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Bachchan has claimed to have been banned by film press during the emergency years for his family's friendship with Indira Gandhi.
Bachchan has been accused of using the slogan "blood for blood" in the context of the 1984 anti-Sikh riots. Bachchan has denied the allegation. In October 2014, Bachchan was summoned by a court in Los Angeles for "allegedly instigating violence against the Sikh community". Bachchan in an interview with journalist Arnab Goswami offered to fight the case in court and asked the accusers to file the same as also present proof. He was also one of the trustees of the Rajiv Gandhi Foundation.
Humanitarian and social causes.
Bachchan has been involved with many social causes. For example, he donated to clear the debts of nearly 40 beleaguered farmers in Andhra Pradesh and to clear the debts of some 100 Vidarbha farmers. In 2010, he donated to Resul Pookutty's foundation for a medical centre at Kochi, and he has given () to the family of Delhi policeman Subhash Chand Tomar who died after succumbing to injuries during a protest against gang-rape after the 2012 Delhi gang rape case. He founded the Harivansh Rai Bachchan Memorial Trust, named after his father, in 2013. This trust, in association with Urja Foundation, will be powering 3,000 homes in India with electricity through solar energy. In June 2019 he cleared debts of 2100 farmers from Bihar.
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Bachchan was made a UNICEF Goodwill Ambassador for the polio eradication campaign in India in 2002 and an international ambassador in 2005 and a WHO Goodwill Ambassador for awareness of hepatitis in 2017. In 2013, he and his family donated () to a charitable trust, Plan India, that works for the betterment of young girls in India. He also donated () to the Maharashtra Police Welfare Fund in 2013.
Bachchan was the face of the 'Save Our Tigers' campaign that promoted the importance of tiger conservation in India. He supported the campaign by PETA in India to free Sunder, a 14-year-old elephant who was chained and tortured in a temple in Kolhapur, Maharashtra.
In 2014, it was announced that he had recorded his voice and lent his image to the Hindi- and English-language versions of the TeachAids software, an international HIV/AIDS prevention education tool developed at Stanford University. He has been a vocal "brand ambassador" of the Swachh Bharat Mission (SBM) and featured in a few advertisements to promote the campaign.
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In 2020, Bachchan was helping the Government of India promote its public health message concerning COVID-19 before he and some members of his family became infected. He was hospitalised with reported mild symptoms of the disease on 11 July. He was discharged from hospital on 2 August. During the pandemic he lent his support by donating oxygen concentrators and 250 million rupees in various forms.
Personal life.
Bachchan has been married to veteran actress and politician Jaya Bhaduri since 3 June 1973, and together they have two children; Shweta, an author, journalist and former model and Abhishek, an actor and producer. Abhishek married actress Aishwarya Rai, and they have a daughter named Aaradhya.
Shweta is married to businessman Nikhil Nanda, a grandson of Raj Kapoor from the Kapoor family of actors. They have a daughter, Navya Naveli, and a son, Agastya.
Amitabh's family lives in Mumbai in Maharashtra. His younger brother Ajitabh Bachchan is a businessman. He did business and lived in London for a brief period before returning to live in India. He and his family choose to stay away from the limelight. His wife Ramola is a fashion designer and was active in business. Ajitabh has one son, Bhim, and three daughters Naina, Namrata, and Nilima. Naina is married to actor Kunal Kapoor and they have a son.
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Bachchan is famously rumoured to have had an extramarital affair with actress Rekha from the mid-1970s to the early 1980s after they first acted together in "Do Anjaane", and later in the successful films "Khoon Pasina", "Ganga Ki Saugandh", "Muqaddar Ka Sikandar", "Mr. Natwarlal", "Suhaag", "Ram Balram" and ending in "Silsila", though they have both denied it.
In 2006, Bachchan stated that he is a teetotaler and a non-smoker.
In November 2023, Bachchan gifted his bungalow "Prateeksha", located in Juhu, to his daughter Shweta. The bungalow is worth .
Legacy.
Bachchan is widely regarded as one of the greatest and most influential actors in the history of Indian cinema. He earned respect among critics for his memorable performances and charismatic screen presence, and is considered one of the most respected public figures of India. He is referred to as the "Shahenshah of Bollywood", "Star of the Millennium" or "Big B". He inspired many Indian cinema actors, including Rajinikanth, Chiranjeevi, Akshay Kumar, Pawan Kalyan, Prabhas, Manoj Bajpayee, Ajay Devgn, Mohanlal, Ranveer Singh, Allu Arjun and Yash. French director François Truffaut called him a "one-man industry".
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One of the most successful actors of the 1970s and 1980s, Bachchan appeared in "Box Office India"s "Top Actors" list seventeen times from 1975 to 1991. He topped the list sixteen times (1976–1991).
In 1999, Bachchan was voted the "greatest star of stage or screen" in a BBC "Your Millennium" online poll. The organisation noted that "Many people in the western world will not have heard of [him] ... [but it] is a reflection of the huge popularity of Indian films." In October 2003, "Time" magazine dubbed Bachchan as "the Undisputed Godfather of Bollywood". In April 2005, The Walter Reade Theater of Lincoln Center in New York honoured Bachchan with a special tribute, retrospective—titled "Amitabh Bachchan: The Biggest Film Star in the World".<ref name="thedailybeast.com/newsweek"></ref>
In the early 80s, Bachchan authorised the use of his likeness for the comic book character Supremo in a series titled "The Adventures of Amitabh Bachchan". In May 2014, La Trobe University in Australia named a Scholarship after Bachchan. In June 2000, he became the first living Asian to have been modelled in wax at London's Madame Tussauds Wax Museum. Another statue was installed in New York in 2009, Hong Kong in 2011, Bangkok in 2011, Washington, DC in 2012 and Delhi in 2017.
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In March 2010, Bachchan was named on CNN's list of the "top 25 Asian actors of all time". He was named "Hottest Vegetarian male" by PETA India in 2012. He also won the title of "Asia's Sexiest Vegetarian male" in a contest poll run by PETA Asia in 2008.
In Allahabad, the Amitabh Bachchan Sports Complex and Amitabh Bachchan Road are named after him. A government senior secondary school in Saifai, Etawah is called Amitabh Bachchan Government Inter College. There is a waterfall in Sikkim known as Amitabh Bachchan Falls.
In 2022, on the occasion of Bachchan's 80th birthday, a not-for-profit organisation Film Heritage Foundation announced a film festival as a part of his 11 films collection had been screened in 17 cities across the country shown in limited cinemas.
Biographies.
Several books have been written about Bachchan. The following is the listing of books focused on his life career:
Awards and honours.
Apart from industry awards won for his performances throughout the years, Bachchan has received several honours for his achievements in the Indian film industry. In 1991, he became the first artist to receive the Filmfare Lifetime Achievement Award, which was established in the name of Raj Kapoor. Bachchan was crowned as Superstar of the Millennium in 2000 at the Filmfare Awards.
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In 2001, he was honoured with the Actor of the Century award at the Alexandria International Film Festival in Egypt in recognition of his contribution to the world of cinema. Many other honours for his achievements were conferred upon him at several International Film Festivals, including the Lifetime Achievement Award at the 2010 Asian Film Awards.
In 2003, he was conferred with the Honorary Citizenship of the French town of Deauville. The Government of India awarded him with the Padma Shri in 1984, the Padma Bhushan in 2001, the Padma Vibhushan in 2015 and Dadasaheb Phalke Award in 2019. The then-President of Afghanistan awarded him the Order of Afghanistan in 1991 following the shooting of "Khuda Gawah" there. The Government of Madhya Pradesh honoured him with Rashtriya Kishore Kumar Samman for 2002–2003.
France's highest civilian honour, the Officer of the Legion of Honour, was conferred upon him by the French Government in 2007 for his "exceptional career in the world of cinema and beyond". On 27 July 2012, at the age of 69, Bachchan carried the Olympic torch during the last leg of its relay in London's Southwark.
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Allomorph
In linguistics, an allomorph is a variant phonetic form of a morpheme, or in other words, a unit of meaning that varies in sound and spelling without changing the meaning. The term "allomorph" describes the realization of phonological variations for a specific morpheme. The different allomorphs that a morpheme can become are governed by morphophonemic rules. These phonological rules determine what phonetic form, or specific pronunciation, a morpheme will take based on the phonological or morphological context in which it appears.
In English.
English has several morphemes that vary in sound but not in meaning, such as past tense morphemes, plural morphemes, and negative morphemes.
Past tense allomorphs.
For example, an English past tense morpheme is "-ed", which occurs in several allomorphs depending on its phonological environment by assimilating the voicing of the previous segment or the insertion of a schwa after an alveolar stop. A possible set of assimilations is:
The "other than" restrictions above are typical for allomorphy. If the allomorphy conditions are ordered from most restrictive (in this case, after an alveolar stop) to least restrictive, the first matching case usually has precedence. Thus, the above conditions could be rewritten as follows:
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The allomorph does not appear after stem-final although the latter is voiceless, which is then explained by appearing in that environment, together with the fact that the environments are ordered (that is, listed in order of priority). Likewise, the allomorph does not appear after stem-final because the earlier clause for the allomorph has priority. The allomorph does not appear after stem-final voiceless phoneme because the preceding clause for the comes first.
Irregular past tense forms, such as "broke" or "was/were," can be seen as still more specific cases since they are confined to certain lexical items, such as the verb "break," which take priority over the general cases listed above.
Plural allomorphs.
The plural morpheme for regular nouns in English is typically realized by adding an "-s" or "-es" to the end of the noun. However, the plural morpheme actually has three different allomorphs: [-s], [-z], and [-əz]. The specific pronunciation that a plural morpheme takes on is determined by a set of morphological rules such as the following:
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Negative allomorphs.
In English, the negative prefix "in-" has three allomorphs: [ɪn-], [ɪŋ-], and [ɪm-]. The phonetic form that the negative morpheme /ɪn-/ uses is determined by a set of morphological rules; for example:
In Sami languages.
The Sami languages have a trochaic pattern of alternating stressed and unstressed syllables. The vowels and consonants that are allowed in an unstressed syllable differ from those that are allowed in a stressed syllable. Consequently, every suffix and inflectional ending has two forms, and the form that is used depends on the stress pattern of the word to which it is attached. For example, Northern Sami has the causative verb suffix - in which "-" is selected when it would be the third syllable (and the preceding verb has two syllables), and "-" is selected when it would be the third and the fourth syllables (and the preceding verb has three syllables):
The same applies to inflectional patterns in the Sami languages as well, which are divided into even stems and odd stems.
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Stem allomorphy.
Allomorphy can also exist in stems or roots, as in Classical Sanskrit:
There are three allomorphs of the stem, , , and , which are conditioned by the particular case-marking suffixes.
The form of the stem , found in the nominative singular and locative plural, is the etymological form of the morpheme. Pre-Indic palatalization of velars resulted in the variant form , which was initially phonologically conditioned. The conditioning can still be seen in the locative singular form, for which the is followed by the high front vowel .
However, the subsequent merging of and into made the alternation unpredictable on phonetic grounds in the genitive case (both singular and plural) as well as the nominative plural and the instrumental singular. Thus, allomorphy was no longer directly relatable to phonological processes.
Phonological conditioning also accounts for the form in the instrumental plural, in which the assimilates in voicing to the following .
History.
The term was originally used to describe variations in chemical structure. It was first applied to language (in writing) in 1948, by Fatih Şat and Sibel Merve in Language XXIV.
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Allophone
In phonology, an allophone (; from the Greek , , 'other' and , , 'voice, sound') is one of multiple possible spoken soundsor "phones"used to pronounce a single phoneme in a particular language. For example, in English, the voiceless plosive (as in "stop" ) and the aspirated form (as in "top" ) are allophones for the phoneme , while these two are considered to be different phonemes in some languages such as Central Thai. Similarly, in Spanish, (as in "dolor" ) and (as in "nada" ) are allophones for the phoneme , while these two are considered to be different phonemes in English (as in the difference between "dare" and "there").
The specific allophone selected in a given situation is often predictable from the phonetic context, with such allophones being called positional variants, but some allophones occur in free variation. Replacing a sound by another allophone of the same phoneme usually does not change the meaning of a word, but the result may sound non-native or even unintelligible.
Native speakers of a given language perceive one phoneme in the language as a single distinctive sound and are "both unaware of and even shocked by" the allophone variations that are used to pronounce single phonemes.
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History of concept.
The term "allophone" was coined by Benjamin Lee Whorf circa 1929. In doing so, he is thought to have placed a cornerstone in consolidating early phoneme theory. The term was popularized by George L. Trager and Bernard Bloch in a 1941 paper on English phonology and went on to become part of standard usage within the American structuralist tradition.
Complementary and free-variant allophones.
Each time a speaker vocalizes a phoneme, they pronounce it differently from previous iterations. There is debate regarding how real and universal phonemes are (see phoneme for details). Only some of the variation is perceptible to listeners speakers.
There are two types of allophones: complementary allophones and free-variant allophones.
Complementary allophones are not interchangeable. If context requires a speaker to use a specific allophone for a given phoneme (that is, using a different allophone would confuse listeners), the possible allophones are said to be "complementary". Each allophone from a complementary set is used in a specific phonetic context and may be involved in a phonological process.
