text:
Talk:Great Western Railway

Infobox
The Infobox used in this article can be found at Infobox GWR.

Early locos
Quote "After 1902 G. J. Churchward developed a distinctive style of locomotive in 4-4-0 ...".

Should that be 4-4-2?

Songwriter 09:46 5 Jul 2003 (UTC)

 * I had the 4-4-0 "City" class in mind, which (as I understand it) were designed while Dean was still nominally in charge, and built in about 1903. I believe Churchward tried out 4-4-2, bringing over three French "Atlantics", converting Albion to a 4-4-2 as a comparison, and building North Star as a 4-4-2 (though it ended up as a 4-6-0). There may have been other 4-4-2 designs. --rbrwr

 * Ah! I was forgetting about the City class.  I was thinking of North Star in its initial form.  Thank you.

 * Songwriter 13:24 5 Jul 2003 (UTC)

Maarten Tromp
The name of the Flying Dutchman Racehorse came from an old story, and has nothing to do with Maarten Tromp, Trom was never the Flying Dutchman, that story is way older. — Preceding unsigned comment added by 84.80.157.6 (talk) 03:38, 31 December 2015

Czech this out...
At the foot of the wikitext of this article is this line:

Isambard Kingdom Brunel

It does not create a wikilink on the page. Does it have any function? Can I just delete it? -- Verbarson talkedits 21:56, 23 September 2022 (UTC)
 * The link is in the left sidebar, see H:ILL. -- Red rose64 🌹 (talk) 19:39, 24 September 2022 (UTC)
 * If it's supposed to create an inter-language link, then it doesn't work. I suspect there may be a syntax error here. Should the cs be preceded by a colon? Roly (talk) 21:23, 24 September 2022 (UTC)
 * I see it, thank you. And Wikidata cannot do section links, so a local link is needed in this case. The inter language link is there for me, under "Čeština". -- Verbarson  talkedits 21:26, 24 September 2022 (UTC)
 * You're right - my mistake. I didn't recognise the name of the language. Roly (talk) 21:41, 24 September 2022 (UTC)

Clarify, please
As an American railfan myself, I do understand the fascination with minute details of a favorite railway's construction and operation. However, as a reader, I don't enjoy wading through minutiae to get the most basic facts. It seems to me the whole point and purpose of building the GWR was to haul goods and people between Bristol and London; but just when that was finally able to happen is *not at all clear* from this article.

As an Anglophile, I take a kindly interest from across the sea in British railways - the originals! - and it seems to me that a simple, concise sentence in the lede giving the date the road was completed to Bristol, and the date the first regular trains began running through from Paddington to Temple Meads, is not too much to expect from you fellows, with all your great expertise at the ready. So how about it, chaps? You're not going to leave such a simple question for a foreigner to answer, are you? Textorus (talk) 18:32, 20 November 2022 (UTC)
 * Do you mean when the line was opened? It was opened in stages: at Great Western Railway we find
 * The first 22+1/2 mi of line, from Paddington station in London to Maidenhead Bridge station, opened on 4 June 1838.
 * and later in the same section we find
 * The GWR main line remained incomplete during the construction of the 1 mi Box Tunnel, which was ready for trains on 30 June 1841, after which trains ran the 152 mi from Paddington through to Bridgwater.
 * Further extensions were opened at subsequent dates, a full list may be found in MacDermot: Volume I Appendix I (pages 857-870) for lines opened 1838-1863; and Volume II Appendix I (pages 595-633) for lines opened 1863-1920. -- Red rose64 🌹 (talk) 21:23, 20 November 2022 (UTC)
 * Bridgwater and the Box Tunnel - you Brits know where those places are, and their relation to Bristol and the line of the railway - but the rest of the world has no idea. It's rather unkind to throw around geographic names that a general reader will have to hunt up.  Much nicer for you to simply state the plain basic facts in the lede, as I said above.  An encyclopedia exists to inform, not mystify its readers.  And no, I did not ask about when the line first opened, I clearly asked when it was completed.  Two simple questions that do not need elaborate explanations or documentation.  Textorus (talk) 22:09, 20 November 2022 (UTC)
 * Box Tunnel is linked, as is Bridgwater in the preceding sentence:
 * ... the Bristol and Exeter Railway (B&ER), the first section of which from Bristol to Bridgwater was opened on 14 June 1841.
 * We don't repeat links unnecessarily, see WP:OVERLINK. -- Red rose64 🌹 (talk) 22:45, 20 November 2022 (UTC)
 * Maybe so, but you DO confuse your readers unnecessarily. Exeter is south of Bristol; London is east.  It does not necessarily follow that the Bristol and Exeter is a component of the route to/from London.  But hey, mate, if it's just too hard for you to write one simple sentence explaining what I asked for - which I assure you many other readers in and out of the UK would also like to see - then forget about it.  You keep the article just the way you like it, and we'll all go read about something else.  Textorus (talk) 15:58, 21 November 2022 (UTC)
 * I hope this suits: It was founded in 1833, received its enabling Act of Parliament on 31 August 1835 and ran its first trains in 1838 with the initial route completed between London and Bristol in 1841. Geof Sheppard (talk) 17:11, 21 November 2022 (UTC)

"Great Western Railway/GA1" listed at Redirects for discussion
An editor has identified a potential problem with the redirect Great Western Railway/GA1 and has thus listed it for discussion. This discussion will occur at until a consensus is reached, and readers of this page are welcome to contribute to the discussion. Regards, SONIC 678 01:47, 8 January 2023 (UTC)

MacDermot
The Internet Archive has two volumes of MacDermot's History of the Great Western Railway. The second volume, naturally, is named "Vol. II", but the first volume is named "Vol. I Part I". Is there a "Vol. I Part II", or is Part II the same as Vol. II? -- Verbarson talkedits 11:27, 9 July 2024 (UTC)
 * There are two editions.
 * The first edition, published in 1927-31, was two volumes but three physical books - volume I, which was published in 1927 and covered the period to 1863, was bound as Volume I Part I and Volume I Part II but these two were sold as a pair - the pagination continued across the split so the page numbers are unique to Vol. I even if you don't know which of the two parts the page is in. Both Prts have a Contents, but only Part II has an index. Volume II, which was published in 1931 and covered the 1863-1921 period, was a single physical book, so has no part numbering. Its pagination restarts at 1.
 * The second edition, published in the 1960s, was revised by O.S. Nock, and not only is the pagination completely different, volume I is now bound as a single physical book. A Volume III was also added, taking the story from 1921 to 1947. -- Red rose64 🌹 (talk) 12:39, 9 July 2024 (UTC)
 * Thanks for that. Therefore the "Vol. I Part I" in archive.org, which has no index, is indeed only Part I, and "Vol. I Part II" is not in the archive. "Vol. II" is present, as is Nock's "Vol. III".
 * Since "Vol. I Part I" takes the history up to 1863, and "Vol. II" picks up from 1863, what is in "Vol. I Part II"? Judging by the contents list of "Vol. II", it would be more detailed coverage of services, locomotives and rolling stock. Is that so? -- Verbarson talkedits 14:48, 9 July 2024 (UTC)
 * I'm not at home right now, I'll check later. -- Red rose64 🌹 (talk) 18:16, 9 July 2024 (UTC)
 * Here are the cite templates that I normally use:
 * Note that I don't distinguish the two Parts of vol. 1, since the pagination is continuous (see below). I don't have the second editions of these two volumes, but I do have vol. 3:
 * Both parts of Vol. I take the story up to 1863-64, ending in one sense with the amalgamation of the GWR, West Midland Railway (WMR) and South Wales Railway in 1863, and in another sense with the retirement of Charles A. Saunders, who had been Secretary of the GWR from before its incorporation until 1864. Part I (pages i-xvi and 1-456 plus a fold-out map of the system as of 1855) is a largely chronological history of the development and expansion of the GWR during this period, and includes previous histories of railways that amalgamated or were absorbed before 1863, such as the Shrewsbury and Birmingham Railway and Shrewsbury and Chester Railway. Part II (fold-out map as of 1863, pages i-x and 457-902) begins with the pre-amalgamation histories of the WMR and SWR, and continues with chapters about signalling, services, staff, locomotives and rolling stock. It also includes appendices and the index. -- Red rose64 🌹 (talk) 21:16, 9 July 2024 (UTC)
 * Thanks for bringing this together so comprehensively. -- Verbarson talkedits 21:50, 9 July 2024 (UTC)
 * Both parts of Vol. I take the story up to 1863-64, ending in one sense with the amalgamation of the GWR, West Midland Railway (WMR) and South Wales Railway in 1863, and in another sense with the retirement of Charles A. Saunders, who had been Secretary of the GWR from before its incorporation until 1864. Part I (pages i-xvi and 1-456 plus a fold-out map of the system as of 1855) is a largely chronological history of the development and expansion of the GWR during this period, and includes previous histories of railways that amalgamated or were absorbed before 1863, such as the Shrewsbury and Birmingham Railway and Shrewsbury and Chester Railway. Part II (fold-out map as of 1863, pages i-x and 457-902) begins with the pre-amalgamation histories of the WMR and SWR, and continues with chapters about signalling, services, staff, locomotives and rolling stock. It also includes appendices and the index. -- Red rose64 🌹 (talk) 21:16, 9 July 2024 (UTC)
 * Thanks for bringing this together so comprehensively. -- Verbarson talkedits 21:50, 9 July 2024 (UTC)
 * Thanks for bringing this together so comprehensively. -- Verbarson talkedits 21:50, 9 July 2024 (UTC)

title: Talk:Great Western Railway


text:
GWR 111 The Great Bear

The Great Bear, number 111, was a locomotive of the Great Western Railway. It was the first 4-6-2 (Pacific) locomotive used on a railway in Great Britain, and the only one of its type built by the GWR.

