beautiful and clearly much more efficient, so no cheating is needed :). — Preceding unsigned comment added by 83.179.7.128 (talk) 10:41, 18 February 2012 (UTC)
 * The simplified version can be simplified a bit further – the first pair of parens is not necessary, too: 15 / (7 - (1 + 1)) * 3 - (2 + 1 + 1) --CiaPan (talk) 07:03, 1 October 2018 (UTC)

 * As I perceive the example, it is designed to avoid the necessity of applying any precedence rules, not expressed by parentheses. I think this gets especially important in connection with unary operators, where the precedence is not always absolutely clear. Possibly, the whole expression should be parenthesized, too, it would then contain seven (binary) operators (taking "-" as one of them) and seven parens-pairs. Personally, I would prefer to have the "-" as unary, writing ((((15 / (7+(-(1 + 1)))) * 3)) + (-(2 + (1 + 1)))), or more algebraically, introducing the multiplicative inverse as second unary operator, instead of the binary division:
 * $$((((15 * ((7+(-(1 + 1)))))^{-1} * 3)) + (-(2 + (1 + 1)))).$$
 * In this context it is not about simplifying, but about machine-readability, and precedence rules are ugly to implement. Purgy (talk) 07:55, 1 October 2018 (UTC)

Lisp and other 'prefix' languages
The mention of Lisp doesn't seem relevant, because Lisp doesn't use parentheses-free Polish notation even when possible. The Lisp version of infix expression 5 • 2 ÷ 3 + 8 ÷ 7 is (+ (* 5 (/ 2 3)) (/ 8 7)), not + * / 2 3 5 / 8 7. This is in contrast to stack-based, prefix languages like Forth, which really use reverse Polish notation. 152.1.137.158 (talk) 15:06, 15 April 2016 (UTC)

Wrong evaluation algorithm
The current evaluation algorithm that process the expression from left to right is wrong. Counterexample: infix notation: 2*(5*2 + 1) prefix notation: * 2 + * 5 2 1 expected evaluation: 22 obtained evaluation: 12 actually evaluated expression: (2 + 5*2)*1

The "push-down automaton with shift reduce rules" is the correct algorithm for this situation. This algorithm needs a finite state control that keeps track of what is on top of stack, and typically, the current state also need to be pushed on the stack. I guess it may be implemented with a operand counter. It can be a rather complex algorithm, therefore removal may be a better solution. Proto8170 (talk) 07:57, 29 September 2018 (UTC)

 * I'm not really into single stepping this "algorithm", and I also do not want to involve myself in checking your results. I'm also no expert in " shift reduce rules", but introduced the DPDA in the text. Your remarks about the finite control (keeping track, pushing states, operand counter) rather confuse me, and I object to this being a "complex algorithm". I would not object to removing this elaborate example, but in case it is right, some readers might lose a guide. Purgy (talk) 12:42, 1 October 2018 (UTC)

 * You're right, the algorithm is wrong. I did the calculation step-by-step on your example and confirmed your result. Anyway, as far as I can see, the whole section #Explanation as well as #Prefix evaluation algorithm together with its subsection #Example possibly fulfill WP:NOR criteria for what should not appear in Wikipedia. It's a pity, the more I myself expanded some part of them – but they actually remain absolutely unsourced. --CiaPan (talk) 20:40, 1 October 2018 (UTC)

 * With three editors talking about deletion of the example, I simply was bold. However, I object to removing #Explanation as well as the whole former #Prefix evaluation algorithm. It never would come to my mind to consider this as "original research", these are trivial consequences ("simple calculations") of the way the notation is set up, where there are certainly thousands of reliable sources in the wild. I'd assume there must be even a Knuth among them. Purgy (talk) 07:04, 2 October 2018 (UTC)

"Noitaton hsilop" listed at Redirects for discussion
An editor has identified a potential problem with the redirect Noitaton hsilop and has thus listed it for discussion. This discussion will occur at Redirects for discussion/Log/2022 September 7 until a consensus is reached, and readers of this page are welcome to contribute to the discussion. –LaundryPizza03 ( d c̄ ) 02:59, 7 September 2022 (UTC)

Implementations
No love for APL? 2A01:CB0C:CD:D800:D890:8BF2:2502:B9F0 (talk) 07:54, 16 September 2022 (UTC)

"Noitaton Hsilop" listed at Redirects for discussion
An editor has identified a potential problem with the redirect Noitaton Hsilop and has thus listed it for discussion. This discussion will occur at Redirects for discussion/Log/2022 September 16 until a consensus is reached, and readers of this page are welcome to contribute to the discussion. Steel1943 (talk) 22:04, 16 September 2022 (UTC)

title: Talk:Polish notation


text:
Li River (disambiguation)

Li River (漓江) is a river in Guangxi, China, famous for its scenery.

Li River may also refer to:

 * Lishui River (澧水) or Li River, in Hunan, China
 * Li River (Thailand), tributary of the Ping River in Thailand

title: Li River (disambiguation)


text:
Limit ordinal

In set theory, a limit ordinal is an ordinal number that is neither zero nor a successor ordinal. Alternatively, an ordinal λ is a limit ordinal if there is an ordinal less than λ, and whenever β is an ordinal less than λ, then there exists an ordinal γ such that β < γ < λ. Every ordinal number is either zero, or a successor ordinal, or a limit ordinal.

For example, the smallest limit ordinal is ω, the smallest ordinal greater than every natural number. This is a limit ordinal because for any smaller ordinal (i.e., for any natural number) n we can find another natural number larger than it (e.g. n+1), but still less than ω. The next-smallest limit ordinal is ω+ω. This will be discussed further in the article.

