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Wind Horse

The wind horse is a flying horse that is the symbol of the human soul in the shamanistic tradition of East Asia and Central Asia. In Tibetan Buddhism, it was included as the pivotal element in the center of the four animals symbolizing the cardinal directions and a symbol of the idea of well-being or good fortune. It has also given the name to a type of prayer flag that has the five animals printed on it.

Depending on the language, the symbol has slightly different names.

 * , pronounced lungta, Tibetan for "wind horse"
 * хийморь, Khiimori, literally "gas horse," semantically "wind horse," colloquial meaning soul.

In Tibetan usage
In Tibet, a distinction was made between Buddhism (, literally "divine dharma") and folk religion (, "human dharma"). Windhorse was predominantly a feature of the folk culture, a "mundane notion of the layman rather than a Buddhist religious ideal," as Tibetan scholar Samten G. Karmay explains.

However, while "the original concept of rlung ta bears no relation to Buddhism," over the centuries it became more common for Buddhist elements to be incorporated. In particular, in the nineteenth century lamas of the Rimé movement, particularly the great scholar Ju Mipham, began to "create a systematic interweaving of native shamanism, oral epic, and Buddhist tantra, alchemical Taoism, Dzogchen, and the strange, vast Kalachakra tantra," and windhorse was increasingly given Buddhist undertones and used in Buddhist contexts.

Windhorse has several meanings in the Tibetan context. As Karmay notes, "the word [ windhorse ] is still and often mistakenly taken to mean only the actual flag planted on the roof of a house or on a high place near a village. In fact, it is a symbol of the idea of well-being or good fortune. This idea is clear in such expressions as rlung rta dar ba, the 'increase of the windhorse,' when things go well with someone; rlung rta rgud pa, the 'decline of windhorse,' when the opposite happens. The colloquial equivalent for this is lam ’gro, which also means luck."

Origination
In his 1998 study The Arrow and the Spindle, Karmay traces several antecedents for the wind horse tradition in Tibet. First, he notes that there has long been confusion over the spelling because the sound produced by the word can be spelt either klung rta "river horse" or rlung rta "wind horse". In the early twentieth century the great scholar Jamgon Ju Mipham Gyatso felt compelled to clarify that in his view rlung rta was preferable to klung rta, indicating that some degree of ambiguity must have persisted at least up to his time.

Karmay suggests that "river horse" (klung rta) was actually the original concept, as found in the Tibetan nag rtsis system of astrology imported from China. The nag rtsis system has four basic elements: srog (vital force), lu (wylie: lus, body), wangtang (wylie: dbang thang, "field of power"), and lungta (wylie: klung rta, river horse). Karmey suggests that klung rta in turn derives from the Chinese idea of the lung ma, "dragon horse," because in Chinese mythology dragons often arise out of rivers (although druk [wylie:  'brug] is the Tibetan for dragon, in some cases they would render the Chinese lung phonetically). Thus, in his proposed etymology the Chinese lung ma became klung rta which in turn became rlung rta. Samtay further reasons that the drift in understanding from "river horse" to "wind horse" would have been reinforced by associations in Tibet of the "ideal horse" (rta chogs) with swiftness and wind.

Symbolism and the lhasang ritual
On prayer flags and paper prints, windhorses usually appear in the company of the four animals of the cardinal directions, which are "an integral part of the rlung ta composition": garuda or kyung, and dragon in the upper corners, and White Tiger and Snow Lion in the lower corners. In this context, the wind horse is typically shown without wings, but carries the Three Jewels, or the wish fulfilling jewel. Its appearance is supposed to bring peace, wealth, and harmony. The ritual invocation of the wind horse usually happens in the morning and during the growing moon. The flags themselves are commonly known as windhorse. They flutter in the wind, and carry the prayers to heaven like the horse flying in the wind.

The garuda and the dragon have their origin in Indian (both Buddhist and Hindu) and Chinese mythology, respectively. However, regarding the origin of the animals as a tetrad, "neither written nor oral explanations exist anywhere" with the exception of a thirteenth-century manuscript called "The Appearance of the Little Black-Headed Man" (dBu nag mi'u dra chag), and in that case a yak is substituted for the snow lion, which had not yet emerged as the national symbol of Tibet. In the text, a nyen (wylie: gNyan, mountain spirit ) kills his son-in-law, Khri-to, who is the primeval human man, in a misguided attempt to avenge his daughter. The nyen then is made to see his mistake by a mediator and compensates Khri-to's six sons with the gift of the tiger, yak, Garuda, dragon, goat, and dog. The first four brothers then launch an exhibition to kill robbers who were also involved with their mother's death, and each of their four animals then becomes a personal drala (wylie: dgra bla, "protective warrior spirit") to one of the four brothers. The brothers who received the goat and dog choose not to participate, and their animals therefore do not become drala. Each of the brothers represents one of the six primitive Tibetan clans (bod mi'u gdung drug), with which their respective animals also become associated.

The four animals (with the snow lion replacing the yak) also recur frequently in the Epic of King Gesar and sometimes Gesar and his horse are depicted with the dignities in place of the windhorse. In this context the snow lion, garuda and dragon represent the Ling (wylie: Gling) community from which Gesar comes, while the tiger represents the family of the Tagrong (wylie: sTag rong), Gesar's paternal uncle.

The wind horse ceremonies are usually conducted in conjunction with the lhasang ( "smoke offering to the gods") ritual, in which juniper branches are burned to create thick and fragrant smoke. This is believed to increase the strength in the supplicator of the four nag rtsis elements mentioned above. Often the ritual is called the risang lungta, the "fumigation offering and (the throwing into the wind or planting) of the rlung ta high in the mountains." The ritual is traditionally "primarily a secular ritual" and "requires no presence of any special officiant whether public or private." The layperson entreats a mountain deity to "increase his fortune like the galloping of a horse and expand his prosperity like the boiling over of milk.

Chögyam Trungpa
The late 20th-century Tibetan Buddhist master Chögyam Trungpa incorporated variants of many of the elements above, particularly windhorse, drala, the four animals (which he called "dignities"), wangtang, lha, nyen and lu, into a secular system of teachings he called Shambhala Training. It is through Shambhala Training that many of the ideas above have become familiar to westerners.

Heraldry
The wind horse is a rare element in heraldry. It is shown as a strongly stylized flying horse with wings. The most common example is the emblem of Mongolia.

title: Wind Horse


text: User talk:64.24.211.143

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

title: User talk:64.24.211.143


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Kyle of Lochalsh line

The Kyle of Lochalsh line is a primarily single-track railway line in the Scottish Highlands, from Dingwall to Kyle of Lochalsh. Many of the passengers are tourists, but there are also locals visiting Inverness for shopping, and commuters. All services are provided by ScotRail and run beyond Dingwall to Inverness. In the past there were some through services to and from Glasgow, Edinburgh or Aberdeen. None of the line is electrified, and all trains on the line are diesel-powered, as are all other trains in the Scottish Highlands.

Route
The Kyle of Lochalsh line runs east-west and links the town of Dingwall, on the east coast of the Highlands at the tip of the Cromarty Firth, with the village of Kyle of Lochalsh on the west coast, close to the Isle of Skye. The line lies entirely within the former county of Ross and Cromarty, part of the modern-day Highland council area.

Dingwall–Achnasheen: Easter Ross
The route begins at Dingwall station – a junction station with the Far North Line, which runs (mostly) along the Moray Firth and links Inverness with Wick and Thurso. Almost immediately north of Dingwall, the two lines diverge at Dingwall Junction and the line to Kyle of Lochalsh takes a sharp left turn to head west.

Initially, the single-track line briefly follows the course of the A834 road until it abruptly curves off to the north, crossing over the River Peffery, only to turn west again. There used to be a short branch line here that went straight on towards Strathpeffer; this branch closed to passengers in 1946 and closed completely in 1951. The line to Kyle, meanwhile, bypasses the town about 1 mi to the north; Achterneed station existed along this stretch and also served Strathpeffer until it too closed in 1964. Achterneed is one of only three stations on the main line to have been closed, and one of two that were never reopened.

The line then continues west, climbing at gradients as steep as 1 in 50, until it passes close to the summit of Raven Rock where it starts descending. It eventually meets the Black Water – a tributary of the River Conon – and follows it upstream alongside the A832 road. The railway and the road both skirt the southern edge of Loch Garve and then turn northwest, approaching the first open station on the line – Garve. This was supposed to be site of a junction with the Garve and Ullapool Railway to the port village of Ullapool but, despite securing government approval, this line was never built.

