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User:Vuara/Who really invented the alphabet

Copyright © 2002 The International Herald Tribune | www.iht.com

So who really invented the alphabet? Stephanie Saldana The Daily Star March 18, 2002 Lebanese, Syrians and Egyptians all vie for a piece of ABC history Ask the folks in Byblos who invented the alphabet and chances are high that they’ll claim they did. Up and down the cobbled alleys of the souq, shop windows display tablets proclaiming the first alphabet as Phoenician, and locals insist that the earliest remnants of it were unearthed in ruins nearby.

“Of course it was invented here,” said souvenir shop owner Tony Karam from behind the counter of his shop downtown.

If the Phoenicians invented the alphabet in Byblos, apparently no one ever told that to the Syrians hanging out near their port city of Lattakia. Here, outside of the archaeological site of Ras Shamra, locals peddle postcards headlined Earliest Alphabet in the World, but display a picture of a different alphabet altogether: the Ugaritic.

Local guide Saji Qorqmaz, who leads tours through the crumbling Royal Palace where that alphabet was discovered, holds fast to his own explanations of alphabetic origins. “The idea for the alphabet was created in Egypt, the invention was in Ugarit, and the distribution was in Byblos,” he said. Byblos? Ugarit? Egypt? If the alphabet is really as easy as ABC, how did so many people become confused about its origins? According to Jo Ann Hackett, professor of Near Eastern languages at Harvard University and an expert on the alphabet, Syria and Lebanon might both have claims to developing “an alphabet,” but today scholars are looking toward Egypt for true alphabetic origins.

“The Ugaritic alphabet and the Phoenician, or linear alphabet, were separate inventions, so they can’t really be compared as if they were on the same timeline,” she said in an interview via email. “Still, both the Syrians and perhaps the Lebanese can claim that their ancestors developed ‘an’ alphabet.”

Robert Fradkin, professor of Asian and East European languages at the University of Maryland, agrees. “Quite a controversy indeed, but I don’t think it’s worth arguing over who was first, as if ‘the alphabet’ was a conscious concrete goal like a race to land a man on the moon,” he said. “It was part of a large cultural trend.”

While tour guides might be anxious to build on earliest alphabet hype, scholars argue that the search for the origins of the alphabet involves far more than merely digging up and deciphering old inscriptions. The alphabet evolved over thousands of years, possibly in response to trade in the ancient Middle East. The fact that people, products and alphabets moved from place to place makes it nearly impossible for archaeologists to be certain if the alphabets they dig up originated where they found them, or were carried there from somewhere else.

“How did the alphabet develop? There is no final or conclusive evidence on the origin of the alphabet,” said Helen Sader, professor at the American University of Beirut and an expert on Semitic languages. “What is certain is that it did not develop overnight.”

Recently Yale Egyptologist John Darnell stumbled upon evidence that may shed light upon the alphabet debate. Surveying ancient travel routes in southern Egypt in 1993-94, he and his wife Deborah came upon strange graffiti marked into walls near Wadi al-Hol located across from the ancient city of Thebes.

In 1999, scholars determined that the graffiti was an alphabet that predates the Byblos Phoenician example by 800 years. Not yet deciphered, the Semitic script, written with Egyptian influences between 1900-1800 BC, seems to have been developed by Semitic people working in Egypt. Unable to read thousands of Egyptian pictographs, Semites may have developed their own crude alphabet for communication.

Yet like most things involving the alphabet, scholars disagree on origins.

“We don’t actually know where this alphabet was invented,” said Hackett of the finds. Bruce Tuckerman, who photographed the inscriptions, told The New York Times wryly: “This is fresh meat for the alphabet people.”

The Egyptian discovery may help scholars understand why Phoenicians in Byblos used the alphabet they did some 800 year later. Scholars believe that Darnell’s alphabet  based partially on sounds represented by Egyptian pictographs, may have traveled north over centuries toward Lebanon, changing and modernizing along the way.

Evidence of an alphabet dating from 1600 BC  200 years after the Wadi al-Hol alphabet  has been discovered by archaeologists in Semitic speaking territory in the Sinai peninsula and farther north in the Syria-Palestine region occupied by Canaanites. Not only do these alphabets bear similarities to those of Wadi al-Hol, but they also appear to be the ancestors of what would later become the Phoenician alphabet, the most famous inscription of which was found in Byblos on the tomb of Ahram dating from 1000 BC.

“The linear (Phoenician) alphabet seems to have been developed by Semites in Egypt and adapted by Canaanites,” said Sader, adding that evidence for this development was found mainly in Palestine in the 13th and 12th centuries BC. The Phoenicians adapted the script even further, laying the foundations for the Greek and Latin alphabets.

As to why so many Lebanese still believe that Phoenicians invented the alphabet, Sader blames the Greeks. “Today nobody believes that one man sat down and had the genius to invent the alphabet … Greek legend attributes the discovery of the alphabet to the Phoenicians, because they did not know of the development of their alphabet before then,” she said. “What the Phoenicians have done is … spread the alphabet through all of Europe.”

While this clears up the confusion between Lebanon, Palestine and Egypt, it still doesn’t explain how Syrians found their way into the alphabet soup. Strangely, the story of Syria’s claims to creating the alphabet involve not just another country, but different people and another alphabet altogether.

In the late 1940s, archaeologists excavating in the Royal Palace of Ras Shamra in coastal Syria uncovered something rather extraordinary  an entire library of ancient clay tablets, sacred and administrative documents impressed with unusual wedge shaped letters. Further investigation revealed that these shapes were in fact the components of what would later be known as the “Ugaritic” alphabet, a simplified system of 30 symbols, each symbol representing a different consonant sound of the local Ugaritic language. Developed between the 14th and 12th centuries BC, the Ugaritic alphabet was in use at virtually the same time as the predecessors of the Phoenician or “linear” alphabet. By the 14th century, communities in the Middle East were using different alphabets simultaneously.

Unlike the linear or “Phoenician” alphabet, which seems to have developed from Egypt, partially from pictographs, the Ugaritic is a cuneiform alphabet based on wedge shaped consonants, with origins that remain mysterious to this day. That means that while Syrians can’t claim to have the earliest alphabet in the world, they can at least claim the earliest known “cuneiform” alphabet.

Yet even this could change.

Scholars admit that, limited by archaeology, they may never understand the origins of the alphabet. And in the meantime, this won’t keep tour guides from claiming the alphabet as their own.

“Guides all want to be proud of their own place  in Syria you’ll hear Ugarit, in Lebanon you’ll hear Byblos, in Egypt you’ll hear I don’t know what,” admitted Waad Khalife, a Byblos tour guide.

“Colleagues and local civilians are not the most objective in their jobs.”


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Talk:Anna Chalon

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1977 Memphis State Tigers football team

The 1977 Memphis State Tigers football team represented Memphis State University (now known as the University of Memphis) as an independent during the 1977 NCAA Division I football season. In its third season under head coach Richard Williamson, the team compiled a 6–5 record and outscored opponents by a total of 228 to 194. The team played its home games at Liberty Bowl Memorial Stadium in Memphis, Tennessee.

The team's statistical leaders included Lloyd Patterson with 1,336 passing yards, James King with 626 rushing yards, Earnest Gray with 826 receiving yards, and Rusty Bennett with 60 points scored (21 extra points, 13 field goals).