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Otherwise, allophones are "free-variant"; speakers choose an allophone by habit or preference.
Allotone.
An allotone is a tonic allophone, such as the neutral tone in Standard Mandarin.
Examples.
English.
There are many allophonic processes in English: lack of plosion, nasal plosion, partial devoicing of sonorants, complete devoicing of sonorants, partial devoicing of obstruents, lengthening and shortening vowels, and retraction.
Because the choice among allophones is seldom under conscious control, few people realize their existence. English-speakers may be unaware of differences between a number of (dialect-dependent) allophones of the phoneme :
In addition, the following allophones of /t/ are found in (at least) some dialects of American(ised) English;
However, speakers may become aware of the differences iffor examplethey contrast the pronunciations of the following words:
A flame that is held in front of the lips while those words are spoken flickers more for the aspirated "nitrate" than for the unaspirated "night rate." The difference can also be felt by holding the hand in front of the lips. For a Mandarin-speaker, for whom and are separate phonemes, the English distinction is much more obvious than for an English-speaker, who has learned since childhood to ignore the distinction.
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One may notice the (dialect-dependent) allophones of English such as the (palatal) alveolar "light" of "leaf" as opposed to the velar alveolar "dark" in "feel" found in the U.S. and Southern England. The difference is much more obvious to a Turkish-speaker, for whom and are separate phonemes, than to an English speaker, for whom they are allophones of a single phoneme.
These descriptions are more sequentially broken down in the next section.
Rules for English consonant allophones.
Peter Ladefoged, a renowned phonetician, clearly explains the consonant allophones of English in a precise list of statements to illustrate the language behavior. Some of these rules apply to all the consonants of English; the first item on the list deals with consonant length, items 2 through 18 apply to only selected groups of consonants, and the last item deals with the quality of a consonant.
These descriptive rules are as follows:
Other languages.
There are many examples for allophones in languages other than English. Typically, languages with a small phoneme inventory allow for quite a lot of allophonic variation: examples are Hawaiian and Pirahã. Here are some examples (the links of language names go to the specific article or subsection on the phenomenon):
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Representing a phoneme with an allophone.
Since phonemes are abstractions of speech sounds, not the sounds themselves, they have no direct phonetic transcription. When they are realized without much allophonic variation, a simple broad transcription is used. However, when there are complementary allophones of a phoneme, the allophony becomes significant and things then become more complicated. Often, if only one of the allophones is simple to transcribe, in the sense of not requiring diacritics, that representation is chosen for the phoneme.
However, there may be several such allophones, or the linguist may prefer greater precision than that allows. In such cases, a common convention is to use the "elsewhere condition" to decide the allophone that stands for the phoneme. The "elsewhere" allophone is the one that remains once the conditions for the others are described by phonological rules.
For example, English has both oral and nasal allophones of its vowels. The pattern is that vowels are nasal only before a nasal consonant in the same syllable; elsewhere, they are oral. Therefore, by the "elsewhere" convention, the oral allophones are considered basic, and nasal vowels in English are considered to be allophones of oral phonemes.
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In other cases, an allophone may be chosen to represent its phoneme because it is more common in the languages of the world than the other allophones, because it reflects the historical origin of the phoneme, or because it gives a more balanced look to a chart of the phonemic inventory.
An alternative, which is commonly used for archiphonemes, is to use a capital letter, such as /N/ for [m], [n], [ŋ].
In rare cases, a linguist may represent phonemes with abstract symbols, such as dingbats, to avoid privileging any particular allophone.
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Affix
In linguistics, an affix is a morpheme that is attached to a word stem to form a new word or word form. The main two categories are derivational and inflectional affixes. Derivational affixes, such as "un-", "-ation", "anti-", "pre-" etc., introduce a semantic change to the word they are attached to. Inflectional affixes introduce a syntactic change, such as singular into plural (e.g. "-(e)s"), or present simple tense into present continuous or past tense by adding "-ing", "-ed" to an English word. All of them are bound morphemes by definition; prefixes and suffixes may be separable affixes.
Affixes, infixes and their variations.
Changing a word by adding a morpheme at its beginning is called "prefixation", in the middle is called "infixation", and at the end is called "suffixation".
"Prefix" and "suffix" may be subsumed under the term "adfix", in contrast to "infix."
When marking text for interlinear glossing, as shown in the third column in the chart above, simple affixes such as prefixes and suffixes are separated from the stem with hyphens. Affixes which disrupt the stem, or which themselves are discontinuous, are often marked off with angle brackets. Reduplication is often shown with a tilde. Affixes which cannot be segmented are marked with a back slash.
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Lexical affixes.
Semantically speaking, "lexical affixes" or "semantic affixes", when compared with free nouns, often have a more generic or general meaning. For example, one denoting "water in a general sense" may not have a noun equivalent because all the nouns denote more specific meanings such as "saltwater", "whitewater", etc. (while in other cases the lexical suffixes have become grammaticalized to various degrees.) Although they behave as incorporated noun roots/stems within verbs and as elements of nouns, they never occur as freestanding nouns. Lexical affixes are relatively rare and are used in Wakashan, Salishan, and Chimakuan languages — the presence of these is an areal feature of the Pacific Northwest of North America - where they show little to no resemblance to free nouns with similar meanings. Compare the lexical suffixes and free nouns of Northern Straits Saanich written in the Saanich orthography and in Americanist notation:
Some linguists have claimed that these lexical suffixes provide only adverbial or adjectival notions to verbs. Other linguists disagree, arguing that they may additionally be syntactic arguments just as free nouns are and, thus, equating lexical suffixes with incorporated nouns. Gerdts (2003) gives examples of lexical suffixes in the Halkomelem language (the word order here is verb–subject–object):
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In sentence (1), the verb "wash" is šak’ʷətəs where šak’ʷ- is the root and -ət and -əs are inflectional suffixes. The subject "the woman" is łə słeniʔ and the object "the baby" is łə qeq. In this sentence, "the baby" is a free noun. (The niʔ here is an auxiliary, which can be ignored for explanatory purposes.)
In sentence (2), "baby" does not appear as a free noun. Instead it appears as the lexical suffix -əyəł which is affixed to the verb root šk’ʷ- (which has changed slightly in pronunciation, but this can also be ignored here). The lexical suffix is neither "the baby" (definite) nor "a baby" (indefinite); such referential changes are routine with incorporated nouns.
Orthographic affixes.
In orthography, the terms for affixes may be used for the smaller elements of conjunct characters. For example, Maya glyphs are generally compounds of a "main sign" and smaller "affixes" joined at its margins. These are called "prefixes, superfixes, postfixes," and "subfixes" according to their position to the left, on top, to the right, or at the bottom of the main glyph. A small glyph placed inside another is called an "infix." Similar terminology is found with the conjunct consonants of the Indic alphabets. For example, the Tibetan alphabet utilizes prefix, suffix, superfix, and subfix consonant letters.
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Allegory
As a literary device or artistic form, an allegory is a narrative or visual representation in which a character, place, or event can be interpreted to represent a meaning with moral or political significance. Authors have used allegory throughout history in all forms of art to illustrate or convey complex ideas and concepts in ways that are comprehensible or striking to its viewers, readers, or listeners.
Writers and speakers typically use allegories to convey (semi-) hidden or complex meanings through symbolic figures, actions, imagery, or events, which together create the moral, spiritual, or political meaning the author wishes to convey. Many allegories use personification of abstract concepts.
Etymology.
First attested in English in 1382, the word "allegory" comes from Latin "allegoria", the latinisation of the Greek ἀλληγορία ("allegoría"), "veiled language, figurative", literally "speaking about something else", which in turn comes from ἄλλος ("allos"), "another, different" and ἀγορεύω ("agoreuo"), "to harangue, to speak in the assembly", which originates from ἀγορά ("agora"), "assembly".
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Types.
Northrop Frye discussed what he termed a "continuum of allegory", a spectrum that ranges from what he termed the "naive allegory" of the likes of "The Faerie Queene", to the more private allegories of modern paradox literature.
In this perspective, the characters in a "naive" allegory are not fully three-dimensional, for each aspect of their individual personalities and of the events that befall them embodies some moral quality or other abstraction; the author has selected the allegory first, and the details merely flesh it out.
Classical allegory.
The origins of allegory can be traced at least back to Homer in his "quasi-allegorical" use of personifications of, e.g., Terror (Deimos) and Fear (Phobos) at Il. 115 f. The title of "first allegorist", however, is usually awarded to whoever was the earliest to put forth allegorical interpretations of Homer. This approach leads to two possible answers: Theagenes of Rhegium (whom Porphyry calls the "first allegorist," Porph. Quaest. Hom. 1.240.14–241.12 Schrad.) or Pherecydes of Syros, both of whom are presumed to be active in the 6th century B.C.E., though Pherecydes is earlier and as he, is often presumed to be the, first writer of prose. The debate is complex, since it demands that we observe the distinction between two often conflated uses of the Greek verb "allēgoreīn," which can mean both "to speak allegorically" and "to interpret allegorically."
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In the case of "interpreting allegorically," Theagenes appears to be our earliest example. Presumably in response to proto-philosophical moral critiques of Homer (e.g., Xenophanes fr. 11 Diels-Kranz), Theagenes proposed symbolic interpretations whereby the Gods of the Iliad actually stood for physical elements. So, Hephestus represents Fire, for instance (for which see fr. A2 in Diels-Kranz). Some scholars, however, argue that Pherecydes cosmogonic writings anticipated Theagenes allegorical work, illustrated especially by his early placement of Time (Chronos) in his genealogy of the gods, which is thought to be a reinterpretation of the titan Kronos, from more traditional genealogies.
In classical literature two of the best-known allegories are the Cave in Plato's "The Republic" (Book VII) and the story of the stomach and its members in the speech of Menenius Agrippa (Livy ii. 32).
Among the best-known examples of allegory, Plato's Allegory of the Cave, forms a part of his larger work "The Republic." In this allegory, Plato describes a group of people who have lived chained in a cave all of their lives, facing a blank wall (514a–b). The people watch shadows projected on the wall by things passing in front of a fire behind them and begin to ascribe forms to these shadows, using language to identify their world (514c–515a). According to the allegory, the shadows are as close as the prisoners get to viewing reality, until one of them finds his way into the outside world where he sees the actual objects that produced the shadows. He tries to tell the people in the cave of his discovery, but they do not believe him and vehemently resist his efforts to free them so they can see for themselves (516e–518a). This allegory is, on a basic level, about a philosopher who upon, finding greater knowledge outside the cave of human understanding, seeks to share it as is his duty, and the foolishness of those who would ignore him because they think themselves educated enough.
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In Late Antiquity Martianus Capella organized all the information a fifth-century upper-class male needed to know into an allegory of the wedding of Mercury and "Philologia", with the seven liberal arts the young man needed to know as guests. Also, the Neoplatonic philosophy developed a type of allegorical reading of Homer and Plato. As scholars of allegory point out, ”the literal reading of a text has its counter-part in allegorical interpretation. This way of reading, which must have started with the first readers of Homer and found a fertile ground in Philo's allegorical commentaries on the Bible, was amazingly natural for Proclus, whose writings and commentaries represent the last phases of late antique philosophy, and particularly of the relation between philosophy and rhetoric.”
Biblical allegory.
Other early allegories are found in the Hebrew Bible, such as the extended metaphor in Psalm 80 of the vine and its impressive spread and growth, representing Israel's conquest and population of the Promised Land. Also allegorical is Ezekiel 16 and 17, wherein the capture of that same vine by the mighty Eagle represents Israel's exile to Babylon.
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Allegorical interpretation of the Bible was a common early Christian practice and continues. For example, the recently re-discovered Fourth Commentary on the Gospels by Fortunatianus of Aquileia has a comment by its English translator: "The principal characteristic of Fortunatianus' exegesis is a figurative approach, relying on a set of concepts associated with key terms in order to create an allegorical decoding of the text."
Medieval allegory.
Allegory has an ability to freeze the temporality of a story, while infusing it with a spiritual context. Medieval thinking accepted allegory as having a "reality" underlying any rhetorical or fictional uses. The allegory was as true as the facts of surface appearances. Thus, the Papal Bull "Unam Sanctam" (1302) presents themes of the unity of Christendom with the pope as its head in which the allegorical details of the metaphors are adduced as facts on which is based a demonstration with the vocabulary of logic: ""Therefore" of this one and only Church there is one body and one head—not two heads as if it were a monster... If, then, the Greeks or others say that they were not committed to the care of Peter and his successors, they "necessarily" confess that they are not of the sheep of Christ." This text also demonstrates the frequent use of allegory in religious texts during the Medieval Period, following the tradition and example of the Bible.
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In the late 15th century, the enigmatic "Hypnerotomachia", with its elaborate woodcut illustrations, shows the influence of themed pageants and masques on contemporary allegorical representation, as humanist dialectic conveyed them.
The denial of medieval allegory as found in the 12th-century works of Hugh of St Victor and Edward Topsell's "Historie of Foure-footed Beastes" (London, 1607, 1653) and its replacement in the study of nature with methods of categorisation and mathematics by such figures as naturalist John Ray and the astronomer Galileo is thought to mark the beginnings of early modern science.