Beyond Garve, the railway and the A832 continue westwards, away from the Black Water whose source lies to the north. Soon, the line meets Loch Luichart – the source of the River Conon itself – and follows its northern edge; Lochluichart station is located at the northwestern tip of the loch. This station was moved to this location from its original site in 1954 as a result of a hydroelectric scheme, which raised the water level of the loch. From here, the line continues to follow several of the Conon's tributaries, passing by Loch a' Chuilinn and Loch Achanalt until it reaches Achanalt station near the mouth of the River Bran. The track then follows the course of this river for about 6 mi until the village of Achnasheen, near the eastern end of Loch a' Chroisg. The station at Achnasheen, like Garve, was to be the site of a junction: the proposed Loch Maree and Aultbea Railway was to run between Achnasheen and the small fishing village of Aultbea, but the line never received government approval.

Down the line from Achnasheen the line turns southwest, parting ways with the A832 which continues westwards; the railway now parallels the A890 road instead.

Achnasheen–Kyle of Lochalsh: Wester Ross
A few miles southwest of Achnasheen the track reaches its highest point above sea level, as it leaves the drainage basin of the River Conon (which flows to the Cromarty Firth on the east coast) and enters the basin of the River Carron (whose estuary is on the west coast). The line meets the River Carron itself at Loch Scaven near its source, and then follows the course of the river downstream.

Close to the point where the Carron is joined by the Alltan na Feola stream lies the site of the former Glencarron station; this small halt closed in 1964, although some drivers continued to stop at the station unofficially, refusing to acknowledge the station's closure, until as late as the 1990s. The next open station on the line is Achnashellach, some 12 mi down the line from Achnasheen; this is the longest distance between two existing consecutive stations on the line. The line then skirts the northwestern edge of Loch Dùghaill and continues to follow the River Carron until reaching Strathcarron station, where the river ends as it flows into Loch Carron, a sea inlet. From here, the railway runs along the southern coastline of Loch Carron, and continues to hug the coast all the way until the terminus at Kyle of Lochalsh (except briefly near Plockton).

A short distance from Strathcarron the line reaches another station, Attadale, located near the mouth of the river of the same name. Just southwest of the station, the line passes through an avalanche shelter – an unusual tunnel-like structure, approximately 250 m, which also carries the A890 and is partially open on the loch-side; it was built in 1978 to prevent rocks from falling onto the road and track. The line then continues for nearly 5 mi until it reaches Stromeferry station, adjacent to a former ferry port which linked the area with North Strome on the opposite side of the loch. Occasionally the ferry link reopens on a temporary basis, when the A890 is closed due to landslips. At Stromeferry the A890 turns south; from here, the railway does not parallel any major roads, instead simply following the coast.

The next station on the line is Duncraig, which was built as a private, single-platform halt to serve Duncraig Castle; it was not made available for the public until 1949, more than 50 years after opening. Similarly to Glencarron, the station closed in 1965 but continued to be served unofficially, as drivers refused to acknowledge the station's closure; however, unlike Glencarron, Duncraig eventually reopened officially, in 1976. From here it is just over 1 mi until the next station at Plockton; this is the shortest distance between any two stations on the line. Plockton station is actually located about 0.6 mi south of the main part of the village itself, although it lies adjacent to both the Plockton High School and the Plockton Airstrip.

The penultimate station en route is Duirinish, which is also a short distance away from Plockton; the station primarily serves the villages of Duirinish and Drumbuie. From here, the line runs in a generally southerly direction, although the exact heading varies significantly as the track closely follows the jagged coast. The railway leaves the coast of Loch Carron just before entering the village of Kyle of Lochalsh; it terminates at Kyle of Lochalsh station, built on a pier right on the edge of Loch Alsh, just 750 m away from the Isle of Skye which can be seen across the loch.

Infrastructure
The full line between Dingwall and Kyle of Lochalsh is 63 mi. It is almost entirely single-track, except for four double-track passing loops at Dingwall, Garve, Achnasheen and Strathcarron, and the two platforms and two sidings at Kyle of Lochalsh. The entire line is unelectrified.

The whole line, together with the Far North Line, is signalled using the Radio Electronic Token Block system, which is very cost-effective in both implementation and maintenance, but significantly limits the capacity of the lines.

Along the route there are 29 bridges, 31 cuttings, and a single tunnel.

History
The route was built in two parts: the Dingwall and Skye Railway, between Dingwall and Stromeferry, opened on 19 August 1870, while the Kyle of Lochalsh Extension (Highland Railway) took the line beyond Stromeferry to Kyle of Lochalsh on 2 November 1897. Dingwall station itself had been open since 1862, as an intermediate station on the Inverness and Ross-shire Railway (part of the modern-day Far North Line).

The Strathpeffer Branch operated between 1885 and 1951.

In 1933, the London, Midland and Scottish Railway introduced two named trains on the line, The Hebridean and The Lewisman.

In July 1939 a landslide between Attadale and Stomeferry derailed an engine and six freight vans. The landslide was caused by recent heavy rains.

In 1949 it was planned to relocate Lochluichart station to allow the flooding of the area by the Glascarnoch-Luichart-Torr Achilty hydroelectric scheme. On 3 May 1954 a new station was opened as Lochluichart. The deviation required about 2 mi on stone-pitched embankments and in rock cuttings, a 100 ft bridge over the River Conon and a 36 ft bridge.

In the 1960s the line was listed to be closed under the Reshaping of British Railways report; however it was reprieved and services continued.

In 1970, British Rail wanted to close the line when Ross and Cromarty council voted to create a new £460,000 ferry terminal at Ullapool (43 nmi from Stornoway) replacing that at Kyle of Lochalsh (71 nmi from Stornoway). In December 1971 it was reported that the costs of operating the line were £318,000 per annum, with revenue of £51,000 per annum , and the Secretary of State for Transport agreed that the line should close, but a spirited local campaign again succeeded in reversing this decision and keeping it open.

In February 1989 the bridge over the River Ness in Inverness was washed away, leaving both the Kyle line and the Far North Line stranded, but new Class 156 "Sprinter" trains were brought over by road, and a temporary yard was built to service them at Muir of Ord. The line reopened in May 1990.

Services
As of April 2022, the Monday−Saturday service pattern on the line consists of four trains per day running eastbound from Kyle of Lochalsh to Inverness (via Dingwall and the Far North Line), and four trains per day westbound from Inverness to Kyle of Lochalsh. On Sundays there is just one train per day each way, increasing to two per day during the summer months. ScotRail operates all services on the line with its Class 158/7 "Express Sprinter" diesel multiple units.

All services call at every intermediate station en route, although Lochluichart, Achanalt, Achnashellach, Attadale, Duncraig and Duirinish stations are request stops: passengers wishing to board the train at these stations must flag the train by raising their arm, while those wishing to alight must inform the on-board train supervisor to arrange for the train to stop. If there are no passengers wishing to get on or off the train at a request stop, it will pass through without stopping.

Services between Inverness and Kyle of Lochalsh typically have a journey time of about 2 hours 40 minutes end-to-end.

Passenger volumes

 * Stations between Inverness and Dingwall are also included for reference, as all trains on the line also call there
 * Stations in italics are request stops
 * The statistics cover twelve-month periods that start in April

Future
In the Scottish Government's National Transport Strategy, published in February 2020, it was stated that the line would not be electrified with overhead lines, but rather, an alternative to diesel traction will be used for the route.

Kyle of Lochalsh line in film and books
The Kyle of Lochalsh line was featured in Eddie McConnell's lyrical documentary The Line to Skye (1973) with commentary by Scottish writer William McIlvanney, commissioned as part of Ross & Cromarty's campaign to keep the line open at a time when it was threatened with closure. The film follows the train from Inverness to Kyle of Lochalsh, describing the communities, landscape and wildlife along its route, while contrasting the frustration of motorists with the relaxation of the journey by rail.

In Stephen Durrell's 1939 documentary West of Inverness, the importance of the Kyle of Lochalsh line to the crofters of the West Highlands is demonstrated through its role of transporting passengers, mail, parcels, food and livestock to and from their communities. The film shows the LMS steam locomotives that operated the line at this time.

In the episode of Great Railway Journeys of the World "Confessions of a Trainspotter" (1980), Michael Palin travels from London to the Kyle of Lochalsh and returns with the railway station's sign.

Video 125 Ltd. produced a driver's eye view documentary of the line in 1987, when the service was still operated using loco-hauled trains, in this case motive power being provided by Class 37 no. 37262 named Dounreay after the nuclear power station. Narration was by Paul Coia.

Nicholas Whittaker travelled the line both ways during the summer of 1973, an experience he wrote about in his 1995 book Platform Souls.