Origins
There are differing views as to why Churchward and the GWR should have built a Pacific locomotive in 1908 when current and future locomotive practice for the railway was centred on the 4-6-0 wheel arrangement. One suggestion is that The Great Bear was built in 1908 to satisfy demands from the directors for the largest locomotive in Britain, and much was made of the locomotive by the GWR's publicity department. However, O. S. Nock was adamant that the design "was entirely due to Churchward, and not to outside influences that pressed the project upon him". Nock regarded the locomotive as "primarily an exercise in boiler design", with Churchward looking forward to a time when his Star Class locomotives could no longer cope with increasing loads. Others have referred to a statement made to the GWR board in 1906 about the GWR-designed 4-4-2 North Star, where Churchward stated that a 4-6-2 would be bigger than required at that time but that such a design was being prepared. The order for The Great Bear was placed in January 1907.

Design
The front-end layout of the class was the same as that for the Star Class except that Churchward fitted 15 in diameter cylinders, the maximum possible without fouling the rear wheels of the front bogie. However, the design of the boiler was entirely new, and with a barrel of 23 ft in length, which was exceptionally long both by contemporary and later standards. The main reason Churchward adopted the 4-6-2 wheel arrangement was to enable him to fit a wide firebox over the trailing wheels. With a firebox surface of 182 sqft, this was a 17.5% increase in size compared to the Star Class. It was also built with a Swindon No. 1 superheater.

Power classification
With the introduction of Great Western Railway Power Classification in 1920, the power classification was "Special" (denoted by a black "+" on the red route availability disc, ) although the tractive effort of 27800 lbf fell within the range for "D".

Performance
In service, the performance of The Great Bear proved to be disappointing and not a significant improvement on existing classes. "The excessive tube and barrel length of 23 feet made for bulk rather than efficiency". Also, the axle boxes of the trailing wheels tended to become overheated due to their proximity to the firebox. Churchward attempted to improve the locomotive's performance by adding a Swindon No. 3 Superheater in 1913 and top-feed apparatus. However, the excellent performance of the Star Class and the advent of the First World War brought a stop to further experimentation without significant improvement.

Route availability
In addition to the disappointing performance, the locomotive had a highly restrictive route availability which limited its usefulness. The 20 LT axle load restricted it to the Paddington to Bristol main line, although it was once recorded to have travelled as far west as Newton Abbot. The GWR route availability colour code for The Great Bear was Red.

Publicity value
Although not a technical success, The Great Bear was considered the company's flagship locomotive from its introduction until Churchward's retirement in 1922. With the introduction of 4073 Caerphilly Castle in 1923 with a higher tractive effort, The Great Bear ceased to have any publicity value and became an embarrassment. It was due for heavy repairs in January 1924 and so was withdrawn from service by Churchward's successor Charles Collett. It had run 527,272 miles by this time. Its regular engine driver was Thomas Blackall, originally from Aston Tirrold, Oxfordshire.

Rebuilding
"The front portion of the original frames and the number plates were used again but probably little else". No. 111 emerged as a 4-6-0 in the Castle Class, given the name Viscount Churchill. Thereafter, the GWR did not use the Pacific wheel arrangement. No. 111 was withdrawn in July 1953 and scrapped later that year. One of the original nameplates is in the Science Museum.

Assessment
According to Cecil J. Allen, "The Great Bear was one of the very few locomotive types that Swindon has produced, and in particular among the Churchward designs, to which the word 'failure' could be applied." Authorities differ as to Churchward's attitude to his locomotive. According to Le Fleming, "his dislike of 'The Bear' was well known", but Nock said that he had "a deep affection for the engine", although he came to regard it as "a white elephant" rather than a "Great Bear". He was disappointed to hear of The Great Bear's destruction, and, upon hearing of Nigel Gresley's plans to construct a Pacific for the Great Northern Railway, is said to have replied: "What did that young man want to build it for? We could have sold him ours!"

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

title: GWR 111 The Great Bear


text:
Rákoskeresztúr

Rákoskeresztúr (Gerersdorf) is a former town in Hungary now part of District XVII of Budapest. Rákoskeresztúr was united with Budapest on January 1, 1950.

Background
The first written mark (the name Pousarakusa, in modern Hungarian Pósarákosa) was a title-deed written in 1265. The name was given by the region's first occupant. In that title-deed the region was given to the Crusaders of Upper-Heviz. The village was almost destroyed in the Turkish assault. In 1662, only eight peasant- and 2 cotter families lived in it. From 1727 to 1950, it was counted as a town. In 1880, Rákoshegy and Rákosliget are cut off from Rákoskeresztúr. In 1950, Rákoskeresztúr, Rákoshegy, Rákosliget and the newly built Rákoskert were joined together as the XVII. district of Budapest.

title: Rákoskeresztúr


text:
User:Cemalokmen

A university student in economics depertment in Ankara/TURKEY.

title: User:Cemalokmen


text:
Kemal Derviş

Kemal Derviş (10 January 1949 – 8 May 2023) was a Turkish economist and politician who was head of the United Nations Development Programme. He was honored by the government of Japan for having "contributed to mainstreaming Japan's development assistance policy through the United Nations". In 2005, he was ranked 67th in the Top 100 Public Intellectuals Poll conducted by Prospect and Foreign Policy magazines. He was vice president and director of the global economy and development program at the Brookings Institution and part-time professor of international economics at the Graduate Institute of International and Development Studies in Geneva.

In March 2015, Derviş agreed to become the Deputy Prime Minister of Turkey responsible for the economy in a cabinet led by Republican People's Party (CHP) leader Kemal Kılıçdaroğlu should his party form the government after the general election to be held in June. He declined to become a Member of Parliament however, stating that he would prefer to participate in the cabinet from outside the Parliament.

Early life
Kemal Derviş was born on 10 January 1949 in Istanbul, Turkey, to an Albanian and Georgian father and a German mother. From his father's side, he is a descendant of Ottoman Grand Vizier Halil Hamid Pasha (1736–1785); and of Ottoman military physician Asaf Derviş Pasha (1868–1928) who is regarded as the founder of modern gynaecology in Turkey.

Political career
Derviş took office as Minister of State for Economic Affairs in Turkey on 13 March 2001, when Bülent Ecevit was Prime Minister. Derviş is credited with being the architect of Turkey's successful three-year economic recovery program launched in that year. The health condition of elder statesman Bülent Ecevit, the Prime Minister and leader of the party led to rumours that his Deputy Prime minister and Minister of State, Hüsamettin Özkan, was plotting to replace him. As a result, Özkan was forced to resign, prompting nearly half of DSP's parliamentarians to follow him, including İsmail Cem, the Minister of Foreign Affairs. Özkan, Zeki Eker, Cem and Kemal Derviş, the Minister of State in charge of economy, then decided to establish a new social democratic party. İsmail Cem became the leader of the New Turkey Party (YTP).

However, the party showed signs of organizational weakness. Moreover, Derviş changed his mind and joined the Republican People's Party (CHP) instead. As a result, the YTP performed dismally in the 2002 general election (receiving only 1.2% of the eligible votes cast) and again in the 2004 local elections. In October 2004, the YTP was merged into the Republican People's Party (CHP). Before being named to head the United Nations Development Programme (UNDP), he was a member of the Turkish parliament, and a member of the joint commission of the Turkish and European Parliaments. He was a member of the Convention on the Future of Europe. A member of the Advisory Group at the Center for Global Development, member of the Task Force on Global Public Goods and the Special Commission on the Balkans and associated with the Economics and Foreign Policy Forum in Istanbul, Derviş was instrumental in strengthening Turkey's prospects of starting membership negotiations with the European Union.

Strobe Talbott announced that Derviş joined the Brookings Institution on 30 March 2009 as vice president and director of the Global Economy and Development program.

On 10 June 2020, he published a Project Syndicate article titled "Less Globalization, More Multilateralism." Derviş was also a regular contributor to Project Syndicate from 2003 to 2023.

Studies and World Bank career
Kemal Derviş completed his early education in Institut Le Rosey. He later earned his bachelor (1968) and master's degrees (1970) in economics from the London School of Economics. He received his PhD in economics from Princeton University in 1973 after completing a doctoral dissertation titled "Substitution, employment and intertemporal equilibrium in a non-linear multi-sector planning model for Turkey." From 1973 to 1976, he was member of the economics faculty of the Middle East Technical University in Ankara, Turkey, and served also as an advisor to Bülent Ecevit during and after his Prime Ministerial duties. From 1976 to 1978, he was member of the faculty, Department of Economics at the Princeton University. In 1977, he joined the World Bank, where he worked until he returned to Turkey in 2001. At the World Bank, he held various positions, including civision chief for industrial and trade strategy and director for the Central Europe Department after the fall of the Berlin Wall. In 1996, he became vice-president of the World Bank for the Middle East and North Africa Region, and in 2000, vice-president for poverty reduction and economic management.

Ministry of Economic Affairs
When Derviş became Turkey's minister of economic affairs in March 2001, after a 22-year career at the World Bank, the country was facing its worst economic crisis in modern history and prospects for success were uncertain. Derviş used his independence from domestic interests and support of domestic reformers and civil society to push through a stabilization program with far-reaching structural changes and bank reforms that protected state banks from political use. Derviş also strengthened the independence of the central bank and initiated deep structural reforms in agriculture, energy and the budget process. These reforms, and his reputation and high-level contacts in the U.S. and Europe, is said to have helped him to mobilize $20 billion in new loans from the International Monetary Fund and the World Bank. Rapid economic growth resumed in 2002 and inflation came down from an average of nearly 70 percent in the 1990s to 12 percent in 2003; interest rates fell and the exchange rate for the Turkish lira stabilized.

Derviş resigned from his ministerial position on 10 August 2002 and was elected to parliament on 3 November of that year as a member of the main opposition Republican People's Party.

United Nations Development Program
On 5 May 2005, the United Nations General Assembly, representing 191 countries, unanimously confirmed Kemal Derviş as the Administrator of the United Nations Development Program, which is also the chairperson of the United Nations Development Group. Derviş started his four-year term on 15 August 2005. The UNDP Administrator is the third-highest-ranking official in the United Nations, after the Secretary-General and the Deputy Secretary-General.

In 2006, United Nations Secretary-General Kofi Annan appointed Derviş to a High-level Panel on United Nations Systemwide Coherence, which was set up to explore how the United Nations system could work more coherently and effectively across the world in the areas of development, humanitarian assistance and the environment.

