the-french-artist/wikipedia_20220301.simple_sentence_embeddings huggingface dataset:
S/2004 S 4 
 It was seen while J. N. Spitale was trying to confirm the orbit of another object,  that was seen 5 hours earlier just on the farther edge of the F ring.
S/2004 S 4 
 Notably, an imaging sequence covering an entire orbital period at 4 km resolution taken on 15 November, 2004 failed to find the object.
S/2004 S 4 
 An interpretation where S3 and S4 are or were a single object on a F-ring crossing orbit is also possible.
S/2004 S 4 
 Such an object might also be orbiting at a bit different inclination to the F ring, thereby not actually passing through the ring material even though it was being seen both radially inward and outward of it.
S/2004 S 6 
 It was first seen by scientists in pictures taken by the Cassini-Huygens probe on October 28, 2004, and announced on 8 November that year.
S/2004 S 6 
 It appears to be the best tracked object in this area with at least five possible sightings in the period till late 2005.
S/2004 S 6 
 In comparison, two objects in the F ring's area ( and ) that were first seen months earlier have not been found again with any confidence.
S/2004 S 6 
 Nevertheless, it continues to be unclear whether there is a solid core to  or whether it is just a dust clump that will disappear in years or months.
S/2004 S 6 
 Notably, an imaging sequence covering an entire orbital period at 4 km resolution taken on 15 November, 2004 (soon after 's discovery) failed to find the object, while it has been seen again later.
S/2004 S 6 
 The lighting conditions in 's part of the orbit were different during these two sightings, however, with the discovery being made when the area was strongly backlit by the sun.
S/2004 S 6 
 A suggested resolution of the absence in November is that 's visibility is primarily due to a diffuse cloud of fine dust that is much brighter in forward scattered light (the conditions of the discovery image), and that the solid core (if any) is small.
S/2004 S 6 
 Careful calculations show that the object periodically plows through the ring material, coming within 1.5 km of the densest core e.g. on 9 April, 2005.
S/2004 S 6 
 It has been suggested that a spiral structure in the thinnest material around the F ring may have been a result of this.
Joel Hastings Metcalf 
 He served as a Unitarian minister in Burlington, Vermont and then later in Taunton, Massachusetts, Winchester, Massachusetts and Portland, Maine.
Joel Hastings Metcalf 
 He found or co-found many comets, such as 23P/Brorsen-Metcalf and 97P/Metcalf-Brewington; he also found many asteroids.
Gräfendorf 
 Gräfendorf is a community in Main-Spessart in the Regierungsbezirk of Lower Franconia (Unterfranken) in Bavaria, Germany and a member of the Verwaltungsgemeinschaft (Administrative Community) of Gemünden am Main.
Gräfendorf 
 The community has the following Gemarkungen (traditional rural cadastral areas) and Ortsteile: Gräfendorf, Michelau an der Saale, Schonderfeld, Weickersgrüben, Wolfsmünster.
Imaginary number 
 Imaginary numbers are numbers that are made from combining a real number with the imaginary unit, called i, where i is defined as .
Imaginary number 
 They are defined separately from the negative real numbers in that they are a square root of a negative real number (instead of a positive real number).
Imaginary number 
 This is not possible with real numbers, as there is no real number that will multiply by itself to get a negative number (e.g.,  and ).
Imaginary number 
 One way of thinking about imaginary numbers is to say that they are to negative numbers what negative numbers are to positive numbers.
Imaginary number 
 Similarly, if we say "go east by -i mile", it means the same as if we had said "go south by 1 mile".
Imaginary number 
 If we say "go east by 1 + i miles" it means the same as if we had said "go east by one mile and north by one mile".
Imaginary number 
 Multiplying two imaginary numbers is a lot like multiplying a positive number with a negative number.
Imaginary number 
 If we say "go east by 2 × -3 miles", it means "rotate all of the way around (so that you are now facing west) and go 2×3 = 6 miles".
Imaginary number 
 If we say go "east by 2×3i miles", it means the same as if we had said "rotate until you are facing north, and then go 2×3 = 6 miles"
Imaginary number 
 Subtractions such as 5 - 9 used to be impossible until negative numbers were invented, just as taking the square root of a negative number used to be impossible until imaginary numbers were invented.
Imaginary number 
 This is why mathematicians invented the imaginary number, i, and said that it is the main square root of −1.