As with the other railway lines of the western Highlands (the West Highland Railway and the Callander and Oban Railway), John Thomas wrote a comprehensive and highly readable history, The Skye Railway.

title: Kyle of Lochalsh line


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Albert Szent-Györgyi Medical University

Albert Szent-Györgyi Medical University was originally established in Kolozsvár, then in Austria-Hungary, later Romania, in 1872. After World War I, it was moved to Szeged. Since 1921 great advances have been made in the development of the University. Most of the University buildings have preserved their original, harmonized style, providing a true University atmosphere of tradition.

Setting and architecture
Preclinical departments of the Faculty of Medicine are situated around Cathedral (Dóm) Square. The University Hospitals, housing the clinical departments, occupy the land between the Cathedral and River Tisza, which is a calm, peaceful area of the old town. Some of the preclinical departments are accommodated in other buildings; however, even off-campus departments of the Medical University (such as Anatomy and Forensic Medicine) are within easy access from the city center (10 minutes by tram).

Notable professors
Many notable professors have been members of the faculty, including:
 * József Mátyás Baló (pathology)
 * Béla Issekutz and Nicholas (Miklós) Jancsó (pharmacology)
 * Dezső Miskolczy (neurology)
 * István Rusznyák and Géza Hetényi (internal medicine)
 * György Ivanovics (microbiology)
 * Albert Szent-Györgyi (medical chemistry); the university recently assumed his name. He was awarded the Nobel Prize in 1937 for his achievements in biochemistry.

Notable researchers
Among other notable people, the following researchers have been honorary doctors of the university:
 * S. Bonfils, Paris, France,
 * Ludwig Demling, Erlangen-Nuremberg, Germany,
 * Egon Diczfalusy, Stockholm, Sweden,
 * Francis (Ferenc) Földes, New York, United States,
 * Ryszard Jerzy Gryglewski, Kraków, Poland,
 * Paul Janssen, Beerse, Belgium,
 * Helmuth Kala, Halle, Germany,
 * K. Kovács, Toronto, Ontario, Canada,
 * E. Körber, Tübingen, Germany,
 * W. Kreutzberg, Munich, Germany,
 * J. M. Krueger, Pullman, USA,
 * G. Lajtha, Manchester, England,
 * M. McMahon, Leeds, England,
 * Sh. Massry, Los Angeles, USA,
 * J. Nakamura, Missoula, USA,
 * P. Pflegel, Greifswald, Germany,
 * P. Rakic, New Haven, USA,
 * J. Roelandt, Rotterdam, The Netherlands,
 * H. L. Sheehan, Liverpool, England,
 * B. F. Straub, Budapest, Hungary,
 * T. Symington, London, England,
 * D. De Wied, Utrecht, The Netherlands,
 * J. R. Wolff, Göttingen, Germany.

Faculty of Pharmacy
The Faculty of Pharmacy was founded in 1957. Since 1921, more than 4000 pharmacists have received their diplomas (Master of Pharmacy) and 400 pharmacists have been awarded a university doctorate in pharmacy. In recent years, 94 foreign students from 24 countries have received pharmaceutical diplomas through government-sponsored exchange programs. A number of young foreign pharmacists currently take part in different post-graduate courses.

Education today
The Albert Szent-Györgyi Medical University is the regional center of health care for southern Hungary, offering wide-ranging cooperation and collaboration with surrounding hospitals and research institutes. As stated earlier the once independent university is now a faculty of the University of Szeged.

title: Albert Szent-Györgyi Medical University


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Sloane Street

Sloane Street is a major London street in the Royal Borough of Kensington and Chelsea which runs north to south, from Knightsbridge to Sloane Square, crossing Pont Street about halfway along.

History
Sloane Street takes its name from Sir Hans Sloane, who purchased the surrounding area in 1712. Many of the properties in the street still belong to his descendants, the Earls Cadogan, via their company Cadogan Estates.

Sloane Street has long been a fashionable shopping street, especially the northern section closest to Knightsbridge, which is known informally as Upper Sloane Street. Since the 1990s Sloane Street's status has increased further, and it is now on a par with Bond Street, which has been London's most exclusive shopping street for two centuries. The street has flagship stores for many of the world's most famous brands in fashion.

In popular culture
Sloane Street, along with Sloane Square, also gives its name to "Sloane Rangers", originally applied to the stereotypical kind of young upper class English ladies seen in the area. The expression was roughly the female equivalent to the term "Hooray Henry", used to describe brash, upper-class young English public school boys, although this term is not geographically restricted and is used all over the UK.

Real estate ownership and character
During the 1990s, Dubai's ruling Al Maktoum family, led by Mohammed bin Rashid Al Maktoum, bought most of the properties on the west side of Sloane Street at the Knightsbridge end. The National Bank of Dubai opened its first overseas branch in London to serve the many UAE-based visitors who rent these properties in summer. The Jumeirah Carlton Tower Hotel is owned by the hotels arm of Dubai Holding Company, which is also controlled by Sheikh Mohammed.

The northern half of the street is near Knightsbridge and is home to a few smart, more modern residential blocks, all with 24-hour porterage, the Cadogan Hotel and Millennium Hotel. Harrods lies next to Hans Place immediately to the west along Basil Street and Hans Crescent, and Lowndes Square lies to the east. Harvey Nichols lies at the corner of Knightsbridge and Sloane Street.

The southern half of the street has much more individual character, with a number of typical Pont Street Dutch style red brick buildings, built in the 19th century by Earl Cadogan, which house elegant apartments. In the most exclusive residential area of the street, which is between Sloane Square and Cadogan Place, some of the residences have remained as whole houses.

Notable buildings
Notable buildings include:
 * Holy Trinity Sloane Street by the Victorian architect J.D. Sedding
 * The Danish Embassy designed by Arne Jacobsen (shared with the Embassy of Iceland)
 * 51-52 Sloane Street, the Embassy of Peru.
 * 64 Sloane Street, designed by Fairfax Blomfield Wade-Palmer.
 * 190-192 Sloane Street.
 * 123 Sloane Street.
 * 139 Sloane Street.

title: Sloane Street


text: Template:Campaignbox Axis–Soviet War

title: Template:Campaignbox Axis–Soviet War


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Johann Leonhard Hug

Johann Leonhard Hug (1 June 1765 in Constance – 11 March 1846 in Freiburg im Breisgau), was a German Roman Catholic theologian, orientalist and biblical scholar.

Life
In 1783 he entered the University of Freiburg, where he became a pupil in the seminary for the training of priests, and soon distinguished himself in classical and Oriental philology as well as in biblical exegesis and criticism. In 1787 he became superintendent of studies in the seminary, and held this appointment until the breaking up of the establishment in 1790. In the following year he was called to the Freiburg chair of Oriental languages and Old Testament exegesis; to the duties of this post were added in 1793 those of the professorship of New Testament exegesis.

Declining calls to Breslau, Tübingen, and thrice to Bonn, Hug continued at Freiburg for upwards of thirty years, taking an occasional literary tour to Munich, Paris or Italy. In 1827 he resigned some of his professorial work, but continued in active duty until in the autumn of 1845 he fell ill and died on 11 March 1846. Johann Martin Augustin Scholz was his pupil.

Works
Hug's earliest publication was the first installment of his Einleitung; in it he argued against Johann Gottfried Eichhorn in favour of the "borrowing hypothesis" of the origin of the Synoptic Gospels, maintaining the priority of Matthew, and asserting that the present Greek text was the original.

His subsequent works were dissertations on the origin of alphabetical writing (Die Erfindung der Buchstabenschrift, 1801), on the antiquity of the Codex Vaticanus (1810), and on ancient mythology (Untersuchungen über den Mythos der berühmtern Völker der alten Welt. Vorzüglich der Griechen; dessen Entstehen, Veränderungen und Innhalt, 1812); a new interpretation of the Song of Solomon (Des hohe Lied in einer noch unversuchten Deutung, 1813), to the effect that the lover represents King Hezekiah, while by his beloved is intended the remnant left in Israel after the deportation of the ten tribes; and treatises on the indissoluble character of the matrimonial bond (De conjugii christiani vinculo indissolubili commentatio exegetica, 1816) and on the Alexandrian version of the Pentateuch (1818).

His Einleitung in die Schriften des Neuen Testaments, his major work, was completed in 1808 (fourth German edition, 1847; English translations by Daniel Guilford Wait, London, 1827, and by David Fosdick and Moses Stuart, New York, 1836; French partial translation by J. E. Cellerier, Geneva, 1823). In the portion relating to the history of the text he holds it to have been current up to the middle of the 3rd century only in a common edition, of which recensions were afterwards made by Hesychius, an Egyptian bishop, by Lucian of Antioch and by Origen.