In 2009, Derviş decided not to seek a second term as Administrator of UNDP.

Personal life
Kemal Derviş spoke Turkish, German, English and French fluently. He was married to Catherine Derviş, an American citizen.

According to press reports, when he was still single and working at the World Bank, Derviş had an affair with a married female subordinate (her identity was not revealed) who reportedly later started working at the IMF. This was speculated by the media as the possible reason why Derviş, despite being seen by many as the right person for the job, decided not to become a candidate to succeed Dominique Strauss-Kahn as the next managing director of the IMF, a position which was eventually taken by Christine Lagarde.

Kemal Derviş died in Washington, D.C., on 8 May 2023, at the age of 74.

Honors

 * JPN Kyokujitsu-sho 1Class BAR.svg Order of the Rising Sun, Grand Cordon (Japan), 2009.
 * Order of Civil Merit (Spain) - Crosses.svg Order of Civil Merit, Grand Cross (Spain), 2011.

title: Kemal Derviş


text:
Yantai

Yantai, formerly known as Chefoo, is a coastal prefecture-level city on the Shandong Peninsula in northeastern Shandong province of People's Republic of China. Lying on the southern coast of the Bohai Strait, Yantai borders Qingdao on the southwest and Weihai on the east, with sea access to both the Bohai Sea (via the Laizhou Bay and the Bohai Strait) and the Yellow Sea (from both north and south sides of the Shandong Peninsula). It is the largest fishing seaport in Shandong. Its population was 6,968,202 during the 2010 census, of whom 2,227,733 lived in the built-up area made up of the 4 urban districts of Zhifu, Muping, Fushan and Laishan.

Names
The name Yantai ( lit. "Smoke Tower") derives from the watchtowers constructed on Mount Qi in 1398 under the reign of the Hongwu Emperor of the Ming dynasty. The towers were used to light signal fires and send smoke signals, called langyan from their supposed use of wolf dung for fuel. At the time, the area was troubled by the Japanese pirates (Wokou), initially raiders from the warring states in Japan but later principally disaffected Chinese. It was also formerly romanized as Yen-tai.

The major district of Yantai is Zhifu, which used to be the largest independent city in the area. It was variously romanized as Chefoo, Che-foo, Chi-fu, and Chih-fou. Although this name was used for the city by foreigners prior to the Communist victory in the Chinese Civil War, the locals referred to the settlement as Yantai throughout.

History

During the Xia and Shang dynasties, the region was inhabited by indigenous people vaguely known to the Chinese as the "Eastern Barbarians" (Dongyi). Under the Zhou, they were colonized and sinicized as the state of Lai. Lai was annexed by Qi in 567 BC. Under the First Emperor (Shi Huangdi), the area was administered as the Qi Commandery. Under the Han, this was renamed as the Donglai Commandery. Following the Three Kingdoms period, the area was organized by the Jin as the Donglai Kingdom or Principality, later returning to prefecture status as a jùn and then zhōu. Under the Tang and during the Five Dynasties and Ten Kingdoms period, it was known as Deng Prefecture and organized with the Henan Circuit. It was then organized as the Laizhou and then, under the Qing, Dengzhou Prefecture.

Up to the 19th century, however, the Zhifu area consisted of nothing but small unwalled fishing villages of little importance. Under the Ming, these were first troubled by the "Dwarf Pirates" and then by the overreacting "Sea Ban", which required coastal Chinese to give up trading and most fishing and relocate inland upon pain of death.

Following the Second Opium War, the Qing Empire was obliged to open more treaty ports by the unequal 1858 Treaty of Tianjin, including Tengchow (now Penglai). Its port being found inadequate, Zhifu—about 30 mi away—was selected to act as the seat of the area's foreign commerce. The mooring was at considerable distance from shore, necessitating more time and expense in loading and unloading, but the harbor was deep and expansive and business grew rapidly. The harbor opened in May 1861, with its status as an international port affirmed on 22 August. The official decree was accompanied by the construction of the Donghai Customs House. It quickly became the residence of a circuit intendant ("taotai"), customs house, and a considerable foreign settlement located between the old native town and the harbor. Britain and sixteen other nations established consulates in the town. The town was initially expanded with well-laid streets and well-built stone houses, even for the poorer classes, a Catholic and a Protestant church were erected, and a large hotel did business with foreigners who employed the town as a summer resort. The principal traders were the British and Americans, followed by the Germans and Thais. In the 1870s, the principal imports were woolen and cotton goods, iron, and opium and the principal exports were tofu, soybean oil, peas, coarse vermicelli, vegetables, and dried fruit from Zhifu itself, raw silk and straw braid from Laizhou, and walnuts from Qingzhou. The town also traded Chinese liquors and sundries for the edible seaweed grown in the shallows of the Russian settlements around Port Arthur (now Dalian's Lüshunkou District). In 1875, the murder of the British diplomat Augustus Margary in Tengchong, Yunnan, led to a diplomatic crisis that was resolved in Zhifu by Thomas Wade and Li Hongzhang the next year. The resultant Chefoo Convention gave British subjects extraterritoriality throughout China and exempted the foreign merchants' enclaves from the likin tax on internal commerce. Its healthy situation and good anchorage made it a favorite coaling station for foreign fleets, giving it some importance in the conflicts over Korea, Port Arthur, and Weihaiwei. Award-winning Chefoo bobbin lace was produced following the introduction of the craft by British missionaries, reportedly becoming a popular export. Chefoo lace was exhibited at the 1904 St. Louis World's Fair.

Yantai received German economic activities and investments for about 20 years. In the run-up to the First World War, its trade continued to grow but was limited by the poor roads of the area's hinterland and the necessity of using pack animals for portage. The trade items remained largely the same as before. After the Germans were defeated by Allied forces in World War I, Qingdao and Yantai were occupied by the Japanese, who turned Yantai into a summer station for their Asian fleet. They also set up a trading establishment in the town. The different foreign influences that shaped this city are explored at the Yantai Museum, which used to be a guild hall. However, the city's colourful history has not left a distinctive architectural mark, there has never been a foreign concession, and though there are a few grand 19th-century European buildings, most of the town is of much more recent origin. After 1949, the town's name was changed from Chefoo to Yantai, and it was opened to the world as an ice-free trade port in 1984.

On 12 November 1911, the eastern division of Tongmeng Hui declared itself a part of the revolutionary movement. The next day, it established the Shandong Military Government (山東軍政府) and, the day after that, renamed itself the Yantai Division of the Shandong Military Government (山東煙台軍政分府). In 1914, Jiaodong Circuit (膠東道) was established with Yantai as the capital. Jiaodong Circuit was renamed Donghai Circuit (東海道) in 1925. On 19 January 1938, Yantai participated as part of an anti-Japanese revolutionary committee.

After the creation of the People's Republic of China, Yantai was officially awarded city status with the outlying towns of Laiyang and Wendeng tacked on as "Special Regions" (专区) in 1950. Wendeng was merged into Laiyang six years later, and this larger Laiyang Special Region was combined with Yantai City to become Yantai Prefecture (烟台地区). Yantai is of strategic importance to China's defense, as it and Dalian, directly across the Bohai Sea from it, are primary coastal guard points for Beijing. In November 1983, the prefecture became a prefecture-level city.

Geography
Yantai is located along the north coast of the Shandong Peninsula, south of the junction of Bohai Sea and Yellow Sea and parallel to the southern coast of Liaoning. The topographical breakdown consists of: About 2643.60 km2 is urbanized. Only Qixia City is located entirely inland. All other county-level entities are coastal, with Changdao consisting entirely of islands. The total coastline of the prefecture is 909 km.
 * 36.62% mountainous
 * 39.7% hilly
 * 50.23% plain
 * 2.90% basin

The summits in the hill country vary from 100 - 300 m; the average peak in the mountainous region is 500 m, and the highest point of elevation is the summit of Mount Kunyu at 922.8 m.

There are 121 rivers over 5 km in length, the largest being: The core of the old town of Zhifu was located above the mouth of the Yi (, Yí Hé).
 * Wulong River (五龙河)
 * Dagu River (大沽河)
 * Dagujia River (大沽夹河)
 * Wang River (王河)
 * Jie River (界河)
 * Huangshui River (黄水河)
 * Xin'an River (辛安河)

Climate
Yantai has a monsoon-influenced climate which under the Köppen climate classification, Yantai falls within either a hot-summer humid continental climate (Dwa) if the 0 °C isotherm is used or a humid subtropical climate (Cwa) if the -3 °C isotherm is used. Summers are hot, humid, and rainy while winters are cold and dry.

Administration
The prefecture-level city of Yantai administers 12 county-level divisions, including 5 districts, 6 county-level cities, and one development zone. (开发区)

 * Zhifu District (芝罘区)
 * Fushan District (福山区)
 * Muping District (牟平区)
 * Laishan District (莱山区)
 * Penglai District (蓬莱区)
 * Laiyang City (莱阳市)
 * Laizhou City (莱州市)
 * Zhaoyuan City (招远市)
 * Qixia City (栖霞市)
 * Haiyang City (海阳市)
 * Longkou City (龙口市)
 * Yantai Economic and Technological Development Zone
 * Yantai Hi-tech Industrial Development Zone

These are further divided into 148 township-level divisions, including 94 towns, six townships, and 48 subdistricts.

Economy

Yantai is currently the second largest industrial city in Shandong, next to Qingdao. However, the region's largest industry is agriculture. It is famous throughout China for a particular variety of apple and Laiyang pear, and is home to the country's largest and oldest grape winery, Changyu.

The county-level city of Longkou is well known throughout China for its production of cellophane noodles.

Power
Yantai derives most of its energy from a large coal power plant using bituminous coal, and fitted with coal gasification technology to minimize pollution. The plant is located close to Yantai port. An attempt to switch northern China from coal to natural gas resulted in shortages, and in 2017 the Chinese government implemented a new plan to convert half of northern China to clean energy for winter heating. Haiyang, a city under Yantai's prefecture, is anticipated to meet its total winter heating needs with nuclear power by 2021.