Using the von Neumann definition of ordinals, every ordinal is the well-ordered set of all smaller ordinals. The union of a nonempty set of ordinals that has no greatest element is then always a limit ordinal. Using von Neumann cardinal assignment, every infinite cardinal number is also a limit ordinal.

Alternative definitions
Various other ways to define limit ordinals are:
 * It is equal to the supremum of all the ordinals below it, but is not zero. (Compare with a successor ordinal: the set of ordinals below it has a maximum, so the supremum is this maximum, the previous ordinal.)
 * It is not zero and has no maximum element.
 * It can be written in the form ωα for α > 0. That is, in the Cantor normal form there is no finite number as last term, and the ordinal is nonzero.
 * It is a limit point of the class of ordinal numbers, with respect to the order topology. (The other ordinals are isolated points.)

Some contention exists on whether or not 0 should be classified as a limit ordinal, as it does not have an immediate predecessor; some textbooks include 0 in the class of limit ordinals while others exclude it.

Examples
Because the class of ordinal numbers is well-ordered, there is a smallest infinite limit ordinal; denoted by ω (omega). The ordinal ω is also the smallest infinite ordinal (disregarding limit), as it is the least upper bound of the natural numbers. Hence ω represents the order type of the natural numbers. The next limit ordinal above the first is ω + ω = ω·2, which generalizes to ω·n for any natural number n. Taking the union (the supremum operation on any set of ordinals) of all the ω·n, we get ω·ω = ω2, which generalizes to ωn for any natural number n. This process can be further iterated as follows to produce:

 * $$\omega^3, \omega^4, \ldots, \omega^\omega, \omega^{\omega^\omega}, \ldots, \varepsilon_0 = \omega^{\omega^{\omega^{~\cdot^{~\cdot^{~\cdot}}}}}, \ldots$$

In general, all of these recursive definitions via multiplication, exponentiation, repeated exponentiation, etc. yield limit ordinals. All of the ordinals discussed so far are still countable ordinals. However, there is no recursively enumerable scheme for systematically naming all ordinals less than the Church–Kleene ordinal, which is a countable ordinal.

Beyond the countable, the first uncountable ordinal is usually denoted ω1. It is also a limit ordinal.

Continuing, one can obtain the following (all of which are now increasing in cardinality):

 * $$\omega_2, \omega_3, \ldots, \omega_\omega, \omega_{\omega + 1}, \ldots, \omega_{\omega_\omega},\ldots$$

In general, we always get a limit ordinal when taking the union of a nonempty set of ordinals that has no maximum element.

The ordinals of the form ω²α, for α > 0, are limits of limits, etc.

Properties
The classes of successor ordinals and limit ordinals (of various cofinalities) as well as zero exhaust the entire class of ordinals, so these cases are often used in proofs by transfinite induction or definitions by transfinite recursion. Limit ordinals represent a sort of "turning point" in such procedures, in which one must use limiting operations such as taking the union over all preceding ordinals. In principle, one could do anything at limit ordinals, but taking the union is continuous in the order topology and this is usually desirable.

If we use the von Neumann cardinal assignment, every infinite cardinal number is also a limit ordinal (and this is a fitting observation, as cardinal derives from the Latin cardo meaning hinge or turning point): the proof of this fact is done by simply showing that every infinite successor ordinal is equinumerous to a limit ordinal via the Hotel Infinity argument.

Cardinal numbers have their own notion of successorship and limit (everything getting upgraded to a higher level).

Indecomposable ordinals
Additively indecomposable

A limit ordinal α is called additively indecomposable if it cannot be expressed as the sum of β < α ordinals less than α. These numbers are any ordinal of the form $$\omega^\beta$$ for β an ordinal. The smallest is written $$\gamma_0$$, the second is written $$\gamma_1$$, etc.

Multiplicatively indecomposable

A limit ordinal α is called multiplicatively indecomposable if it cannot be expressed as the product of β < α ordinals less than α. These numbers are any ordinal of the form $$\omega^{\omega^\beta}$$ for β an ordinal. The smallest is written $$\delta_0$$, the second is written $$\delta_1$$, etc.

Exponentially indecomposable and beyond

The term "exponentially indecomposable" does not refer to ordinals not expressible as the exponential product (?) of β < α ordinals less than α, but rather the epsilon numbers, "tetrationally indecomposable" refers to the zeta numbers, "pentationally indecomposable" refers to the eta numbers, etc.

title: Limit ordinal


text:
Licchavis of Nepal

The Licchavis of Nepal (also Lichchhavi, Lichavi) was a kingdom which existed in the Kathmandu Valley, Nepal from approximately 450 CE to 750 CE. The Licchavi clan originated from the Licchavis of Vaishali in modern-day Bihar, and conquered the Kathmandu Valley. The Licchavis were ruled by a maharaja, aided by a prime minister and other royal officials, but in practice local communities were controlled by caste councils.

The ruling period of this dynasty was called the Golden Period of Nepal. A table of the evolution of certain Gupta characters used in Licchavi inscriptions prepared by Gautamavajra Vajrācārya can be found online.

Records
It is believed that a branch of the Licchavi clan, having lost their political fortune and military power in Vaishali (Bihar), came to Kathmandu and married with the ruling Queen, Mandeva Shree Vogini of the Nagvanshi clan beginning their rule in Nepal. Source. They also battled with local militias in Chyasal to gain control of Nepal. In the Buddhist Pali canon, the Licchavi are mentioned in a number of discourses, most notably the Licchavi Sutta, the popular Ratana Sutta and the fourth chapter of the Petavatthu. The Mahayana Vimalakirti Sutra also spoke of the city of Vaishali as where the lay Licchavi bodhisattva Vimalakirti was residing.