From 1828 until it ceased to be published in 1834, Hug was a regular contributor to the Zeitschrift für die Geistlichkeit des Erzbisthums Freyburg. Hug was also the first editor (from 1839 until his death in 1846) of the newly founded Zeitschrift für Theologie, published by the Catholic Theological Faculty in Freiburg.
 * Hug's introduction to the New Testament, transl. by D. Fosdick and Moses Stuart, Andover 1836
 * Die mosaische Geschichte des Menschen, Frankfurt 1793;
 * Die Ursprünge der menschlichen Erkenntnis, Basel 1796;
 * Einleitung in die Schriften des Neuen Testaments, 2 Te., 1808 (18472);
 * De antiquitate Codicis Vaticani commentatio, Freiburg: Herder 1810;
 * Untersuchungen über den Mythos der berühmtern Völker der alten Welt Vorzüglich der Griechen; dessen Entstehen, Veränderungen und Innhalt, Freiburg 1812 (18232);
 * Das hohe Lied einer noch unversuchten Deutung, 1813;
 * J. L. M., Schutzschr. f. seine Deutung des Hhld. u. dessen weitere Erl., Freiburg 1815;
 * De conjugii christiani vinculo indissolubili commentatio exegetica, 1816;
 * De Pentateuchi versione Alexandrina commentatio, 1818;
 * Gutachten über das Leben Jesu v. David Friedrich Strauß (1835), 2 Te., 1840–44 (l8542)

title: Johann Leonhard Hug


text:
Wikipedia:Articles for deletion/Flarion

 This page is an archive of the discussion about the proposed deletion of the article below. This page is no longer live. Further comments should be made on the article's talk page rather than here so that this page is preserved as an historic record. The result of the debate was Keep. Rje 05:48, Feb 16, 2005 (UTC)

Flarion
Vanity. Not especially notable. — Trilobite (Talk) 16:47, 6 Feb 2005 (UTC)

This page is now preserved as an archive of the debate and, like some other VfD subpages, is no longer 'live'. Subsequent comments on the issue, the deletion, or the decision-making process should be placed on the relevant 'live' pages. Please do not edit this page.
 * Vague and with unverifiable claims. Delete. Uncle G 17:46, 2005 Feb 6 (UTC)
 * Keep. It gets an impressive total of 81,000 Google hits. I've cleaned up the article with information from their website. This company seems to be making news all over the Internet. Unless someone with more knowledge of the telecommunications market assures this is just hype, I'm voting to keep. JoaoRicardo 19:09, 6 Feb 2005 (UTC)
 * I find it amusing that when (aside from articles and prepositions) the only two words in common across the versions are "company" and "wireless", this is still "clean up" rather than "complete rewrite". ☺  You're too modest.  Much better.  Verifiable and specific.  Keep. Uncle G 00:34, 2005 Feb 7 (UTC)
 * Comment. Thanks Uncle G and Samaritan. :-) JoaoRicardo 02:48, 7 Feb 2005 (UTC)
 * Great catch JoaoRicardo! Keep. Samaritan 00:22, 7 Feb 2005 (UTC)
 * Keep, notable, needs expansion. Megan1967 01:38, 7 Feb 2005 (UTC)
 * Keep. Thanks to the good work by Joao Ricardo. 220.244.224.72 16:36, 11 Feb 2005 (UTC)
 * Oops that was me. Capitalistroadster 17:32, 11 Feb 2005 (UTC)
 * Keep and allow for organic growth. GRider\talk 22:10, 7 Feb 2005 (UTC)

title: Wikipedia:Articles for deletion/Flarion


text: Category:Superior Software games

title: Category:Superior Software games


text:
Shackleton Ice Shelf

Shackleton Ice Shelf is an extensive ice shelf fronting the coast of East Antarctica from 95° E to 105° E. It extends for an along-shore distance of about 384 km, projecting seaward about 145 km in the western portion and 64 km in the east. It occupies an area of 33,820 km2. It is part of Mawson Sea and separates the Queen Mary Coast to the west from the Knox Coast of Wilkes Land to the east.

Discovery and naming
The existence of this ice shelf was first made known by the USEE under Charles Wilkes who mapped a portion of it from the Vincennes in February 1840. It was explored by the Australian Antarctic Expedition under Douglas Mawson (1911–14) who named it for Sir Ernest Shackleton. The extent of the ice shelf was mapped in greater detail in 1955, using aerial photography obtained by US Navy Operation Highjump, 1946–47. Further mapping by the Soviet Expedition of 1956 showed the portion eastward of Scott Glacier to be a part of this ice shelf.

Important Bird Area
A 500 ha site (-64.98861°N, 96.15583°W) on the ice shelf has been designated an Important Bird Area (IBA) by BirdLife International because it supports a breeding colony of some 6,500 emperor penguins, based on 2009 satellite imagery.

title: Shackleton Ice Shelf


text:
Hocine Aït Ahmed

Hocine Aït Ahmed (حسين آيت أحمد; 20 August 1926 – 23 December 2015) was an Algerian politician. He was founder and leader until 2009 of the historical political opposition in Algeria.

Life
Aït Ahmed was born at Aït Yahia in 1926.

He was one of the main leaders of the National Liberation Front (FLN) in the Algerian War, and was arrested along with Ahmed Ben Bella, Mohamed Boudiaf, Mostefa Lacheraf, and Mohamed Khider after France hijacked the airplane the FLN leaders bound for Tunisia, and directed it to occupied Algiers.

After the Algerian War, Aït Ahmed resigned from the Provisional Government of the Algerian Republic (GPRA) and all the organs of the new power during the crisis of the summer of 1962. In September 1963, he founded the Socialist Forces Front (FFS), which sought political pluralism in political life locked by the single party system.

Arrested and sentenced to death in 1964, he escaped from the El Harrach prison on May 1, 1966. Exiled in Switzerland, he became a doctor of law. After the riots of 1988, the Algerian president Chadli Bendjedid proposed a new constitution calling for political pluralism. Aït Ahmed was invited to return to his country, where he came back in December 1989, at the head of the FFS, but again left his country after the assassination of the President, Mohamed Boudiaf, in June 1992. He repeatedly returned to Algeria since then, including during the 50th anniversary of the outbreak of the war of liberation (November 1, 1954). Aït Ahmed died at the age of 89 in Lausanne, Switzerland on 23 December 2015.

title: Hocine Aït Ahmed


text: Talk:Shackleton Ice Shelf

title: Talk:Shackleton Ice Shelf


text:
Roger O. Egeberg

Roger Olaf Egeberg, M.D. (13 November 1902 – 13 September 1997 Washington, D.C.) was an American medical educator, administrator and advocate of public health. He was General Douglas MacArthur's personal physician during World War II in the Pacific theater. His other roles included Assistant Secretary for Health and Scientific Affairs in the Department of Health, Education, and Welfare (now the United States Department of Health and Human Services) during the Nixon administration and Dean of the University of Southern California's medical school.

Early life and family
Egeberg was born in Chicago, Illinois to Hans Olaf Egeberg (1875-1932) and Ulrikka Rostrup Egeberg (1875-1932) (née Nielsen), a Norwegian immigrant family. Egeberg married a Canadian sculptor, Margaret Chahoon (25 August 1904 - 31 March 2011), in 1929. Together, they had a son and three daughters.

Education and career
Egeberg received a bachelor's degree in 1925 from Cornell University where he was a member of the Quill and Dagger society. He earned his medical degree in 1929 at Northwestern University school of medicine. He became an internist and joined the faculty of Western Reserve University School of Medicine.

Military service
During World War II, Egeberg was a member of the 4th General Hospital which was sent to Australia. From there he transferred to Milne Bay, Papua New Guinea (PNG) where he organised field stations and was a malaria control officer. Through determined attempts to control illnesses such as malaria and sexually transmitted diseases in PNG, Egeberg was noticed by MacArthur who made him his personal physician and aide-de-camp. Egeberg rose to the rank of colonel and was awarded the Bronze Star Medal and the Legion of Merit. At the end of the war, Egeberg treated the Prime Minister of Japan, Hideki Tojo who had shot himself. Tojo was later hanged.

Academic positions
After the war, Egeberg was Chief of Medicine at Wadsworth General Hospital, head of County-University of Southern California Medical Center (1959) and Dean, USC School of Medicine (1964). After working for Nixon, Egeberg took a professorial chair at Georgetown University. In his later career, he advocated for the advanced training of doctors in geriatric medicine.