Modern allegory.
Since meaningful stories are nearly always applicable to larger issues, allegories may be read into many stories which the author may not have recognized. This is allegoresis, or the act of reading a story as an allegory. Examples of allegory in popular culture that may or may not have been intended include the works of Bertolt Brecht, and even some works of science fiction and fantasy, such as "The Chronicles of Narnia" by C. S. Lewis.
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The story of the apple falling onto Isaac Newton's head is another famous allegory. It simplified the idea of gravity by depicting a simple way it was supposedly discovered. It also made the scientific revelation well known by condensing the theory into a short tale.
Poetry and fiction.
While allegoresis may make discovery of allegory in any work, not every resonant work of modern fiction is allegorical, and some are clearly not intended to be viewed this way. According to Henry Littlefield's 1964 article, L. Frank Baum's "The Wonderful Wizard of Oz", may be readily understood as a plot-driven fantasy narrative in an extended fable with talking animals and broadly sketched characters, intended to discuss the politics of the time. Yet, George MacDonald emphasized in 1893 that "A fairy tale is not an allegory."
J. R. R. Tolkien's "The Lord of the Rings" is another example of a well-known work mistakenly perceived as allegorical, as the author himself once stated, "...I cordially dislike allegory in all its manifestations, and always have done so since I grew old and wary enough to detect its presence. I much prefer history – true or feigned – with its varied applicability to the thought and experience of readers. I think that many confuse applicability with allegory, but one resides in the freedom of the reader, and the other in the purposed domination of the author."
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Tolkien specifically resented the suggestion that the book's One Ring, which gives overwhelming power to those possessing it, was intended as an allegory of nuclear weapons. He noted that, had that been his intention, the book would not have ended with the Ring being destroyed but rather with an arms race in which various powers would try to obtain such a Ring for themselves. Then Tolkien went on to outline an alternative plot for "Lord of The Rings", as it would have been written had such an allegory been intended, and which would have made the book into a dystopia. While all this does not mean Tolkien's works may not be treated as having allegorical themes, especially when reinterpreted through postmodern sensibilities, it at least suggests that none were conscious in his writings. This further reinforces the idea of forced allegoresis, as allegory is often a matter of interpretation and only sometimes of original artistic intention.
Like allegorical stories, allegorical poetry has two meanings – a literal meaning and a symbolic meaning.
Some unique specimens of allegory can be found in the following works:
Art.
Some elaborate and successful specimens of allegory are to be found in the following works, arranged in approximate chronological order:
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Allotropy
Allotropy or allotropism () is the property of some chemical elements to exist in two or more different forms, in the same physical state, known as allotropes of the elements. Allotropes are different structural modifications of an element: the atoms of the element are bonded together in different manners.
For example, the allotropes of carbon include diamond (the carbon atoms are bonded together to form a cubic lattice of tetrahedra), graphite (the carbon atoms are bonded together in sheets of a hexagonal lattice), graphene (single sheets of graphite), and fullerenes (the carbon atoms are bonded together in spherical, tubular, or ellipsoidal formations).
The term "allotropy" is used for elements only, not for compounds. The more general term, used for any compound, is polymorphism, although its use is usually restricted to solid materials such as crystals. Allotropy refers only to different forms of an element within the same physical phase (the state of matter, such as a solid, liquid or gas). The differences between these states of matter would not alone constitute examples of allotropy. Allotropes of chemical elements are frequently referred to as "polymorphs" or as "phases" of the element.
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For some elements, allotropes have different molecular formulae or different crystalline structures, as well as a difference in physical phase; for example, two allotropes of oxygen (dioxygen, O2, and ozone, O3) can both exist in the solid, liquid and gaseous states. Other elements do not maintain distinct allotropes in different physical phases; for example, phosphorus has numerous solid allotropes, which all revert to the same P4 form when melted to the liquid state.
History.
The concept of allotropy was originally proposed in 1840 by the Swedish scientist Baron Jöns Jakob Berzelius (1779–1848). The term is derived . After the acceptance of Avogadro's hypothesis in 1860, it was understood that elements could exist as polyatomic molecules, and two allotropes of oxygen were recognized as O2 and O3. In the early 20th century, it was recognized that other cases such as carbon were due to differences in crystal structure.
By 1912, Ostwald noted that the allotropy of elements is just a special case of the phenomenon of polymorphism known for compounds, and proposed that the terms allotrope and allotropy be abandoned and replaced by polymorph and polymorphism. Although many other chemists have repeated this advice, IUPAC and most chemistry texts still favour the usage of allotrope and allotropy for elements only.
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Differences in properties of an element's allotropes.
Allotropes are different structural forms of the same element and can exhibit quite different physical properties and chemical behaviours. The change between allotropic forms is triggered by the same forces that affect other structures, i.e., pressure, light, and temperature. Therefore, the stability of the particular allotropes depends on particular conditions. For instance, iron changes from a body-centered cubic structure (ferrite) to a face-centered cubic structure (austenite) above 906 °C, and tin undergoes a modification known as tin pest from a metallic form to a semimetallic form below 13.2 °C (55.8 °F). As an example of allotropes having different chemical behaviour, ozone (O3) is a much stronger oxidizing agent than dioxygen (O2).
List of allotropes.
Typically, elements capable of variable coordination number and/or oxidation states tend to exhibit greater numbers of allotropic forms. Another contributing factor is the ability of an element to catenate.
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Examples of allotropes include:
Metals.
Among the metallic elements that occur in nature in significant quantities (56 up to U, without Tc and Pm), almost half (27) are allotropic at ambient pressure: Li, Be, Na, Ca, Ti, Mn, Fe, Co, Sr, Y, Zr, Sn, La, Ce, Pr, Nd, Sm, Gd, Tb, Dy, Yb, Hf, Tl, Th, Pa and U. Some phase transitions between allotropic forms of technologically relevant metals are those of Ti at 882 °C, Fe at 912 °C and 1,394 °C, Co at 422 °C, Zr at 863 °C, Sn at 13 °C and U at 668 °C and 776 °C.
Most stable structure under standard conditions.<br>
Structures stable below room temperature.<br>
Structures stable above room temperature.<br>
Structures stable above atmospheric pressure.
Nanoallotropes.
In 2017, the concept of nanoallotropy was proposed. Nanoallotropes, or allotropes of nanomaterials, are nanoporous materials that have the same chemical composition (e.g., Au), but differ in their architecture at the nanoscale (that is, on a scale 10 to 100 times the dimensions of individual atoms). Such nanoallotropes may help create ultra-small electronic devices and find other industrial applications. The different nanoscale architectures translate into different properties, as was demonstrated for surface-enhanced Raman scattering performed on several different nanoallotropes of gold. A two-step method for generating nanoallotropes was also created.
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Agathocles of Syracuse
Agathocles (, "Agathoklḗs"; 361–289 BC) was a tyrant of Syracuse from 317 BC and king of much of Sicily from 304 BC until his death. Agathocles began his career as a military officer, and raised his profile as a supporter of the democratic faction in Syracuse against the oligarchic civic government. His opponents forced him into exile and he became a mercenary leader. He eventually made his way back to Syracuse and was elected as a general. A few years later he took control through a coup d'état. In practice he was a tyrant, although a democratic constitution theoretically remained in force.
Agathocles had led a long, costly war against the Carthaginians, who ruled the western half of Sicily between 311 and 306 BC. In a military campaign he led the invasion of Carthage's North African heartland in 310 BC. After initial successes he abandoned his army in Africa and returned to Sicily in 307 BC, where he made peace with the Carthaginians and restored the "status quo ante bellum". He then assumed the royal title and managed to bring almost the entire Greek portion of Sicily, and part of Calabria, under his control. Agathocles came close to of bringing the entirety of Magna Graecia under his control but his attempt to establish a dynasty fell apart as a result of conflict within his family.
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Biography.
Agathocles was a son of Carcinus, who came from Rhegium. Carcinus was expelled from his hometown, so he migrated to Thermae Himeraeae and married a local citizen woman. Thermae, which was located on the north coast of Sicily, belonged to the western part of the island, which was under Carthaginian control. The couple had two sons, Antander and Agathocles. In 343 BC, when Agathocles was around eighteen years old, the family re-settled in Syracuse. Carcinus had answered a call from the commander Timoleon, which had overthrown the tyrannical regime of Dionysius II. Timoleon sought new citizens for the city, which had been depopulated by the civil wars. Thus, Carcinus and Agathocles acquired Syracusan citizenship. According to the sources, Carcinus was a potter and Agathocles followed him in his profession. Modern historians generally argue that he must have been a wealthy man who owned a pottery workshop. In later times, Agathocles frequently advertised his lower class origins and used them as part of his self-presentation as a ruler, since performative modesty and presenting himself as a man of the people would be important parts of his persona.
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Agathocles began his military career during Timoleon's rule. He initially served as a soldier and then as an officer. Later, after Timoleon's death in 337 BC, Agathocles participated in an expedition against Acragas and began a relationship with the general, Damas, who promoted him to chiliarch. After Damas' death, Agathocles married his widow. This made him one of the richest men in Syracuse, which gave him a good platform to begin his political ascent.
After Timoleon's death, Syracuse descended into the traditional conflict between democrats and oligarchs. The oligarchs had the upper hand and ruled the city as a club, called "the Six Hundred." Agathocles' elder brother, Antander, was elected to a generalship, during this period, so he must have had good relationships with members of the ruling circle. Agathocles, on the other hand, spoke in the people's assembly and placed himself on the side of the opposition democrats, but he was unable to overcome their power. After a successful campaign to defend Croton in southern Italy from the Bruttii, he denied an award for bravery which he felt he had earnt. After this, he openly opposed the government and openly accused the leading oligarchs, Sosistratus and Heracleides, of seeking to become tyrants. These accusations were not successful and the two oligarchs solidified their power. Agathocles' situation in Syracuse was then untenable and he declared that he was compelled to leave the city. This does not necessarily mean that he was formally exiled.
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Double exile.
Agathocles went to southern Italy, where he led the life of a mercenary captain. At the same time, he built up an independent power base, as preparation for a return to Syracuse. His first military effort was a failure, however: he attempted to bring the major city of Croton in Calabria under his control by force, probably in alliance with the local democrats, but he was completely defeated and had to flee with his surviving followers to Tarentum. The Tarentines accepted him into their mercenary forces, but they distrusted him because of his ambition and plots, which led to his dismissal. After this, he gathered together democrats who had been expelled from their cities by local oligarchs. An opportunity appeared at Rhegium, the hometown of Agathocles' father. There, the democrats were in power, but the city was attacked by forces led by the Syracusan oligarchs, who wanted to help the local oligarchs take power by force. Agathocles defeated this Syracusan expeditionary force, which destabilised Sosistratus and Heracleides' position in Syracuse and as a result they were overthrown in a coup. The democrats returned to power and drove the leading oligarchs out of Syracuse. The exiled oligarchs allied themselves with the Carthaginians. These developments allowed Agathocles to return home around 322 BC.
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Agathocles distinguished himself in the subsequent battles against the Carthaginians and oligarchs, but did not manage to acquire a leading position in the city. Instead, the Syracusans chose to request a commander from their mother city, Corinth, in accordance with a law established by Timoleon. The Corinthians sent one Acestorides, who organised an amnesty for the oligarchs, made peace with the Carthaginians, and exiled Agathocles. The radical democrats were forced out and a moderate oligarchy was established. Acestorides even attempted to have Agathocles assassinated. Agathocles established a private army, apparently funded from his own assets. He took advantage of the fact that the Syracusans were considered oppressive by other cities in Sicily and successfully presented himself as a supporter of these cities' interests against the Syracusans. He managed to take over Leontini and even led an attack on Syracuse. The situation became so tenuous for the oligarchs in Syracuse that they reached out to the Carthaginians for help.
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Agathocles outpaced the oligarchs. He negotiated with the Carthaginian commander in Sicily, Hamilcar, and convinced him to withdraw. Allegedly, they had concluded a personal agreement to support each other in establishing themselves as sole rulers of their respective cities. After the loss of Carthaginian support, Syracuse was isolated. The citizens, who did not really wish to fight for oligarchy, agreed to allow Agathocles to return home. He swore the Syracuse "great oath", promising that he would not establish a tyranny. After that, he was elected commander in chief of the Syracusan army in 319/318 BC.
Seizure of power.
The position of Agathocles within the city of Syracuse was initially that of a regular military commander, with wide but limited powers. His title was General and Guardian of the Peace (). In Syracuse, the surviving oligarchs banded together as "The Six Hundred" and continued to oppose him. Agathocles took advantage of the conflicts between the Syracusans and the non-Greek Sicels and between the rich and poor within Syracuse to overcome these opponents. On the pretext of taking military action against external enemies, he was able to gather a powerful force, which was loyal only to him, without raising suspicion.