In the 4th century CE, during the reign of the Gupta emperor Samudragupta, the "Nepalas" are mentioned among the tribes subjugated by him:

"(Samudragupta, whose) formidable rule was propitiated with the payment of all tributes, execution of orders and visits (to his court) for obeisance by such frontier rulers as those of Samataṭa, Ḍavāka, Kāmarūpa, Nēpāla, and Kartṛipura, and, by the Mālavas, Ārjunāyanas, Yaudhēyas, Mādrakas, Ābhīras, Prārjunas, Sanakānīkas, Kākas, Kharaparikas and other (tribes).""

- Lines 22–23 of the Allahabad pillar inscription of Samudragupta (r.c.350-375 CE).

Samudragupta was a son of the Gupta Emperor Chandragupta I and the Licchavi princess Kumaradevi. Gold coins bearing portraits of Chandragupta and Kumaradevi have been discovered at Mathura, Ayodhya, Lucknow, Sitapur, Tanda, Ghazipur, and Varanasi in Uttar Pradesh; Bayana in Rajasthan; and Hajipur in Bihar. The obverse of these coins depicts portraits of Chandragupta and Kumaradevi, with their names in the Gupta script. The reverse shows a goddess seated on a lion, with the legend "Li-ccha-va-yah" ( 𑁊 , "the Lichchhavis").

The earliest known physical record of the kingdom is an inscription of Mānadeva, which dates from 464. It mentions three preceding rulers, suggesting that the Licchavi dynasty began in the late 4th century.

Government
The Licchavi were ruled by a Maharaja ("great king"), who was aided by a prime minister, in charge of the military and of other ministers. Nobles known as samanta influenced the court whilst simultaneously managing their own landholdings and militia. At one point, between approximately 605 and 641, a prime minister called Amshuverma assumed the throne.

The population provided land taxes and conscript labour (vishti) to support the government. Most local administration was performed by village heads or leading families. Many kings ruled but the popular ones were Manadeva, Amshuverma etc.

Economy
The economy was agricultural, relying on rice and other grains as staples. Villages (grama) were grouped into dranga for administration. Lands were owned by the royal family and nobles. Trade was also very important, with many trading settlements.

Domain
Settlements already filled the entire valley during the Licchavi period. Further settlement extended east toward Banepa, west toward Tistung Deurali, and northwest toward present-day Gorkha.

Rulers
The following list was adapted from The Licchavi Kings, by Tamot & Alsop, and is approximate only, especially with respect to dates.
 * 185 Jayavarmā (also Jayadeva I)
 * Vasurāja (also Vasudatta Varmā)
 * c. 400 Vṛṣadeva (also Vishvadeva)
 * c. 425 Shaṅkaradeva I
 * c. 450 Dharmadeva
 * 464-505 Mānadeva I
 * 505-506 Mahīdeva (few sources)
 * 506-532 Vasantadeva
 * Manudeva (probable chronology)
 * 538 Vāmanadeva (also Vardhamānadeva)
 * 545 Rāmadeva
 * Amaradeva
 * Guṇakāmadeva
 * 560-565 Gaṇadeva
 * 567-c. 590 Bhaumagupta (also Bhūmigupta, probably not a king)
 * 567-573 Gaṅgādeva
 * 575/576 Mānadeva II (few sources)
 * 590-604 Shivadeva I
 * 605-621 Aṃshuvarmā
 * 621 Udayadeva
 * 624-625 Dhruvadeva
 * 631-633 Bhīmārjunadeva, Jiṣṇugupta
 * 635 Viṣṇugupta - Jiṣṇugupta
 * 640-641 Bhīmārjunadeva / Viṣṇugupta
 * 643-679 Narendradeva
 * 694-705 Shivadeva II
 * 713-733 Jayadeva II
 * 748-749 Shaṅkaradeva II
 * 756 Mānadeva III
 * 826 Balirāja
 * 847 Baladeva
 * 875–879 Mandeva IV

title: Licchavis of Nepal


text:
Martha Lane Fox

Martha Lane Fox, Baroness Lane-Fox of Soho,  (born 10 February 1973) is a British businesswoman, philanthropist and public servant. She co-founded Last Minute during the dotcom boom of the early 2000s and has subsequently served on public service digital projects. She sits on the boards of WeTransfer and Chanel, as well as being a trustee of The Queen's Commonwealth Trust. She previously served on the board of Channel 4.

She entered the House of Lords as a crossbencher on 26 March 2013, becoming its youngest female member; she was appointed Chancellor of the Open University on 12 March 2014. In October 2019, she was named by media and marketing publication The Drum as the most influential woman in Britain's digital sector from the past quarter of a century.

Education and early life
Born in London, Lane Fox is the daughter of academic and gardening writer Robin Lane Fox, the scion of an English landed gentry family seated at Bramham Park. She was privately eduated at Oxford High School, an all-girls in Oxford, and at Westminster School in London with a coeducational sixth form. She read Ancient and Modern History at the University of Oxford where she was an undergraduate student of Magdalen College, Oxford graduating with a lower second class honours Bachelor of Arts (BA) degree; as per tradition [citation needed], her BA was promoted to a Master of Arts (MA) degree.