Nixon administration
From 1969 to 1971, Egeberg was the Assistant Secretary for health and scientific affairs in the Department of Health, Education and Welfare. In this role, he was an advocate for expanding public health care and argued for the financing of medical programs (through the Office of Health Care Financing). During this time, Egeberg visited the USSR and developed a professional relationship with Boris Vasilevich Petrovsky, the Soviet minister of health. In the spring of 1970, while requesting $100 million to train more doctors and nurses, Egeberg alleged the Health, Education and Welfare Secretary, Robert H. Finch, and the department's Under Secretary, John C. Veneman, were not considering his advice on health matters and that Nixon's advisers were ignoring him. He said,
 * "The White House just doesn't appreciate, doesn't know, what is going on in the health field."

also,
 * "I just can't get through to Ehrlichman," (referring to John D. Ehrlichman, the president's chief aide for domestic matters.)

and,
 * "I may be fired because of my words and actions, but I won't quit."

Officials of the department, including Finch, expressed dissatisfaction with Egeberg's managerial skills. From 1971 to 1977, Egeberg was the health secretary's special assistant for health policy and special consultant to the president in health affairs. In 1976 and 1977, he was also special assistant for health education.

Marijuana
In 1970, Egeberg introduced an amendment to legislation governing penalties for marijuana offences. The nature of a conviction for possession of marijuana was changed from felony to misdemeanor. The committee reviewing the Controlled Substances Act requested Egeberg's advice on how marijuana should be regulated. After Egeberg wrote to Harley O. Staggers, chairman of the house committee on interstate and foreign commerce, marijuana was temporarily placed in Schedule I, the most tightly-controlled category of drugs. He wrote,
 * "Dear Mr. Chairman, In a prior communication, comments requested by your committee on the scientific aspects of the drug classification scheme incorporated in H.R. 18583 were provided. This communication is concerned with the proposed classification of marihuana...It is presently classed in schedule I(C) along with its active constituents, the tetrahydrocannibinols and other psychotropic drugs...Some question has been raised whether the use of the plant itself produces "severe psychological or physical dependence" as required by a schedule I or even schedule II criterion.  Since there is still a considerable void in our knowledge of the plant and effects of the active drug contained in it, our recommendation is that marihuana be retained within schedule I at least until the completion of certain studies now underway to resolve the issue. If those studies make it appropriate for the Attorney General to change the placement of marihuana to a different schedule, he may do so in accordance with the authority provided under section 201 of the bill."

Egeberg intended for marijuana to remain in Schedule I only until the Shafer Commission completed its report. However, Nixon refused to implement the Commission's recommendation that marijuana be legalized.

Books

 * The General: MacArthur and the Man He Called 'Doc.'  (1984 Hippocrene Books) ISBN 0882548549, ISBN 978-0882548548
 * Reaching for the world: early memories. (2000, Washington Expatriates Press) ISBN 096090624X, ISBN 978-0960906246

External sources

 * "Two national officials who advocated drug policy reform pass away'' National Drug Strategy Network.
 * Gettman, Jon Science and the end of marijuana prohibition
 * Obituary NY Times. Accessed 28 June 2012.
 * Interview with Roger O. Egeberg 30 July 1991. Accessed 28 June 2012.

title: Roger O. Egeberg


text:
Gortyna, Arcadia

Gortyna (Γόρτυνα), is a former municipality in Arcadia, Peloponnese, Greece. Since the 2011 local government reform it is part of the municipality Megalopoli, of which it is a municipal unit. The municipal unit has an area of 116.205 km2. Its seat was in the village Karytaina. The name of the municipality was taken from the ancient city of Gortys.

Subdivisions
The municipal unit Gortyna is subdivided into the following communities (constituent villages in brackets):
 * Atsicholos
 * Karytaina (Karytaina, Kalyvakia, Karvounari)
 * Katsimpalis
 * Kotili (Kotili, Palatos, Strongylo)
 * Kourounios
 * Kyparissia
 * Mavria
 * Sarakini (Sarakini, Kryonero, Palaiokastro)
 * Vlachorraptis
 * Zoni

Ancient Gortys
The ancient city Gortys was located in the valley of the river Lousios. It reputedly was founded by Gortys, son of Stymphalus, a legendary king of Arcadia. When Megalopolis was founded in the 4th century BC, many inhabitants moved to the new city, but Gortys was still inhabited in the 2nd century AD, a village belonging to Megalopolis then. Ancient Gortys was known for its Temple of Asclepius. The ruins of Gortys have been excavated between 1940 and 1956. They are located near the road from Atsicholos to Elliniko. The remains of several fortifications, temples and baths have been found.

Geography
The territory of the municipal unit Gortyna is very mountainous: the Mainalo lies to the northeast, and the Lykaion to the southwest. The rivers Lousios and Alfeios flow through it and have created deep gorges. The plain of Megalopoli lies to the southeast. Gortyna borders on Elis to the west, and Messenia to the southwest. Gortyna is about 12 km northwest of Megalopoli, 12 km south of Dimitsana, 30 km west of Tripoli, 50 km north of Kalamata and 60 km southeast of Pyrgos.

title: Gortyna, Arcadia


text:
Talk:Split-quaternion

Name
I think split-quaternion would be a better name for this page; mostly for naming consistency with split-complex number. We could then do split-octonion as well. As you've pointed out all these structures have numerous names; we should, however, strive for some consistency. -- Fropuff 16:52, 2005 Feb 6 (UTC)

I believe the hyphen goes against standard mathematical practice. It should be "split quaternion", "split octonion", "split complex number", etc.  See mathematics papers like this:

https://www.jstor.org/stable/24898658

or this:

https://arxiv.org/pdf/1203.0688

or many more. John Baez (talk) 05:40, 21 October 2019 (UTC)

"Hyperbolic Quaternion" ambiguity
(19 June 2006)

I see that there is a potential ambiguity about the term "Hyperbolic quaternion". The reference I've added to the split-quaternion site refers to hyperbolic quaternions from the hypernumbers program only, and not to the hyperbolic quaternions as they were defined in the 19th century. I hope that my wording is clear and the reference is therefore not ambiguous. In addition, I've explicitely added hyperbolic quaternions to the referenced hypernumbers page (as an example), and am also referencing split-quaternions / coquaternions from there.

While I am open to any wording or placement adjustment, I see this as a correct and valid statement, and see the reference therefore as applicable, useful, and reasonable. I would be glad to discuss any concern. Hypernumbers in general are actively discussed in the "hypernumbers" Yahoo(R) group. Thanks, Jens.

 * I've done some layout clean-up, as a step in the right direction, hopefully. Comments are invited. Thanks, Jens Koeplinger 02:08, 19 August 2006 (UTC)

re: Clifford algebras
Since Clifford algebras are a more advanced concept than a particular 4-dimensional real algeba, the introduction of the extra concept in the introductory paragraph amounts to obscurantism. Clear expository principles should prevail over the urge to link in an already well-funded research area. The better we describe the lower-dimensional algebras, the firmer will be the foundation for higher study. So, I have removed the Clifford algebra link from the first paragraph and replaced it with a more elementary and concrete reference.Rgdboer 01:59, 30 March 2007 (UTC)

 * I've put it back again. The point is that identifying the Clifford algebra(s) immediately tags what this algebra is about, what it is likely to be useful for, and how it compares to other hypercomplex numbers or quaternion variants.  It means that somebody who can read a Clifford algebra classification knows exactly what to expect to find in the article.

 * So seeing Cℓ2,0(R), one can read off immediately that this is going to be the natural algebra for describing vectors and directed areas in 2d, and their behaviour under reflections and rotations; and co-ordinate transformations on hyperbolic surfaces in 3d through the isomorphism with Cℓ01,2(R). Seeing Cℓ1,1(R), one can read off immediately that this is going to be a natural algebra for describing vectors and areas on surfaces with one real and one hyperbolic coordinate; and through the isomorphism with Cℓ02,1(R), it's going to relate co-ordinate transformations on hyperbolic surfaces in 3d with the alternative metric convention (+,+,-), rather than (-,-,+).

 * As for Clifford algebras being obscurantist, I agree that IMO the current version of the Clifford algebra article starts at much too abstract, too all-encompassing, too mathemematically sophisticated a level.  But that is a problem with the current article, not with the topic.  If you look at hypercomplex number, you can start to see how useful the Clifford algebra classifications can be for making sense of all these algebras, and linking them all together with a systematic contextualised approach.  I'm also going to put in some work on the geometric algebra article, which has potential to become the consolidated entry-level way in to study algebras like this one, and the geometric uses to which they can be put.  See for example the first couple of chapters of the Cambridge "Physical applications of geometric algebra" course, linked at Geometric_algebra for how it ties everything together.