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In 317/6 or 316/5 BC, Agathocles used this force to launch a coup. At a meeting that the leading members of the opposition party had been invited to, he accused around forty of the oligarchs there of planning an attack on him and had them arrested and executed on the spot. His trumpeters gave the sign for battle and a general slaughter took place in the city, in which the wealthy and their supporters were the main victims. Their houses were plundered. According to Diodorus Siculus's account, over 4,000 people were killed, purely because they belonged to the upper class. More than 6,000 people escaped from the city, even though the gates had been locked. They mostly fled to Agrigentum.
Finally, Agathocles called an assembly of the people, in which he presented himself as a saviour of democracy in the face of the oligarchs and announced that he would retire from his position and return to private life. His followers responded by calling on him to take over the leadership of the state. He responded that he was willing to be general once more, but only if he could hold the role without any colleagues, as General with unlimited power (). This was the title that the earlier ruler Dionysius I had used as the legal basis for his tyranny. The people elected him to this position and also entrusted him with a general "management of the city" (). After this he announced a cancellation of debts and redistribution of the land, two planks of the traditional populist programme.
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Rulership.
War with Carthage followed. In 311 BC Agathocles was defeated in the Battle of the Himera River and besieged in Syracuse. In 310 BC he made a desperate effort to break through the blockade and attack Carthage. He landed at Cape Bon in August 310 BC, and was able to defeat the Carthaginians for the first time, and establish a camp near Tunis. He then turned east and tried to take over coastal trading cities such as Neapolis and Hadrumetum, and on this occasion concluded an alliance with Ailymas, king of the Libyans according to Diodorus of Sicily, in an attempt to surround and isolate Carthage. After capturing Hadrumetum, Thapsus and other coastal towns, Agathocles turned his attention to central Tunisia. Before or during this campaign, he broke his alliance with Ailymas, whom he pursued and killed, but he kept his Numidian army, including war chariots they built.
In 309/8 BC, Agathocles began trying to sway Ophellas, ruler of Cyrenaica, as he was likely to prove a useful ally in Agathocles' war against the Carthaginians. To gain his allegiance, he promised to cede to Ophellas whatever conquests their combined forces might make in Africa, reserving to himself only the possession of Sicily. Ophellas gathered a powerful army from the homeland of his wife Euthydike (a descendant of Miltiades), Athens, where many citizens felt disgruntled after having lost their voting rights. Despite the natural obstacles that presented themselves on his route, Ophellas succeeded in reaching the Carthaginian territories after a toilsome and perilous march of more than two months. He was received by Agathocles with every demonstration of friendship, and the two armies encamped near each other, but a few days later, Agathocles betrayed his new ally by attacking the camp of the Cyrenaeans and having Ophellas killed. The Cyrenean troops, left without a leader, went over to Agathocles.
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After several victories, he was finally completely defeated (307 BC) and fled secretly to Sicily. After concluding peace with Carthage in 306 BC, Agathocles styled himself king of Sicily in 304 BC, and established his rule over the Greek cities of the island more firmly than ever. A peace treaty with Carthage left him in control of Sicily east of the Halycus River. Even in his old age, he displayed the same restless energy and is said to have been contemplating a fresh attack on Carthage at the time of his death.
His last years were plagued by ill health and the attempted usurpation of his throne by his grandson Archagathus, whom Diodorus Siculus states had him poisoned; however Justinius and the majority of modern historians assert he died a natural death (presumably from cancer of the jaw). He was a born leader of mercenaries, and he did not shrink from cruelty for the purposes to royal power. Agathocles restored the Syracusan democracy on his deathbed and did not want his grandson to succeed him as king.
Family.
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Agathocles was married three times. His first wife was the widow of his patron Damas, by whom he had two sons:
Agathocles' second wife was Alcia, with whom he had two children:
Agathocles' third wife was Theoxena, who was the second daughter of Berenice I and her first husband Philip and thus a stepdaughter of Ptolemy I Soter, king of Egypt. She escaped to Egypt with their two children following Agathocles' death in 289 BC:
Legacy.
Agathocles was cited as an example "Of those who become princes through their crimes" in chapter 8 of Niccolò Machiavelli's treatise on politics - "The Prince" (1513).
He was described as behaving as a criminal at every stage of his career. Machiavelli claimed:
Machiavelli goes on to reason that Agathocles' success, in contrast to other criminal tyrants, was due to his ability to commit his crimes quickly and ruthlessly, and states that cruelties are best used when they
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Economy of Alberta
The economy of Alberta is the sum of all economic activity in Alberta, Canada's fourth largest province by population. Alberta's GDP in 2018 was CDN$338.2 billion.
Although Alberta has a presence in many industries such as agriculture, forestry, education, tourism, finance, and manufacturing, the politics and culture of the province have been closely tied to the production of fossil energy since the 1940s. Alberta—with an estimated 1.4 billion cubic metres of unconventional oil resource in the bituminous oil sands—leads Canada as an oil producer.
In 2018, Alberta's energy sector contributed over $71.5 billion to Canada's nominal gross domestic product. According to Statistics Canada, in May 2018, the oil and gas extraction industry reached its highest proportion of Canada's national GDP since 1985, exceeding 7% and "surpass[ing] banking and insurance" with extraction of non-conventional oil from the oilsands reaching an "impressive", all-time high in May 2018. With conventional oil extraction "climbed up to the highs from 2007", the demand for Canadian oil was strong in May.
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From 1990 to 2003, Alberta's economy grew by 57% compared to 43% for all of Canada—the strongest economic growth of any region in Canada. In 2006 Alberta's per capita GDP was higher than all US states, and one of the highest figures in the world. In 2006, the deviation from the national average was the largest for any province in Canadian history. Alberta's per capita GDP in 2007 was by far the highest of any province in Canada at C$74,825 (approx. US$75,000). Alberta's per capita GDP in 2007 was 61% higher than the Canadian average of C$46,441 and more than twice that of all the Maritime provinces. From 2004 to 2014 Alberta's "exports of commodities rose 91%, reaching $121 billion in 2014" and 500,000 new jobs were created. In 2014, Alberta's real GDP by expenditure grew by 4.8%, the strongest growth rate among the provinces." In 2017, Alberta's real per capita GDP—the economic output per person—was $71,092, compared to the Canadian average of $47,417. In 2016, Alberta's A grade on its income per capita was based on the fact that it was almost "identical" to that of the "top peer country"—Ireland.
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The energy industry provided 7.7% of all jobs in Alberta in 2013, and 140,300 jobs representing 6.1% of total employment of 2,286,900 in Alberta in 2017. The unemployment rate in Alberta peaked in November 2016 at 9.1%. Its lowest point in a ten-year period from July 2009 to July 2019, was in September 2013 at 4.3%. The unemployment rate in the spring of 2019 in Alberta was 6.7% with 21,000 jobs added in April. By July 2019, the seasonally adjusted unemployment rate had increased to 7.0%.
By August 2019, the employment number in Alberta was 2,344,000, following the loss of 14,000 full-time jobs in July, which represented the "largest decline" in Canada according to Statistics Canada.
Beginning in June 2014, the record high volume of worldwide oil inventories in storage—referred to as a global oil glut—caused crude oil prices to collapse at near ten-year low prices. By 2016 West Texas Intermediate (WTI)—the benchmark light, sweet crude oil—reached its lowest price in ten years—US$26.55. In 2012 the price of WTI had reached US$125 and in 2014 the price was $100. By February 2016 the price of Western Canadian Select WCS—the Alberta benchmark heavy crude oil—was US$14.10—the cheapest oil in the world.
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By 2016 West Texas Intermediate (WTI)—the benchmark light, sweet crude oil—reached its lowest price in ten years—US$26.55. In 2012 the price of WTI had reached US$125 and in 2014 the price was $100. By February 2016 the price of Western Canadian Select WCS—the Alberta benchmark heavy crude oil—was US$14.10—the cheapest oil in the world. Alberta boom years from 2010 to 2014 ended with a "long and deep" recession that began in 2014, driven by low commodity pricing ended in 2017. By 2019—five years later—Alberta was still in recovery. Overall, there were approximately 35,000 jobs lost in mining, oil and gas alone. Since 2014, sectors that offered high-wage employment of $30 and above, saw about 100,000 jobs disappear—"construction (down more than 45,000 jobs), mining, oil and gas (down nearly 35,000), and professional services (down 18,000)," according to the economist, Trevor Tombe. There was a decrease in wages, in the number of jobs, and in the number of hours worked. The total loss of incomes from "workers, business, and government" amounted to about 20 percent or about CDN$75 billion less per year. The total loss of incomes from "workers, business, and government" amounted to about 20 percent or about CDN$75 billion less per year. Since 2011, prices have increased in Alberta by 18%. However, a typical worker in Alberta still earns more than a typical worker in all the other provinces and territories.
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By March 2016, Alberta lost over 100,000 jobs in the oil patch. In spite of the surplus with the low price of WCS in 2015—99% of Canada's oil exports went to the United States and in 2015 Canada was still their largest exporter of total petroleum—3,789 thousand bpd in September—3,401 thousand bpd in October up from 3,026 thousand bpd in September 2014. By April 2019, two of the major oil companies, still had thousands of workers—Suncor had about 12,500 employees and Canadian Natural Resources had about 10,000 full-time employees.
Alberta has the "lowest taxes overall of any province or territory" in Canada, due in part to having high resource tax revenues. However, overall tax revenues from oil royalties and other non-renewable sources has fallen steeply along with the drop in global oil prices. For example, in 2013, oil tax revenues brought in 9.58 billion, or 21% of the total Provincial budget, whereas in 2018 it had fallen to just 5.43 billion, or 11% of the Provincial budget.
In the spring of 2020, Alberta's economy suffered from the economic fallout of both the COVID-19 pandemic and the 2020 Russia–Saudi Arabia oil price war."
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Current overview.
According to ATB Financial's Vice President and Chief Economist—Todd Hirsch, who spoke during an April 2, 2020, webinar hosted by the Calgary Chamber of Commerce, the COVID-19 pandemic in Alberta and its "economic fallout will permanently reshape our economy." Hirsch said that he expects that the resulting contraction in Alberta's economy will be the "worst...Alberta has ever seen."
The global price of oil decreased dramatically because of the combination of COVID-19 pandemic and the 2020 Russia–Saudi Arabia oil price war. In March 2020, the United States benchmark crude oil EWest Texas Intermediate (WTI)—upon which Alberta's benchmark crude oil Western Canadian Select (WCS) price is based—dropped to an historical below of US$20 a barrel. The price of WCS bitumen-blend crude was US$3.82 per barrel by the end of March.
In 2018, the low price of heavy oil negatively impacted Alberta's economic growth.
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In 1985, Alberta's energy industry accounted for 36.1% of the provinces $66.8 billion GDP. In 2006, the mining, oil and gas extraction industry accounted for 29.1% of GDP; by 2012 it was 23.3%; in 2013, it was 24.6% of Alberta's $331.9 billion GDP, and in 2016, the mining, oil and gas extraction industry accounted for about 27.9% of Alberta's GDP.
By comparison, "In 2017, the federal, provincial and territorial governments spent some $724 billion on programs and more than $58 billion on interest payments on their public debt, which, combined, amounted to about 36 percent of Canada’s gross domestic product (GDP). Their combined borrowing that year was $27 billion, and their net financial debt at year-end stood at around $1.2 trillion, about 54 percent of GDP."
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Since 2014, sectors that offered high-wage employment of $30 and above, saw about 100,000 jobs disappear—"construction (down more than 45,000 jobs), mining, oil and gas (down nearly 35,000), and professional services (down 18,000)."
Alberta's deficit.
Alberta's net debt was $27.5 billion by March 2019, which represents the end of the 2018-19 fiscal year (FY). By November 2018, Alberta's government expenditures were $55 billion while the revenue was about $48 billion, according to a report by the University of Calgary's School of Public Policy (SPP) economist, Trevor Tombe. Capital investment amounted to $4.3 billion. The provincial government employs more than "210,000 full-time equivalent workers across hundreds of departments, boards and other entities." Tombe, cited a $8.3 billion deficit in his November report, prior to the release in February 2019 of the corrected deficit figures, which was "$1.9 billion less in 2018-19 than originally expected", —$6.9-billion deficit instead of the original $8.8-billion".
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Alberta's current deficit is "unusual for the province", says Tombe in 2018. During the financial crisis, Alberta's "net asset position equivalent to 15 per cent of GDP"−it "owned more financial assets than it owed in debt."
In 2009 Alberta had $31.7 billion in financial assets.
Alberta's credit rating.
On December 3, 2019, Moody's downgraded Alberta's credit rating from Aa2 stable from Aa1 negative and "downgraded the long-term debt ratings of the Alberta Capital Finance Authority and the long-term issuer rating of ATB Financial to Aa2 from Aa1." The agency said that there is a "structural weakness in the provincial economy that remains concentrated and dependent on non-renewable resources ... and remains pressured by a lack of sufficient pipeline capacity to transport oil efficiently with no near-term expectation of a significant rebound in oil-related investments...Alberta's oil and gas sector is carbon-intensive and Alberta's greenhouse gas emissions are the highest among provinces. Alberta is also susceptible to natural disasters including wildfires and floods which could lead to significant mitigation costs by the province."
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Alberta's real per capita GDP.