Imaginary number 
 The square root of −1 is not a real number, so this definition creates a new type of number, just like fractions create numbers like 2/3 that are not counting numbers like 4 or 10, and negative numbers create numbers that are less than 0.
Imaginary number 
 Sometimes, mathematicians seem rather comfortable using a number that is so unusual, but the name imaginary should not fool you because i is as valid a number as 3 or 145,379.
Imaginary number 
 electrical engineers need i to understand how an electric circuit will work when they are designing it (electrical engineers use j instead of i to avoid confusion with the symbol for the current).
Imaginary number 
 certain branches of physics such as quantum physics and high energy physics use i as often as they use any other regular number.
Eric Maskin 
 He is the Albert O. Hirschman Professor of Social Science at the Institute for Advanced Study, and a visiting Professor at Princeton University.
Eric Maskin 
 Maskin was born in New York City, New York on December 12, 1950, to a non-religious Jewish family, and grew up in Alpine, New Jersey.
Eric Maskin 
 He graduated from Tenafly High School in Tenafly, New Jersey in 1968, and then studied at Harvard University where he received his A.B. and Ph.D. After he got his Ph.D., Maskin went to the University of Cambridge in 1976 where he was a research fellow at Cambridge College.
Eric Maskin 
 He taught at Massachusetts Institute of Technology from 1977-1984 and from 1985-2000 at Harvard, where he was the Louis Berkman Professor of Economics.
Eric Maskin 
 He has studied a wide range of subjects in economic theory, such as game theory, the economics of incentives, and contract theory.
Eric Maskin 
 He is particularly well known for his work on mechanism design/implementation theory and dynamic games.
Eric Maskin 
 His current research projects include comparing different rules for elections, the causes of inequality and studying coalition formation.
Eric Maskin 
 He is a Fellow of the American Academy of Arts and Sciences, Econometric Society, and the European Economic Association, and a Corresponding Fellow of the British Academy.
Eric Maskin 
 Software, semiconductor, and computer industries have made many inventions in the past when patent laws have been weak, he argued. "
Roger Myerson 
 Roger Bruce Myerson (born 29 March 1951) is an American economist and co-winner, with Leonid Hurwicz and Eric Maskin, of the 2007 Nobel Prize in Economics "for having laid the foundations of mechanism design theory."
Roger Myerson 
 He has made contributions as an economist, as an applied mathematician, and as a political scientist.
Roger Myerson 
 He attended Harvard University, where he received his A.B., S.M. (1973), and Ph.D. (1976), all in applied mathematics.
Roger Myerson 
 From 1976 to 2001, he was a professor of economics at Northwestern University's Kellogg School of Management.
Roger Myerson 
 Currently, he is the Glen A. Lloyd Distinguished Service Professor of Economics at the University of Chicago.
Roger Myerson 
 Among his scientific contributions to game theory and mechanism design, the following are noteworthy:
Roger Myerson 
 "Refinements of the Nash Equilibrium Concept," International Journal of Game Theory 7 (1978), 73-80.
Roger Myerson 
 "Bayesian Equilibrium and Incentive Compatibility," in Social Goals and Social Organization, edited by L. Hurwicz, D. Schmeidler, and Hugo Sonnenschein, Cambridge University Press (1985), 229-259.
Roger Myerson 
 He wrote a general textbook on game theory in 1991, and has also written on the history of game theory, including his review of the origins and significance of noncooperative game theory.
Roger Myerson 
 Myerson has worked on economic analysis of political institutions and written several major survey papers:
Roger Myerson 
 "Analysis of Democratic Institutions: Structure, Conduct, and Performance," Journal of Economic Perspectives 9:1 (1995), 77-89.
Roger Myerson 
 "Economic Analysis of Political Institutions: An Introduction,"  Advances in Economic Theory and Econometrics: Theory and Applications, volume 1, edited by D. Kreps and K. Wallis (Cambridge University Press, 1997), pages 46–65.
Roger Myerson 
 His recent work on democratization has raised critical questions about American policy in occupied Iraq.
Mario Capecchi 
 Capecchi is  Distinguished Professor of Human Genetics and Biology at the University of Utah School of Medicine, which he joined in 1973.
Mario Capecchi 
 His father, Luciano Capecchi, was an Italian airman who was reported as missing in action in the Western Desert Campaign.
Mario Capecchi 
 His mother, Lucy Ramberg, was the American-born daughter of Impressionist painter Lucy Dodd Ramberg and German  archaeologist Walter Ramberg.