Yantai Economic and Technological Development Area
Yantai Economic and Technological Development Area is one of the earliest approved state-level economic development zones in China. It now has a planned area of 10 km2 and a population of 115,000. It lies on the tip of the Shandong Peninsula facing the Yellow Sea. It adjoins downtown Yantai, merely 6 kilometers away from Yantai Port and 6 kilometers away from Yantai Railway Station (not to be confused with Yantai South Railway Station).

Yantai Export Processing Zone
Yantai Export Processing Zone (YTEPZ) is one of the first 15 export processing zones approved by the State Council. The total construction area of YTEPZ is 4.17 km2, in which the initial zone covers 3 km2. After developing for several years, YTEPZ is completely constructed. At present, the infrastructure has been completed, with standard workshops of 120000 m2 and bonded warehouses of 40000 m2. Up to now, owing to an excellent investment environment, YTEPZ has attracted investors from foreign countries and regions such as Japan, Korea, Singapore, Hong Kong, Taiwan, Sweden, the United States, Canada, etc., as well as domestic investors, to operate in the zone.

Education
The following is a list of prominent Yantai higher education institutions.
 * Yantai University
 * Ludong University
 * Shandong Institute of Business and Technology

China Agricultural University and Binzhou Medical College house campuses in Yantai.

It houses a Korean international school, Korean School in Yantai.

Chefoo School previously educated foreign children.

Transport
Yantai Penglai International Airport provides scheduled flights to major airports in China as well as Seoul, Osaka, and Hong Kong. The Lancun–Yantai railway ends at Yantai. The Qinggrong Intercity Railway, the first intercity high-speed railway in Shandong Province, has been put into operation, cutting the travel time of the fastest train from Qingdao to Yantai from about 4 hours and 30 minutes to about 1 hour and 15 minutes.

Tourism

Penglai City's Dan Cliffs is said to be the departure point of the Eight Immortals on their trip to the Conference of the Magical Peach. It is important to note that Penglai is around 80 km from the city centre of Yantai.

Yangma Island is located in the north of Muping District, Yantai and has a large area. The climate on the island is pleasant, with no severe cold in winter and no scorching heat in summer, making it suitable for leisure and vacation. It can be called the Maldives in China. Yangma Island has a long history. It is said that Emperor Qin Shihuang raised royal horses here during his eastward tour and was named the "Royal Horse Island", hence the name of Yangma Island.

Notable people

 * Qiu Chuji (1148–1227), leading Quanzhen Taoist priest and founder of Dragon Gate Taoism
 * Qi Jiguang (1528–1588), Ming dynasty military general most remembered for defending coastal China against Japanese pirates
 * Wang Yirong (1845–1900), Qing dynasty official and historian who was first to recognize the oracle bone script
 * Henry Luce (1898–1967), founder of Time Magazine, Sports Illustrated, and owned many magazine publications such as Life Magazine
 * Peter Stursberg (1913–2014), Canadian writer and journalist
 * Chou Wen-chung (1923–2019), composer
 * Liu Zewen (b. 1943), artist
 * Lin Qingxia (b. 1954), actress
 * Wang Zhengpu (b. 1963), politician
 * Dong Jun (b.1963), People's Liberation Army Navy commander
 * Li Yunze (b. 1970), politician and first post 70's ministerial-level leader
 * Huo Jianhua (b. 1979), actor
 * Wang Yaping (b. 1980), People's Liberation Army Astronaut Corps astronaut
 * Fan Bingbing (b. 1981), actress
 * Guanqun Yu (b. 1982), Opera singer
 * Zhao Yingzi (b. 1990), actress

title: Yantai


text:
Zhifu Island

Zhifu Island or North Island, is an islet with historical significance in Shandong Province, China. The name of the islet Chefoo was generalized to mean the entire Yantai region in older western literature.

Etymologies
Possibilities include:
 * 1) "A Barrier in the Shape of a Magical Plant"
 * 2) * Zhi is a magical and powerful plant, which the island's shape resembles
 * 3) * Fu a barrier of ocean
 * 4) A magical mountain name (significance unknown)
 * 5) * From Qin Dynasty's Zhifu (之罘), officially changed to the present character in late Qing Dynasty.

Administration
Administratively, Zhifu Island is a part of Dàtuǎn Village (大疃村), Xingfu Sub-district, Zhifu District, Yantai City, Shandong Province. Dàtuǎn has a part on the mainland, where the offices and most residents are.

History
Archeological excavations have uncovered over 200 artifacts, including stone axes, and short axes (錛 : Bēn), pottery fragments, bone needles, and bone hairpins. These and Carbon-14 dating indicated that the island has been settled since the Neolithic period.

People were buried here during the Zhou Dynasty, including Duke Kang of Qi, who died on the island in 379 BC. The ruins of the cemetery still exist today. The Lord Yang Temple (陽主廟 Yángzhǔ Miào) was built during the early Zhou Dynasty by rulers of the State of Qí in honor of Lord Yang, the fifth deity of the Eight Divine Generals (八神將).

Because of a legend of a Mountain of Immortality, China's first emperor Qin Shi Huang visited the island three times looking for the elixir. He left a couple of stone inscriptions that are still visible today: Today, there are places like Shihuang Avenue (始皇道 Shihuang Dao), and Fish-shooting Tower (射魚台 Sheyu Tai) named after the emperor. Having failed to discover the elixir, Qin Shihuang dispatched the court sorcerer Xu Fu from Yantai, to sail away and find the elixir of life with hundreds of men and women.
 * During his second visit in 218 BC, he left the inscription: "Arrived at Fu, and carved the stone" (登之罘，刻石).
 * The last time he visited (210 BC) he wrote: "Came to Fu, saw an enormous stone, and shot one fish" (至之罘，見巨石，射殺一魚).

After performing a ceremony in the Yangzhu Temple, Emperor Wudi of the Han Dynasty also left an inscription in 94 BC: "Arrived at Zhifu, which floats on Great Ocean. Mountains call out 'Ten thousand years!" (登芝罘，浮大海，山稱萬歲).

Now, the island is mainly a tourist attraction where clams and abalones can be fished here in abundance.

Geography
Located in Bohai Sea, the island is 4 km from Downtown Zhifu and is 10 km x 1 km. Part of Public Road No. 26 connects the western end of the island and the north part of the mainland peninsula. Originally, the island was disconnected from the mainland, but for a period of millennium of years, the sand and soil in the ocean floor built up a 600-metre wide pathway. Thus the island is called the "Mainland-connecting Island" in Chinese (陸連島); it could even be considered a small peninsula.

The island's largest mountain is Laoye Mountain (老爺山 Lǎoyé Shān) at 294.1m. The Old Lady Stone (婆婆石 Pópó Shí) is on a cliff, at 43.49 metres above sea level, named because of its resemblance to a woman hugging the ocean waves. The southern part of the island is forested.

title: Zhifu Island


text:
Talk:Exponentiation by squaring

Untitled
Maybe you should add a link to the Peasant multiplication in Ancient_Egyptian_multiplication —Preceding unsigned comment added by 85.250.163.119 (talk) 10:21, 23 August 2008 (UTC)

I guess we should present the iterative version of this algorithm:

power(x,n) is computed as long as n is not negative assign 1 to result as long as n is positive assign result*x to result if n is odd assign x*x to x       assign the truncated to next integer of n diveded by 2 to n     return result

Robert Dober 2003-07-05 MEDST

This is the 2^k-ary method with k=1 so it is covered. However, the current presentation hides this; when I have time, I will improve it.Fizban99 (talk) 11:07, 23 January 2010 (UTC)

Never mind, and there is even an error in my algorithm, really well done Robert, sorry for the noise :(

Robert Dober 2003-07-05 MEDST

Article incomplete
One aspect of this subject not mentioned is that this binary algorithm doesn't get to the exponent as fast as possible. For example:

1. x^62 => x^31*x^31 2. x^31 => x*x^30 3. x^30 => x^15*x^15 4. x^15 => x*x^14 5. x^14 => x^7*x^7 6. x^7 => x*x^6 7. x^6 => x^3*x^3 8. x^3 => x*x^2 9. x^2 => x*x

but assuming we remember all exponents we've previously created...

1. x*x => x^2 2. x^2*x^2 => x^4 3. x^4*x^4 => x^8 4. x^8*x^8 => x^16 5. x^4*x^16 => x^20 6. x^20*x^20 => x^40 7. x^20*x^40 => x^60 8. x^2*x^60 => x^62

This takes one step less. I have some more information on this if it would be interesting to have here. This isn't exactally exponentiating by squaring, but along the same lines.

---Jay

Yes, this would be interesting! Especially if there is (as I would expect) a quick systematic way to get at the fastest method, then this should be mentioned in the article as a variation. (And even if there's not a fast alternative algorithm, then this fact can still be mentioned.) Is this the addition chain exponentiation that Henrygb linked? -- Toby Bartels 19:58, 7 Aug 2004 (UTC)

 * Yes, both of these are considered addition chains. It is considered hard to generate minimal addition chains (where one takes the absolute least number of steps required to perform the exponentiation).  In other words, there's a ton of setup that goes into generating these minimal chains, but they execute faster than any other addition chain.  That makes them useless when only a single exponentiation is being performed, as so much time is spent in the setup.  Binary addition chains (which is what this article is about) require no setup and are close enough to minimal to make them useful.  Note that in the above example, there was only a one step difference.  Such a binary addition chain executes somewhat more slowly than a minimal-length chain, but the time saved in skipping initial setup causes the net speed to be in the binary chain's favor. -- Vesta 09:12, 16 Aug 2004 (UTC)

 * As an aside, by definition exponentiation by squaring is a variation of addition chain exponentiation, not the other way around. :) -- Vesta 09:14, 16 Aug 2004 (UTC)

Iterative version useful?
It doesn't use recursion, which increases the speed even further.