 * If you read that link, I hope you'll agree that it ought to be much more easy for students to study all the examples of geometric algebras together, understanding their geometric uses in a systematic way, rather than trying to pick them off in an ad-hoc unconnected way one by one. Jheald 07:48, 30 March 2007 (UTC)

 * I side with Rgdboer, Clifford algebras are only one out of many aspects of approaching coquaternions, historically and algebraically. The current article mentions the various isomorphisms in a way that is scattered out throughout the article, which is a problem. I believe that this article needs much rework. However, I am very concerned about the current edits in the hypercomplex number article by Jheald. The article suddently becomes an article on Clifford algebras, rather than an overview article. I have voiced my concern there. Thanks, Koeplinger 19:36, 30 March 2007 (UTC)

Name of this article: James Cockle's ring or something more modern?
There is a long tradition in astronomy and mathematics that a discoverer has the rights to name his discovery. In that tradition the original title of this page is Coquaternion. Recently the page was moved to Split-quaternion on the grounds that this term is more commonly used, though no evidence was provided. Within WP there are several pages dealing with naming disputes, though the particulars of other disputes seem irrelevant here. Advice given is that a resolution through dialogue is preferable to polling. On the side of "coquaternion" one can note the twin status of this ring with Hamilton's by its appearance as real matrices (2 x 2) when re-arranged. If you happen by this talk page, click the edit button and contribute to this stand-off: discoverer's designation or "split-quaternion", what do you think? >>Rgdboer 21:22, 19 May 2007 (UTC)
 * My vote, for the moment anyway, would be to stick with co-quaternion, because I don't (yet) see why the characterisation of this algebra as the result of applying the Cayley-Dickson process to the algebra Cl1,0(R) is particularly interesting. If material were to be added to the article to motivate why "splitness" is an gives useful/meaningful/interesting insight into the features of the algebra, I'd happily reconsider.  But as the article stands at the moment, renaming to "split quaternion" seems not appropriate, given the balance of properties the article focusses on.  Jheald 22:05, 19 May 2007 (UTC)

 * An apologetic entry: I am the miscreant who moved this page from coquaternion to split-quaternion. The naming of things seems to generate more discussion than anything else on wikipedia. Anyway, I don't have a particularly strong opinion, so I will try to bow out gracefully with a few comments. First of all I disagree that there is a tradition in mathematics that a discoverer names their discovery. In fact normally, someone else names it after the discoverer. Second, as far as I am aware, co-quaternion is rarely used in mathematics these days. It may be used in astronomy, but this is beyond my expertise. The "See also" section of this article indicates why the "split" terminology is gaining ground. This is associated with the idea of the split form of a semisimple Lie algebra. Finally, I have no desire to create a stand-off. If there is consensus to move this page back, then so be it. If not, I am more than willing to improve the article, add historical information on the terminology, and replace "co" by "split" where appropriate. Geometry guy 22:39, 19 May 2007 (UTC)

 * A note on what it is about this algebra that associates it with "split form of a semisimple Lie algebra" would be a useful addition to this article, whatever it ends up being called. I can't say it's obvious to me from any of the "see also" articles, and the idea of a "split form" doesn't seem to be mentioned in the semisimple Lie algebra.  So further explanation of this concept, and hence of the name "split quaternion" would be welcome, regardless of what the article's final naming.  Jheald 00:09, 20 May 2007 (UTC)

 * To try to answer my own question, (and to see if I can correctly interpret what G-guy wrote), I think the "split" comes in when we identify this algebra as parametrising rotations. Whereas on the one hand the quaternions can be identified with Cℓ03,0(R), ie the even Clifford sub-algebra that is associated with rotations in a space with the pure signature (+,+,+), on the other hand the split-quaternions can be identified with Cℓ02,1(R) and Cℓ01,2(R) - rotations (partially hyperbolic) in 3d pseudo-Euclidean space with the split signature (+,+,-) or (+,-,-).

 * This is analogous to complex numbers being identified with Cℓ02,0(R) - rotations in 2D space with the pure signature (+,+), whereas split-complex numbers are identified with Cℓ01,1(R) - hyperbolic rotations in 2D pseudo-Euclidean space with the split signature (+,-).

 * Is that a fair understanding of the word "split" ?

 * Split-octonians can't be associated with any Clifford algebra, because they aren't associative. But they're the next step in applying the Cayley-Dickson construction which gives the chain split-complex -> split-quaternion -> split-octonian.  So that is the interpretation of "split" there.  Is this correct, or are there further implications and connections that I'm not yet seeing?  Jheald 08:45, 20 May 2007 (UTC)

 * According to Split-complex number the term "split" comes from the "signature" of the number system; however, no reference is provided, and it is also not clear which definition signature is meant. It appears to me that the definition of signature using 2-forms gives reason to the term "split", where complex numbers would have signature (+,+), split-complex numbers would have (+,-), quaternions (+,+,+,+), split-quaternions (+,+,-,-), and so forth (applying the Cayley-Dickson construction). The lower dimensional constructs are e.g. contained in Clifford algebras, however, the classifying construction is Cayley-Dickson on split-complex numbers. We should be careful not to mention Clifford algebras too early, thereby overstating their relation. Clifford algebras are important, and there is an overlap in two constructs (split-complex and split-quaternions), but that's where it ends. Thanks, Jens Koeplinger 15:04, 20 May 2007 (UTC)

 * IMHO the move from "Coquaternion" to "Split-quaternion" is not entirely unfounded, since interest in split-complex algebras has grown considerably in physics in recent years (e.g. click here for a search on "split octonion" at http://arxiv.org/find/grp_q-bio,grp_cs,grp_physics,grp_math,grp_nlin/1/all:+AND+octonion+split/0/1/0/all/0/1 arxiv.org]). This could underwrite notability of the newer term. Nevertheless, my vote for this article would still go towards keeping it at "Coquaternion", due to naming by the discoverer), and mention the identity with split-quaternions in the article. I've just not seen the new term "split-quaternion" used enough on its own (I've seen "split-octonions" and in general "split-complex" algebras more frequently). Thanks, Jens Koeplinger 01:31, 20 May 2007 (UTC)

 * Surely another apology is due from me for dropping the term "split form" into the conversation without providing links or explanations, and promptly promising to bow out! I've been kind of busy...
 * First split signature, for inner products (by which I mean nondegenerate symmetric bilinear forms), refers to inner products with signature (p,p), (p,p+1) or (p+1,p), i.e., equal or nearly equal numbers of pluses and minuses. As Jens points out, the split algebras have natural (i.e., automorphism-invariant) inner products of signature (1,1), (2,2) and (4,4), just as the "pure" algebras have inner products of signature (2,0), (4,0) and (8,0).
 * Second the associated Lie groups O(p,p) and O(p,p+1), and their Lie algebras, turn out to be the so called split forms. The articles on Lie theory seem to be rather undeveloped so far, but the article Real_form_of_a_complex_Lie_algebra at least redirects to a useful list. The "split form" is the real form whose real rank is equal to its complex rank. Roughly speaking, this means that the elements of a Cartan subalgebra have real eigenvalues, i.e., their characteristic polynomials split over the reals (hence the name). For example, the split form of sl(n,C) is sl(n,R).
 * The automorphism groups of the split quaternions and the split octonians are subgroups of O(2,2) and O(4,4), and are themselves split forms, namely SO(1,2), and the split form of G_2.
 * Finally, as noted by Jheald, the association with Clifford algebras (when it exists) also involves Clifford algebras associated to split signature inner products. This is related to the appearance of SO(1,2) above.
 * The serendipitous consonance of language between split signature and split form is one of the reasons the terminology has become popular, indeed, I claim, dominant.
 * PS. I support the merge with para-quaternion. Geometry guy 16:22, 20 May 2007 (UTC)
 * Thanks a lot for providing more info on where the naming "split" comes from! As it looks, we're today having the terms "split-quaternion" and "para-quaternion" used in different research contexts, yet describing an isomorphic algebra. Certainly nothing anyone would have apologize for ... it looks like a decision on which is the "better" term is doomed already. Thanks, Jens Koeplinger 01:14, 21 May 2007 (UTC)
 * para- is used to some extent in geometry (paraconformal or paraquaternionic manifolds), but I don't think it is used so much in algebra.
 * Anyway, in case it is not clear, I would be in favour of para- and co- redirecting to split-. At some stage, it might be nice to have a page analogous to normed division algebra which lists all the split algebras, and their properties. The Cayley-Dickson process also discusses the split case. I find the "split" terminology more descriptive and hence more neutral, but I'll be curious to see whether I have provided enough mathematical justification to satisfy Rgdboer's concerns.