title: 1977 Memphis State Tigers football team


text:
Atlas Shrugged/Synopsis/Chapters 6-10

=Atlas Shrugged, Part 1, Chapters 6-10=

Section 161: Part 1, Chapter 6, Section 1

 * Plot summary:
 * At the expense of postponing the myriad commercial tasks that must still be done, Hank Rearden reluctantly attends a party thrown by his wife on their wedding anniversary. Lillian Rearden has invited her circle of friends, which includes the "heart of the country's culture", the so-called intellectual elite whose opinions are shaping the times.  This is a bit of an insult, though, as the whole country is falling apart.  As these friends speak, we are introduced to the ideas that are causing the collapse of society:
 * Dr. Simon Pritchett, the nation's leading philosopher, declares that man is a miserable bit of protoplasm, there are no standards, reason is a superstition, the purpose of philosophy is to prove we can know nothing and that there is no meaning to be found in life, and that when people realize this they will be more "tractable."
 * Balph Eubank is the literary leader of the age (albeit, his books do not sell), declares that suffering is the essence of life, and that free will, achievement, and happiness are laughable concepts of old literature. Plot, he says, is a primitive vulgarity in literature. Moreover, life is about suffering and frustration, that the only thing to live for is brotherlove.  He later says, that the machine age has destroyed man's humanity, observing that Dagny Taggett runs a railroad rather than practicing the beautiful art of the handloom and bearing children.
 * Bertram Scudder, the editor, declares that property rights are a superstition. Moreover, even though he has written an editorial filled with groundless insults against Rearden, he is present at Rearden's party.
 * Claude Slagenhop, president of Friends of Global Progress, declares that need is the only consideration, that an empty belly is a fact, and that this consideration justifies anything, that ideas are just hot air - that right is whatever is good for society, and that the people have the right to seize what they need.
 * All of them are introduced in the context of their pro-Equalization of Opportunity Bill views.
 * Rearden is shocked by the arrival of Dagny Taggart. When they talk he is formal and distant, quite unlike the easy manner that characterized their business dealings.  Dagny is taken aback by his manner and is puzzled when he gives her the cold shoulder throughout the evening.
 * Rearden argues with Lillian after he discovers she has invited Bertram Scudder to the party. Scudder had trashed Rearden in an article.  He cannot understand why she would invite a man who is so hostile to him, and why Lillian seems to enjoy his anger.  He thinks there is some riddle to her character that he should try to understand, but he cannot accept the insanity that would make it possible for her to take pleasure in his fury.
 * Just then, Francisco d'Anconia enters, who will in due time provide Rearden with the answer to this riddle. A self-made man, Rearden despises Francisco as a worthless profligate who does not know how to deserve the great gift of inherited wealth.  He tells Lillian to "keep that man away from me."  But Francisco has come for the specific purpose of meeting Rearden, and it is only a matter of time until he corners him.
 * First, though, Francisco circulates, and as Lillian's friends spout out their inanities, he glibly refutes them. When James Taggart confronts him about the failure of the San Sebastian Mines, Francisco justifies his actions as being in accords with the "virtue" of the times.
 * Francisco tells a disbelieving and frustrated Taggart that the San Sebastian Mines is the "practical realization of the highest moral order." Frisco has taken no personal interest, is completely selfless in it; he has eliminated the useless presence of the exploiter-owner. He has hired based on need, rather than ability. Focusing on the livelihood on the employees, he has constructed a settlement for his employees regardless of the place's potential for copper. He has not profited, but has loss - as human beings should, according to the morality of the times, for privation and imperfection are man.
 * When Francisco does meet Rearden, their talk is prolific. Francisco asks why Rearden is willing to support those who are helpless, who never show their gratitude towards him, and who, in fact, openly denounce him as an evil exploiter.  He leaves this an open question.  Rearden at this point of the story is aware that there is something wrong with the world, but does not know what, while Francisco does know.  In this, their first meeting, Francisco tries to place in Rearden's mind the seeds of understanding.  The reader is in the same position as Rearden, and the scene is meant to do the same for the reader, preparing us for the explicit revelation of Galt's Speech.  Francisco leaves Rearden with two ambiguous facts:
 * They have a terrible weapon against Rearden, and the evidence for this is his unhappiness.
 * He warns Rearden about the sin of forgiveness. He also asserts that everything Rearden had said to him is true, except his belief that the commercial is evil. As Francisco leaves him, Rearden is filled with a feeling of wishing him to stay, for, unbeknownst to him, Francisco has given him the beginnings of a moral sanction.
 * Dagny approaches Rearden, attempting to make smalltalk with him by commenting on the debasing nature of his guests, casually stating her belief that celebration should only be done by those who mean it, implying that the drudgery of the milieu is due to their attempt to be more senseless and meaningless than usual. When Rearden denies that they're missing something, a frustrated and confused Dagny leaves, wandering into a group of "respectable women." She hears a fable of John Galt, as the millionaire who had found Atlantis and lost it all in the process. Francisco is nearby, and he asserts his belief of her story, although Dagny finds it another ludicrous myth.
 * As the scene reaches a climax, Halley's music, as remixed into cacaphony by an inept Mort Liddy, permeates the room. Dagny is leaving the party before she loses her composure. What she has slowly come to realize is that she came to the party hoping to make Rearden aware of her as a woman, not just a business partner.  She was distraught when Rearden responds to her with indifference, and upset when Francisco is the only one who sees her as an object of sexual desire--she is also angered that Francisco would call her appearance a waste, that the heroes would have to succumb to wasting their time in miasmaic milieus such as this party of aimless people.  She has also been pushed to the edge by the inane ramblings of Lillian's guests.  As she walks out, she is pushed over the edge when she hears Mort Liddy's bastardized treatment of her favorite song, Halley's Fourth Concerto.  At that moment, Dagny hears Lillian denigrating the bracelet of Rearden Metal that she has been wearing all night as a joke, carefully pronouncing its oddity in the midst of an extravagant display of excessive jewelry.  Lillian jokes that it is supposed to be priceless because it is the first thing ever made from Rearden Metal, but she would gladly exchange it for a common diamond bracelet any time.  In an act of supreme audacity, Dagny removes her diamond bracelet and offers it in exchange, saying that if Lillian is not a coward she would take the offer.  Lillian is taken aback but accepts the trade, not realizing that this act would ultimately undermine her secret weapon against Rearden.  Hank Rearden is furious at Dagny's gall, for the trade symbolizes Lillian's passing her status of "wife" to Dagny.  Rearden's guilt manifests in his acting like the ideal husband throughout the rest of the evening.  (This scene symbolizes Rand's theory of sex that will be elucidated in the next section.)

 * The following Places in Atlas Shrugged are used as settings in this section:
 * Rearden's home in Philadelphia.

 * The following Characters in Atlas Shrugged appear in this section:
 * Balph Eubank
 * Bertram Scudder
 * Betty Pope
 * Businessman 1
 * Young Woman who blushes when she admits she cannot understand how life is to be lived with nothing but frustraction and suffering
 * Claude Slagenhop
 * Dagny Taggart
 * Gwen Ives
 * Hank Rearden
 * Hugh Akston
 * James Taggart
 * John Galt - legend mentioned
 * Lillian Rearden
 * Mort Liddy
 * Mrs. Whitcomb
 * Newspaperman 1
 * Philip Rearden
 * Ragnar Danneskjold
 * Simon Pritchett
 * Spinster
 * Wesley Mouch - mentioned
 * Francisco d'Anconia
 * Richard Halley - mentioned

 * The following bills appear in this section
 * Equalization of Opportunity Bill - first mentioned

 * The following groups appear in this section
 * Friends of Global Progress

 * Quotations:
 * "I am in favor of a free economy. A free economy cannot exist without competition. Therefore, men must be forced to compete. Therefore, we must control men in order to force them to be free." - Dr. Pritchett (127)
 * "Plot is a primitive vulgarity in literature" - Balph Eubank
 * "Quite so. Just as logic is a primitive vulgarity in philosophy." - Dr. Pritchett
 * "Just as melody is a primitive vulgarity in music." - Mort Liddy (129)
 * "Need is the only consideration. If people are in need, we've got to seize things first and talk about it afterwards." - Claude Slagenhop (130)
 * "But surely you wouldn't want me to do anything about it. My mines and your railroad were seized by the will of the people. You wouldn't want me to oppose the will of the people, would you?" - Francisco d'Anconia to James Taggart (137)
 * "Isn't it generally conceded that when you hire a man for a job, it is his need that counts, not his ability? Doesn't everyone believe that in order to get the goods, all you have to do is need them? I have carried out every moral precept of our age, I expected gratitude and a citation of honor. I do not understand why I am being damned." - Francisco d'Anconia (138)
 * "To me, there's only one form of human depravity - the man without a purpose." - Hank Rearden (142)
 * "If one's actions are honest, one does not need the predated confidence of others, only their rational perception. The person who craves a moral blank check of that [the confidence] kind has dishonest intentions."

Section 162: Part 1, Chapter 6, Section 2

 * Plot summary
 * After the anniversary party, late in the evening, Hank Rearden enters his wife's bedroom with the pretext of having sex with her. Yet, he is disgusted by Lillian, not caring to admit his defeat by leaving.  Lillian accedes perfunctorily, and starts talking about the party, because talking is what people are supposed to do before making love.  As she jabbers, Rearden wonders why she married him, and recalls the details of their courtship and early marriage.  He thinks about what a torture it has become, pretending that he and Lillian still find their marriage and their sex life rewarding.  By the time she is done talking, Rearden has lost his desire and returns to his own room.  It is his first glimpse of the premise, from Rand's sexual theory, that one's sexual desires are an expression of one's values.

 * The following Places in Atlas Shrugged are used as settings in this section:
 * Lillian Rearden's bedroom.

 * The following Characters in Atlas Shrugged appear in this section:
 * Hank Rearden
 * Lillian Rearden
 * Balph Eubank - mentioned
 * Bertram Scudder - mentioned
 * Dagny Taggart - mentioned
 * Francisco d'Anconia - mentioned
 * Mrs. Weston - mentioned
 * Simon Pritchett - mentioned
 * Simons - mentioned

Section 171: Part 1, Chapter 7, Section 1

 * Plot summary:
 * Dagny Taggart visits the construction site of the Rio Norte Line near the Wyatt oil fields. Construction is being supervised by Ben Nealy, who is incompetent but the best contractor Dagny could find.  She meets Ellis Wyatt who indicates he now knows what she is, and that he respects her.  Hank Rearden is also on hand, designing a Rearden Metal bridge to show off his new metal.  The two get along as they always had, as if the party had never happened.
 * Rearden mentions he is flying back east, and Dagny asks if she can go back with him. He tells her no, because he is flying to Minnesota before heading to New York.  Later at the airfield, Dagny discovers Rearden was lying -- that he did fly straight to New York.  Dagny has no clue why Rearden would flat out lie to her.
 * The following Places in Atlas Shrugged are used as settings in this section:
 * Laying of the new Rio Norte Line track near the Wyatt oil fields in Colorado.
 * The following Characters in Atlas Shrugged appear in this section:
 * Airport attendant 1
 * Ben Nealy
 * Chief Engineer 2
 * Dagny Taggart
 * Ellis Wyatt
 * Hank Rearden
 * Francisco d'Anconia - mentioned
 * Dick McNamara - mentioned.
 * Mr. Coleman - mentioned.
 * Mr. Mowen
 * Nat Taggart's son - mentioned.
 * Orren Boyle - mentioned
 * Mysteries
 * Why Rearden lies to Dagny about his flying directly to New York.