Is it useful at all, though? To take the example from the article, x^1000000 requires 41 multiplications (and even fewer recursive calls than that). If you calculate x^1000000 for any x bigger than 1, the relative time spent on calls will be completely negligible. Fredrik | talk 16:40, 17 Feb 2005 (UTC)
 * If the function is executed every millisecond or so, it's probably very useful. 190.60.93.218 (talk) 17:27, 9 September 2013 (UTC)
 * Not likely unless you're using an exceptionally slow computer. I ran a test on a rather slow (1.7 GHz) iMac and found the difference between iterating 41 times in a loop vs. recursing was about 76 nanoseconds.  If that happened every millisecond, it would be a performance decrease of less than one hundredth of one percent.  Mnudelman (talk) 18:09, 3 January 2016 (UTC)

Those code snippets are "yowch"
The following Haskell code implements this algorithm in just 3 lines of code:

power b 0         = 1 power b e | even e =    power (b*b) (e `div` 2) power b e | odd e = b * power (b*b) (e `div` 2)

The following code is tail-recursive, so it uses less stack space:

power' r b 0         = r power' r b e | even e = power'  r    (b*b) (e `div` 2) power' r b e | odd e = power' (r*b) (b*b) (e `div` 2) power   b e          = power'  1     b     e

The above will work for any type of b that the * operator is defined on (any type in the Num class). It can be generalized to use any function in place of multiplication:

power f r b 0         = r power f r b e | even e = power'  r      (f b b) (e `div` 2) power f r b e | odd e = power' (f r b) (f b b) (e `div` 2)

The original function is now power (*) 1, and, say, multiplication can be implemented as power (+) 0. --Ihope127 02:13, 12 April 2006 (UTC) (edited 14:43, 12 April 2006 (UTC))

Far too many examples
The article needs to be severely cut down. Most wikipedia math articles could use more examples, but this page has far too many examples. The same ground is covered repeatedly. 165.189.91.148 20:54, 10 May 2006 (UTC)

Text Concatenation
This algorithm is unsuitable for text concatenation. Instead, the following algorithm is more efficient:

function repeat ( s, n ) { if ( s == "" || n < 1 ) return ""; if ( n == 1 ) return s;  var res = s;   for ( var i = 2 ; i < n ; i *= 2 ) res = res + res; return res + res.substr( 0, s.length * n - res.length ); }

Results of binary decomposition assume a slightly different algorithm
The case for n=1 is missing in the original definition of the algorithm. I realize it's probably obvious, but it should probably be included for completeness. In fact, why bother with restricting the odd case to n>2 at all (since it reduces to 'x' anyway for n=1) and just use what's below instead?

\mbox{Power}(x,\,n)= \begin{cases} 1, & \mbox{if }n\mbox{ = 0} \\ \mbox{Power}(x^2,\,n/2), & \mbox{if }n\mbox{ is even} \\ x\times\mbox{Power}(x^2,\,(n-1)/2), & \mbox{if }n\mbox{ is odd} \end{cases} $$

But I have a bigger concern, and that's the fact that the definition given above doesn't result in an expression with the same economy that the binary decomposition does. When I found that the binary decomposition of the expression results in one with fewer multiplications, I was confused. I asked myself why a better definition wasn't given instead, one which results in the same number of multiplications as the binary decomposition, but without the intermediate expression. It seems cumbersome to apply the above definition to get one expression, then go through the manual process of binary decomposition of that to get a more economical expression (which is the way it was done in the examples in the article). So why not use the following definition instead:

\mbox{Power}(x,\,n)= \begin{cases} 1, & \mbox{if }n\mbox{ = 0} \\ (\mbox{Power}(x,\,n/2))^2, & \mbox{if }n\mbox{ is even} \\ x\times(\mbox{Power}(x,\,(n-1)/2))^2, & \mbox{if }n\mbox{ is odd} \end{cases} $$

For instance, in the case of x100, the expression it produces requries 8 multiplications, while the expression produced by the first definition requires 15 multiplications. (For either definition, an extra multiplication is saved by recognizing that Power(x,n)=x Power(x,1)=x (sorry, typo), and treating it as a fourth case.)

Does anyone have any objections to me updating the definition in the article with this updated one? I think it would reduce some confusion.

--Paul 06:53, 7 March 2007 (UTC)

Agreed. Also I fail to see the need for multiple recursive definitions on the page. I merged the content.Fizban99 (talk) 10:54, 23 January 2010 (UTC)

Text application
I don't understand at all how the text application applies at all to the article. I recommend deletion.

R00723r0 08:58, 15 July 2007 (UTC)

Exponentiation can be viewed as multiplying exponents. Multiplying can be viewed as adding exponents (i.e., logarithms). The text application leverages this by viewing concatenation as a variant of multiplication. Then the same techniques that are used for exponentiation (and thus that are available to multiplying exponents where "multiplying exponents" is just another name for exponentiation) are now available to multiplying strings. Thus it is quite related and should stay as is. —optikos (talk) 03:48, 17 June 2008 (UTC)

No R00723r0 is quite correct. This is original research that is not related to exponentiation. Please provide a citation of where it has been published before that shows the relation. Furthermore it is a terrible way to do string repetition as it assumes that the copy/append operations are unit-time, where-as in most implementations they would be linear time over the length of the operands. As a result, in any run-time where the linear component dominates over the fixed start-up cost, or in any run-time over large enough operands (ie asymptotically) this method is *slower* than the naive approach of allocating a buffer and then looping over the repeated string to fill it. I have removed this section pending some sort of citation to show that it is not original research. Amoss (talk) 12:38, 9 April 2009 (UTC)

Programming
I think it would be a good idea to stick to one programming language throughout the article, or even just a pseudo-language. Furthermore, I don't think most people can benefit from Javascript examples.

R00723r0 09:03, 15 July 2007 (UTC)

 * I agree, please just use pseudo-code. Binary exponentiation is simple enough that we hardly need to get into the syntax of any particular programming language du jour.  24.61.43.18 15:36, 14 August 2007 (UTC)
 * Your comment did benefit me ironically, since you said there was a JavaScript implementation out there thus making me search for this implementation and helping me out understand 190.60.93.218 (talk) 17:32, 9 September 2013 (UTC)
 * More importantly, getting into the syntax of a particular language adds greater complexity to an algorithm's description, languages limit rather than expand the mathematical approach. In reality the only time to be giving an algorithm description in a specific language is if you are targeting developing the algorithm that language, as Wikipedia is not a StackOverflow this should never happen. JSory (talk) 07:50, 16 March 2023 (UTC)

Simpler
Why unroll the recursion manually? This is simpler:

\mbox{Power}(x,\,n)= \begin{cases} 1, & \mbox{if }n\mbox{ = 0} \\ x\times\mbox{Power}(x,\,n-1), & \mbox{if }n\mbox{ is odd} \\ \mbox{Power}(x,\,n/2)^2, & \mbox{if }n\mbox{ is even} \end{cases} $$ For "n=0" and "n is odd", this is standard recursive exponentiation. Just "n is even" case is optimized, according to:

x^n=x^{n/2} \times x^{n/2} $$ exe (talk) 18:08, 22 May 2008 (UTC)

I believe the reason is that the former emphasizes you get precisely lg n calls to the function, facilitating the analysis.Fizban99 (talk) 10:48, 23 January 2010 (UTC)

Underlying idea: I'd like to add one logical step
This is the current version: $$ x^n= \begin{cases} 1,                                         & \mbox{if }  n = 0   \\ 1/x^{-n},                                       & \mbox{if }  n < 0   \\ x \cdot \left( x^{\frac{n-1}{2}} \right)^2, & \mbox{if } n \mbox { is odd} \\ \left( x^{\frac{n}{2}} \right)^2,           & \mbox{if }n\mbox{ is even} \end{cases} $$

But I feel that the third equation could be modified to say

$$ x^n= \begin{cases} 1,                                         & \mbox{if }  n = 0   \\ 1/x^{-n},                                       & \mbox{if }  n < 0   \\ x \cdot x^{n-1}, & \mbox{if } n \mbox { is odd, i.e. } n - 1 \mbox{ is even} \\ \left( x^{\frac{n}{2}} \right)^2,           & \mbox{if }n\mbox{ is even} \end{cases} $$

That would make this equation a lot clearer, and the next step follows by the fourth equation, instead of having both in one step. It should be noted that the algorithm makes both steps at once for increased performance, though. —Preceding unsigned comment added by 134.96.57.229 (talk) 18:03, 6 February 2011 (UTC)

I didn't really see the post above, so sorry for that. I'm still all for the change though, especially now that we're talking about "underlying idea" instead of the actual algorithm used lateron. Also, for the logarithmic time you don't need to divide the argument by 2 on every iteration; You merely have to do so every O(1) steps. --134.96.57.229 (talk) 18:09, 6 February 2011 (UTC)

Underlying idea: Negative Exponent
Seeing how there is an edit war between those who believe that

$$ x^n = 1/{x^n} $$

And those who know that

$$ x^n = 1/{x^{-n}} $$

Just look at this:

$$x^n = 1/x^{-n}$$

Multiply both sides by $$ x^{-n}$$ and you get

$$x^n \cdot x^{-n} = 1$$

Product with same base allows contraction of exponents, such that

$$x^{n + \left(-n\right)} =  1$$

Performing the addition yields

$$x^0 =  1 = 1$$

which is true by reflexivity.

The other one only works for $$n=0$$ or $$x=1$$.