Mario Capecchi 
 During World War II, his mother was sent to the Dachau concentration camp, as punishment for handing out pamphlets and belonging to an anti-Fascist group.
Mario Capecchi 
 Before her arrest she had sold her belongings and gave the money to a poor family near Bolzano, to give her son a place to live.
Mario Capecchi 
 At four-and-a-half years old he was left to live on the streets of northern Italy for the next four years, living in various orphanages and roving through towns with groups of other homeless children.
Mario Capecchi 
 She finally found him in a hospital bed in Reggio Emilia, ill with a fever and living one bowl of chicory coffee and bread crust each day.
Mario Capecchi 
 In 1946 his uncle, Edward Ramberg, an American physicist at RCA, sent his mother money to return to the United States.
Mario Capecchi 
 Mario and his mother moved to Pennsylvania to live at a cooperative community which had been started by his uncle.
Mario Capecchi 
 In 1960 Capecchi came to MIT as a graduate student to study physics and mathematics, but he soon became interested in molecular biology.
Mario Capecchi 
 After the Nobel committee announced that Capecchi had won the Nobel prize, an Austrian woman named Marlene Bonelli claimed that Capecchi was her long-lost half-brother, which he acknowledged was true.
Mario Capecchi 
 The work on gene targeting and knockout mice won the 2007 Nobel Prize in Physiology or Medicine, jointly with Martin Evans and Oliver Smithies.
Mario Capecchi 
 2001 – Albert Lasker Award for Basic Medical Research, co-winner with Martin Evans and Oliver Smithies.
Wizard 
 Wizards are often depicted as having a special connection to supernatural beings, such as gods or fairies, or as such supernatural beings themselves.
Wizard 
 Dumbledore (from the Harry Potter series) and Gandalf (from Tolkien's Middle Earth) are fictional examples of "good" wizards.
Wizard 
 Wizards are often depicted as old men with long, flowing beards, and wearing a large-brimmed hat, a thick cloak and holding a staff.
Wizard 
 This may be due to descriptions of Odin the Wanderer, a god from Norse mythology who often disguised himself thus, in order to pass through the lands of men unnoticed.
Wizard 
 Wizards, when they are named thus, are almost always portrayed as male, but some fictional or mythical female characters seem to play the same role, sometimes as a foil character to a male wizard or other character.
Wizard 
 Nowadays, the term "wizard" is also used for someone whose accomplishments are due to unusual skill or creativity.
Kaunas 
 Kaunas, also known by several other names, is the second biggest city in Lithuania and used to be a temporary capital.
Kaunas 
 Kaunas is found at the point where the two biggest Lithuanian rivers, the Nemunas and the Neris, meet.
Warp drive 
 A well-known one is found in the Star Trek universe, where faster-than-light travel is needed to tell the story.
Warp drive 
 However, warp technology as a fictional idea has been an interesting way of shaping the story line to let spaceships move at speeds greater than 186,000 miles per second (speed of light through a vacuum - the known limit of speed in the universe).
Warp drive 
 Warp technology, as the name implies, 'warps space' in effect bringing a destination closer by bending space rather than the traditional 'thruster' means of propelling a spacecraft at high speeds.
Warp drive 
 In the Star Trek universe, for example, the measurement of the speed that the spaceship is moving is called the warp factor.
Warp drive 
 Most of that is pure science fiction, and no solid evidence has been produced of a true "warp drive" on a large scale.
Warp drive 
 In the field of Quantum Mechanics physicists have produced tiny wormholes, but they don't warp space time in the same way the "warp drive" concept does, rather they connect two separate points of spacetime through quantum entanglement.
Warp drive 
 Also, there seems to be a lack of clarity as to what a warp drive is because some argue with a warp drive we would travel at incredible speeds, however if the concept is to warp gravity and "fold" it in on itself then it's not speed that's traveled but rather distance that was removed.
Christian Heinrich Friedrich Peters 
 Christian Heinrich Friedrich Peters (September 19, 1813–July 18, 1890) was a German-American astronomer, and one of the first to find asteroids.
Christian Heinrich Friedrich Peters 
 He was born in Schleswig-Holstein, then part of Denmark but later part of Germany, and later studied under Carl Friedrich Gauss.
Christian Heinrich Friedrich Peters 
 He spoke many languages and spent time in Italy and Ottoman Turkey before going to the United States in 1854.