 * Quotations:
 * "muscles - that's all it takes to build anything in the world" - Ben Nealy (154)
 * "I never believed that story. I thought by the time the sun was exhausted, men would find a substitute" - Hank Rearden (162)

Section 172: Part 1, Chapter 7, Section 2
"Judgement to determine right and wrong, vision to see the truth, courage to act upon it, dedication to that which is good, integrity to stand by the good at any price."
 * Plot summary:
 * Jim tries to trap Dagny into appearing on a radio program to debate Bertram Scudder by promising she'd be there. When she discovers that the topic is 'Is Rearden Metal a lethal product of greed?' she bails out of the car, considering such a ridiculous question to be non-debatable.
 * She visits a diner in a slum area and hears more myths about John Galt, including one that he found the Fountain of Youth, but never came back because he couldn't bring it back.
 * The following Places in Atlas Shrugged are used as settings in this section:
 * New York City streets
 * A Diner in a run-down section of New York City.
 * The following Characters in Atlas Shrugged appear in this section:
 * Bertram Scudder - mentioned
 * Dagny Taggart
 * Jim Taggart
 * Various people in the diner
 * John Galt - legend mentioned
 * Quotations:
 * "You go through life looking for beauty, for greatness, for some sublime achievement, and what do you find? A lof of trick machinery for making upholstered cars - or inner-spring mattresses" - Bum in diner (168)
 * "What is morality?" she asked.

Section 173: Part 1, Chapter 7, Section 3

 * Plot summary:
 * Dr. Potter tries to convince Rearden to take his metal off the market, because it will make the State Science Institute, a government research facility, look bad for its failure to produce any serious new developments in metallurgy over the past few years. Rearden refuses, even after Dr. Potter tries to bribe him into selling all rights to the metal to the government.
 * The following Places in Atlas Shrugged are used as settings in this section:
 * Rearden's Office at Rearden Steel in Pennsylvania.
 * The following Characters in Atlas Shrugged appear in this section:
 * Dr. Potter
 * Hank Rearden

Section 174: Part 1, Chapter 7, Section 4

 * Plot summary:
 * Eddie Willers informs Dagny that the State Science Institute has released a sham condemnation of Rearden Metal that has no actual facts as to any problems with the metal, but essentially an innuendo of doubt as to whether it is safe or not.
 * Dagny visits the Institute to try to find out why the statement was made. The Director of the Institute, Dr. Robert Stadler, refuses to denounce the statement, which was made without his knowledge or consent, even though he knows it to be untrue, because to denounce the statement would destroy the institute, which is all he cares about.
 * Dr. Stadler doesn't really have any concern as to how people are going to think about the false statement his institute has made, because he has essentially lost faith in humanity. He notes when he was at the Patrick Henry University he had three star pupils: Francisco d'Anconia who become a worthless playboy; Ragnar Danneskjöld who become a pirate; and a third very promising student who went nowhere.
 * The following Places in Atlas Shrugged are used as settings in this section:
 * Dagny's Office at Taggart Transcontinental in New York City
 * Dr. Stadler's Office at the State Science Institute in New Hampshire.
 * The following Characters in Atlas Shrugged appear in this section:
 * Dagny Taggart
 * Eddie Willers
 * Dr. Robert Stadler
 * Francisco d'Anconia - mentioned
 * Ragnar Danneskjöld - mentioned
 * Quotations:
 * "What is happening to people? ...how could they accept it? Didn't they read it? Didn't they see? Don't they think?" - Eddie Willers (175)
 * "Men are not open to truth or reason. They cannot be reached by a rational argument. The mind is powerless against them. Yet we have to deal with them. If we want to accomplish anything, we have to deceive them into letting us accomplish it. Or force them. They understand nothing else." - Dr. Stadler (180)

Section 175: Part 1, Chapter 7, Section 5

 * Plot summary:
 * When Conway refuses to sell to Taggart Transcontinental the rails of his Phoenix-Durango Line and Taggart Transcontinental becomes unable to finish the construction of the Rio Norte line, but is also in the precarious position if they don't finish it the railroad will collapse, Jim Taggart develops a strange case of flu and runs off to the mansion on the old Taggart Estate. Dagny delivers an ultimatum: she will finish the Rio Norte Line herself, on her own terms, disassociating herself and the publically notorious project from Taggart Transcontinental.  She also demands Eddie Willers be appointed Vice President of Operations in her absence (but it will actually still be her running the company, just nobody will admit it.)  In deciding what to call the new railroad she will operate, when suggesting her own name, Jim feels that her using her own name will suggest there is a connection between the two companies (which everyone will know but nobody will admit).  Flippantly, she suggests calling the line The John Galt line, and decides to use that name.
 * The following Places in Atlas Shrugged are used as settings in this section:
 * The Taggart Estate on the Hudson River.
 * The following Characters in Atlas Shrugged appear in this section:
 * Dagny Taggart
 * Jim Taggart
 * Eddie Willers - mentioned

Section 176: Part 1, Chapter 7, Section 6

 * Plot summary:
 * Dagny spends time selling bonds to finance the construction of the John Galt Line. Through a desperate display of emotional turmoil, Francisco d'Anconia struggles in his refusal to purchase the bonds for reasons he cannot say.  Dagny reduces herself to begging, hoping that Francisco will have pity for her cause -- he has already thrown away many more millions of dollars in his depraved endeavors.  Tortured that he cannot tell Dagny the full truth behind his refusal, he gives her one crucial hint -- "that contradictions do not exist, whenever you believe you've found one, check your premises."   He is shocked when he finds out the name of the railroad, because she did it for the effect, that it represents "the hopeless" and suggests that if it is that way, let John Galt come and claim his line.  Francisco's response is, "He will."
 * Dagny visits Rearden to place the "first official order" for Rearden Metal rails for the John Galt Line. Dagny shows Rearden a list of the Line's bondholders upon request.  The bondholders are the remaining great businesses from Colorado and other places have put up their own money to have the line built. In contrast to Francisco's tortured refusal to Dagny's begging, Hank Rearden makes an unsolicited offer to buy the largest block of bonds, not because he's offering her charity, but because he knows he will make a big profit off her work. (In their conversation, it is revealed that the bonds are convertible and high-yield.)
 * The following Places in Atlas Shrugged are used as settings in this section:
 * The John Galt Line office in New York City.
 * Rearden's Office at Rearden Steel in Pennsylvania.
 * The following Characters in Atlas Shrugged appear in this section:
 * Dagny Taggart
 * Francisco d'Anconia
 * Hank Rearden
 * Quotations:
 * "Contradictions do not exist. Whenever you think that you are facing a contradiction, check your premises. You will find that one of them is wrong." - Francisco d'Anconia (188)

Section 177: Part 1, Chapter 7, Section 7

 * Plot summary:
 * Rearden's mother - against Rearden's wishes that his family does not visit the mills without asking him first - comes to see him. She wants Rearden to give his skillless brother Philip a job in the steel mill. Rearden refuses because Philip can't do the work.  His mother tries to manipulate Rearden by saying he only thinks of justice and has no love.  To the astonishment of is mother, Rearden responds saying, "Mother, I'm running a steel plant--not a whorehouse." His mother retaliates by saying, "What are... your mills--a holy temple of some kind?" Despite her tone, Rearden finds himself agreeing in the sacredness of his mills. His mother attempts to broach up morality, "Don't you ever think of people and of your moral duties?" Rearden says that if he ever gives a job to Philip, he wouldn't be able to face any competent man who needs work and deserves it. His mother then attempts to warp morality with the statement that, "Virtue is the giving of the undeserved." Rearden ends the meeting with finality, "You don't know what you're saying. I'm not able ever to despise you enough to believe that you mean it."
 * Rearden next has a meeting with Mr. Ward, the honest owner of a family-owned plant that makes harvest equipment. Ward has spent months trying to get a meeting with Rearden -- his goal being to explain the full truth of his situation, that just a little bit of Rearden steel would keep his company running, and he would be ever so grateful. Although his plant is already running at maximum, Rearden agrees to help. Ward's appearance and manner of speech is a stark contrast to Rearden's mother; Ward is fully conscious of his position, that though he owns a successful plant, he is in a position of a beggar, while Rearden's mother, who is the real beggar, acts as if Rearden owes her his success.
 * The following Places in Atlas Shrugged are used as settings in this section:
 * The mill floor at Rearden Steel in Pennsylvania.
 * The following Characters in Atlas Shrugged appear in this section:
 * Phillip Rearden - Mentioned
 * Rearden's Mother
 * Hank Rearden
 * Quotations:
 * "That's why I can't talk to you - because you're not human. You have no pity, no feeling for your brother, no compassion for his feelings" - Rearden's Mother (196)
 * "If you loved your brother, you'd give him a job he didn't deserve, precisely because he didn't deserve it - that would be true love and kindness and brotherhood. Else what's love for? If a man deserves a job, there's no virtue in giving it to him. Virtue is the giving of the undeserved." - Rearden's Mother (197)