--134.96.57.229 (talk) 18:43, 6 February 2011 (UTC)

Basic method
Nothing explains better than an example, especially for those of us who aren't especially fast learners or who don't think recursively. So, I'm inserting an example at the beginning that shows what's really going on. It's based on the way I've implemented exponentiation by squaring in many languages (as well as computing terms in a Lucas sequence - same idea, but with subscripts instead of exponents). I hope this makes the basic method clearer. MathPerson (talk) 19:56, 3 April 2017 (UTC)

This first section of the article says: The method is based on the observation that, for a positive integer n, we have
 * $$ x^n=

\begin{cases} x \, ( x^{2})^{\frac{n - 1}{2}}, & \mbox{if } n \mbox{ is odd} \\ (x^{2})^{\frac{n}{2}}, & \mbox{if } n \mbox{ is even}. \end{cases} $$

No, it isn't. You don't compute $$x^{10}$$ by raising $$x^2$$ to the 5th power. You get $$x^{10}$$ by squaring $$x^5$$. Also, the recursive methods shown only obscure the issue. MathPerson (talk) 23:12, 20 May 2019 (UTC)

Least significant bit is first
Despite the language that indicates that bits are examined left to right, the first bit tested in the exponent is the least significant bit, when the test is for whether n is odd or even. This should be fixed in the description, yes? — Q uantling (talk | contribs) 22:39, 15 May 2022 (UTC)
 * The article is correct for the description of the computation (look at he example for a verification). However, in recursive programming, tests are done from right to left for building the stack, and the reverse order is used for computing. This may be confusing. So, I agree that this part of the article deserves to be rewritten. But this cannot be done by changing few words only. D.Lazard (talk) 09:22, 16 May 2022 (UTC)
 * Thank you, good point. The confusion comes in part because many of these algorithms are written for non-ALGOL-like languages.  We could replace them with something much simpler like this C/C++ snippet

double power(double x, int n) { if (n < 0) { n = -n; x = 1 / x;     } double y = 1.0; while (n > 0) { if (n & 1) // if n is odd y *= x;       x *= x;        n /= 2; // rounds down }     return y;    }
 * ... or perhaps the equivalent in something like Python. No recursion, no confusion about the bit order, straightforward.  What do you think?  — Q uantling (talk | contribs) 22:40, 16 May 2022 (UTC)
 * I disagree with the use of a specific programming language (see MOS:MATH), and pseudocode must be used as far as possible. In any case, the pseudocode style must be coherent through the article, and this is not even the case in
 * However, things are worse than a single coding-style issue: Several distinct algorithms are presented as if they were the same. Some algorithms use explicitly the binary representation of the exponents, and therefore cannot be easily used one many programming languages; other algorithms use simply a parity test for exponents, and are therefore easier to implement. Also, some algorithms, such a the non-tail recursive one, use the formula $$ x^n=

\begin{cases} x \, ( x^{2})^{\frac{n - 1}{2}}, & \mbox{if } n \mbox{ is odd} \\ (x^{2})^{\frac{n}{2}}, & \mbox{if } n \mbox{ is even}, \end{cases} $$ while other algorithms use $$ x^n= \begin{cases} x \, ( x^{\frac{n - 1}{2}})^{2}, & \mbox{if } n \mbox{ is odd} \\ (x^{\frac{n}{2}})^{2}, & \mbox{if } n \mbox{ is even}. \end{cases} $$ In one case, the last multiplication in the case of an odd exponent use the initial $x$, while a different multiplier is used in the iterative algorithm and the tail-recursive one without accumulators.
 * So, a major rewrite is needed. As I am not willing to do it now, I will tag the article with a link to this section. D.Lazard (talk) 10:34, 17 May 2022 (UTC)
 * I have rewritten section . Nevertheless I have left the tag confusing, since much work is needed for clarifying the other sections. Also, I have removed the example, since I do not know how to give an example that is more informative than the given explanations. D.Lazard (talk) 16:27, 17 May 2022 (UTC)
 * Excellent, thank you! — Q uantling (talk | contribs) 18:10, 17 May 2022 (UTC)
 * I tried to extend your excellent prose a little. Please edit as you see fit.  — Q uantling (talk | contribs) 18:48, 17 May 2022 (UTC)

Use of the binary representation of the exponent
Although it contains some interesting content, I'll revert the last edit by. The reasons are as follows.

The main features of this edit is to introduce from the beginning the binary representation of the exponent, and to use the technical language of language theory ("prefix" and "suffix"). This is not useful for section, and therefore could be confusing or too technical for most readers.

IMO, the content added by Quantling could be the starting point of a lacking section that could be called as the heading of this thread. This section summarized as follows: In, the bits of the exponent are implicitly used by starting with the less significant one. If one can access to these bits in the opposite order (either with a precomputation or using primitive of assembly language), one may obtain another algorithm that requires exactly the same number of arithmetic operations (this is the algorithm used in the example that I have removed by my edit). Then the pseudocode of this algorithm should be presented. It is also possible to compare this pseudocode with a variant of the algorithm of that uses a bit access.

Such a section could be also useful for making sections 3 and 4 easier to understand. D.Lazard (talk) 16:41, 18 May 2022 (UTC)

 * If you have the chance to follow through on this vision, it would be much appreciated! — Q uantling (talk | contribs) 20:55, 18 May 2022 (UTC)

Magma
Switching in "magma" for "semigroup" doesn't appear to work. While the former is, in some sense, a generalization of the latter, it appears that the binary operator for a magma is not required to be associative. As such, an expression such as $x3$ does not appear to be well defined because $x • (x • x)$ and $(x • x) • x$ are not necessarily equal. In particular, it appears that exponentiation by squaring is not going to be meaningful for a magma. — Q uantling (talk | contribs) 12:50, 6 October 2023 (UTC)

 * The IP user that I reverted was aware of that, as they switched to "magmas where the operation has the property of power associativity". This was not the reason of my revert. The reason is that few people know this structure, and, AFAIK, there are no common examples of exponentiation by squaring in a structure that is not a semigroup. Exponentiation of matrices is an important example where the multiplication is not the operation of a group, and elliptic curves are examples that are not rings and where the method is used. So, there is no reason for such a generalization in the lead. However, I am not opposed to add somewhere in the body the remark that "magmas where the operation has the property of power associativity" are the most general structures where the method works. D.Lazard (talk) 13:51, 6 October 2023 (UTC)
 * Thank you for clarifying that. I added a mention of magma and made some other edits to the article.  As always, please feel free to edit further, undo, comment here, ....  Thank you — Q uantling (talk | contribs) 16:02, 6 October 2023 (UTC)

title: Talk:Exponentiation by squaring


text:
William Dunbar

William Dunbar (1459 or 1460 – by 1530) was a Scottish makar, or court poet, active in the late fifteenth and early sixteenth centuries. He was closely associated with the court of King James IV and produced a large body of work in Scots distinguished by its great variation in themes and literary styles. He was probably a native of East Lothian, as assumed from a satirical reference in The Flyting of Dumbar and Kennedie. His surname is also spelt Dumbar.

Biography
Dunbar first appears in the historical record in 1474 as a new student or determinant of the Faculty of Arts at the University of St Andrews. Since the customary age for entering a Scottish university at this time was fourteen, a birth-date of 1459 or 1460 has been assumed. At St Andrews, he obtained a bachelor's degree in 1477 and a master's degree in 1479. Details from his later life suggest that he was ordained as a priest at some point, but the date is unknown.

In 1491 and 1492, Dunbar accompanied an embassy to Denmark and France in an unknown capacity. In 1501 and 1502, he participated in an embassy to England in the staff of Andrew Forman, Bishop of Moray.

From 1500 the poet was employed at the court of King James in a role for which he received an annual pension. His duties are not recorded; he is referred to only as a servitour or servant; but it is to this period that the bulk of his poetry can be dated. Several of Dunbar's poems were included in the Chepman and Myllar prints of 1508, the first books to be printed in Scotland.

In 1510, his pension was set at the substantial annual sum of eighty pounds Scots. In comparison, Dunbar's contemporary Hector Boece received an annual salary of £26 13s for his role as Principal of King's College, Aberdeen.

The last reliable reference to Dunbar is in the Treasurer's Accounts for May 1513, where he is recorded receiving payment of his pension. James died at Flodden in September of the same year. In the dislocation that followed, the Treasurer's accounts cease for a period and, when resumed in 1515, Dunbar is no longer recorded as being employed by the crown.

A poem, Quhen the Governour Past in France, describing the departure of the Regent Albany for France in 1517, is attributed to Dunbar in the Maitland Manuscripts, suggesting that he was still active at the time. But in Sir David Lyndsay's work The Testament and Complaynt of the Papyngo of 1530, Dunbar is referred to as being deceased. The exact date of his death remains unknown.

Dunbar's poetry
William Dunbar's poetry contained a wide variety of subjects, moods and metres. He wrote many devout religious works and noble courtly pieces but he also produced comic pieces which often made use of scurrilous elements and uninhibited language.

Commemorative and occasional works
Some of Dunbar's poems were clearly commissioned to mark public events. His allegory The Thrissil and the Rois commemorated the marriage of Margaret of England to King James in 1503 while the Eulogy to Bernard Stewart, Lord of Aubigny welcomed the arrival of a distinguished Franco-Scottish soldier as the French ambassador in 1508. Local events were also marked such as the visit of Queen Margaret to the 'blyth and blissful burgh of Aberdein' in 1511.

The poem "In Honour of the City of London", of the medieval urban description genre, was made into a cantata of the same name by William Walton in 1937.

Religious and moral works
Dunbar was an ordained priest of the Roman Catholic Church in Scotland and several of his works have religious subject matter. Rorate Celi Desuper, Of the Passioun of Christ and Done is a Battell on the Dragon Blak deal with the Nativity, Passion and Resurrection respectively. Ane Ballat of Our Lady is a hymn in praise of the Blessed Virgin. The Table of Confession discusses sin and confession.

Poems with a secular moral theme also occur in his work such as Of Deming and the trilogy of short pieces Of Discretioun in Asking, Of Discretioun in Geving and Of Discretioun in Taking.

Dunbar's poems The Tabill Of Confessioun, Rorate Celi Desuper and Done Is A Battell On The Dragon Blak were included in the "Ballatis of Theologie" section of the Bannatyne Manuscript.

Court entertainment
Many of the poet's pieces appear to provide entertainment for the King, the Queen and his fellow courtiers with comic elements as a recurring theme. The well known Ane Dance in the Quenis Chalmer is a comic satire of court life. The notorious flyting with Kennedy was an exchange of outrageous poetic insults with his fellow makar Walter Kennedy while The Dance of the Seven Deadly Sins is a series of comic scenes set in Hell.

Poems in the tradition of courtly love are represented in Dunbar's work including a short lyric Sweit Rois of Vertew and the extended allegory The Goldyn Targe.

Other court entertainments were more personal. Of James Dog and its sequel He Is Na Dog, He Is a Lam describe the poet's dealings with the keeper of the Queen's wardrobe.