In 2006 Alberta's per capita GDP was higher than all US states, and one of the highest figures in the world. In 2006, the deviation from the national average was the largest for any province in Canadian history. In 2007, Alberta's per capita GDP in 2007 was C$74,825 (approx. US$75,000)—by far the highest of any Canadian province—61% higher than the Canadian average of C$46,441 and more than twice that of all the Maritime provinces. In 2017, Alberta's real per capita GDP—the economic output per person—was $71,092, compared to the Canadian average of $47,417. Alberta's A grade on its income per capita was based on the fact that it was almost "identical" to that of the "top peer country" in 2016, Ireland.
In 2017, Alberta's real per capita GDP—the economic output per person—was $71,092 compared to the Canadian average output per person of $47, 417 and Prince Edward Island at $32,123 per person. Since at least 1997, Alberta's per capita GDP has been higher than that of any other province. In 2014, Alberta's reached its highest gap ever—$30,069—between its real capita GDP and the Canadian average.
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According to the Conference Board of Canada, in 2016 Alberta earned an "A grade with income per capita almost identical to the top peer country, Ireland." In 2016 income per capita in Alberta was $59,259.
Alberta's GDP compared to other provinces.
A table listing annual ""Gross domestic product (GDP) at basic prices, by industry, provinces and territories (x 1,000,000)." from 2014 through 2018 with value chained to 2012 dollars.
Source: Statistics Canada: GDP (totals),
Economic geography.
Alberta has a small internal market, and it is relatively distant from major world markets, despite good transportation links to the rest of Canada and to the United States to the south. Alberta is located in the northwestern quadrant of North America, in a region of low population density called the Interior Plains. Alberta is landlocked, and separated by a series of mountain ranges from the nearest outlets to the Pacific Ocean, and by the Canadian Shield from ports on the Lakehead or Hudson Bay. From these ports to major populations centres and markets in Europe or Asia is several thousands of kilometers. The largest population clusters of North America (the Boston – Washington, San Francisco - San Diego, Chicago – Pittsburgh, and Quebec City – Windsor Corridors) are all thousands of kilometers away from Alberta. Partly for this reason, Alberta has never developed a large presence in the industries that have traditionally started industrialization in other places (notably the original Industrial Revolution in Great Britain) but which require large labour forces, and large internal markets or easy transportation to export markets, namely textiles, metallurgy, or transportation-related manufacturing (automotives, ships, or train cars).
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Agriculture has been a key industry since the 1870s. The climate is dry, temperate, and continental, with extreme variations between seasons. Productive soils are found in most of the southern half of the province (excluding the mountains), and in certain parts of the north. Agriculture on a large scale is practiced further north in Alberta than anywhere else in North America, extending into the Peace River country above the 55th parallel north. Generally, however, northern Alberta (and areas along the Alberta Rockies) is forested land and logging is more important than agriculture there. Agriculture is divided into primarily field crops in the east, livestock in the west, and a mixture in between and in the parkland belt in the near north.
Conventional oil and gas fields are found throughout the province on an axis running from the northwest to the southeast. Oil sands are found in the northeast, especially around Fort McMurray (the Athabasca Oil Sands).
Because of its (relatively) economically isolated location, Alberta relies heavily on transportation links with the rest of the world. Alberta's historical development has been largely influenced by the development of new transportation infrastructure, (see "trends" below). Alberta is now served by two major transcontinental railways (CN and CP), by three major highway connections to the Pacific (the Trans-Canada via Kicking Horse Pass, the Yellowhead via Yellowhead Pass and the Crowsnest via Crowsnest Pass), and one to the United States (Interstate 15), as well as two international airports (Calgary and Edmonton). Also, Alberta is connected to the TransCanada pipeline system (natural gas) to Eastern Canada, the Northern Border Pipeline (gas), Alliance Pipeline (gas) and Enbridge Pipeline System (oil) to the Eastern United States, the Gas Transmission Northwest and Northwest Pipeline (gas) to the Western United States, and the McNeill HVDC Back-to-back station (electric power) to Saskatchewan.
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Economic regions and cities.
Since the days of early agricultural settlement, the majority of Alberta's population has been concentrated in the parkland belt (mixed forest-grassland), a boomerang-shaped strip of land extending along the North Saskatchewan River from Lloydminster to Edmonton and then along the Rocky Mountain foothills south to Calgary. This area is slightly more humid and treed than the drier prairie (grassland) region called Palliser's Triangle to its south, and large areas of the south (the "Special Areas") were depopulated during the droughts of the 1920s and 30s. The chernozem (black soil) of the parkland region is more agriculturally productive than the red and grey soils to the south. Urban development has also been most advanced in the parkland belt. Edmonton and Red Deer are parkland cities, while Calgary is on the parkland-prairie fringe. Lethbridge and Medicine Hat are prairie cities. Grande Prairie lies in the Peace River Country a parkland region (with isolated patches of prairie, hence the name) in the northwest isolated from the rest of the parkland by the forested Swan Hills. Fort McMurray is the only urbanized population centre in the boreal forest which covers much of the northern half of the province.
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Calgary and Edmonton.
The Calgary and Edmonton regions, by far the province's two largest metropolitan regions, account for the majority of the province's population. They are relatively close to each other by the standards of Western Canada and distant from other metropolitan regions such as Vancouver or Winnipeg. This has produced a history of political and economic rivalry and comparison but also economic integration that has created an urbanized corridor between the two cities.
The economic profile of the two regions is slightly different. Both cities are mature service economies built on a base of resource extraction in their hinterlands. However, Calgary is predominant in hosting the regional and national headquarters of oil and gas exploration and drilling companies. Edmonton skews much more towards governments, universities and hospitals as large employers, while Edmonton's suburban fringes (e.g. Fort Saskatchewan, Nisku, Strathcona County (Refinery Row), Leduc, Beaumont, Acheson) are home to most of the province's manufacturing (much of it related to oil and gas).
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Calgary-Edmonton Corridor.
The Calgary-Edmonton Corridor is the most urbanized region in the province and one of the densest in Canada. Measured from north to south, the region covers a distance of roughly . In 2001, the population of the Calgary-Edmonton Corridor was 2.15 million (72% of Alberta's population). It is also one of the fastest-growing regions in the country. A 2003 study by TD Bank Financial Group found the corridor was the only Canadian urban centre to amass a U.S. level of wealth while maintaining a Canadian-style quality of life, offering universal health care benefits. The study found GDP per capita in the corridor was 10% above average U.S. metropolitan areas and 40% above other Canadian cities at that time.
Calgary–Edmonton rivalry.
Seeing Calgary and Edmonton as part of a single economic region as the TD study did in 2003 was novel. The more traditional view had been to see the two cities as economic rivals. For example, in the 1980 both cities claimed to be the "Oil Capital of Canada".
Background.
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Alberta has always been an export-oriented economy. In line with Harold Innis' "Staples Thesis", the economy has changed substantially as different export commodities have risen or fallen in importance. In sequence, the most important products have been: fur, wheat and beef, and oil and gas.
The development of transportation in Alberta has been crucial to its historical economic development. The North American fur trade relied on birch-bark canoes, York boats, and Red River carts on age-old Native trails and buffalo trails to move furs out of, and European trade goods into, the region. Immigration into the province was eased tremendously by the building of the Canadian Pacific Railway's transcontinental line across southern Alberta in 1880s. Commercial farming became viable in the area once the grain trade had developed technologies to handle the bulk export of grain, especially hopper cars and grain elevators. Oil and gas exports have been possible because of increasing pipeline technology.
Prior to the 1950s, Alberta was a primarily agricultural economy, based on the export of wheat, beef, and a few other agricultural products. The health of economy was closely bound up with the price of wheat.
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In 1947 a major oil field was discovered near Edmonton. It was not the first petroleum find in Alberta, but it was large and spawned an industry that significantly altered the economy of the province (and coincided with growing American demand for energy). Since that time, Alberta's economic fortunes have largely tracked the price of oil, and increasingly natural gas prices. When oil prices spiked during the 1967 Oil Embargo, 1973 oil crisis, and 1979 energy crisis, Alberta's economy boomed. However, during the 1980s oil glut Alberta's economy suffered. Alberta boomed once again during the 2003-2008 oil price spike. In July 2008 the price of oil peaked and began to decline, and Alberta's economy soon followed suit, with unemployment doubling within a year. By 2009 with natural gas prices at a long-term low, Alberta's economy was in poor health compared to before, although still relatively better than many other comparable jurisdictions. By 2012 natural gas prices were at a ten-year low and the Canadian dollar was highly valued compared to the U.S. dollar, but then oil prices recovered until June 2014.
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The spin-offs from petroleum allowed Alberta to develop many other industries. Oilpatch-related manufacturing is an obvious example, but financial services and government services have also benefited from oil money.
A comparison of the development of Alberta's less oil and gas-endowed neighbours, Saskatchewan and Manitoba, reveals the role petroleum has played. Alberta was the least-populous of the three Prairie Provinces in the early 20th century, but by 2009, Alberta's population was 3,632,483, approximately three times as much as either Saskatchewan (1,023,810) or Manitoba (1,213,815).
Employment.
Alberta's economy is a highly developed one in which most people work in services such as healthcare, government, or retail. Primary industries are also of great importance, however.
By March 2016 the unemployment rate in Alberta rose to 7.9%— its "highest level since April 1995 and the first time the province’s rate has surpassed the national average since December 1988." There were 21,200 fewer jobs than February 2015. The unemployment rate was expected to average 7.4% in 2016. The Canadian Association of Petroleum Producers (CAPP) claimed that Alberta lost 35,000 jobs in 2015–25,000 from the oil services sector and 10,000 from exploration and production. Full-time employment increased by 10,000 in February 2016 after falling 20,000 in both December 2015 and January 2016. The natural resources industry lost 7,400 jobs in February. "Year-over-year (y/y), the goods sector lost 56,000 jobs, while the services sector gained 34,800." In 2015 Alberta's population increased by 3,900. While Alberta had a reprieve in job loss in February 2016—up 1,400 jobs after losing jobs in October, November, December 2015 and January 2016—Ontario lost 11,200 jobs, Saskatchewan lost 7,800 jobs and New Brunswick lost 5,700 jobs.
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The unemployment rate in spring 2019 in Alberta was 6.7% with 21,000 jobs added in April; in Calgary it was 7.4%, in Edmonton it was 6.9%, in Northern Alberta it was 11.2%, and in Southern Alberta it was 7.8%. By July 2019, the seasonally adjusted unemployment rate had increased to 7.0%, which represented an increase of 0.3% from the previous year. The unemployment rate in Alberta peaked in November 2016 at 9.1%. Its lowest point in a ten-year period from July 2009 to July 2019 was in September 2013 at 4.3%.
By August 2019, the employment number in Alberta was 2,344,000, following the loss of 14,000 full-time jobs in July, which represented that the "largest decline" in Canada according to Statistics Canada.
Employment by industry, Alberta – seasonally adjusted (000s)
Extraction industries.
According to the Government of Alberta, the "mining and oil and gas extraction industry accounted for 6.1% of total employment in Alberta in 2017". By April 2019, there were about 145,100 people working directly with the oil and gas industry. In 2013, there were 171,200 people employed in the mining and oil and gas extraction industry.
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In 2007 there were 146,900 people working in the mining and oil and gas extraction industry.
Largest employers of Alberta.
According to "Alberta Venture" magazine's list of the 50 largest employers in the province, the largest employers are:
Sectors.
Oil and gas extraction industries.
In 2018, Alberta's energy sector contributed over $71.5 billion to Canada's nominal gross domestic product. In 2006, it accounted for 29.1% of Alberta's GDP; by 2012 it was 23.3%; in 2013, it was 24.6%, and in 2016 it was 27.9%. According to Statistics Canada, in May 2018, the oil and gas extraction industry reached its highest proportion of Canada's national GDP since 1985, exceeding 7% and "surpass[ing] banking and insurance". with extraction of non-conventional oil from the oilsands reaching an "impressive", all-time high in May 2018. With conventional oil extraction "climbed up to the highs from 2007", the demand for Canadian oil was strong in May.
Alberta is the largest producer of conventional crude oil, synthetic crude, natural gas and gas products in the country. Alberta is the world's 2nd largest exporter of natural gas and the 4th largest producer. Two of the largest producers of petrochemicals in North America are located in central and north central Alberta. In both Red Deer and Edmonton, world class polyethylene and vinyl manufacturers produce products shipped all over the world, and Edmonton's oil refineries provide the raw materials for a large petrochemical industry to the east of Edmonton. Since the early 1940s, Alberta had supplied oil and gas to the rest of Canada and the United States. The Athabasca River region produces oil for internal and external use. The Athabasca Oil Sands contain the largest proven reserves of oil in the world outside Saudi Arabia.
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The Athabasca Oil Sands (sometimes known as the Athabasca Tar sands) have estimated unconventional oil reserves approximately equal to the conventional oil reserves of the rest of the world, estimated to be . With the development of new extraction methods such as steam-assisted gravity drainage (SAGD), which was developed in Alberta, bitumen and synthetic crude oil can be produced at costs close to those of conventional crude. Many companies employ both conventional strip mining and non-conventional in situ methods to extract the bitumen from the oil sands. With current technology and at current prices, about of bitumen are recoverable. Fort McMurray, one of Canada's fastest growing cities, has grown enormously in recent years because of the large corporations which have taken on the task of oil production. As of late 2006 there were over $100 billion in oil sands projects under construction or in the planning stages in northeastern Alberta.