Christian Heinrich Friedrich Peters 
 Working at Hamilton College in Clinton, New York (near Utica), he was a good finder of asteroids, finding 48 of them, beginning with 72 Feronia in 1861 and ending with 287 Nephthys in 1889.
Christian Heinrich Friedrich Peters 
 He was involved in litigation in 1889 with his old assistant Charles A. Borst, and the "Great Star-Catalog Case" Peters v. Borst went before the Supreme Court of New York.
Christian Heinrich Friedrich Peters 
 After his death, the judgement was ultimately reversed on appeal and a new trial was ordered, but it never took place.
Christian Heinrich Friedrich Peters 
 Besides asteroids, he co-found the Periodic comet 80P/Peters-Hartley, and also found different nebulae and galaxies.
Soest, Germany 
 Soest is along the Hellweg road, about 50 kilometres east of Dortmund and about 50 kilometres west of Paderborn.
Soest, Germany 
 Due to the fertile soil the area around Soest was used long before 836 when the village is first mentioned in the Dagobertsche Schenkung, although the origin of this document is historically unknown.
Soest, Germany 
 But there is no doubt that Soest has been lived in for a long time; excavations in the last two decades have uncovered signs of people living in Soest more than 4000 years ago.
Soest, Germany 
 In the 11th and 12th century Soest grew a lot, making it one of the biggest cities in Westphalia with some 10,000 citizens.
Soest, Germany 
 A self-confident Soest from 1444 to 1449 freed itself from the Bishop of Cologne, who controlled Westphalia (the so-called Soester Fehde).
Soest, Germany 
 This was a Pyrrhic victory, however; the city had shown itself strong enough to defy the powerful Archbishop of Cologne, but lost much of its trade: the "freed" town was two-thirds surrounded by territories with other rulers.
Soest, Germany 
 When the last Duke of Cleves died in 1609 that dukedom was taken by Brandenburg and after a short siege Soest was added into it.
Soest, Germany 
 During and after the Thirty Years' War, Soest lossed a lot of people and influence; at the lowest point in 1756 it had only 3,600 citizens.
Soest, Germany 
 However, the industrialization of the Ruhr area did not reach Soest, which continued to be a small city.
Soest, Germany 
 From about 1953 to 1971 there was a big garrison of Canadian soldiers and their families stationed at Soest (with the Canadian camps just east of the city in Bad Sassendorf) as well as Werl and Hemer-Iserlohn and Deilinghofen to the south west.
Soest, Germany 
 From 1971-1993 the old Canadian properties, such as the Married Quarters along Hiddingser Weg, south of the B-1, were used by British military and families.
Soest, Germany 
 Upon the closing out of Belgian and British army facilities many of these military facilities either became used for civilian purposes or were not used again/destroyed.
Soest, Germany 
 The old CANEX (formerly MLS) (the Canadian Army's food and clothing store for dependent families) was changed to a NAAFI under the British and was finally demolished in 2006.
Soest, Germany 
 In 960, Bruno I, Archbishop of Cologne moved St Patroclus's relics from Troyes and buried them in 964 at St Patroclus's Cathedral in Soest, where he is still today honoured.
Soest, Germany 
 The Cathedral is a beautiful example of early medieval "Romanesque" architecture fashioned from the local greenish sandstone.
Soest, Germany 
 Its big squared bell tower or steeple can be seen for many kilometers, rising up out of the city centre of the old city and a landmark of the Soester Boerde.
Soest, Germany 
 Articles about "Aldegrever and the Protestant Reformation in Soest" / virtual exhibition "Iconoclastic Controversy and sensual pleasure - Heinrich Aldegrever"  with introductory texts and about 170 commented copperplate engravings
History of Europe 
 The history of Europe means all the time since the beginning of written records in the European continent up to the present day.
History of Europe 
 It is traditionally divided into ancient (before the fall of the Western Roman Empire) medieval, and modern (after the fall of Constantinople).
History of Europe 
 Europe's antiquity dates from the Minoan civilization, the Myceneans and later on Homer's Iliad in Ancient Greece of around 700 BC.
History of Europe 
 The Roman Republic was established in 509 BC, which was usurped by Octavian's new Roman Empire at its first century BC peak.
History of Europe 
 The Christian religion was adopted in the fourth century, and in the sixth was organized, within the Empire, by Emperor Justinian I (527–565) with five most important cities: Rome, Constantinople, Antioch, Jerusalem and Alexandria.
History of Europe 
 A new schism within the church's authority in 1054 was added to the earlier division that had persisted since 451.