Section 178: Part 1, Chapter 7, Section 8

 * Plot summary:
 * The Legislature passes the Equalization of Opportunity bill, which will make Rearden unable to operate the other businesses he has as part of his operation. Privately, he feels as if a part of his body has been cut out from under him. In thinking about this he realizes a revelation about a new type of bridge development; he calls Dagny to tell her about it.
 * The following Places in Atlas Shrugged are used as settings in this section:
 * Rearden's Office at the steel mill in Pennsylvania.
 * The following Characters in Atlas Shrugged appear in this section:
 * Dagny Taggart
 * Hank Rearden
 * Mr. Ward
 * Rearden's Secretary Gwen
 * Wesley Mouch - Mentioned
 * Quotations:
 * "I don't like people who talk too much about how everything they do is just for the sake of others. It's not true, and I don't think it would be right if it were true." - Mr. Ward (199)

Section 181: Part 1, Chapter 8, Section 1

 * Plot summary:
 * Eddie is ashamed to see The Worker whom he's known for years, because for the moment, Eddie is Vice President of Operations of Taggart Transcontinental while Dagny has been disentitled of her position, and while it would be an honor for him to be a stooge for her, in some undefined way he feels he is a (greasy) stooge for Jim Taggart.
 * Eddie tells The Worker how Dwight Sanders has taken over the bankrupt United Locomotive Works so they should soon be receiving new Diesel locomotives. He also mentions that Sanders is now crucially important to Taggart Transcontinental -- the new line will need diesels from him.
 * While updating The Worker on the strategic needs of the company, Eddie broaches up the truth of the matter: that, all around, the great men are forced to relinquish their status, while lesser men become their stooges.
 * Eddie ends the conversation with the naming of the line -- the John Galt Line. Eddie doesn't like the name, but The Worker does.
 * The following Places in Atlas Shrugged are used as settings in this section:
 * Employee Cafeteria of Taggart Transcontinental in New York City
 * The following Characters in Atlas Shrugged appear in this section:
 * Eddie Willers
 * The Worker
 * Dwight Sanders - mentioned

Section 182: Part 1, Chapter 8, Section 2

 * Plot summary:
 * Dagny, dead tired after an endless workday at John Galt, Inc., slumps her head down in need of a hero's viaticum: someone she could love, a strong man who would bring out the best in her. As she raises her head, she sees a shadow indicating some person is thinking of walking into her office. The man who is about to enter the office stops at the door, then changes his mind and walks away. Instead of feeling the fear of a potential intruder, Dagny runs out but finds no one out there; all she can see is the empty street and the entrance to the Taggart Transcontinental Building's train tunnels.
 * The following Places in Atlas Shrugged are used as settings in this section:
 * Offices of The John Galt Line in New York City.
 * The following Characters in Atlas Shrugged appear in this section:
 * Dagny Taggart
 * Shadow Man

Section 183: Part 1, Chapter 8, Section 3

 * Plot summary:
 * Rearden, required to do so because of the Equalization of Opportunity Law, sells his iron ore mines to a friend of his family, Paul Larkin, and hates having to do so because he sees Larkin as unworthy. When Larkin says that he will always consider the mines to belong to Rearden, that this ownership business is a mere legal triviliaty, Rearden declares one of his foundational principles: "Either I own a property or I don't (208)." The truth of the matter is that, now that he has the official rights, Larkin can do whatever he wants against Rearden. Rearden does not want to be at anyone's mercy. Moreover, unlike Dagny, he will not allow anyone -- least of all Larkin -- to be his stooge.
 * When Rearden sells his coal mines to Ken Dannager, it's almost painless, because he respects Dannager. But, when Dannager offers to sell Rearden coal at cost, Rearden refuses and even offers to pay more for the coal. Rearden wants the small triumph of having defeated the irascible incumbents by paying a worthwhile man the money he's worth -- and since he's paying all the incompetent men the market value, he'd have to hike up the price to meet Dannager's worth.
 * Summoned by Rearden for a last-minute business venture, Eddie Willers eats breakfast at Rearden's suite at the Wayne-Falkland Hotel in New York. Rearden recognizes that Taggart Transcontinental is in financial trouble and cannot pay its first payment coming up in a week for Rearden Metal. On account of his metal, he proposes to give the railroad a six month delay in paying its bills.  Eddie thanks him profusely, but Rearden makes it clear to him that this is not an act of charity -- Rearden has received a lot of money, which he cannot use, from the purchases of his mines and ores from the looters, and giving Taggart Transcontinental a break is a sort of fuel in his fight against the looters.
 * The following Places in Atlas Shrugged are used as settings in this section:
 * Rearden's Office at Rearden Steel in Pennsylvania
 * Ken Dannager's Office at Dannager Coal Company in Pennsylvania
 * Rearden's hotel room in the Wayne-Falkland Hotel in New York City.
 * The following Characters in Atlas Shrugged appear in this section:
 * Hank Rearden
 * Paul Larkin
 * Ken Dannager
 * Eddie Willers
 * Jim Taggart - mentioned
 * Quotations:
 * And the government, he [Rearden] thought suddenly, the money now given to him as payment for his property, where had that come from? Whose work had provided it? (209)

Section 184: Part 1, Chapter 8, Section 4

 * Plot summary:
 * Public Opinion - without any evidence or proof - is that the Rearden Metal rail of the John Galt line will break or fail, and that the Rearden Metal bridge will collapse. Jim Taggart informs Dagny he's afraid of public opinion. Dagny tells him how their ancestor, Nat Taggart, only envied one of his competitors, who said, "The public be damned!" because he wished he had said it.
 * A delegate of the Union of Railroad Engineers tries to blackmail Dagny by saying they won't allow her to run trains on the John Galt Line, whereupon she orders him out of her office. He changes his tone when she refuses to acceed to his blackmail.  She states she won't make anyone work on the train, she will ask for volunteers.
 * In putting out a request for volunteers, Eddie Willers informs Dagny that with the exception of three men who are unreachable, every single engineer on Taggart Transcontinental volunteered to drive the first train on the John Galt Line.
 * Dagny announces casually to a packed audience of railroad engineers that she will also be aboard that first train, but her casual attitude fools no one, they all expected her to go.
 * The following Places in Atlas Shrugged are used as settings in this section:
 * Jim Taggart's Office at Taggart Transcontinental in New York City
 * Offices of the John Galt Line in New York City
 * Eddie Willer's Office at Taggart Transcontinental in New York City
 * The following Characters in Atlas Shrugged appear in this section:
 * Dagny Taggart
 * James Taggart
 * Eddie Willers
 * Union Shop Steward
 * Room full of train engineers

Section 185: Part 1, Chapter 8, Section 5

 * Plot summary:
 * Dagny Holds a press conference to announce the opening of the John Galt Line and welcomes the press to be in Cheyenne, Wyoming for the first train, which will not be a passenger special with celebrities and politicians, but a freight express, running at an average speed of 100MPH. She also announces she will be aboard the train.
 * Hank Rearden is present at the press conference, and announces that he, too, will ride the first train of The John Galt Line.
 * The following Places in Atlas Shrugged are used as settings in this section:
 * Offices of the John Galt Line in New York City
 * The following Characters in Atlas Shrugged appear in this section:
 * Dagny Taggart
 * Several Reporters
 * Hank Rearden

Section 186: Part 1, Chapter 8, Section 6

 * Plot summary:
 * Dagny and Hank arrive at the station in Cheyenne on July 22nd where the first trip on the John Galt line will begin. Eddie Willers is representing Taggart Transcontinental because Dagny has forbidden Jim to come stating, "If you come, Jim, I'll have you thrown out of your own station. This is one event you're not going to see"
 * Many reporters are at the scene. The ebulliance of the moment has torn away their usual disinterested pessimism. Laughingly, in defiance of the doom the media's groundlessly predicted, one photographer exclaims, "Can't you people look doomed, please? I know that's what the editor wants." One cynical reporter who's had years of success writing the kind of dribble expected and wanted by the media proclaims, "I know what I'd like to be: I wish I could be a man who covers news. (223)" Finally, before they take off the pressing question "Who is John Galt?" is asked by a reporter. Dagny turns to him and proclaims "We are!"
 * Though the press wants multiple shots to choose from, Eddie Willers refuses to cut the ribbon multiple times for photo opportunities to avoid being a "phony." In one fell swoop, he cuts the ribbon and orders the driver Pat Logan to "Open her up!" Thus, begins the first ride on the John Galt Line.
 * The following Places in Atlas Shrugged are used as settings in this section:
 * The Taggart Station in Cheyenne, Wyoming
 * The following Characters in Atlas Shrugged appear in this section:
 * Dagny Taggart
 * Hank Rearden
 * Pat Logan
 * Eddie Willers
 * Various reporters