Another factor determining the viability of oil extraction from the oil sands was the price of oil. The oil price increases since 2003 made it more than profitable to extract this oil, which in the past would give little profit or even a loss.
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Alberta's economy was negatively impacted by the 2015-2016 oil glut with a record high volume of worldwide oil inventories in storage, with global crude oil collapsing at near ten-year low prices. The United States doubled its 2008 production levels mainly due to substantial improvements in shale "fracking" technology, OPEC members consistently exceeded their production ceiling, and China experienced a marked slowdown in economic growth and crude oil imports.
Mining and Oil and Gas Extraction Industry (2017)
Natural gas.
Natural gas has been found at several points, and in 1999, the production of natural gas liquids (ethane, propane, and butanes) totalled , valued at $2.27 billion. Alberta also provides 13% of all the natural gas used in the United States.
Notable gas reserves were discovered in the 1883 near Medicine Hat. The town of Medicine Hat began using gas for lighting the town, and supplying light and fuel for the people, and a number of industries using the gas for manufacturing.
One of North America's benchmarks is Alberta gas-trading price—the AECO "C" spot price.
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In 2018, 69% of the marketable natural gas in Canada was produced in Alberta. Forty nine per cent of Alberta's natural gas production is consumed in Alberta. In Alberta, the average household uses of natural gas annually. Domestic demand for natural gas is divided across sectors, with the highest demand—83% coming from "industrial, electrical generation, transportation and other sectors," and 17 percent going towards residential and commercial sectors.
Of the provinces, Alberta is the largest consumer of natural gas at 3.9 billion cubic feet per day.
By August 2019, the "Financial Post" said that "AECO daily and monthly natural gas prices" were at the lowest they have been since 1992. Canada's largest natural gas producer, Canadian Natural Resources Ltd., announced in early August that it had "shut in gas production of 27,000 million cubic feet per day because of depressed prices. Previously natural gas pipeline drilled in the southern Alberta and shipped to markets in Eastern Canada. By 2019, the entire natural gas industry had was primarily operating in northwestern Alberta and northeastern B.C., which resulted in strained infrastructure.
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By 2019, the entire natural gas industry had was primarily operating in northwestern Alberta and northeastern B.C., which resulted in strained infrastructure. New systems will not be complete until 2021 or 2023. In September 25, 2017 Alberta's benchmark AECO natural gas prices fell into "negative territory – "meaning producers have had to pay customers to take their gas". It happened again in early October with the price per gigajoule dropping to -7 cents. TransCanada (now TC Energy Corp)—which "owns and operates Alberta's "largest natural gas gathering and transmission system, interrupted its pipeline service in the fall of 2017 to complete field maintenance on the Alberta system. In July 2018, RS Energy Group's energy analyst Samir Kayande, said that faced with a glut of natural gas across North America, the continental market price was $3 per gigajoule. Alberta is "awash" with natural gas but faces pipeline bottlenecks. CEOs of nine Alberta natural gas producers requested the Kenney government to mandate production cuts to deal with the crisis. CEOs of nine Alberta natural gas producers requested the Kenney government to mandate production cuts to deal with the crisis. On June 30, the AECO price of gas dropped to 11 cents per gigajoule, because of maintenance issues with the pipeline giant TC Energy Corp.
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In 2003 Alberta produced of marketable natural gas. That year, 62% of Alberta's natural gas was shipped to the United States, 24% was used within Alberta, and 14% was used in the rest of Canada. In 2006, Alberta consumed of natural gas. The rest was exported across Canada and to the United States. Royalties to Alberta from natural gas and its byproducts are larger than royalties from crude oil and bitumen. In 2006, there were 13,473 successful natural gas wells drilled in Alberta: 12,029 conventional gas wells and 1,444 coalbed methane wells. There may be up to of coalbed methane in Alberta, although it is unknown how much of this gas might be recoverable. Alberta has one of the most extensive natural gas systems in the world as part of its energy infrastructure, with of energy related pipelines.
Coal.
Coal has been mined in Alberta since the late 19th century. Over 1800 mines have operated in Alberta since then.
The coal industry was vital to the early development of several communities, especially those in the foothills and along deep river valleys where coal was close to the surface.
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Alberta is still a major coal producer, every two weeks Alberta produces enough coal to fill the Sky Dome in Toronto.
Much of that coal is burned in Alberta for electricity generation. By 2008, Alberta used over 25 million tonnes of coal annually to generate electricity. However, Alberta is set to retire coal power by 2023, ahead of 2030 provincial deadline.
Alberta has vast coal resources and 70 per cent of Canada's coal reserves are located in Alberta. This amounts to 33.6 Gigatonnes.
Vast beds of coal are found extending for hundreds of miles, a short distance below the surface of the plains. The coal belongs to the Cretaceous beds, and while not so heavy as that of the Coal Measures in England is of excellent quality. In the valley of the Bow River, alongside the Canadian Pacific Railway, valuable beds of anthracite coal are still worked. The usual coal deposits of the area of bituminous or semi-bituminous coal. These are largely worked at Lethbridge in southern Alberta and Edmonton in the centre of the province. Many other parts of the province have pits for private use.
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Electricity.
, Alberta's generating capacity was 16,261 MW, and Alberta has about of transmission lines.
Alberta has 1491 megawatts of wind power capacity.
Production of electricity in Alberta in 2016 by source:
Alberta has added 9,000 MW of new supply since 1998.
Peak for power use in one day was set on July 9, 2015 – 10,520 MW.
Mineral mining.
Building stones mined in Alberta include Rundle stone, and Paskapoo sandstone.
Diamonds were first found in Alberta in 1958, and many stones have been found since, although to date no large-scale mines have been developed.
Manufacturing.
The Edmonton area, and in particular Nisku is a major centre for manufacturing oil and gas related equipment. As well Edmonton's Refinery Row is home to a petrochemical industry.
According to a 2016 Statistics Canada report Alberta's manufacturing sales year-over-year sales fell 13.2 per cent, with a loss of almost four per cent from December to January. Alberta's economy continued to shrink because of the collapse of the oil and gas sector. The petroleum and coal product manufacturing industry is now third— behind food and chemicals.
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Biotechnology.
Several companies and services in the biotech sector are clustered around the University of Alberta, for example ColdFX.
Food processing.
Owing to the strength of agriculture, food processing was once a major part of the economies of Edmonton and Calgary, but this sector has increasingly moved to smaller centres such as Brooks, the home of XL Foods, responsible for one third of Canada's beef processing in 2011.
Transportation.
Edmonton is a major distribution centre for northern communities, hence the nickname "Gateway to the North". Edmonton is one of CN Rail's most important hubs. Since 1996, Canadian Pacific Railway has its headquarters in downtown Calgary.
WestJet, Canada's second largest air carrier, is headquartered in Calgary, by Calgary International Airport, which serves as the airline's primary hub. Prior to its dissolution, Canadian Airlines was headquartered in Calgary by the airport. Prior to its dissolution, Air Canada subsidiary Zip was headquartered in Calgary.
Agriculture and forestry.
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Agriculture.
In the past, cattle, horses, and sheep were reared in the southern prairie region on ranches or smaller holdings. Currently Alberta produces cattle valued at over $3.3 billion, as well as other livestock in lesser quantities. In this region irrigation is widely used. Wheat, accounting for almost half of the $2 billion agricultural economy, is supplemented by canola, barley, rye, sugar beets, and other mixed farming. In 2011, Alberta producers seeded an estimated total of to spring wheat, durum, barley, oats, mixed grains, triticale, canola and dry peas. Of the total seeded area, 94 per cent was harvested as grains and oilseeds and six per cent as greenfeed and silage. Saudi Arabia is a major export target especially for wheat and processed potato products. SA having decided to phase out their own forage and cereal production, Alberta expects this to be an opportunity to fill livestock feed demand in the kingdom.
Agriculture has a significant position in the province's economy. Over three million cattle are residents of the province at one time or another, and Albertan beef has a healthy worldwide market. Although beef could also be a major export to Saudi Arabia, as with wheat and potatoes above, market access is lacking at the moment. Nearly one half of all Canadian beef is produced in Alberta. Alberta is one of the prime producers of plains buffalo (bison) for the consumer market. Sheep for wool and lamb are also raised.
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Wheat and canola are primary farm crops, with Alberta leading the provinces in spring wheat production, with other grains also prominent. Much of the farming is dryland farming, often with fallow seasons interspersed with cultivation. Continuous cropping (in which there is no fallow season) is gradually becoming a more common mode of production because of increased profits and a reduction of soil erosion. Across the province, the once common grain elevator is slowly being lost as rail lines are decreased and farmers now truck the grain to central points.
Clubroot ("Plasmodiophora brassicae") is a costly disease of "Brassicaceae" here including canola. In several experiments by Peng "et al.", out of fungicides, biofungicides, inoculation with beneficial microbes, cultivar resistance, and crop rotation, only genetic resistance combined with more than two years rotation worked "susceptible" cultivars rotated with other crops did not produce enough improvement.
Alberta is the leading beekeeping province of Canada, with some beekeepers wintering hives indoors in specially designed barns in southern Alberta, then migrating north during the summer into the Peace River valley where the season is short but the working days are long for honeybees to produce honey from clover and fireweed. Hybrid canola also requires bee pollination, and some beekeepers service this need.
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Forestry.
The vast northern forest reserves of softwood allow Alberta to produce large quantities of lumber, oriented strand board (OSB) and plywood, and several plants in northern Alberta supply North America and the Pacific Rim nations with bleached wood pulp and newsprint.
In 1999, lumber products from Alberta were valued at $4.1 billion of which 72% were exported around the world. Since forests cover approximately 59% of the province's land area, the government allows about to be harvested annually from the forests on public lands.
Services.
Despite the high profile of the extractive industries, Alberta has a mature economy and most people work in services. In 2014 there were 1,635.8 thousand people employed in the services-producing sector. Since then, the number has steadily increased to 1754.8 thousand jobs by August 2019, which is an increase of 16.7 thousand jobs from August 2018 This includes wholesale and retail trade; transportation and warehousing; finance, insurance, real estate, rental and leasing; professional, scientific and technical services; business, building and other support services; educational services; health care and social assistance; information, culture and recreation; accommodation and food services; other services (except public administration) and public administration.
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Finance.
The TSX Venture Exchange is headquartered in Calgary. The city has the second highest number of corporate head offices in Canada after Toronto, and the financial services industry in Calgary has developed to support them. All major banks including the Big Five maintain corporate offices in Calgary, along with smaller banks such as Equitable Group. Recently there has also been a number of fintech companies founded in Calgary such as the National Digital Asset Exchange and Neo Financial, founded by the Skip-the-Dishes team.
One of Canada's largest accounting firms, MNP LLP, is also headquartered in Calgary.
Edmonton hosts the headquarters of the only major Canadian banks west of Toronto: Canadian Western Bank, and ATB Financial, as well as the only province-wide credit union, Servus Credit Union.
Government.
Despite Alberta's reputation as a "small government" province, many health care and education professionals are lured to Alberta from other provinces by the higher wages the Alberta government is able to offer because of oil revenues. In 2014 the median household income in Alberta was $100,000 with the average weekly wage at $1,163—23 per cent higher than the Canadian national average.
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In their May 2018 report co-authored by C. D. Howe Institute's President and CEO, William B.P. Robson, evaluating "the budgets, estimates and public accounts" of 2017/18 fiscal year that were tabled by senior governments in the Canadian provinces and the federal government in terms of reporting financial information, appropriately, with transparency, and in a timely fashion, Alberta and New Brunswick ranked highest. The report also said that, prior to 2016, Alberta had scored poorly in comparison with other provinces, because of "confusing array of "operating," "saving" and "capital" accounts that were not Public Sector Accounting Standards (PSAS) consistent." but since 2016, Alberta has received A-plus grades. The report said that Alberta and New Brunswick in FY2017 provided "straightforward reconciliations of results with budget intentions, their auditors record no reservations, and their budgets and public accounts are timely."
Technology.
Alberta has a burgeoning high tech sector, including prominent technology companies iStockPhoto, Shareworks, Benevity, and Attabotics in Calgary, and Bioware and AltaML in Edmonton. Growth in Calgary's technology sector, particularly at Benevity, fueled predictions of a modest economic recovery in February 2020.
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Augustin-Louis Cauchy
Baron Augustin-Louis Cauchy ( , , ; ; 21 August 1789 – 23 May 1857) was a French mathematician, engineer, and physicist. He was one of the first to rigorously state and prove the key theorems of calculus (thereby creating real analysis), pioneered the field complex analysis, and the study of permutation groups in abstract algebra. Cauchy also contributed to a number of topics in mathematical physics, notably continuum mechanics.
A profound mathematician, Cauchy had a great influence over his contemporaries and successors; Hans Freudenthal stated:
Cauchy was a prolific worker; he wrote approximately eight hundred research articles and five complete textbooks on a variety of topics in the fields of mathematics and mathematical physics.