Career
Lane Fox joined information technology and media consulting firm Spectrum, where she met Brent Hoberman. In 1998, Lane Fox and Hoberman founded Last Minute, an online travel and gift business. She stepped down as managing director in 2003. Last Minute was bought by Sabre Holdings in 2005.

Following her departure from Last Minute, Lane Fox was tipped to take over day-to-day operations at Selfridges but was involved in a car accident before she could assume that role. At the suggestion of advertising executive Julian Douglas, Fox teamed up with Nick Thistleton to launch karaoke company Lucky Voice. In 2007, Lane Fox joined the board of Marks & Spencer.

From 2009 to 2013, she was the Digital Champion for the UK and helped to create the Government Digital Service – this team launched gov.uk, and was given the task of spearheading a two-year campaign to improve computer literacy. The following year she was assigned to establish the Digital Public Services Unit within the Cabinet Office. and invited to sit on the Cabinet Office Efficiency and Reform Board. The following month Lane Fox was honoured by David Cameron for her "Manifesto for a Networked Nation", a challenge to increase British internet engagement. She resigned from her position as Digital Champion in late 2013.

She entered the House of Lords as a crossbencher on 26 March 2013, becoming its youngest female member. In her maiden speech, she addressed the need for digital literacy in all sectors of the economy. That same year the Open University appointed her Chancellor. In the run-up to the Scottish independence referendum of 2014, Lane Fox signed an open letter opposing Scottish independence.

In 2017, Lady Lane-Fox was appointed a member of the Joint Committee on National Security Strategy. In 2018, she was appointed Non-Executive Director of Chanel as well as Donmar Warehouse and a Trustee of the Queen's Commonwealth Trust. Lane Fox continues to be a Patron of AbilityNet, Reprieve, Camfed and Just for Kids Law. She joined the board of social network Twitter in June 2016. In 2020, Lane Fox was appointed to the board of directors of the company WeTransfer.

Charity work
Lady Lane-Fox is an advocate for such causes as human rights, women's rights, and social justice. In 2007, she founded Antigone, a grant-making trust to support charities based in the United Kingdom. She is a patron of Reprieve, a legal action charity, and CAMFED, an organization dedicated to fighting poverty, HIV, and AIDS in rural Africa through an emphasis on education of young women. She is also patron of the charity Just for Kids Law, which supports children and young people in London, as well as fighting for wider reform on behalf of young people across the UK.

When the telecommunications company Orange withdrew its longstanding support for the Orange Prize, Lane Fox was one of several benefactors, along with Cherie Blair and Joanna Trollope, who offered to sustain the contest until another major sponsor could be found.

Honours and awards
Lane Fox was appointed Commander of the Most Excellent Order of the British Empire (CBE) in the 2013 New Year Honours for "services to the digital economy and charity". In February 2013 she was assessed to be one of the 100 most powerful women in the United Kingdom by Woman's Hour on BBC Radio 4. In the same month it was announced that she was to be created a life peer to sit as a crossbencher in the House of Lords. She was also recognized as one of the BBC's 100 women of 2013.

On 25 March 2013, she was created a Life Peer as Baroness Lane-Fox of Soho, of Soho in the City of Westminster, and was introduced in the House of Lords the next day. On 29 October 2015, Lane Fox was ranked 15th on the Richtopia list of 100 Most Influential British Entrepreneurs. In February 2016, Lane Fox was elected a Distinguished Fellow of BCS, The Chartered Institute for IT, after being nominated by The Duke of Kent.

In October 2019, Lane Fox was named by media and marketing publication The Drum, in association with the Futures Network, Innovate Her and WACL, as the most influential woman in Britain's digital sector from the past quarter of a century. She was elected an Honorary Fellow of the Royal Academy of Engineering in 2023.

Personal life
Lane Fox lives in Marylebone, London, with her partner Chris Gorell Barnes. Their identical twin sons, Milo and Felix, were born in 2016. In May 2004, she was severely injured in a car accident in the tourist resort of Essaouira in Morocco and was flown to England for treatment at John Radcliffe Hospital, Oxford, and later Wellington Hospital in London. She was discharged from hospital in December 2005.

title: Martha Lane Fox


text:
Vanara

In Hinduism, Vanara (वानर) are either monkeys, apes, or a race of forest-dwelling people.

In the epic the Ramayana, the Vanaras help Rama defeat Ravana. They are generally depicted as humanoid apes, or human-like beings.

Etymology
There are three main theories about the etymology of the word "Vanara":

 * Aiyanar suggests that vanara means "monkey" derived from the word vana ("forest"), Literally meaning "belonging to the forest" Monier-Williams says it is probably derived from vanar (lit. "wandering in the forest") and means "forest-animal" or monkey.
 * Devdutt Pattanaik suggests that it derives from the words vana ("forest"), and nara ("man"), thus meaning "forest man" and suggests that they may not be monkeys, which is the general meaning.
 * It may be derived from the words vav and nara, meaning "is it a man?" (meaning "monkey") or "perhaps he is man".

Identification

Although the word Vanara has come to mean "monkey" over the years and the Vanaras are depicted as monkeys in the popular art, their exact identity is not clear. According to the Ramayana, Vanaras were shapeshifters. In the Vanara form, they had beards with extended sideburns, narrowly shaved chin gap, and no moustache. They had a tail and razor-sharp claws. Their skin and skeleton were inforced with an indestructible Vajra, which no earthly element could penetrate. Unlike other exotic creatures such as the rakshasas, the Vanaras do not have a precursor in the Vedic literature. The Ramayana presents them as humans with reference to their speech, clothing, habitations, funerals, weddings, consecrations etc. It also describes their monkey-like characteristics such as their leaping, hair, fur and a tail. Aiyanagar suggests that though the poet of the Ramayana may have known that vanaras were actually forest-dwelling people, he may portrayed them as real monkeys with supernatural powers and many of them as amsas (portions) of the gods to make the epic more "fantastic".