Satires and commentary on public life
A recurring theme in Dunbar's work is satire. He satirised colleagues of whom he disapproved such as in The Fenyeit Freir of Tungland and he urged the burgesses of Edinburgh to show greater civic pride in To the Merchantis of Edinburgh. Tydings Fra The Sessioun criticised corruption in the Court of Session. In The Treatise of Mr. Andro Kennedy, he directs satire at a member of the court of James IV.

Some of Dunbar's satirical poems are preserved in the Bannatyne Manuscript, including The Dregy of Dunbar, The Twa Cummeris, and The Flyting of Dumbar and Kennedie to name a few.

Petitions to the King and personal affairs
William Dunbar was willing to reveal his personal affairs in his poetry and a number of his works are petitioned to the King asking for personal advancement. He often requested to be appointed to an office in the church, which he refers to as a benefice. A typical example is Quone Mony Benefices Vakit. On other occasions, his requests were more modest. In The Petition of The Gray Horse, Auld Dunbar the poet asked the King for a new suit of clothes to mark Christmas. The poem Schir, Ye Have Mony Servitouris makes clear his comparative value to the king and country.

Elsewhere, Dunbar seemed to reveal other aspects of his private life. His famous Memento mori poem Lament for the Makaris eulogised his fellow Scottish poets who had passed away. Meditatioun In Wyntir considers ageing and the poet's frustrated ambitions while On His Heid-Ake is apparently an attempt to excuse a lack of productivity by recounting a migraine.

Work and influence
Dunbar's reputation among his immediate successors was considerable. By later criticism, stimulated in some measure by Scott's eulogy that he is "unrivalled by any which Scotland has produced", he has held the highest place among the makars.

One hundred and one poems have been ascribed to Dunbar. Of these at least ninety are generally accepted as his; of the eleven attributed to him, it would be hard to say that they should not be considered authentic. Most doubt has clung to his verse tale The Freiris of Berwik, so much so that it seems unlikely that he was the author. The only copy manuscript of this text is in French, and although the style is very close to that of Dunbar's, it is unlikely that he was the author of this anonymous text.

Dunbar's chief allegorical poems are The Goldyn Targe and The Thrissil and the Rois. The motif of the former is the poet's futile endeavour, in a dream, to ward off Dame Beauty's arrows by Reason's "scheld of gold." When wounded and made prisoner, he discovers the true beauty of the lady: when she leaves him, he is handed over to Heaviness. The noise of the ship's guns, as the company sails off, wakes the poet to the real pleasures of a May morning. Dunbar works on the same theme in a shorter poem, known as Beauty and the Prisoner. The Thrissil and the Rois is a prothalamium in honour of King James and Queen Margaret.

The greater part of Dunbar's work is occasional — personal and social satire, complaints, orisons and pieces of a humorous character. His best-known orison, usually remembered as Timor mortis conturbat me which is repeated as the fourth line of each verse, is titled Lament for the Makaris and takes the form of prayer in memory of the medieval Scots poets.

The humorous works show Dunbar at his finest. The best specimen of this work, of which the outstanding characteristics are sheer whimsicality and topsy-turvy humour, is The Ballad of Kynd Kittok. This strain runs throughout many of the occasional poems, and is not wanting in odd passages in Dunbar's contemporaries; and it has the additional interest of showing a direct historical relationship with the work of later Scottish poets, and chiefly with that of Robert Burns. Dunbar's satire often becomes invective. Examples of this type are The Satire on Edinburgh, The General Satire, the Epitaph on Donald Owre, and the powerful vision of The Dance of the Sevin Deidlie Synnis. Two satirical ballads lampoon a colleague at court, the would-be aviator John Damian. In The Flyting of Dunbar and Kennedy, an outstanding specimen of a favourite northern form, analogous to the continental estrif, or tenzone, he and his rival reach a height of scurrility which is certainly without parallel in English literature. This poem has the additional interest of showing the antipathy between the Middle Scots-speakers in the Lothians and the Galwegian Gaelic-speaking population of Carrick, in the south of Ayrshire, where Walter Kennedy was from.

"Back to Dunbar"
For the Scottish Literary Renaissance in the mid-twentieth century, Dunbar was a touchstone. Many tried to imitate his style, and "high-brow" subject matter, such as Hugh MacDiarmid and Sydney Goodsir Smith. As MacDiarmid himself said, they had to go "back to Dunbar". To make Dunbar more accessible to the modern reader Selected Poems of William Dunbar: An Interlinear Translation was published by Lawrence Siegler in 2010.

Dunbar is commemorated in Makars' Court, outside The Writers' Museum, Lawnmarket, Edinburgh.

Works

 * Ane Dance in the Quenis Chalmer
 * The Dregy Of Dunbar
 * The Fenyeit Freir of Tungland
 * The Flyting of Dumbar and Kennedie
 * The Twa Cummeris
 * The Goldyn Targe
 * He Is Na Dog, He Is a Lam
 * On His Heid-Ake
 * Of Ane Blak-Moir
 * Of James Dog
 * Lament for the Makaris (Timor mortis conturbat me)
 * Meditatioun In Wyntir
 * The Petition of The Gray Horse, Auld Dunbar
 * Remonstrance to the King (Schir, ye have mony servitouris)
 * The Thrissil and the Rois
 * The Tua Mariit Wemen and the Wedo

title: William Dunbar


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An Alan Smithee Film: Burn Hollywood Burn

An Alan Smithee Film: Burn Hollywood Burn (stylized on-screen as Burn Hollywood Burn) is a 1997 American mockumentary black comedy film directed by Arthur Hiller, written by Joe Eszterhas and starring Eric Idle as a director unfortunately named Alan Smithee, a traditional pseudonym used in Hollywood for directors disowning a project. The film follows Smithee as he steals the negatives to his latest film and goes on the run.

An Alan Smithee Film: Burn Hollywood Burn was universally panned by critics and tanked at the box office. It won five awards (including Worst Picture) at the 19th Golden Raspberry Awards. The film's creation set off a chain of events which led the Directors Guild of America to officially discontinue the Alan Smithee credit in 2000 after its use for decades when an American director disavowed a film. The plot, about a director attempting to disown a film, described the film's own production; Hiller requested that his name be removed after witnessing the final cut, and he is credited as Alan Smithee. Burn Hollywood Burn was also the final film produced by Cinergi Pictures to be released before the company declared bankruptcy.

Plot
Challenger Films producers Jerry Glover and James Edmunds hire acclaimed English editor Alan Smithee to direct Trio, a blockbuster action film starring Sylvester Stallone, Whoopi Goldberg, and Jackie Chan. Though only hired due to his inexperience, which the producers believe will make him controllable, Smithee becomes invested in the project.

Edmunds makes frequent changes to the film, hiring many additional writers to retool the script and giving Smithee frequent notes during production. Between this and frequent interference from the film's stars, Smithee becomes withdrawn. Edmunds hires prostitute Michelle Rafferty to seduce a drunken Smithee, who is in an unhappy marriage, so he can acquire blackmail material. Michelle is captivated by Smithee's kind spirit, and develops feelings for him.

Smithee realizes he has lost control over Trio, and voices his concerns to Edmunds, who advises him to take his name off the film and use the DGA pseudonym - which he cannot do, as it is also 'Alan Smithee.' After Stallone requests they cut one of Chan's lines in the film, Smithee offers to make the edit and drop the master off at the lab for duplication, instead stealing it and running away.

As Challenger instructs security foreman Sam Rizzo to organize a search for Smithee, he calls into Larry King, and in the middle of a mental breakdown, announces his intention to burn the film so it may not be released. At a gas station, he is spotted by Stagger Lee, a member of the African American Guerilla Film Family, whom he quickly befriends. Smithee is put in touch with famed indie directors the Brothers brothers, who relate to his plight and schedule a meeting with Glover and Edmunds to negotiate.

Glover offers the brothers a three-picture deal if they return the master as-is, but they refuse, insisting that Smithee be given final cut on Trio. Though claiming to accept this offer, Glover has Rizzo follow the brothers back to their house, where the police search for the master. Smithee exits through a back window and drives to the La Brea Tar Pits, where he finally burns the film as promised. He appears on Larry King again, in-person, to defend his actions, explaining that "they killed [Trio], I ended its suffering."

Attorney Robert Shapiro negotiates for Smithee to be sent to a psychiatric hospital in England in lieu of criminal charges, as the King interview has led Smithee to be regarded as a hero by the public. Glover and Edmunds compete in a bidding war with producer Robert Evans to secure Smithee's life story for a film adaptation, which Smithee sells on the condition that the Brothers brothers direct with final cut. The producers decide that Smithee, with his newfound reputation, is now a valuable property, and offer him a film deal. At the hospital, Michelle reconciles with Smithee as he discusses plans for his new film, Duo.

Cast
• Eric Idle as Alan Smithee

• Ryan O'Neal as James Edmunds

• Coolio as Dion Brothers

• Chuck D as Leon Brothers

• Richard Jeni as Jerry Glover

• Leslie Stefanson as Michelle Rafferty

• Sandra Bernhard as Ann Glover

• Cherie Lunghi as Myrna Smithee

• Harvey Weinstein as Sam Rizzo

• Gavin Polone as Gary Samuels

• MC Lyte as Sista Tu Lumumba

• Marcello Thedford as Stagger Lee

• Nicole Nagel as Aloe Vera

• Stephen Tobolowsky as Bill Bardo

• Erik King as Wayne Jackson

• Dina Spybey as Alessandra Cameos as themselves • Sylvester Stallone

• Whoopi Goldberg

• Jackie Chan

• Robert Evans

• Robert Shapiro

• Shane Black

• Mario Machado

• Lisa Canning

• Joe Eszterhas

• Larry King

• Peter Bart

• Dominick Dunne

• Billy Bob Thornton

• Billy Barty

• Norman Jewison (uncredited)

Production
The film was written (and produced, though he was not credited for it) by Joe Eszterhas, who became the first person to win four Golden Raspberry awards for a single film: Worst Picture, Worst Screenplay and both Worst Supporting Actor and Worst New Star for a brief cameo appearance (he also received a co-nomination for the Worst Screen Couple award, since An Alan Smithee Film: Burn Hollywood Burn was nominated for "any two people appearing together onscreen"; although the movie did not "win" in this category). The released film credits the Alan Smithee pseudonym as director because Arthur Hiller, the film's real director, objected to the way Eszterhas recut the film, and as a result, had his name removed. In his autobiography, Hollywood Animal, Eszterhas claims that Hiller still sat in the editing room with him to make certain suggestions. In his entry on An Alan Smithee Film: Burn Hollywood Burn for his "My Year of Flops" column in The A.V. Club, pop culture critic Nathan Rabin sarcastically commented that Hiller's decision to use the Alan Smithee credit was "very transparently not a stupid, stupid gimmick to raise interest in a terrible film".