 * Thanks again for the additional info. I've looked around a bit at topics where there are - in the widest sense - many individual "components" that are part in several different "programs" (like split-quaternion/split-complex extension, para-quaternion/paraquaternionic manifold, etc). I've come across chemicals, like e.g. Hydrogen, where its key properties are contained in a template insert on the right. Maybe that's what we need for our number systems? We cuold e.g. make one template for co-/split-/para-quaternion, list all its other classifications (including Clifford, Lie), its algebraic properties. Then, we could actually leave the individual pages for co/split/paraquaternion, list a bit of history and how it came that it has its different names etc. You pointed out yet another place at which the split-complex contruction is contained, so we might be able to remove the repeated explanation of it away from split-complex number, split-octonion, and Cayley-Dickson construction and instead have one article that is referenced from the template insert. ... Along these lines ... Obviously, some more planning is needed, since many pages are affected. ... We do want to make sure that all the different names for the same thing are represented reasonably, in particular how it came like it; but at the same time offer a one-click link to the related program (whether Cliffor, split-, para-, or whatever other).
 * This is good stuff, I'm glad I won't be getting bored over the summer :) - - - Thanks, Jens Koeplinger 12:50, 21 May 2007 (UTC)

Inner products
My thanks to G-guy for his clarification about the inner products/norms. One question, though. I know that for Clifford algebras, I can compute the signature ||s||2 for each base s of the algebra, by starting with the known quadratic forms for vector bases, ||p||2 = +1 or -1, and then using the fact that under Clifford multiplication of elements these signatures also multiply, ||pq||2 = ||p||2||q||2, revealing the signatures for bivector and higher bases.

But when one of these algebras cannot be related to a Clifford algebra (or half a Clifford algebra), where then do the signatures for its bases come from. Are they then implicit in the definition of the algebra? Or are they a further choice still to be settled, after the composition rules of the algebra have been fixed? -- Cheers, James Jheald 23:29, 22 May 2007 (UTC).

 * For (split-)octonions the quadratic form is still multiplicative; Cayley-Dickson constructs beyond that, however, don't have a multiplicative modulus at all, so I've got to pass your question on. I've never seen a thing like split-sedenions. Has anyone seen investigation into split-(2^N)-ions with N>3? Thanks, Jens Koeplinger 01:12, 23 May 2007 (UTC)

Second question, what is the right word for ||s||2 ? For s a general member of a Clifford algebra, I think it equals $$\langle s \tilde{s} \rangle_0$$ where s~ is the reverse of s, and <>0 means scalar part of. This can also be written $$ (s \,\,\lrcorner\,\, \tilde{s})$$ where $$\lrcorner$$ is the contractive inner product.

I'm wary about calling it a norm or a modulus, because no square root is taken, and because ||s||2 could be negative. It's not simply a run-of-the-mill inner product, because of the need to include the reversal operation. Quadratic form might be right, but does this not more naturally suggest just s2, without the reversal, and/or including non-scalar terms? Jheald 08:49, 23 May 2007 (UTC)

 * Either square-norm or quadratic form will do: the problem with the former is that it seems to suggest nonnegativity (but then so does the notation ||s||2); the problem with the latter is that it does not specify nondegeneracy. The $$\langle s \tilde{s} \rangle_0$$ notation is just a clean way of writing this square norm: expanded with respect to a suitable basis for the Clifford algebra, it will be a sum of s_i^2 terms (with signs). The reversal is a red herring as well: this is needed in the positive definite case, when $$\langle s \tilde{t} \rangle_0$$ is an inner product on the Clifford algebra. Geometry guy 13:26, 23 May 2007 (UTC)

 * Hmmm. I think you're going a bit fast, saying the reversal is just a red herring.  The two most usual inner products, at least for real Clifford algebras, are sums over the contributions for each pair of grades k and l of the general multivectors A and B, the contributions being as follows:
 * for the contractive product (the "computer scientist's inner product"),
 * $$ \langle A \rangle_k \,\,\lrcorner\,\, \langle B \rangle_l = \langle AB \rangle_{k-l} $$  (zero if l < k),
 * for the dot product (the "physicist's inner product"),
 * $$ \langle A \rangle_k \cdot \langle B \rangle_l = \langle AB \rangle_{|k-l| \,\,\,\, l,k\neq 0} $$
 * Neither contains reversal; but reversal is nevertheless required to get the right signs on the contribution to the square norm from bivectors and higher grade bases: if A=e1e2 then $$A \,\,\lrcorner\,\, A = A^2 = (\mathbf{e}_1 \mathbf{e}_2) (\mathbf{e}_1 \mathbf{e}_2) = - \mathbf{e}_1^2 \mathbf{e}_2^2$$. But $$||A||^2 = \langle A \tilde{A} \rangle = (\mathbf{e}_1 \mathbf{e}_2) (\mathbf{e}_2 \mathbf{e}_1) = + \mathbf{e}_1^2 \mathbf{e}_2^2$$.  So the square-norm is rather a special product.

 * Secondly, I'm also wondering if I may have been too hasty in asserting that ||PQ||2 = ||P||2||Q||2 for general multivectors P and Q. ||PQ||2 = $$\langle P Q \tilde{Q} \tilde{P} \rangle_0$$; whereas  ||P||2||Q||2 = $$\langle P \langle Q \tilde{Q}\rangle_0 \tilde{P} \rangle_0$$.  And in general $$Q \tilde{Q} \neq \langle Q \tilde{Q}\rangle_0$$.  The two will be equal if Q is a blade -- ie if it can be factorised as a pure Clifford product of vectors.  But if Q is not a blade, then $$Q \tilde{Q}$$ may contain cross terms which are not of grade 0.  However, it seems very likely that application of an appropriate P and P~ may rotate these extra cross terms into resulting terms which are of grade 0.  Such contributions would break the equality ||PQ||2 = $$\langle P Q \tilde{Q} \tilde{P} \rangle_0$$.  Does this mean I've missed something?  Or is that equality, which I have jumped to, not necessarily a generally correct assertion? Jheald 00:28, 24 May 2007 (UTC)

 * Thanks for pointing these out, but I would call these interior products rather than inner products, since they are not scalar-valued, although one could take the scalar part to obtain an inner product. This would differ from a definition using reversion by switching some signs according to the grade mod 4. One could also use conjugation instead of reversion to get other signs. I agree that it is most natural to use reversion.
 * For the second question, you are right that the equality does not always hold, cf. Hurwitz's theorem for composition algebras. Geometry guy 14:46, 28 May 2007 (UTC)

Reconsider name
The title of this article should be coquaternion because: Respectfully,Rgdboer (talk) 01:56, 16 February 2010 (UTC)
 * The split prefix signifies reducibility of the algebra to a direct sum of smaller algebras, and this algebra is not so reducible.
 * The discoverer named the algebra "coquaternions", and the only reference for "split-quaternion", Rosenfeld (1988), does not justify that name. Though Rosenfeld poses as a historian, the History does not mention the 1849 discovery.

In 1993 Rosenfeld collaborated with M.A. Akivis to write Elie Cartan (1869 - 1951) which mentions split-quaternions on page 68. This time the mention is flawed by a misprint:
 * $$i^2 = -1,\ e^2 = 1,\ i e = e i = f.$$

However, the next sentence says "This algebra is isomorphic to the algebra R2 of real matrices of the second order." Without this sentence he would appear to contradict himself since the equations are appropriate for tessarines. Neither of these Rosenfeld sources have a methodical development of algebra; rather they both string along a text of historical references. Thus they are not helpful for a reader studying structure. The call for consistency in terminology should outweigh the flawed Rosenfeld sources.Rgdboer (talk) 21:25, 25 August 2010 (UTC)
 * editingRgdboer (talk) 21:36, 25 August 2010 (UTC)

Having just gone over some literature on composition algebras, it appears that three of seven composition algebras over the real field are called "split algebras". The algebra of the present article is one of them. Considering this literature, the request to reconsider coquaternion is withdrawn.Rgdboer (talk) 01:43, 27 January 2012 (UTC)

Kinematics
One could argue that the kinematics this algebra represents is that of a two-dimensional Lorentz space, with the root of -1 representing a rotation in this space.