According to one theory, the Vanaras are semi-divine creatures. This is based on their supernatural abilities, as well as descriptions of Brahma commanding other deities to either bear Vanara offspring or incarnate as Vanaras to help Rama in his mission. The Jain re-tellings of Ramayana describe them as a clan of the supernatural beings called the Vidyadharas; the flag of this clan bears monkeys as emblems.

G. Ramdas, based on Ravana's reference to the Vanaras' tail as an ornament, infers that the "tail" was actually an appendage in the dress worn by the men of the Savara tribe. (The female Vanaras are not described as having a tail. ) According to this theory, the non-human characteristics of the Vanaras may be considered artistic imagination. In Sri Lanka, the word "Vanara" has been used to describe the Nittaewos mentioned in the Vedda legends.

In the Ramayana
Vanaras are created by Brahma to help Rama in battle against Ravana. They are powerful and have many godly traits. Taking Brahma's orders, the gods began to parent sons in the zion of Kishkindha (identified with parts of present-day Karnataka, Andhra Pradesh, and Maharashtra). Rama first met them in Dandaka Forest, during his search for Sita. An army of Vanaras helped Rama in his search for Sita, and also in battle against Ravana, Sita's abductor. Nala and Nila built a bridge over the ocean so that Rama and the army could cross to Lanka. As described in the epic, the characteristics of the Vanara include being amusing, childish, mildly irritating, badgering, hyperactive, adventurous, bluntly honest, loyal, courageous, and kind.

Other texts
The Vanaras also appear in other texts, including Mahabharata. The epic Mahabharata describes them as forest-dwelling, and mentions their being encountered by Sahadeva, the youngest Pandava.

Shapeshifting
In the Ramayana, the Vanara Hanuman changes shape several times. For example, while he searches for the kidnapped Sita in Ravana's palaces on Lanka, he contracts himself to the size of a cat, so that he will not be detected by the enemy. Later on, he takes on the size of a mountain, blazing with radiance, to show his true power to Sita.

Notable Vanaras

 * Angada, son of Vali, successor of Sugriva, who helped Rama find his wife Sita
 * Anjana, Hanuman's mother
 * Hanuman, devotee of the god Rama and son of Vayu
 * Kesari, Hanuman's father
 * Mainda and Dvivida, sons of Ashvins
 * Macchanu, son of Hanuman (per the Cambodian and Thai versions)
 * Makardhwaja, son of Hanuman (per the Indian versions)
 * Nala, son of Vishwakarma
 * Nila, son of Agni
 * Rumā, wife of Sugriva
 * Sharabha, son of Parjanya
 * Sugriva, king of Kishkindha, son of Surya
 * Sushena, son of Varuna
 * Taar, son of Brihaspati
 * Tara, wife of Vali
 * Vali, Sugriva's brother and son of Indra

title: Vanara


text:
Poleshuks

The Poleshuks, also known as Polesians (, палешукі, полещуки) are the indigenous population of Polesia (also known as  Polesie and Polissia). Their native speech forms a dialect continuum between the Ukrainian and Belarusian languages and includes recently codified West Polesian, as well as many local variations and sub-dialects.

History
Since the interbellum, the Poleshuks started developing a sense of identity, influenced by the ethnic politics of the Second Polish Republic within the Polesie Voivodeship. The voivodship had the sparsest population and among the lowest levels of prosperity, due to its adverse climatic and agricultural (soil) conditions. A 1923 Polish statistical document said that 38.600 of 880.900 of population in Polesie Voivodeship (about 4%) were identified as Polezhuks, who self-identified their ethnicity in the census as tutejszy ("local"). The document noted that they were using East Slavic dialects, transitional between Ukrainian and Belarusian, sometimes identified as a separate Polesian language. In the 1931 Polish Census the question about ethnicity was replaced with the question about mother tongue. As a result, 62.5% of population identified their language as tutejszy ("local"). (14.5% declared Polish and 10.0% declared Yiddish or Hebrew as mother tongue.) That some respondents declared their language as Belarusian or Ukrainian was interpreted as the formation of the corresponding ethnic consciousness in the area. Currently the ethnic group of Poleshuks is considered one of the distinct cultural and ethnic identities in the area, while most of the population of the Belarusian, Polish and Ukrainian parts of the region of Polesie have assimilated with the respective nations, as well as with Russian ethnos. At the end of the 1980s, there was a minor campaign in Soviet Byelorussia for the creation of a standard written language for the dialect based on the dialects of Polesia launched by Belarusian writer Nikolai Shelyagovich and his associates as part of his activities for the recognition of Poleshuks as a separate ethnicity and for their autonomy. However, they received almost no support and the campaign eventually melted away.

title: Poleshuks


text:
Polesia

Polesia, Polissia, Polesie, or Polesye is a natural (geographic) and historical region in Eastern Europe within the bigger East European Plain, including part of Eastern Poland and the Belarus–Ukraine border region.

Extent
One of the largest forest areas on the continent, Polesia is located in the southwestern part of the Eastern-European Lowland, the Polesian Lowland. On the western side, Polesia originates at the crossing of the Bug River valley in Poland and the Pripyat River valley of Western Ukraine. The swampy areas of central Polesia are known as the Pinsk Marshes (after the major local city of Pinsk). Large parts of the region were contaminated after the Chernobyl disaster and the region now includes the Chernobyl Exclusion Zone and Polesie State Radioecological Reserve, named after the region.