Section 187: Part 1, Chapter 8, Section 7

 * Plot summary:
 * Dagny and Hank ride the first train on the John Galt line with Pat Logan driving the train at an unprecedented 100 mph. Taggart workers and local townspeople line the sides of the track along the way to celebrate -- and to act as guards of honor. In the blink of an eye, they cross the bridge made of Rearden Metal without any trouble and arrive at Wyatt Junction. Wyatt and other industrialists greet and congratulate Hank and Dagny.
 * Hank, Dagny, and Wyatt have dinner together at Wyatt's mansion out in the woods. Wyatt has provided them a sanctuary away from the mindless media that will, doubtlessly, be bandwagoning on the heroes' success they had denied as impossible, just a few hours ago. This is the first time Rearden has seen Wyatt in person -- and Wyatt appears as his true happy self, unmarred by his usual mask of anger. The success of the John Galt Line has made Wyatt boundlessly happy, but his happiness quickly diminishes when his old pessimistic bitterness returns -- that this will not last.
 * Wyatt shows Hank and Dagny to where they will be staying and Hank and Dagny consummate their love for each other. See Ayn Rand's Theory of Sex
 * The following Places in Atlas Shrugged are used as settings in this section:
 * The first train of the John Galt Line
 * Wyatt Junction
 * The following Characters in Atlas Shrugged appear in this section:
 * Dagny
 * Hank Rearden
 * Pat Logan
 * Ellis Wyatt
 * Various industrialists

Section 191: Part 1, Chapter 9, Section 1

 * Plot summary:
 * Rearden and Dagny put into words the differing yet similar nature of their "love" for each other. Rearden views the act of sex that he has succumbed to as depraved, yet he needs her, wants it, while Dagny views it as the joy to look forward to, the goal of arduous work. Each of them finds in the other a worthwhile mate to render mutual pleasures to.
 * The following Places in Atlas Shrugged are used as settings in this section:
 * Dagny's apartment
 * The following Characters in Atlas Shrugged appear in this section:
 * Hank Rearden
 * Dagny Taggart
 * James Taggart
 * Board of Taggart Transcontinental (mentioned)
 * Dr. Simon Pritchett (mentioned)
 * The following quotations appear in this section:
 * "Nothing's important" - James Taggart (242)
 * "I saw pictures of New York and I thought, somebody built those buildings - he didn't just sit and whine that the kitchen was filthy and the roof leaking and the plumbing clogged and it's a goddamn world and ... we were stinking poor and not giving a damn about it. That's what I couldn't take - that they didn't give a damn." - Cherryl Brooks (245)
 * "He didn't do it for any noble purpose, he did it just for his own profit. He's never done anything for any other reason." - Jim to Cherryl
 * "What's wrong with that, Mr. Taggart?" - Cherryl to Jim (246)
 * "There are no absolutes - as Dr. Pritchett has proved irrefutably." - James Taggart (248)
 * "Unhappiness is the hallmark of virtue, If a man is unhappy, really, truly unhappy, it means that he is a superior sort of person" - James Taggart (248)
 * "The worst thing about people is not the insults they hand out, but the compliments" - Hank Rearden (259)

Section 192: Part 1, Chapter 9, Section 2

 * Plot summary:
 * James Taggart finds himself wandering down a slum street plagued with a discontent he cannot pinpoint, succumbing to feelings of contempt and disgust in lieu of cogent thoughts. The setting is dark, the weather damp; Taggart has a cold, and he can't find his handkerchief. With the task of purchasing paper tissues and the malice of hoping the store will be out of business soon, he walks into a dime store in the district, the only spot of light in the dark decay of the slum neighborhood. The contrast between the dark decay of the slums that Taggart walks into and the brightness of the dime store sharpens the difference between Brooks and Taggart. Brooks, an innocent salesgirl at the dime store, is naive enough to see in Taggart a genuine hero. Taggart is amused by her ignorance and also drawn to her by it. Moreover, she does not regard him with the secret contempt of fellow looters, who know that Taggart's so-called "greatness" is gained in underhand tricks, rather than genuinely. Having been askew by the media's muckracking of Taggart as one of the supporters of the John Galt Line, she views him as one of the truly heroic. Taggart's true motive, however, is not to deceive himself that he is great. Although a part of him seems to want greatness, as if jealous of Rearden's ability to invent that metal, he wouldn't be happy if he receives that greatness because it's unearned--but he does not know this, as he lets feelings bypass thoughts. Taggart's true motive is feeling the superiority that he has something over her--that he's deceived her. To him, she is a girl with the same spirit of the heroes he despises, and deceiving her, to him, is like putting something over the heroes. When he brings her back home, having resisted the "customary action" of taking advantage of her sexually, she praises him, saying that anyone else would have. Taggart smugly asks if she would have, and Brooks runs away, abashed and ashamed. Taggart is satisfied that he has rendered the feelings of the profane into the sacred spirit Brooks represents.
 * The following Places in Atlas Shrugged are used as settings in this section:
 * Dime store in the slums
 * James Taggart's living room
 * The following Characters in Atlas Shrugged appear in this section:
 * James Taggart
 * Cherryl Brooks (first appearance)
 * Ragnar Danneskjold (mentioned)
 * Orren Boyle (mentioned)
 * Dr. Floyd Harris (mentioned)
 * Dr. Simon Pritchett (mentioned)
 * The following pieces of Literature in Atlas Shrugged appear in this section:
 * The Metaphysical Contradictions of the Universe by Dr. Simon Pritchett

Section 193: Part 1, Chapter 9, Section 3

 * Plot summary:
 * As Dagny and Rearden talk about the aftermath of the success of the John Galt Line, they realize that their love for each other is based on a mutual capitalistic gauge of each other's worth. This scene is in stark juxtaposition to the one before, as unlike Taggart/Brooks, Dagny/Rearden worship each other in a worthwhile pride of mutual strength, while Taggart toys with Brooks' ignorance, letting a faked sense of pride win over his feelings.
 * The following Places in Atlas Shrugged are used as settings in this section:
 * Philadelphia
 * The following Characters in Atlas Shrugged appear in this section:
 * Hank Rearden
 * Dagny Taggart
 * Francisco D'Anconia (elliptical reference as Dagny's former lover)

Section 194: Part 1, Chapter 9, Section 4

 * Plot summary:
 * The Quinn Ball Bearing Company is yet another company leaving their homestate to join the incipient wealth in Colorado. Mowen complains about how everyone is leaving for Colorado. The low-labor worker explains that it's due to the Equalization of Opportunity Bill forbidding others from owning more than one business. Mowen whines about how someone should do something about the world. He likes the worker, as the worker makes him feel safe. The worker states that Mowen wouldn't care what happens to the world. The worker turns out to be Owen Kellogg.
 * Mowen mentions that Wesley Mouch, the man whom James Taggart liked for being reticent, becomes Top-Coordinator of the Bureau of Economic Planning and National Resources.
 * The following Places in Atlas Shrugged are used as settings in this section:
 * Quinn Ball Bearing Company of Connecticut
 * Amalgamated Switch and Signal Company (mentioned)
 * The following Characters in Atlas Shrugged appear in this section:
 * Mr. Mowen
 * Owen Kellogg
 * Dan Conway (mentioned)
 * Orren Boyle (mentioned)
 * Wesley Mouch (mentioned)

Section 195: Part 1, Chapter 9, Section 5

 * Plot summary:
 * The shackles of orthodox depravity that restrain Rearden from his full happiness are beginning to crack, as he lets his love for Dagny push aside the burden of public scandal. He wants Dagny to wear the bracelet of Rearden Metal in public. He also wants to take her on a vacation. This will be their only break, as there is a plethora of business jam-packed into the next three years.
 * The following Places in Atlas Shrugged are used as settings in this section:
 * Dagny's apartment
 * John Galt. Inc. building (briefly)
 * The following Characters in Atlas Shrugged appear in this section:
 * Dagny Taggart
 * Hank Rearden
 * Francisco D'Anconia (mentioned)