History of Europe 
 The Fall of Constantinople in 1453 showed the military weakness of the Christians in Eastern Europe.
History of Europe 
 Europe awoke from the medieval period through rediscovery of classical learning, much of which had been kept alive in the Muslim world while the Western church had rejected much of it as paganry.
History of Europe 
 The Renaissance was followed by the Protestant Reformation, as priest Martin Luther attacked Papal authority.
History of Europe 
 The Thirty Years War, the Treaty of Westphalia and the Glorious Revolution prepared for expansion and enlightenment.
History of Europe 
 The Industrial Revolution, beginning in Great Britain, allowed masses of people, not just the rich, to escape for the first time from lives of being always poor and barely able to afford either food or shelter.
History of Europe 
 The early British Empire split as its colonies in America revolted to establish their own representative government.
History of Europe 
 Political change in continental Europe was spurred by the French Revolution, as people cried out for liberté, egalité, fraternité (liberty, equality, brotherhood).
History of Europe 
 The French leader, Napoleon Bonaparte, conquered and reformed the social structure of the continent through war up to 1815, when he met his final defeat at the Battle of Waterloo and was sent away into exile.
History of Europe 
 As more and more small property holders were granted the vote, especially in France and the UK, socialist and trade union activity developed and revolution gripped Europe in 1848.
History of Europe 
 After the Franco-Prussian War, Italy and Germany were formed, each from groups of smaller countries which spoke the same languages, in 1870 and 1871.
History of Europe 
 Conflict intensified across the globe, in a chase for empires, where powerful countries turned less powerful ones into colonies, until the outbreak, in 1914, of the biggest war that had ever been fought up to that point in time.
History of Europe 
 In the desperation of war, the Russian Revolution promised the people "peace, bread and land" and led to the end of the Russian Empire and its replacement by the formation of the Soviet Union.
History of Europe 
 The defeat of Germany came at the price of economic destruction, which was formally written into the Treaty of Versailles in 1919 where it was stated that the First World War had been entirely the fault of Germany and its allies and demanded that they pay back the entire amount the war had cost.
History of Europe 
 The Great Depression began in 1929, brought about in part by the economic problems caused by the attempt to force Germany to pay for the war and in part by trade restrictions.
History of Europe 
 The governments soon fell into two main groups, those who believed in freedom and human rights and those who followed fascism.
History of Europe 
 These two deeply different views led to a Second World War, which most people who write history feel began in Europe when Germany invaded Poland in 1939, but soon spread to most of the countries in the world.
History of Europe 
 It took in wars which were already happening in other places, most notably the war between Japan and China.
History of Europe 
 After this war Socialism spread to Central and Eastern Europe, including the relatively new Eastern European countries of Yugoslavia, Bulgaria, Romania, Albania, and in Asia North Vietnam and North Korea, and, slightly later, to Cuba in the Carribean Sea very near to North America.
History of Europe 
 The conflict between the advocates of a capitalist and a socialist economy and political system led to the Cold War, a forty-year argument between the United States and the Soviet Union, two of the countries which had worked together to win the Second World War and the two which had come out of it with the most powerful military forces.
History of Europe 
 People across the world feared a nuclear war because of the tension, and Europe, divided by the Iron Curtain, was assumed to be a probable battleground.
History of Europe 
 Communism became less attractive when it became clear that it could promote economic growth less effectively than the capitalistic Western states and that it was not suited for a reform that allowed freedom of speech for everyone.
History of Europe 
 Therefore, the Soviet Union forced Hungary to give up its reform in 1956, it favoured the building of the Berlin Wall in 1961 and it stopped reform in Czechoslovakia in 1968.
History of Europe 
 When in 1988/89 the Soviet leader Gorbachev made clear that he would not force the countries of the East block to stick to Communism the Berlin Wall was torn down in 1989 and the Soviet Union collapsed (1991).
Peace of Westphalia 
 The Peace of Westphalia refers to the pair of peace treaties, the Treaty of Osnabrück and the Treaty of Münster, signed on May 15 and October 24 of 1648, which ended both the Thirty Years' War and the Eighty Years' War.
Peace of Westphalia 
 The treaties involved the Holy Roman Emperor, Ferdinand III Habsburg, the other German princes, Spain, France, Sweden and representatives of the Dutch Republic.
Peace of Westphalia 
 The Treaty of the Pyrenees, signed in 1659, ending the war between France and Spain, is also often considered part of the overall accord.