Name
The names Polesia/Polissia/Polesye, etc. may reflect the Slavic root les 'forest', and the Slavic prefix po- 'on, in, along'. Inhabitants of Polesia are called Polishchuks.

History
In ancient times, the areas of today's western and west-central Polesia were inhabited by the people of the Milograd culture, the Neuri.

In the late Middle Ages Polesia became part of the Grand Duchy of Lithuania, following it into the Polish–Lithuanian Commonwealth (1569). Polesia was largely part of Poland from 1921 to 1939, when the country's largest provinces bore that name.'' Polesia has rarely been a separate administrative unit. However, there was a Polesie Voivodeship during the Second Polish Republic, as well as a Polesia Region in Byelorussian SSR. From 1931 to 1944, it was explicitly mentioned as constituent part of the short-lived (Byzantine Rite) Ukrainian Catholic Apostolic Exarchate of Volhynia, Polesia and Pidliashia. Since the end of World War II, the region of Polesie or Polesia has encompassed areas in eastern Poland, southern Belarus, and northwestern Ukraine.

Geography
Polesia is a marshy region lining the Pripyat River (Pripyat Marshes) in Southern Belarus (Brest, Pinsk, Kalinkavichy, Gomel), Northern Ukraine (in the Volyn, Rivne, Zhytomyr, Kyiv and Chernihiv Oblasts), and partly in Poland (Lublin). It is a flatland within the drainage basins of the Western Bug and Prypyat rivers. The two rivers are connected by the Dnieper-Bug Canal, built during the reign of Stanislaus II of Poland, the last king of the Polish–Lithuanian Commonwealth.

Notable tributaries of the Pripyat are the Horyn, Stokhid, Styr, Ptsich, and Yaselda rivers. The largest towns in the Pripyat basin are Pinsk, Stolin, Davyd-Haradok. Huge marshes were reclaimed from the 1960s to the 1980s for farmland.

The region is subdivided into several subregions among which are:
 * Poland
 * Western Polesia
 * Ukraine
 * Volhynian Polissia
 * Little Polissia, a.ka. Lviv Polissia
 * Zhytomyr Polissia
 * Kyiv Polissia
 * Chernihiv Polissia
 * Novhorod-Siverskyi Polissia
 * Belarus
 * Brest Paliessie
 * Zaharodzie
 * Prypiat Paliessie
 * Mazyr Paliessie
 * Homiel Paliessie

Chernobyl disaster
This region suffered severely from the Chernobyl disaster. Huge areas were polluted by radioactive elements. The most polluted part includes the Chernobyl Exclusion Zone and the adjacent Polesie State Radioecological Reserve. Some other areas in the region are considered unsuitable for living as well.

Tourism
The Polish part of the region includes the Polesie National Park (Poleski Park Narodowy), established 1990, which covers an area of 97.6 km2. This and a wider area adjoining it (up to the Ukrainian border) make up the UNESCO-designated West Polesie Biosphere Reserve, which borders a similar reserve (the Shatskiy Biosphere Reserve) on the Ukrainian side. There is also a protected area called Pribuzhskoye-Polesie in the Belarusian part of the region.

The wooden architecture structures in the region were added to the UNESCO World Heritage Tentative List on 30 January 2004 in the Cultural category.

title: Polesia


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Sugriva

Sugriva (सुग्रीव, ), is a character In the ancient Hindu epic Ramayana. He is the younger brother of Vali, whom he succeeded as ruler of the vanara kingdom of Kishkindha. Rumā is his wife. He is a son of Surya, the Hindu deity of the sun. As the king of the vanaras, Sugriva aided Rama in his quest to liberate his wife Sita from captivity at the hands of the rakshasa king Ravana.

Nomenclature
He is also known as Sugriwa, Su-khrip, Sugeep, Sukhreeb, Creole: Soogrim, Sangkip, Sugrīwũdu, Sukkrivan, Thugyeip, Sugreeva or Sugreev. Malayalam:Sugreevan.

Legend
The story of Sugriva is part of Ramayana and in an abbreviated version, is also present in the Mahabharata.

The king of Kishkindha, Vrikshraja, was a divine creature born from Brahma's tilaka. He had the body of a human and face and tail of a monkey. He was instructed to roam the forests and kill demons. One day, Vriksharaja entered an enchanted pond, and was transformed into a beautiful lady, attracting the attention of both Indra and Surya. Soon after, they each sired Vali and Sugriva respectively. Vali and Sugriva were born having brute strength, equal to Indra and Surya.

According to a legend from the Kathasaritsagara, Aruna (Hinduism)the sun,the charioteer of Surya, travelled to Devaloka to see the dance of the apsaras. Since men were not allowed to observe the event, Aruna assumed the feminine form of Arunidevi. Observing the beautiful form of Arunidevi, Indra grew infatuated with her, and a child was soon born to them. On the advice of Indra, Arunidevi took the child to Ahalya, leaving it there before the dawn to be brought up by her. This child became Vali. Aruna reported this incident to Surya, who wished to see his female form of Arunidevi as well. Becoming besotted with her, Surya sired a son from her. The child, Sugriva, would also be raised under the care of Ahalya.