Section 196: Part 1, Chapter 9, Section 6

 * Plot summary:
 * After spending an aimless week of wandering, Rearden confronts Dagny with the characteristic restlessness of the heroes, "Does relaxing have to be purposeless?" In reply, Dagny asks him which factory he wants to visit. They start visiting abandoned factories and ore mines. They come across the Twentieth Century Motor Company. But, the rampant decay around the factory is depressing; moreover, it foreshadows the emotional context in which the world's greatest material treasure is to be found. Dagny finds in the company the broken remnants of a motor that would run on static electricity. While all other valuables have been looted from the factory, the significance of the motor has been heartfallingly disregarded, the re-usable parts of the motor having been torn off. Rearden states the good the motor could have done, implying that all the loot taken away from the company wouldn't have been worth the potential of the motor. Those who had run the company to its ends were not capable of realizing the worth of the motor; their lack of judgment parallels that of the incomptency of the incumbents who now hold power over the world.
 * The following Places in Atlas Shrugged are used as settings in this section:
 * Abandoned ore pit in Michigan
 * Anonymous motels in Wisconsin and Michigan
 * The Twentieth Century Motor Company
 * The following Characters in Atlas Shrugged appear in this section:
 * Hank Rearden
 * Dagny Taggart
 * Ted Nielsen (mentioned)
 * Dwight Sanders (mentioned)
 * The following pieces of Literature in Atlas Shrugged appear in this section:

Section 197: Part 1, Chapter 10, Section 1

 * Plot summary:
 * The clerk of the Hall of Records explains that the Twentieth Century Motor Company had been sold out twice, at the same time. Mark Yonts had used the company as collateral for a loan from an Illinois bank and he had sold it to some South Dakotans. The clerk describes Yonts as not the kind of person who operates things, that he "doesn't want to make money, only to get it." The clerk tells them that Yonts had sold the parts of the factory piece-meal after he bought it and that scavengers from Starnesville probably took everything else to use as kindling. He admits that Yonts bought it from a Mayor Bascom of Rome. When the clerk asks Rearden and Dagny what they're looking for, Rearden replies saying that it is a friend they've lost, a friend who used to work at the factory.

 * The following Places in Atlas Shrugged are used as settings in this section:
 * Hall of Records
 * Starnesville (mentioned)
 * The following Characters in Atlas Shrugged appear in this section:
 * People's Mortage Company (mentioned)
 * Twentieth Century Motor Company (mentioned)
 * Mark Yonts (mentioned)
 * Dagny Taggart
 * Hank Rearden
 * Clerk of Hall of Records
 * Mayor Bascom of Rome, Wisconsin (mentioned)
 * The following Quotations appear in this section:
 * "So it seems like everybody owns the place--and nobody" (Clerk describes state of 20th century motor company)
 * "He didn't want to make money, only to get it" (Clerk describes Mark Yonts)(273)

Section 198: Part 1, Chapter 10, Section 2

 * Plot summary:
 * Dagny and Rearden visit Bascom in Rome. Bascom is the type of man who believes that one can only become rich by "cutting corners" and bending laws, and he's open about this, "as if a fellow cheat displaying his shrewdness to his partners in guilt." Bascom rambles on about how he can't stand a man with principles, and Rearden is forced to have to clue him in with questions. Bascom mentions that he managed to take a few items before he sold it to Mark Yonts--Jed Starnes' mahogany desk and a mermaid shower stall. When Rearden figures out to ask him which bankruptcy sale he bought it from, Bascom finally tells that it was from the Community National Bank, run by Eugene Lawson, the banker with a heart. Bascom implies in passing that much of the poverty is because of the crash of the bank. Rearden again tells him that they are looking for a friend. Bascom replies that it must be a good friend if they would go through all this trouble to find him, "you and the charming lady who is not your wife."
 * Rearden is enraged. But, when Dagny asks Bascom why he thinks so, Bascom tells them that married couples don't look as if they have a bedroom on their minds because "in this world, either you're virtuous or you enjoy yourself. Not both."
 * When they leave Bascom, Rearden apologizes to Dagny. Dagny, however, tells him to think through the man's explanation, revealing that Dagny knows the fetters that Hank's family has around him.
 * Rearden gets paranoid about sending their engineers down to sift through the remains of the factory for more details of the motor, fearing that others would find out about their furtive romance. Dagny effortlessly bypasses his pessimism saying she'd call her engineers down here to search the factory, saying that she was on vacation.
 * Dagny reaches a long distance phone to call Eddie. Eddie is panicked, his words foreboding, "I think they're planning to kill Colorado."

 * The following Places in Atlas Shrugged are used as settings in this section:
 * Mayor Bascom's office in Rome, Wisconsin
 * Long-distance telephone station
 * The following Characters in Atlas Shrugged appear in this section:
 * Dagny Taggart
 * Hank Rearden
 * Mayon Bascom
 * Mark Yonts (mentioned)
 * Jed Starnes (mentioned)
 * Community National Bank (mentioned)
 * Eugene Lawson (mentioned)
 * Eddie Willers
 * The following quotations appear in this section:
 * "No principle ever filled anybody's milk bottle" - Mayor Bascom (275)
 * "Don't ever get mad at a man for stating the truth" - Dagny (277)

Section 199: Part 1, Chapter 10, Section 3

 * Plot summary:
 * Dagny returns to New York. She hides the motor in a vault in an abandoned Taggart tunnel that used to hold an emergency electric generator. This is symbolic of the motor's role in the state of things--it has the potential to power the world in this emergency state.
 * The media has muckraked the following:
 * Union of Locomotive Engineers demanding the maximum speed of trains be set at 60 mph.
 * Union of Railway Constructors and Brakemen demand that the trains be reduced to 60 cars. (James Taggart would later argue that because of the massive unemployment, having fewer cars per train would divide up the work.)
 * The neighboring states of Wyoming, New Mexico, Utah, Arizona demand that the number of trains running in Colorado not to exceed the number of trains run in each of neighboring states. (Parallel: Brother's keeper become State's keeper.)
 * Orren Boyle vies for the Preservation of Livelihood Law limiting the production of Rearden Metal to that of the output of other steel mills of equal plant capacity.
 * Mowens demands a Fair Share Law so that every customer of Rearden Metal gets an equal share of it. (Ironically, just a few months ago, he had refused to make switches out of Rearden Metal.)
 * Scudder demands for the Public Stability Law forbidding Eastern businesses from moving out of states.
 * Wesley Mouch, the Top Co-ordinator of the Bureau for Economic Planning and National Resources makes a bunch of ambiguous statements repeating the phrases "emergency powers" and "unbalanced economy."
 * Dagny reminisces about Eddie's despair and James Taggart's response. Taggart had argued for each of the demands above, albeit each one has the potential to destroy Taggart Transcontinental. When confronted with this, Taggart adamantly states that he "fully intends to protect the interests of Taggart Transcontinental." Dagny points out that it is impossible if he intends to kill Colorado. Taggart claims there is no need for panic, that Dagny had predicted disaster for the Anti-dog-eat-dog-rule, but it's yet to come. Dagny points out that that was because she saved them! She ominously points out that if she doesn't save them, who will?
 * All this does not seem real to her while underground. Dagny realizes that finding the man who created the motor is more important than anything, albeit the impending legislature may easily stifle her business.
 * The following Places in Atlas Shrugged are used as settings in this section:
 * Taggart Tunnels
 * The following pieces of legislature are used in this section:
 * Preservation of Livelihood Law (mentioned)
 * Fair Share Law (mentioned)
 * Public Stability Law
 * The following Characters in Atlas Shrugged appear in this section:
 * Union of Locomotive Engineers (mentioned)
 * Union of Railway Constructors and Brakemen (mentioned)
 * Wesley Mouch
 * Bertram Scudder
 * Orren Boyle
 * Mr. Mowen
 * James Taggart
 * Dagny Taggart
 * Hank Rearden (mentioned)
 * Eddie Willers
 * The following quotations appear in this section:
 * "If one of my blast furnaces goes down, will I be able to keep it going by feeding your intention into it?" - Hank Rearden to Paul Larkin (281)
 * "The same kind of brain can't do both. Either you're good at running the mills or you're good at running to Washington" The Purchasing Manager to Rearden (283)
 * "Lillian, what purpose do you live for?" - Hank
 * "What a crude question! No enlightened person would ever ask it." - Lillian
 * "Well, what is it that enlightened people do with their lives?" - Hank
 * "Perhaps they do not attempt to do anything. That is their enlightenment" - Lillian (287)

Section 200: Part 1, Chapter 10, Section 4

 * Plot summary:
 * The section begins with Rearden realizing that he cannot fight both battles: the fight against the incumbent gangs vying for the restrictive laws and the fight against the traditional gangs of ruffians for ore to run his mines. Rearden's purchasing manager would later tell him that he's not the type of man who would win the fight in Washington, that either he's good at running the mills or running to Washington.
 * Larkin, who had bought Rearden's mines c/o The Equalization of Opportunity Bill, has shipped the ore to Boyle instead of Rearden. Moreover, he's using railway transportation instead of lake shipping in order to keep his friendship with Taggart.
 * Rearden has been reduced to furtive bargains with ungainly sources, such as ruffian gangs, to obtain his ore. Rearden finds himself unable to see his own cause as right because he feels guilt for his secret relationship with Dagny. He does not believe in degrees of evil, thus seeing himself as one of the evil ones, he finds himself unable to fully condemn the looters. He would fight as one guilty wretch against the others. But, he finds that it is all worth it because of Dagny.
 * Rearden returns home late. Lillian offers him the duty of a wife, but Rearden, who is now in love with Dagny, is disgusted. Lillian hints at her motive in wanting him--not in the gutter sense. She, like his family, would hold onto him by his sense of duty and guilt, and this is how they are having him.
 * When Lillian finally leaves, Rearden falls asleep consoled by sexy thoughts of Dagny.
 * The following Places in Atlas Shrugged are used as settings in this section:
 * Rearden's Office
 * The following Characters in Atlas Shrugged appear in this section:
 * Paul Larkin
 * Hank Rearden
 * Rearden's Purchasing Manager