Biography.
Youth and education.
Cauchy was the son of Louis François Cauchy (1760–1848) and Marie-Madeleine Desestre. Cauchy had two brothers: Alexandre Laurent Cauchy (1792–1857), who became a president of a division of the court of appeal in 1847 and a judge of the court of cassation in 1849, and Eugene François Cauchy (1802–1877), a publicist who also wrote several mathematical works. From his childhood he was good at math.
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Cauchy married Aloise de Bure in 1818. She was a close relative of the publisher who published most of Cauchy's works. They had two daughters, Marie Françoise Alicia (1819) and Marie Mathilde (1823).
Cauchy's father was a highly ranked official in the Parisian police of the
Ancien Régime, but lost this position due to the French Revolution (14 July 1789), which broke out one month before Augustin-Louis was born. The Cauchy family survived the revolution and the following Reign of Terror during 1793–94 by escaping to Arcueil, where Cauchy received his first education, from his father. After the execution of Robespierre in 1794, it was safe for the family to return to Paris. There, Louis-François Cauchy found a bureaucratic job in 1800, and quickly advanced his career. When Napoleon came to power in 1799, Louis-François Cauchy was further promoted, and became Secretary-General of the Senate, working directly under Laplace (who is now better known for his work on mathematical physics). The mathematician Lagrange was also a friend of the Cauchy family.
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On Lagrange's advice, Augustin-Louis was enrolled in the École Centrale du Panthéon, the best secondary school of Paris at that time, in the fall of 1802. Most of the curriculum consisted of classical languages; the ambitious Cauchy, being a brilliant student, won many prizes in Latin and the humanities. In spite of these successes, Cauchy chose an engineering career, and prepared himself for the entrance examination to the École Polytechnique.
In 1805, he placed second of 293 applicants on this exam and was admitted. One of the main purposes of this school was to give future civil and military engineers a high-level scientific and mathematical education. The school functioned under military discipline, which caused Cauchy some problems in adapting. Nevertheless, he completed the course in 1807, at age 18, and went on to the École des Ponts et Chaussées (School for Bridges and Roads). He graduated in civil engineering, with the highest honors.
Engineering days.
After finishing school in 1810, Cauchy accepted a job as a junior engineer in Cherbourg, where Napoleon intended to build a naval base. Here Cauchy stayed for three years, and was assigned the Ourcq Canal project and the Saint-Cloud Bridge project, and worked at the Harbor of Cherbourg. Although he had an extremely busy managerial job, he still found time to prepare three mathematical manuscripts, which he submitted to the "Première Classe" (First Class) of the Institut de France. Cauchy's first two manuscripts (on polyhedra) were accepted; the third one (on directrices of conic sections) was rejected.
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In September 1812, at 23 years old, Cauchy returned to Paris after becoming ill from overwork. Another reason for his return to the capital was that he was losing interest in his engineering job, being more and more attracted to the abstract beauty of mathematics; in Paris, he would have a much better chance to find a mathematics related position. When his health improved in 1813, Cauchy chose not to return to Cherbourg. Although he formally kept his engineering position, he was transferred from the payroll of the Ministry of the Marine to the Ministry of the Interior. The next three years Cauchy was mainly on unpaid sick leave; he spent his time fruitfully, working on mathematics (on the related topics of symmetric functions, the symmetric group and the theory of higher-order algebraic equations). He attempted admission to the First Class of the Institut de France but failed on three different occasions between 1813 and 1815. In 1815 Napoleon was defeated at Waterloo, and the newly installed king Louis XVIII took the restoration in hand. The Académie des Sciences was re-established in March 1816; Lazare Carnot and Gaspard Monge were removed from this academy for political reasons, and the king appointed Cauchy to take the place of one of them. The reaction of Cauchy's peers was harsh; they considered the acceptance of his membership in the academy an outrage, and Cauchy created many enemies in scientific circles.
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Professor at École Polytechnique.
In November 1815, Louis Poinsot, who was an associate professor at the École Polytechnique, asked to be exempted from his teaching duties for health reasons. Cauchy was by then a rising mathematical star. One of his great successes at that time was the proof of Fermat's polygonal number theorem. He quit his engineering job, and received a one-year contract for teaching mathematics to second-year students of the École Polytechnique. In 1816, this Bonapartist, non-religious school was reorganized, and several liberal professors were fired; Cauchy was promoted to full professor.
When Cauchy was 28 years old, he was still living with his parents. His father found it time for his son to marry; he found him a suitable bride, Aloïse de Bure, five years his junior. The de Bure family were printers and booksellers, and published most of Cauchy's works. Aloïse and Augustin were married on April 4, 1818, with great Roman Catholic ceremony, in the Church of Saint-Sulpice. In 1819 the couple's first daughter, Marie Françoise Alicia, was born, and in 1823 the second and last daughter, Marie Mathilde.
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The conservative political climate that lasted until 1830 suited Cauchy perfectly. In 1824 Louis XVIII died, and was succeeded by his even more conservative brother Charles X. During these years Cauchy was highly productive, and published one important mathematical treatise after another. He received cross-appointments at the Collège de France, and the .
In exile.
In July 1830, the July Revolution occurred in France. Charles X fled the country, and was succeeded by Louis-Philippe. Riots, in which uniformed students of the École Polytechnique took an active part, raged close to Cauchy's home in Paris.
These events marked a turning point in Cauchy's life, and a break in his mathematical productivity. Shaken by the fall of the government and moved by a deep hatred of the liberals who were taking power, Cauchy left France to go abroad, leaving his family behind. He spent a short time at Fribourg in Switzerland, where he had to decide whether he would swear a required oath of allegiance to the new regime. He refused to do this, and consequently lost all his positions in Paris, except his membership of the academy, for which an oath was not required. In 1831 Cauchy went to the Italian city of Turin, and after some time there, he accepted an offer from the King of Sardinia (who ruled Turin and the surrounding Piedmont region) for a chair of theoretical physics, which was created especially for him. He taught in Turin during 1832–1833. In 1831, he was elected a foreign member of the Royal Swedish Academy of Sciences, and the following year a Foreign Honorary Member of the American Academy of Arts and Sciences.
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In August 1833 Cauchy left Turin for Prague to become the science tutor of the thirteen-year-old Duke of Bordeaux, Henri d'Artois (1820–1883), the exiled Crown Prince and grandson of Charles X. As a professor of the École Polytechnique, Cauchy had been a notoriously bad lecturer, assuming levels of understanding that only a few of his best students could reach, and cramming his allotted time with too much material. Henri d'Artois had neither taste nor talent for either mathematics or science. Although Cauchy took his mission very seriously, he did this with great clumsiness, and with surprising lack of authority over Henri d'Artois. During his civil engineering days, Cauchy once had been briefly in charge of repairing a few of the Parisian sewers, and he made the mistake of mentioning this to his pupil; with great malice, Henri d'Artois went about saying Cauchy started his career in the sewers of Paris. Cauchy's role as tutor lasted until Henri d'Artois became eighteen years old, in September 1838. Cauchy did hardly any research during those five years, while Henri d'Artois acquired a lifelong dislike of mathematics. Cauchy was named a baron, a title by which Cauchy set great store.
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In 1834, his wife and two daughters moved to Prague, and Cauchy was reunited with his family after four years in exile.
Last years.
Cauchy returned to Paris and his position at the Academy of Sciences late in 1838. He could not regain his teaching positions, because he still refused to swear an oath of allegiance.
In August 1839 a vacancy appeared in the Bureau des Longitudes. This Bureau bore some resemblance to the academy; for instance, it had the right to co-opt its members. Further, it was believed that members of the Bureau could "forget about" the oath of allegiance, although formally, unlike the Academicians, they were obliged to take it. The Bureau des Longitudes was an organization founded in 1795 to solve the problem of determining position at sea — mainly the longitudinal coordinate, since latitude is easily determined from the position of the sun. Since it was thought that position at sea was best determined by astronomical observations, the Bureau had developed into an organization resembling an academy of astronomical sciences.
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In November 1839 Cauchy was elected to the Bureau, and discovered that the matter of the oath was not so easily dispensed with. Without his oath, the king refused to approve his election. For four years Cauchy was in the position of being elected but not approved; accordingly, he was not a formal member of the Bureau, did not receive payment, could not participate in meetings, and could not submit papers. Still Cauchy refused to take any oaths; however, he did feel loyal enough to direct his research to celestial mechanics. In 1840, he presented a dozen papers on this topic to the academy. He described and illustrated the signed-digit representation of numbers, an innovation presented in England in 1727 by John Colson. The confounded membership of the Bureau lasted until the end of 1843, when Cauchy was replaced by Poinsot.
Throughout the nineteenth century the French educational system struggled over the separation of church and state. After losing control of the public education system, the Catholic Church sought to establish its own branch of education and found in Cauchy a staunch and illustrious ally. He lent his prestige and knowledge to the École Normale Écclésiastique, a school in Paris run by Jesuits, for training teachers for their colleges. He took part in the founding of the Institut Catholique. The purpose of this institute was to counter the effects of the absence of Catholic university education in France. These activities did not make Cauchy popular with his colleagues, who, on the whole, supported the Enlightenment ideals of the French Revolution. When a chair of mathematics became vacant at the Collège de France in 1843, Cauchy applied for it, but received just three of 45 votes.
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In 1848 King Louis-Philippe fled to England. The oath of allegiance was abolished, and the road to an academic appointment was clear for Cauchy. On March 1, 1849, he was reinstated at the Faculté de Sciences, as a professor of mathematical astronomy. After political turmoil all through 1848, France chose to become a Republic, under the Presidency of Napoleon III of France. Early 1852 the President made himself Emperor of France, and took the name Napoleon III.
The idea came up in bureaucratic circles that it would be useful to again require a loyalty oath from all state functionaries, including university professors. This time a cabinet minister was able to convince the Emperor to exempt Cauchy from the oath. In 1853, Cauchy was elected an International Member of the American Philosophical Society. Cauchy remained a professor at the university until his death at the age of 67. He received the Last Rites and died of a bronchial condition at 4 a.m. on 23 May 1857.
His name is one of the 72 names inscribed on the Eiffel Tower.
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Work.
Early work.
The genius of Cauchy was illustrated in his simple solution of the problem of Apollonius—describing a circle touching three given circles—which he discovered in 1805, his generalization of Euler's formula on polyhedra in 1811, and in several other elegant problems. More important is his memoir on wave propagation, which obtained the Grand Prix of the French Academy of Sciences in 1816. Cauchy's writings covered notable topics. In the theory of series he developed the notion of convergence and discovered many of the basic formulas for q-series. In the theory of numbers and complex quantities, he was the first to define complex numbers as pairs of real numbers. He also wrote on the theory of groups and substitutions, the theory of functions, differential equations and determinants.
Wave theory, mechanics, elasticity.
In the theory of light he worked on Fresnel's wave theory and on the dispersion and polarization of light. He also contributed research in mechanics, substituting the notion of the continuity of geometrical displacements for the principle of the continuity of matter. He wrote on the equilibrium of rods and elastic membranes and on waves in elastic media. He introduced a 3 × 3 symmetric matrix of numbers that is now known as the Cauchy stress tensor. In elasticity, he originated the theory of stress, and his results are nearly as valuable as those of Siméon Poisson.
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Number theory.
Other significant contributions include being the first to prove the Fermat polygonal number theorem.
Complex functions.
Cauchy is most famous for his single-handed development of complex function theory. The first pivotal theorem proved by Cauchy, now known as "Cauchy's integral theorem", was the following:
where "f"("z") is a complex-valued function holomorphic on and within the non-self-intersecting closed curve "C" (contour) lying in the complex plane. The "contour integral" is taken along the contour "C". The rudiments of this theorem can already be found in a paper that the 24-year-old Cauchy presented to the Académie des Sciences (then still called "First Class of the Institute") on August 11, 1814. In full form the theorem was given in 1825.
In 1826 Cauchy gave a formal definition of a residue of a function. This concept concerns functions that have poles—isolated singularities, i.e., points where a function goes to positive or negative infinity. If the complex-valued function "f"("z") can be expanded in the neighborhood of a singularity "a" as
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where φ("z") is analytic (i.e., well-behaved without singularities), then "f" is said to have a pole of order "n" in the point "a". If "n" = 1, the pole is called simple.
The coefficient "B"1 is called by Cauchy the residue of function "f" at "a". If "f" is non-singular at "a" then the residue of "f" is zero at "a". Clearly, the residue is in the case of a simple pole equal to
where we replaced "B"1 by the modern notation of the residue.
In 1831, while in Turin, Cauchy submitted two papers to the Academy of Sciences of Turin. In the first he proposed the formula now known as Cauchy's integral formula,
where "f"("z") is analytic on "C" and within the region bounded by the contour "C" and the complex number "a" is somewhere in this region. The contour integral is taken counter-clockwise. Clearly, the integrand has a simple pole at "z" = "a". In the second paper he presented the residue theorem,
where the sum is over all the "n" poles of "f"("z") on and within the contour "C". These results of Cauchy's still form the core of complex function theory as it is taught today to physicists and electrical engineers. For quite some time, contemporaries of Cauchy ignored his theory, believing it to be too complicated. Only in the 1840s the theory started to get response, with Pierre Alphonse Laurent being the first mathematician besides Cauchy to make a substantial contribution (his work on what are now known as Laurent series, published in 1843).