Quarrel between brothers

Vali ruled the kingdom of Kishkindha; his subjects were the vanaras. Tara is his wife. Angada is his son. His son left his house at a very young age and later became a follower of Vaishnavism. A raging demon by the name of Mayavi came to the gates of the capital and challenged Vali to a fight. Vali accepted the challenge, but when he sallied forth, the demon fled in terror into a deep cave. Vali entered the cave in pursuit of the demon, telling Sugriva to wait outside. When Vali did not return and upon hearing demonic shouts in the cave and seeing blood streaming from its mouth, Sugriva concluded that his brother had been slain. With a heavy heart, Sugriva rolled a boulder to seal the cave's opening so as to lock the demon in, returned to Kishkindha, and assumed kingship over the vanaras, taking his brother's wife Tara as his queen. Vali, however, ultimately prevailed in his combat with the demon and returned home. Seeing Sugriva acting as king, he concluded that his brother had betrayed him. Though Sugriva humbly attempted to explain himself, Vali would not listen and exiled Sugriva from the kingdom. To exact his vengeance, Vali forcibly took Sugriva's wife Ruma for his own, and the brothers became bitter enemies. Sugriva went on to live upon the mountain Rishyamukh, the only place on earth that Vali could not tread on. Vali had been previously cursed by Sage Mathanga to be unable to lay a foot on this mountain on pain of death.

Sugriva makes an alliance

In exile, Sugriva made the acquaintance of Rama, the avatar of Vishnu, who is on a quest to rescue his wife Sita from the demon Ravana, king of the rakshasas. Rama promised Sugriva that he would kill Vali and would reinstate Sugriva as the king of the vanaras. Sugriva, in turn, promised to help Rama with his quest.

The Death of Vali

Together, Sugriva and Rama went to seek out Vali. While Rama stood back, Sugriva shouted a challenge and dared him to battle. The brothers rushed at each other, fighting with trees and stones, with fists, nails, and teeth. They were evenly matched and indistinguishable to the observer, until Sugriva's counselor Hanuman, stepped forward and placed a garland of flowers around Sugriva's neck. It is then that Rama emerged with his bow and drove an arrow through Vali's heart. After Vali's death, Sugriva reclaimed the vanara kingdom, took back his first wife, Ruma, and also reclaimed Vali's primary wife, Tara, who became his queen. Her son by Vali, Angada, became the crown prince.

Duel with Lava and Kusha
On Lakshmana's request and after Guru Vasistha's approval, Rama plans to do Ashvamedha yajna. At this auspicious occasion he calls Sugriva along with Angada, Nala, Nila, Jambavantha and Hanuman to come to Ayodhya. Rama greets and hugs Sugriva, Jambavantha and others on their arrival to Ayodhya.

The yajna horse is captured by Lava and Kusha brothers. In the Rama's army the news spreads that two muni kumara's has captured the Yagya's horse. Shatrughana walks and fights with Lava and he is defeated by Lava. Then Lakshamana comes and he is also defeated by Lava due to the fact that he was holding back. Then Bharata asks Rama to give him the permission to go to set horse free from both muni Kumara. Sugriva and Hanuman also request Rama to permit them to go along with Bharata in the battle. Lava and Kusha defeat Bharata and Sugriva and took Hanuman as a prisoner. Hanuman is the only one who knew that Lava and Kusha were sons of his master Rama & Sita and thus allowed himself to be imprisoned by his master's sons.

Retirement
When Rama decided to depart from the world and took samadhi in the Sarayu river, Sugriva also retired from earth and went with his father Surya. He crowned his nephew Angada as the next king of Kishkindha.

Jainism
According to Jain texts, Sugriva is a human being and he took Jain Diksha and attained Moksha from Mangi-Tungi.

Depictions

 * The combat of Sugriva with his brother Vali is a favorite motif of the Khmer sculptors contributing to the Angkorian temples and monuments near Siem Reap in Cambodia.
 * A detailed and moving tympanum at the 10th century Hindu temple of Banteay Srei depicts the combat of the brothers, as well as Rama's intervention and Vali's death in the arms of another vanara.
 * A bas-relief at the 12th-century temple of Angkor Wat shows the fight between the brothers, arrival of Rama and Vali lying on his death-bed, mourned by many other vanaras. Another scene shows Sugriva and Rama entering into their alliance. A large bas-relief depicts the Battle of Lanka between Rama and Sugriva's army of vanaras and Ravana's army of Rakshasas.
 * The fight between Vali and Sugriva is also represented at the lesser-known 13th century Angkorian temple of Preah Pithu.

title: Sugriva


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Palk Strait

The Palk Strait (பாக்கு நீரிணை Pākku Nīriṇai, පෝක් සමුද්‍ර සන්ධිය Pok Samudra Sandhiya) is a strait between the Tamil Nadu state of India and the Jaffna District of the Northern Province of the island nation of Sri Lanka. It connects the Bay of Bengal in the northeast with Palk Bay in the southwest. It is 40 to 85 miles (64 to 137 km) wide and 85 miles long. Several rivers flow into it, including the Vaigai River of Tamil Nadu. The strait is named after Robert Palk, who was a governor of Madras (1755–1763) during the Company Raj period.

The unique feature around Palk Strait is that the waves around it, to its north and south are of high contrast. To the north, the waves of Bay of Bengal are mostly swells waves while that on the south, in Palk Bay, are mostly sea waves. Despite being a sea dominated area, the significant wave heights in Palk Bay regions are relatively low. The average significant wave height in Palk Bay close to Ram Setu is around 0.5 m.

Geography and geology

Palk Bay is studded at its southern end with a chain of low islands and reef shoals that are collectively called Ram Setu or Adam's Bridge. In Hindu Mythology, "Ram Setu" was created by the god Ram. This chain extends between Dhanushkodi on Pamban Island (also known as Rameswaram Island) in Tamil Nadu and Mannar Island in Sri Lanka. The island of Rameswaram is linked to the Indian mainland by the Pamban Bridge.