Section 201: Part 1, Chapter 10, Section 5

 * Plot summary:
 * Dagny meets with Eugene Lawson, who is now a member of the Bureau of Economic Planning and National Resources, one of the controllers of the world. Lawson, thinking she's here to leech dirty news from him, states he is not ashamed of his past presidentship of the Community National Bank of Madison.
 * Dagny inquires about the Twentieth Century Motor Company, but Lawson claims that whatever or whomever she's searching for would be of less importance than a friendship with Wesley Mouch, which he can obtain for her. Dagny believes that he's wrong, that the man she is looking for is more important than anything.
 * The following Places in Atlas Shrugged are used as settings in this section:
 * Lawson's office in Bureau
 * The following Characters in Atlas Shrugged appear in this section:
 * Dagny Taggart
 * Eugene Lawson
 * Lee Hunsacker (mentioned)
 * Wesley Mouch (mentioned)
 * The following quotations appear in this section:
 * "My objective was social progress, human brotherhood and love. Love, Ms. Taggart. That is the key to everything. If men learned to love one another, it would solve all their problems" - Eugene Lawson (290)
 * "I can proudly say that in all of my life I have never made a profit!" - Eugene Lawson
 * "Mr. Lawson, I think I should let you know that of all the statements a man can make, that is the one I consider most despicable." - Dagny (292)

Section 202: Part 1, Chapter 10, Section 6

 * Plot summary:
 * Hunsacker's tag line is "I never had a chance." He tells of a life where, from his perspective, he has been massively cheated on all levels--the wealth entitled to him made impossible because of averse circumstances that seem to reoccur. Hunsacker claims he is the only man who has beaten Midas Mulligan. Upon Mulligan's rejection of a loan to him, Hunsacker had brought his case to court. Hunsacker had appealed to a higher court, when Judge Narrangansett rejected his suit against Mulligan. The higher court reversed Narrangensett's decision.
 * Dagny recalls her memory of Midas Mulligan, a famous banker. He had disappeared, suddenly, without a trace. His company had also liquidated itself suddenly -- every single penny of it liquidated, the company completely wiped out. Narrangansett had disappeared shortly after.
 * Dagny recalls Judge Narrangetsett, the ideally impartial judge who is likened to the blind-folded statue of justice.
 * Dagny manages to get the locations of the Starnes heirs from Hunsacker.
 * The following Places in Atlas Shrugged are used as settings in this section:
 * Hunsacker's squalid home
 * The following Characters in Atlas Shrugged appear in this section:
 * Lee Hunsacker
 * Dagny Taggart
 * Starnes Heirs (mentioned)
 * Midas Mulligan (mentioned)
 * Judge Narrangetsett (mentioned)
 * The following Quotations appear in this section:
 * "Why yes I can," said Midas Mulligan, when he was asked whether he could name a person more evil than the man with a heart closed to pity. "The man who uses another's pity for him as a weapon." (294)
 * "I didn't have much money to spend on such things as laboratories . . . I had to have a brighter color scheme in my office, and a decent modern bathroom with a stall shower. Furthermore, I spent a lot of money on a new cafeteria and a playroom and rest room for the workers. We had to have morale didn't we?" - Lee Hunsacker (298)

Section 203: Part 1, Chapter 10, Section 7

 * Plot summary:
 * Each Starnes heir is akin to a demon of greater evil in hell. They are archetypes of the evil people in the world.
 * Eric would kill himself just to hurt others.
 * Gerald claims that the factory crashed because it was bad. He represents a man who has reversed the proper metaphysics that it is the men who have brought the factory to its current decrepit state that are bad.
 * Ivy installed the creed of communism as the new company plan. She is the epitome of pure evil, from Dagny's perspective.
 * "From each according to his ability, to each according to his need..."
 * "Rewards were based on need; and the penalties on ability... Those who had not produced as much as the vote said they could were fined... It required men to be motivated, not by personal gain, but by a love for their brothers..."
 * Dagny almost murders Ivy, but Ivy gives her a shred of information--of a William Hastings, who had been the chief engineer.
 * The following Places in Atlas Shrugged are used as settings in this section:
 * Flophouse where Gerald crashes in
 * Ivy's stinky bungalow
 * The following Characters in Atlas Shrugged appear in this section:
 * Eric Starnes (mentioned)
 * Gerald Starnes
 * Ivy Starnes
 * Dagny Taggart
 * Jed Starnes (mentioned)
 * William Hastings (mentioned)

Section 204: Part 1, Chapter 10, Section 8

 * Plot summary:
 * Dagny visits the Hastings' home. Mrs. Hastings answers the door. William had died five years ago. Dagny is crestfallen, but she soon finds that the man who had made the motor still exists somewhere. Mrs. Hastings does not know much of her husband's affairs, except once when she was picking him up she saw him with two other men. One a young man, whom William claimed would upturn the world, and the other a venerable old man. It is almost a dead end for Dagny, but Mrs. Hastings remembers that she has seen the man at a diner near the Lennox Foundry.
 * The following Places in Atlas Shrugged are used as settings in this section:
 * the Hasting's modest home in suburbia
 * The following Characters in Atlas Shrugged appear in this section:
 * Lennox Foundry (mentioned)
 * William Hastings (mentioned)
 * Mrs. Hastings
 * Dagny Taggart

Section 205: Part 1, Chapter 10, Section 9

 * Plot summary:
 * Dagny eats the best burger she's ever had at the diner near Lennox Foundry. She finds from the owner and cook that it'll close in a week, after the foundry closes.
 * The owner turns out to be Hugh Akston. He warns her to stop searching for the man who made the motor, that it would be a dead end alley.
 * Dagny leaves, stating that she would still search for him.
 * As she boards the train back to civilization, she hears news of the new directives enacted for emergency measures.
 * As the train speeds by Colorado, Dagny screams, seeing that Wyatt's oil fields are ablaze with fire.
 * The following Places in Atlas Shrugged are used as settings in this section:
 * diner near Lennox Foundry
 * The following Characters in Atlas Shrugged appear in this section:
 * Francisco d'Anconia (mentioned)
 * Ragnar Danneskjold (mentioned)
 * Dagny Taggart
 * Hugh Akston
 * Dr. Stadler (mentioned)
 * The following quotations appear in this section:
 * "If you find it inconceivable that an invention of genius should be abandoned among ruins and that a philosopher should wish to work as a cook in a diner - check your premises. You will find that one of them is wrong." - Hugh Akston to Dagny (308)
 * "I am leaving it as I found it. Take over. It's yours." - Note left by Ellis Wyatt at the foot of the burning hill of Wyatt Oil.

title: Atlas Shrugged/Synopsis/Chapters 6-10


text:
Wikipedia:Articles for deletion/Sarp Levendoğlu

The result was   speedy delete. WP:CSD § FreeRangeFrog croak 22:42, 7 February 2015 (UTC)

Sarp Levendoğlu

 * – ( View AfD View log  Stats )

Another unotable actor here Wgolf (talk) 22:34, 7 February 2015 (UTC)
 * Delete As per nom.Peter Rehse (talk) 22:36, 7 February 2015 (UTC)


text:
User:Jpetersen007/sandbox/Randy Petersen

Randy Petersen Randy Petersen is an American songwriter and producer. He is best known for writing songs for Disney's High School Musical, High School Musical 2, and High School Musical 3: Senior Year. His work includes songs for Pup Star, Pup Star: Better 2Gether, The Lion King 2: Simba's Pride, Aladdin: The Return of Jafar, Hercules (TV series), The Little Mermaid (TV series), and Sister, Sister theme song. His songs are featured on many other movie and television soundtracks.

Along with frequent collaborators Kevin Quinn and Tim Heintz, Randy's work has earned an Emmy nomination and an Annie nomination.