Box office
The film had an estimated budget of $10 million and grossed at least $52,850, as it was released in only 19 theaters.

Critical response
Film critic Roger Ebert, reviewing for the Chicago Sun-Times, gave An Alan Smithee Film: Burn Hollywood Burn a score of zero stars, his lowest possible rating. The film was not merely bad but "incompetent", Ebert wrote, and also seemingly represented a lapse of judgment for Eszterhas who "is sometimes a good writer". In 2005, Ebert included it on his list of most hated films.

The film holds a 7% rating on Rotten Tomatoes, based on 41 reviews, with an average rating of 3.3/10. The site's critical consensus calls it "A witless Hollywood satire whose hammy, obvious jokes are neither funny nor insightful of the movie business." Eric Idle said in various interviews meant to promote the film that "this is rather dreadful".


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Talk:Pan frying

Untitled
I don't think this article is correct - pan-frying is not "frying in minimal oil/fat", at least in American usage. e.g. 3tbsp butter here: http://www.epicurious.com/recipes/food/views/Pan-Fried-Jerusalem-Artichokes-in-Sage-Butter-233715, 5tbsp here http://www.epicurious.com/recipes/food/views/Pan-Fried-Flounder-with-Potatoes-in-Parsley-354529, many more examples at http://www.epicurious.com/tools/searchresults?search=pan+fry&type=simple&threshold=53&att=639. That's much more than "minimal fat" in many of these. Epicurious sources their recipes from Gourmet and Bon Appetit, two of the more prestigious/mainstream cooking magazines, so I am inclined to trust their labels for cooking methods. 66.108.25.34 (talk) 22:08, 25 June 2010 (UTC)

 * The first recipe actually uses one tablespoon of butter, and melts the rest to use as a sauce. "Minimal" fat is a terminology issue - deep frying would use cups or quarts, not tablespoons, and even shallow frying would use more than the five tablespoons called for in the second recipe (five tablespoons of butter in a pan large enough to fry fish isn't a large amount at all). In addition, some foods, like the sausages shown, make their own fat and don't need fat added at all. So maybe a better word than "minimal"? FiveRings (talk) 11:38, 26 June 2010 (UTC)

I have not heard that pan frying is the english word for the french saute. i pan fry my steaks which i use a heavy pan and no added fat. I don't consider this the same technique as sauteing, am I wrong?

 * The article was incorrect. I've taken a shot at revising and expanding it.  It certainly could use more work.

 * I think your confusion stems from the difference between the culinary use of the word fry and more general use. In one sense, fry can be used for nearly all methods of cooking, especially on  the stove top.  As I understand it the more specific definition of frying requires oil to mediate the heat transfer from heat source to food.  The various techniques use more or less oil and have corresponding procedural differences as a result.

 * Sauté comes from the French for jump. Either, depending on who you listen to, the water "jumping" out of the food/pan or the need to keep the food "jumping" around the pan to prevent sticking/burning.

 * As for your steaks: you are what would more accurately be described as browning or searing. VermillionBird 18:31, 20 September 2005 (UTC)

The image of sausages being pan-fried does not match the description. The description indicates that pan-frying uses a quantity of oil sufficient to partially submerge the food. This image indicates only a small amount of oil in the bottom of the pan. Would the image of the sausages be an example of searing or sauteing instead? —Preceding unsigned comment added by 76.122.210.39 (talk) 01:27, 12 June 2009 (UTC)

Breading and Battering
"Foods to be pan-fried are usually covered with a batter or breading." USUALLY? Stub Mandrel (talk) 13:02, 7 February 2017 (UTC)

title: Talk:Pan frying


text:
Platonic epistemology

In philosophy, Plato's epistemology is a theory of knowledge developed by the Greek philosopher Plato and his followers.

Platonic epistemology holds that knowledge of Platonic Ideas is innate, so that learning is the development of ideas buried deep in the soul, often under the midwife-like guidance of an interrogator. In several dialogues by Plato, the character Socrates presents the view that each soul existed before birth with the Form of the Good and a perfect knowledge of Ideas. Thus, when an Idea is "learned" it is actually just "recalled".

Plato drew a sharp distinction between knowledge, which is certain, and mere true opinion, which is not certain. Opinions derive from the shifting world of sensation; knowledge derives from the world of timeless Forms, or essences. In The Republic, these concepts were illustrated using the metaphor of the Sun, the analogy of the divided line, and the allegory of the cave.

Platonic doctrine of recollection
The Platonic doctrine of recollection, or anamnesis is the view that we are born possessing all knowledge and our realization of that knowledge is contingent on our discovery of it. Whether the doctrine should be taken literally or not is a subject of debate. The soul is trapped in the body. The soul was once directly acquainted with the Forms, but it is now embodied. It once knew all of the Forms, but forgot them. Recollection is the process of bringing to our attention this knowledge that we have forgotten. This doctrine implies that nothing is ever learned, it is simply recalled or remembered. In short it says that all that we know already comes pre-loaded on birth and our senses enable us to identify and recognize the stratified information in our mind. Recollection involves, on the one hand, overcoming the deceptions and distractions of the body, but, on the other hand, productively using the body's deceptions to occasion or trigger the episodes of recollection. The main texts that develop the theory of recollection are the Phaedo and Meno, although the theory also plays an important role in the Phaedrus.

Metaphor of the Sun
In the Republic (VI 507b-509c), Plato's character, Socrates, uses the Sun as a metaphor for the source of "intellectual illumination," which he held to be The Form of the Good. The metaphor is about the nature of ultimate reality and how we come to know it. It starts with the eye, which Socrates says is unusual among the sense organs in that it needs a medium, namely light, in order to operate. The strongest and best source of light is the Sun; with it, we can discern objects clearly. Analogously, for intelligible objects The Form of the Good is necessary in order to understand any particular thing. Thus, if we attempt to understand why things are as they are, and what general categories can be used to understand various particulars around us, without reference to any forms (universals) we will fail completely. In contrast, "the domain where truth and reality shine resplendent" is none other than Plato's world of forms, illuminated by the highest of the Forms, that of the Good.

The divided line
In the sixth book of the Republic, the divided line has two parts that represent the intelligible world and the smaller visible world. Each of those two parts is divided, the segments within the intelligible world represent higher and lower forms and the segments within the visible world represent ordinary visible objects and their shadows, reflections, and other representations. The line segments are unequal and their lengths represent "their comparative clearness and obscurity" and their comparative "reality and truth," as well as whether we have knowledge or instead mere opinion of the objects.

Allegory of the cave
In his best-known dialogue, The Republic, Plato drew an analogy between human sensation and the shadows that pass along the wall of a cave - an allegory known as Plato's allegory of the cave.

Charioteer myth
Along with these other allegories, Plato's charioteer myth in the Phaedrus (245c-257b) certainly also deserves mention. The ascent of the mind to celestial and trans-celestial realms is likened to a charioteer and a chariot drawn by two winged horses, one dark and one white. Figuratively represented is the famous Platonic tripartite model of the soul: the charioteer represents reason, or intellect, the dark horse appetitive passions, and the white horse irascible nature. Only by taming and controlling the two horses can the charioteer ascend to the heavens and enjoy a banquet of divine knowledge. Key epistemological features of the charioteer myth are (1) an emphasis, as with the cave allegory, upon true knowledge as ascent, (2) and the need to tame one's passionate nature to obtain true knowledge.

An example: love and wisdom
A good example of how Plato presents the acquiring of knowledge is contained in the Ladder of Love. In Symposium (210a-211b), Plato's Socrates cites the priestess Diotima as defining a "lover" as someone who loves and love as a desire for something that one does not have. According to this ladder model of love, a lover progresses from rung to rung from the basest love to the pure form of love as follows:

 * 1) A beautiful body - The lover begins here at the most obvious form of love.
 * 2) All beautiful bodies - If the lover examines his love and does some investigating, he/she will find that the beauty contained in this beautiful body is not original, that it is shared by every beautiful body.
 * 3) Beautiful souls - After most likely attempting to have every beautiful body, the lover should realize that if a single love does not satisfy, there is no reason to think that many ones will satisfy. Thus, the "lover of every body" must, in the words of Plato, "bring his passion for the one into due proportion by deeming it of little or of no importance."  Instead, the passion is transferred to a more appropriate object: the soul.
 * 4) The beauty of laws and institutions - The next logical step is for the lover to love all beautiful souls and then to transfer that love to that which is responsible for their existence: a moderate, harmonious and just social order.
 * 5) The beauty of knowledge - Once proceeding down this path, the lover will naturally long for that which produces and makes intelligible good social institutions: knowledge.
 * 6) Beauty itself - This is the Form of Beauty. It is not a particular thing that is beautiful, but is instead the essence of beauty.  Plato describes this level of love as a "wondrous vision," an "everlasting loveliness which neither comes nor ages, which neither flowers nor fades."  It is eternal and isn't "anything that is of the flesh" nor "words" nor "knowledge" but consists "of itself and by itself in an eternal oneness, while every lovely thing partakes of it."

Knowledge concerning other things is similarly gained by progressing from a base reality (or shadow) of the thing sought (red, tall, thin, keen, etc.) to the eventual form of the thing sought, or the thing sought itself. Such steps follow the same pattern as Plato's metaphor of the sun, his allegory of the cave and his divided line; progress brings one closer and closer to reality as each step explains the relative reality of the past.

title: Platonic epistemology