The strait is relatively shallow. The region around Ram Setu/Adam's Bridge is typically around 1–3 metres deep, while the central part of the strait is typically around 20 metres deep, with the strait reaching a maximum depth of 35 metres.

Due to lowered sea levels during the Last Glacial Period (115,000-11,700 years Before Present) where sea levels reached a maximum of 120 metres below present values, the entirety of the relatively shallow strait was exposed as dry land. Following the rise to present sea levels during the Holocene, by around 7,000 years ago, the strait became submerged.

History
In 1914, there used to be regular trains from Madras/Chennai to Dhanushkodi, a ferry to Talaimannar on Mannar Island, and then a train to Colombo. In 1964, a cyclone destroyed Dhanushkodi and the railway and caused severe damage along the shores of Palk Strait and Palk Bay. Dhanushkodi was not rebuilt and the railway from Talaimannar to Mahawilachchiya in Sri Lanka was given up due to the civil war (It was later completely rebuilt). At least into the 1970s there was a ferry between small piers in Rameswaram and Talaimannar, but this was discontinued. Ferry service briefly resumed around 2010 but at this time there are no passenger connections across the Strait.

Proposed canal
The shallow waters and reefs of the strait make it difficult for large ships to pass through, although fishing boats and small craft carrying coastal trade have navigated the strait for centuries. Large ships must travel around Sri Lanka. Construction of a shipping canal through the strait was first proposed to the British government of India in 1860, and a number of commissions have studied the proposal up to the present day. The most recent study of the Sethusamudram Shipping Canal Project, as it is now called, was an environmental impact assessment and a technical feasibility study commissioned by the Tamil Nadu government in 2004.

However, the plan encountered opposition from various religious circles. The Indian epic poem Ramayana, written thousands of years ago in Sanskrit and an important Hindu text, recounts how Rama, with the help of an army of vanaras, built a bridge of stones across the sea to Lanka to rescue his wife Sita from the Asura king Ravana. The Ram Karmabhoomi movement, encouraged by a NASA satellite photograph of Rama's Setu, was formed to prevent the shipping canal from being built.

Fixed link
The construction of an Undersea Bed Rail tunnel linking India and Sri Lanka has been proposed that will pass below the Palk Strait.

title: Palk Strait


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Nguni languages

The Nguni languages are a group of Bantu languages spoken in southern Africa (mainly South Africa, Zimbabwe and Eswatini) by the Nguni people. Nguni languages include Xhosa, Hlubi, Zulu, Ndebele, and Swati. The appellation "Nguni" derives from the Nguni cattle type. Ngoni (see below) is an older, or a shifted, variant.

It is sometimes argued that the use of Nguni as a generic label suggests a historical monolithic unity of the people in question, where in fact the situation may have been more complex. The linguistic use of the label (referring to a subgrouping of Bantu) is relatively stable.

From an English editorial perspective, the articles "a" and "an" are both used with "Nguni", but "a Nguni" is more frequent and more correct especially if "Nguni" is pronounced as it is suggested.

Classification
Within a subset of Southern Bantu, the label "Nguni" is used both genetically (in the linguistic sense) and typologically (quite apart from any historical significance).

The Nguni languages are closely related, and in many instances different languages are mutually intelligible; in this way, Nguni languages might better be construed as a dialect continuum than as a cluster of separate languages. On more than one occasion, proposals have been put forward to create a unified Nguni language.

In scholarly literature on southern African languages, the linguistic classificatory category "Nguni" is traditionally considered to subsume two subgroups: "Zunda Nguni" and "Tekela Nguni". This division is based principally on the salient phonological distinction between corresponding coronal consonants: Zunda and Tekela  (thus the native form of the name Swati and the better-known Zulu form Swazi), but there is a host of additional linguistic variables that enables a relatively straightforward division into these two substreams of Nguni.

Tekela languages

 * Bhaca
 * Hlubi
 * Lala
 * Nhlangwini
 * Northern Transvaal Ndebele (Sumayela Ndebele)
 * Phuthi
 * Swazi

Zunda languages

 * Matabele (Ndebele)
 * Southern Ndebele (South African Ndebele)
 * Xhosa
 * Zulu

Note: Maho (2009) also lists S401 Old Mfengu†.

Characteristics
The following aspects of Nguni languages are typical:
 * A 5-vowel system, by merging the near-close and close series of Proto-Bantu. (Phuthi has re-acquired a new series of superclose vowels from Sotho)
 * Spreading of high tones to the antepenultimate syllable.
 * A distinction between high and low tones on noun prefixes, indicating different grammatical roles, accompanied in some cases by an overt pre-prefix called the augment.
 * Development of breathy-voiced consonants, acting as depressor consonants.
 * Development of aspirated consonants.
 * Development of click consonants.

Comparative data
Compare the following sentences:

Note: Xhosa $\langletsh\rangle$ = Phuthi $\langletjh\rangle$ = IPA ; Phuthi $\langletsh\rangle$ = ; Zulu $\langlesh\rangle$ = IPA, but in the environment cited here  is "nasally permuted" to. Phuthi $\langlejh\rangle$ = breathy voiced = Xhosa, Zulu $\langlej\rangle$ (in the environment here following the nasal ). Zulu, Swazi, Hlubi $\langleng\rangle$ =.

Note: Phuthi $\langlekg\rangle$ = IPA.

title: Nguni languages