A discrete Thomas precession can then be quickly derived by multiplying orthogonal boosts and observing the complex term, which would be the sin of half of the rotation angle. — Preceding unsigned comment added by 24.236.65.120 (talk) 04:01, 15 September 2011 (UTC)
 * This interesting observation about application to kinematics may be original research. On the other hand, it may already exist in the vast literature that has been written in the last century or so. In the first case it is inadmissible to this encyclopedia; in the second case it remains to find that note, essay, journal article, or book paragraph that would provide a source to cite in this encyclopedia.Rgdboer (talk) 21:21, 15 September 2011 (UTC)
 * Thomas precession can certainly be analysed using the geometric algebra Cℓ3,1(R) -- see for example the slides for Lecture 10 in this 2001 course on Physical Applications of Geometric Algebra, corresponding to pages 24--26 of Part 2 of the written-up handouts. (A consolidated set of slides for most of the course is also available here).  Googling for "geometric algebra", "Thomas precession" or for "Hestenes", "Thomas precession" produces further write-ups.  Looking at the effect of combining just two boosts to produce a Thomas rotation should also be straightforward.
 * However this can't be shown in Cℓ1,1(R), the algebra most naturally corresponding to split-quaternions, because you need at least two spatial directions as well as a time-like direction to show the precession -- just one is not enough. But perhaps there is a different way to use split quaternions to represent such a space? Jheald (talk) 09:22, 16 September 2011 (UTC)
 * On the other hand, I suppose you can also use the split quaternions to represent Cℓ+2,1(R), the even part of the geometric algebra Cℓ2,1(R). It's the even part that contains boosts and rotations, so that is essentially exactly what you need to look at to consider the result of combining two non-parallel Lorentz boosts.
 * I do think, generally for the article, that relating the split-quaternions to the different Clifford algebras they can stand for, in particular to the particular Clifford algebra that is relevant for a particular application (out of the number of different possibilities), is useful if their applications are going to be presented, because the signature of the Clifford algebra immediately makes clear exactly the way in which the split quaternions are being related to geometric space, from which their capabilities can essentially be read off directly. Jheald (talk) 09:40, 16 September 2011 (UTC)
 * This is the interpretation, as a super algebra of Cℓ+2,1(R), I originally had in mind when I started this, unsigned, above. I will accept this as original research, and not appropriate here. — Preceding unsigned comment added by Utesfan100 (talk • contribs) 18:02, 6 March 2012 (UTC)

Complete rewrite of section "Profile"
I have completely rewritten the section "Profile" which was not understandable, even for a professional mathematician. I have extracted from this mess the results that are of encyclopedic value, but I have presented them in a completely different way (WP:TNT). I have no source for my presentation, but the results are natural enough for having certainly been published before. So, I have tagged it as unreferenced section.

I have removed the parts that seem WP:OR and those that are out-of-scope here. If needed, be free to add content that is relevant to this article, but, if you do that, it should be clear for everybody that the added content is relevant here and is of encyclopedic nature. This means that the removed text must not be added again. D.Lazard (talk) 15:45, 17 February 2021 (UTC)

title: Talk:Split-quaternion


text:
Army of Puerto Rican Occupation Medal

The Army of Puerto Rican Occupation Medal was a service medal of the United States Army which was created by order of the United States War Department on 4 February 1919. A retrospective award created decades after the action commemorated, the medal recognized Army service from 14 August through 10 December 1898 in Puerto Rico. The Army of Puerto Rican Occupation Medal was commemorative by nature although was approved for wear on active military uniforms. A similar medal, the Army of Cuban Occupation Medal was created for occupation service in Cuba following the Spanish–American War. The regulations for the Army of Cuban Occupation Medal were re-written to include regulations for the Army of Puerto Rican Occupation Medal.

Background
Service in Puerto Rico during the Spanish American War was recognized initially by the Spanish Campaign Medal. This medal recognized service between 24 July 1898 and 13 August 1898, as well as those who were embarked on ships headed there during the specified period of time. With the last date of recognition being 13 August, there were some troops who received no medal for their service in Puerto Rico during the immediate period after the end of the Spanish–American War. A similar lack of recognition for service in Cuba was remedied by the creation of the Army of Cuban Occupation Medal in 1915. On 4 February 1919 the order establishing the Army of Cuban Occupation Medal was modified to add regulations and criteria for awarding a service badge for time served in Puerto Rico between 14 August – 10 December 1898. The regulations allowed the awarding of the medals, at government expense, only to those officers and enlisted men who were still actively serving on or after 28 June 1915. Those who had left the service were able to apply for a certificate verifying service from the War Department and then purchase a medal, at cost, after providing the proof of service certificate. It wasn't until an act of congress in 1928 that the War Department was authorized to issue to all those entitled, and their next of kin, any medals to which they might be entitled to include the Army of Puerto Rican Occupation Medal.

Criteria
The medal recognized those service members who had performed military occupation duty in Puerto Rico after the close of the Spanish–American War. For those service members who performed duty both during and subsequent to the Spanish–American War, the Spanish Campaign Medal was also authorized. The qualifying dates for the Army of Puerto Rican Occupation Medal were from 14 August through 10 December 1898. The United States Navy and Marine Corps had no equivalent to the Army of Puerto Rican Occupation Medal.

Appearance
The Army of Puerto Rican Occupation Medal is bronze 1 1/4 inches wide. It has an oxidized matte finish in relief. The obverse of the medal bears a castle in the center with two small round towers at the corners. This obverse is also used on the obverse of the Spanish Campaign Medal. At the top around the outside of the medal is the inscription ARMY OF OCCUPATION OF PORTO RICO (the "Puerto Rico" of the country was spelled using conventions of the time). The date 1898 appears at the bottom. On the left side of the date is a branch of a tobacco plant on the other side is a stalk of sugar cane. The reverse depicts a spread eagle on a trophy consisting of a cannon, six rifles, four standards, an Indian shield, quiver of arrows with three spears, a Cuban machete, and Sulu kris. Below the trophy are the words FOR SERVICE. The reverse is circumscribed by the words UNITED STATES ARMY at the upper half and thirteen five-pointed stars in the lower half. The ribbon is 1 3/8 inches wide in ultramarine blue. At the edges are stripes of old glory red 1/16 inches wide. In the center is a 3/8 inch stripe of old glory red bordered on both sides by 1/16 inch golden yellow stripes.

title: Army of Puerto Rican Occupation Medal


text:
Talk:Stetson Kennedy

Work in progress
This article has a lot of redundancies and is pretty rambling, so I'm working on paring it down. I'm up to the section about infiltrating the KKK, which is a hot mess, and the part of the article he's most known for. There's way too much emphasis on the Freakonomics criticism, which has been solidly shot down in a number of articles in serious academic journals. My goal is to make the section more concise and include more academic sources: Just an FYI. I'm open to suggestions. —PermStrump ( talk )  16:09, 26 August 2017 (UTC)
 * SHARON MONTEITH: "'I second that emotion': a case for using imaginative sources in writing civil rights history", Patterns of Prejudice, 2015 Vol. 49, No. 5, 440–465,
 * John DiNardo. (October 26, 2006) "Freakonomics: Scholarship in the Service of Storytelling", American Law and Economics Review,
 * John DiNardo. (December 2007) "Interesting Questions in Freakonomics Journal of Economic Literature Vol. XLV, pp. 973–1000
 * NANCY GROCE AND STEPHEN WINICK (Ap 2008) "The New Deal at 75: When Art, Culture and Government Intersected." Libr Cong Inf Bull 67 no4
 * https://www.facingsouth.org/2011/08/voices-stetson-kennedy-and-the-pursuit-of-truth.html
 * https://www.theguardian.com/commentisfree/cifamerica/2011/sep/02/protest-florida
 * This is correct. The article is contorted into a discussion of the mistakes made by the guys who wrote Freakonomics. That has very little to do with Kennedy and less of a place on Wikipedia. Trumpetrep (talk) 02:19, 6 May 2024 (UTC)

Criticism
All of the junked material from the Criticism section is here if anyone wants to salvage it. It was so lengthy that it completely threw off the balance of the article.Trumpetrep (talk) 07:02, 24 May 2024 (UTC)

title: Talk:Stetson Kennedy


text: User talk:83.70.245.37

title: User talk:83.70.245.37


text:
West Ice Shelf

The West Ice Shelf is a prominent ice shelf extending about 350 km in an east–west direction along the Leopold and Astrid Coast in East Antarctica between Barrier Bay and Posadowsky Bay, and up to 120 km northwards from the continental margin.

Discovery and naming
The ice shelf was discovered and named by the First German Antarctica Expedition, 1901–1903, under Dr Erich von Drygalski. The toponym describes the direction in which the German expedition first viewed the ice shelf. Their limited westward view became a prolonged one; on February 21, 1902, the ship became stuck in the pack ice, remaining imprisoned there until February 8, 1903.

Important Bird Area
A 416 ha site on sea ice near the north-western margin of the shelf has been designated an Important Bird Area (IBA) by BirdLife International because it supports an emperor penguin colony.

title: West Ice Shelf