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"Cours d'analyse".
In his book "Cours d'analyse" Cauchy stressed the importance of rigor in analysis. "Rigor" in this case meant the rejection of the principle of "Generality of algebra" (of earlier authors such as Euler and Lagrange) and its replacement by geometry and infinitesimals. Judith Grabiner wrote Cauchy was "the man who taught rigorous analysis to all of Europe". The book is frequently noted as being the first place that inequalities, and formula_6 arguments were introduced into calculus. Here Cauchy defined continuity as follows: "The function f(x) is continuous with respect to x between the given limits if, between these limits, an infinitely small increment in the variable always produces an infinitely small increment in the function itself."
M. Barany claims that the École mandated the inclusion of infinitesimal methods against Cauchy's better judgement. Gilain notes that when the portion of the curriculum devoted to "Analyse Algébrique" was reduced in 1825, Cauchy insisted on placing the topic of continuous functions (and therefore also infinitesimals) at the beginning of the Differential Calculus. Laugwitz (1989) and Benis-Sinaceur (1973) point out that Cauchy continued to use infinitesimals in his own research as late as 1853.
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Cauchy gave an explicit definition of an infinitesimal in terms of a sequence tending to zero. There has been a vast body of literature written about Cauchy's notion of "infinitesimally small quantities", arguing that they lead from everything from the usual "epsilontic" definitions or to the notions of non-standard analysis. The consensus is that Cauchy omitted or left implicit the important ideas to make clear the precise meaning of the infinitely small quantities he used.
Taylor's theorem.
He was the first to prove Taylor's theorem rigorously, establishing his well-known form of the remainder. He wrote a textbook (see the illustration) for his students at the École Polytechnique in which he developed the basic theorems of mathematical analysis as rigorously as possible. In this book he gave the necessary and sufficient condition for the existence of a limit in the form that is still taught. Also Cauchy's well-known test for absolute convergence stems from this book: Cauchy condensation test. In 1829 he defined for the first time a complex function of a complex variable in another textbook. In spite of these, Cauchy's own research papers often used intuitive, not rigorous, methods; thus one of his theorems was exposed to a "counter-example" by Abel, later fixed by the introduction of the notion of uniform continuity.
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Argument principle, stability.
In a paper published in 1855, two years before Cauchy's death, he discussed some theorems, one of which is similar to the "Principle of the argument" in many modern textbooks on complex analysis. In modern control theory textbooks, the Cauchy argument principle is quite frequently used to derive the Nyquist stability criterion, which can be used to predict the stability of negative feedback amplifier and negative feedback control systems. Thus Cauchy's work has a strong impact on both pure mathematics and practical engineering.
Published works.
Cauchy was very productive, in number of papers second only to Leonhard Euler. It took almost a century to collect all his writings into 27 large volumes:
His greatest contributions to mathematical science are enveloped in the rigorous methods which he introduced; these are mainly embodied in his three great treatises:
His other works include:
Politics and religious beliefs.
Augustin-Louis Cauchy grew up in the house of a staunch royalist. This made his father flee with the family to Arcueil during the French Revolution. Their life there during that time was apparently hard; Augustin-Louis's father, Louis François, spoke of living on rice, bread, and crackers during the period. A paragraph from an undated letter from Louis François to his mother in Rouen says:
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In any event, he inherited his father's staunch royalism and hence refused to take oaths to any government after the overthrow of Charles X.
He was an equally staunch Catholic and a member of the Society of Saint Vincent de Paul. He also had links to the Society of Jesus and defended them at the academy when it was politically unwise to do so. His zeal for his faith may have led to his caring for Charles Hermite during his illness and leading Hermite to become a faithful Catholic. It also inspired Cauchy to plead on behalf of the Irish during the Great Famine of Ireland.
His royalism and religious zeal made him contentious, which caused difficulties with his colleagues. He felt that he was mistreated for his beliefs, but his opponents felt he intentionally provoked people by berating them over religious matters or by defending the Jesuits after they had been suppressed. Niels Henrik Abel called him a "bigoted Catholic" and added he was "mad and there is nothing that can be done about him", but at the same time praised him as a mathematician. Cauchy's views were widely unpopular among mathematicians and when Guglielmo Libri Carucci dalla Sommaja was made chair in mathematics before him he, and many others, felt his views were the cause. When Libri was accused of stealing books he was replaced by Joseph Liouville rather than Cauchy, which caused a rift between Liouville and Cauchy. Another dispute with political overtones concerned Jean-Marie Constant Duhamel and a claim on inelastic shocks. Cauchy was later shown, by Jean-Victor Poncelet, to be wrong.
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Archimedes
Archimedes of Syracuse ( ; ) was an Ancient Greek mathematician, physicist, engineer, astronomer, and inventor from the ancient city of Syracuse in Sicily. Although few details of his life are known, he is considered one of the leading scientists in classical antiquity. Regarded as the greatest mathematician of ancient history, and one of the greatest of all time, Archimedes anticipated modern calculus and analysis by applying the concept of the infinitely small and the method of exhaustion to derive and rigorously prove many geometrical theorems. These include the area of a circle, the surface area and volume of a sphere, the area of an ellipse, the area under a parabola, the volume of a segment of a paraboloid of revolution, the volume of a segment of a hyperboloid of revolution, and the area of a spiral.
Archimedes' other mathematical achievements include deriving an approximation of pi (), defining and investigating the Archimedean spiral, and devising a system using exponentiation for expressing very large numbers. He was also one of the first to apply mathematics to physical phenomena, working on statics and hydrostatics. Archimedes' achievements in this area include a proof of the law of the lever, the widespread use of the concept of center of gravity, and the enunciation of the law of buoyancy known as Archimedes' principle. In astronomy, he made measurements of the apparent diameter of the Sun and the size of the universe. He is also said to have built a planetarium device that demonstrated the movements of the known celestial bodies, and may have been a precursor to the Antikythera mechanism. He is also credited with designing innovative machines, such as his screw pump, compound pulleys, and defensive war machines to protect his native Syracuse from invasion.
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Archimedes died during the siege of Syracuse, when he was killed by a Roman soldier despite orders that he should not be harmed. Cicero describes visiting Archimedes' tomb, which was surmounted by a sphere and a cylinder that Archimedes requested be placed there to represent his most valued mathematical discovery.
Unlike his inventions, Archimedes' mathematical writings were little known in antiquity. Alexandrian mathematicians read and quoted him, but the first comprehensive compilation was not made until by Isidore of Miletus in Byzantine Constantinople, while Eutocius' commentaries on Archimedes' works in the same century opened them to wider readership for the first time. The relatively few copies of Archimedes' written work that survived through the Middle Ages were an influential source of ideas for scientists during the Renaissance and again in the 17th century, while the discovery in 1906 of previously lost works by Archimedes in the Archimedes Palimpsest has provided new insights into how he obtained mathematical results.
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Biography.
Early life.
Archimedes was born c. 287 BC in the seaport city of Syracuse, Sicily, at that time a self-governing colony in Magna Graecia. The date of birth is based on a statement by the Byzantine Greek scholar John Tzetzes that Archimedes lived for 75 years before his death in 212 BC. Plutarch wrote in his "Parallel Lives" that Archimedes was related to King Hiero II, the ruler of Syracuse, although Cicero suggests he was of humble origin. In the "Sand-Reckoner", Archimedes gives his father's name as Phidias, an astronomer about whom nothing else is known. A biography of Archimedes was written by his friend Heracleides, but this work has been lost, leaving the details of his life obscure. It is unknown, for instance, whether he ever married or had children, or if he ever visited Alexandria, Egypt, during his youth. From his surviving written works, it is clear that he maintained collegial relations with scholars based there, including his friend Conon of Samos and the head librarian Eratosthenes of Cyrene.
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Career.
The standard versions of Archimedes' life were written long after his death by Greek and Roman historians. The earliest reference to Archimedes occurs in the "Histories" by Polybius ( 200–118 BC), written about 70 years after his death. It sheds little light on Archimedes as a person, and focuses on the war machines that he is said to have built in order to defend the city from the Romans. Polybius remarks how, during the Second Punic War, Syracuse switched allegiances from Rome to Carthage, resulting in a military campaign under the command of Marcus Claudius Marcellus and Appius Claudius Pulcher, who besieged the city from 213 to 212 BC. He notes that the Romans underestimated Syracuse's defenses, and mentions several machines Archimedes designed, including improved catapults, crane-like machines that could be swung around in an arc, and other stone-throwers. Although the Romans ultimately captured the city, they suffered considerable losses due to Archimedes' inventiveness.
Cicero (106–43 BC) mentions Archimedes in some of his works. While serving as a quaestor in Sicily, Cicero found what was presumed to be Archimedes' tomb near the Agrigentine gate in Syracuse, in a neglected condition and overgrown with bushes. Cicero had the tomb cleaned up and was able to see the carving and read some of the verses that had been added as an inscription. The tomb carried a sculpture illustrating Archimedes' favorite mathematical proof, that the volume and surface area of the sphere are two-thirds that of an enclosing cylinder including its bases. He also mentions that Marcellus brought to Rome two planetariums Archimedes built. The Roman historian Livy (59 BC–17 AD) retells Polybius' story of the capture of Syracuse and Archimedes' role in it.
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Death.
Plutarch (45–119 AD) provides at least two accounts on how Archimedes died after Syracuse was taken. According to the most popular account, Archimedes was contemplating a mathematical diagram when the city was captured. A Roman soldier commanded him to come and meet Marcellus, but he declined, saying that he had to finish working on the problem. This enraged the soldier, who killed Archimedes with his sword. Another story has Archimedes carrying mathematical instruments before being killed because a soldier thought they were valuable items. Marcellus was reportedly angered by Archimedes' death, as he considered him a valuable scientific asset (he called Archimedes "a geometrical Briareus") and had ordered that he should not be harmed.
The last words attributed to Archimedes are "Do not disturb my circles" (; ), a reference to the mathematical drawing that he was supposedly studying when disturbed by the Roman soldier. There is no reliable evidence that Archimedes uttered these words and they do not appear in Plutarch's account. A similar quotation is found in the work of Valerius Maximus (fl. 30 AD), who wrote in "Memorable Doings and Sayings", "" ("... but protecting the dust with his hands, said 'I beg of you, do not disturb this).
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Discoveries and inventions.
Archimedes' principle.
The most widely known anecdote about Archimedes tells of how he invented a method for determining the volume of an object with an irregular shape. According to Vitruvius, a crown for a temple had been made for King Hiero II of Syracuse, who supplied the pure gold to be used. The crown was likely made in the shape of a votive wreath. Archimedes was asked to determine whether some silver had been substituted by the goldsmith without damaging the crown, so he could not melt it down into a regularly shaped body in order to calculate its density.
In this account, Archimedes noticed while taking a bath that the level of the water in the tub rose as he got in, and realized that this effect could be used to determine the golden crown's volume. Archimedes was so excited by this discovery that he took to the streets naked, having forgotten to dress, crying "Eureka!" (, "heúrēka"!, ). For practical purposes water is incompressible, so the submerged crown would displace an amount of water equal to its own volume. By dividing the mass of the crown by the volume of water displaced, its density could be obtained; if cheaper and less dense metals had been added, the density would be lower than that of gold. Archimedes found that this is what had happened, proving that silver had been mixed in.
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The story of the golden crown does not appear anywhere in Archimedes' known works. The practicality of the method described has been called into question due to the extreme accuracy that would be required to measure water displacement. Archimedes may have instead sought a solution that applied the hydrostatics principle known as Archimedes' principle, found in his treatise "On Floating Bodies": a body immersed in a fluid experiences a buoyant force equal to the weight of the fluid it displaces. Using this principle, it would have been possible to compare the density of the crown to that of pure gold by balancing it on a scale with a pure gold reference sample of the same weight, then immersing the apparatus in water. The difference in density between the two samples would cause the scale to tip accordingly. Galileo Galilei, who invented a hydrostatic balance in 1586 inspired by Archimedes' work, considered it "probable that this method is the same that Archimedes followed, since, besides being very accurate, it is based on demonstrations found by Archimedes himself."
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Law of the lever.
While Archimedes did not invent the lever, he gave a mathematical proof of the principle involved in his work "On the Equilibrium of Planes". Earlier descriptions of the principle of the lever are found in a work by Euclid and in the "Mechanical Problems," belonging to the Peripatetic school of the followers of Aristotle, the authorship of which has been attributed by some to Archytas.
There are several, often conflicting, reports regarding Archimedes' feats using the lever to lift very heavy objects. Plutarch describes how Archimedes designed block-and-tackle pulley systems, allowing sailors to use the principle of leverage to lift objects that would otherwise have been too heavy to move. According to Pappus of Alexandria, Archimedes' work on levers and his understanding of mechanical advantage caused him to remark: "Give me a place to stand on, and I will move the Earth" (). Olympiodorus later attributed the same boast to Archimedes' invention of the "baroulkos", a kind of windlass, rather than the lever.
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