In 2017, Randy added acting credits as the voice of "Shampoo" in Pup Star: Better 2Gether. Early life Randy started playing bass guitar in high school and toured several years in various cover bands. After moving to Los Angeles in 1980 Randy was hired as Sheena Easton's musical director. He later served as music director for Paula Abdul, Toni Childs, and Callaway. By 1990, Randy's songs began appearing in various TV series, animated series and motion pictures.


text:
Wikibooks:Mathematics bookshelf

Basic Math

 * Arithmetic
 * Applied Math Basics
 * Beginning Mathematics
 * Introduction to Mathematics
 * Mental Math
 * Prealgebra for Two-Year Colleges
 * Using an Abacus

Elementary

 * Algebra I - A Verbose Approach
 * Basic Algebra

Intermediate

 * Algebra
 * Intermediate Algebra
 * Theory of equations
 * Prealgebra for Two-Year Colleges

Geometry

 * Geometry for Elementary School
 * Geometry
 * Conic Sections
 * High School Mathematics Extensions

Trigonometry

 * Trigonometry

Discrete Mathematics

 * Discrete mathematics
 * Combinatorics
 * Number Theory
 * Fermat's last theorem

Calculus

 * Calculus
 * Calculus optimization methods

Statistics and Probability

 * Probability
 * Statistics
 * Handbook of Descriptive Statistics

Higher Mathematics

 * Problems in Mathematics

Foundations

 * Set Theory
 * Category theory
 * Mathematical Logic
 * Mathematical Proof
 * Finite Model Theory

Analysis

 * Real Analysis
 * Complex Analysis
 * Functional Analysis
 * Residue Theory
 * Measure Theory
 * UMD Analysis Qualifying Exam

Linear Algebra

 * Linear Algebra

Advanced Algebra

 * Abstract Algebra
 * Ring Theory
 * Introduction to Rings and Algebras

Geometry and Topology

 * Algebraic Geometry
 * Crystallography
 * Topology
 * Combinatorial Topology
 * Differential Geometry
 * Amateur's Guide to Proving the Four Color Theorem

Differential Equations

 * Differential Equations
 * Linear Algebra with Differential Equations
 * Partial Differential Equations

Applied Mathematics

 * Applied Mathematics
 * Introduction to Game Theory
 * Numerical Methods
 * Numerical Methods Qualification Exam Problems and Solutions (University of Maryland)

Program Specific Math

 * A-level Mathematics
 * Advanced A-level Mathematics
 * VCE Mathematical Methods

Misc.

 * Solutions To Mathematics Textbooks
 * Programmed Math
 * Vedic Mathematics
 * Applicable Mathematics
 * Fractals
 * The Book of Mathematical Proofs
 * Solved Question Papers - IIT JEE

cy:Silff lyfrau:Mathemateg de:Regal:Mathematik he:מדף:מתמטיקה it:Wikibooks:Ripiano Matematica 数学 Wiskunde 数学书架

title: Wikibooks:Mathematics bookshelf


text:
ponzare

Etymology
From, from. Compare 🇨🇬, 🇨🇬, 🇨🇬.

Verb

 * 1)  to push forcefully; to strain
 * 2)  to lay an egg

title: ponzare


text:
User:Ncresearcher

Ncresearcher, created on February 7th, 2015, is a user dedicated to informing the users of the internet about new topics that have been previously unfounded on Wikipedia.

title: User:Ncresearcher


text:
User:CooperScience/Hurricane Jerry (2019)

Hurricane Jerry was a Category 2 hurricane which is currently a tropical storm threatening the island of Bermuda. The tenth named storm and fourth hurricane of the 2019 Atlantic hurricane season, Jerry formed from a tropical wave on September 17 over the tropical Atlantic Ocean. Favorable environmental conditions allowed the cyclone to strengthen as it moved westward, and Jerry became a hurricane on September 19. Early the following day, Jerry reached its peak intensity as a Category 2 hurricane, although increasing vertical wind shear caused it to quickly weaken afterward.


text:
Portal talk:French

Renovations
Due to the French Language Division not being used in well over a year, I have decided to put it under heavy renovations. All previous pages have been archived and will remain visible to those who desire to view them. They are the following: Main Page, Topic talk, and the French stream. Readyokaygo (talk) 04:39, 1 July 2012 (UTC)

Wonderful Job
Just looking at how pleasantly arranged and dispayed this page is makes me want to learn French :3 --Simplex (discuss • contribs) 03:31, 24 June 2013 (UTC)

title: Portal talk:French


text:
Martin Evans (cricketer)

Martin James Evans (16 October 1904 – 17 December 1998) was an English first-class cricketer and Royal Navy officer.

Evans was born in October 1904 at Kingsclere, Hampshire. After enlisting in the Royal Navy, he was promoted from the rank of midshipman to sub-lieutenant in July 1925. He made a single appearance in first-class cricket for the Royal Navy against the British Army cricket team at Lord's in 1925. Batting twice in the match, he ended the Royal Navy first-innings not out on 7, while in their second-innings he was dismissed for a single run by Geoffrey Cooke. With the ball, he bowled a total of nine wicketless overs in the Army first-innings, conceding 42 runs. He was promoted to the rank of lieutenant in February 1927, with promotion to the rank of lieutenant commander in February 1935.

Evans served with the Royal Navy in the Second World War, during which he was promoted to the rank of commander in December 1940. During the war he held commands aboard HMS Keppel (D84), HMS Towy and HMS Philante. He was made an OBE in December 1942, before being made a CBE in August 1945. Following the war, he was awarded the Legion of Merit by the United States in May 1946 and promoted to the rank of captain the following month. Evans died in December 1998 at Peasmarsh Place retirement home in the Sussex village of Peasmarsh.

title: Martin Evans (cricketer)


text:
User:Kjcarlson/sandbox

 Article Evaluation
 * "Moral Injury"
 * While evaluating this article, I found the information presented to be extremely sparse. A thorough review of moral injury was not provided. The article does present as neutral, but lacks common perspectives in moral injury research, such as military/combat related moral injury. The links for the citations on the article worked. I think the article could benefit from use of more systematic reviews as sources, as the sources provided seemed very specific. The article's talk page stated that the article was labeled as "Start Class" on the WikiProject Psychology quality scale, meaning that it is "quite incomplete and may or may not cite adequate sources." The quality scale also suggests that the article needs "substantial improvement" on content and organization, which I would agree with. The organization of the topics did not paint a cohesive picture of moral injury.

title: User:Kjcarlson/sandbox


text:
User:DAPJ/sandbox

The Rise of the Synths is an upcoming documentary film directed by Iván Castell and narrated by filmmaker and composer John Carpenter. The film explores the origins and growth of the electronic music genre known as Synthwave, charting its growth in popularity from underground online music scene to recent mainstream exposure following its use in retro-themed soundtracks, notably the 2011 film Drive, and more recently the television series Stranger Things.

Cast
The film contains various interviews with both established and upcoming synthwave artists, exploring their sources of inspiration, ranging from early electronic pioneers such as Giorgio Moroder, Vangelis and Tangerine Dream to a collective love of 1980's films and video games. Artists featuring in the film include:

 * Carpenter Brut

 * Gunship

 * Perturbator

 * Electric Youth

 * The Midnight

 * NINA

 * Power Glove

 * Dance with the Dead

 * Robert Parker

 * Waveshaper

 * OGRE Sound

 * Miami Nights 1984

 * Valerie Collective

 * Laserhawk

 * 80's Stallone

 * John Bergin

 * MPM Soundtracks

 * Night Crawler

 * Scandroid

 * Mecha Maiko

 * GoST

Production
The Rise of the Synths initially began as a crowdfunding campaign on Kickstarter in 2016 before later moving platforms to Indiegogo. The film is due to premiere at the In-Edit Festival in Barcelona on 1 November 2019, followed by its UK premiere at the Doc'n Roll Festival.

Soundtrack
The film's original soundtrack is composed by OGRE Sound. In support of film, Lakeshore Records released an Official Companion Album in 2017, featuring exclusive music from various synthwave artists which received positive reviews.

title: User:DAPJ/sandbox


text:
Abortion in Georgia

Abortion in Georgia may refer to:

 * Abortion in Georgia (country)
 * Abortion in Georgia (U.S. state)

title: Abortion in Georgia


text:
Interpolation and Extrapolation

This course belongs to the track Numerical Algorithms in the Department of Scientific Computing in the School of Computer Science.

In this course, students will learn how to approximate discrete data. Different representations and techniques for the approximation are discussed.

Discrete Data
Discrete data arises from measurements of $$f(x)$$ or when $$f(x)$$ is difficult or expensive to evaluate.

In general, discrete data is given by a set of nodes $$x_i$$, $$i=1 \dots n$$ and the function $$f(x)$$ evaluated at these points: $$f_i = f(x_i)$$, $$i=1 \dots n$$.

In the following, we will refer to the individual nodes and function values as $$x_i$$ and $$f_i$$ respectively. The vectors of the $$n$$ nodes or function values are written as $$\underline{\mathbf x}$$ and $$\underline{\mathbf f}$$ respectively.

We will also always assume that the $$x_i$$ are distinct.

Polynomial Interpolation
Although there are many ways of representing a function $$f(x)$$, polynomials are the tool of choice for interpolation. As the Taylor series expansion of a function $$f(x)$$ around $$0$$ shows, every continuous, differentiable function has a polynomial representation

 * {|border=0

 * $$f(x)$$
 * $$f(0) + f'(0)x + \frac{1}{2}f(0)x^2 + \frac{1}{6}f'(0)x^3 + \dots$$
 * $$\sum_{n=0}^\infty \underbrace{\frac{1}{n!}f^{(n)}(0)}_{=a_n}x^n$$
 * $$\sum_{n=0}^\infty a_n x^n$$
 * }
 * $$\sum_{n=0}^\infty \underbrace{\frac{1}{n!}f^{(n)}(0)}_{=a_n}x^n$$
 * $$\sum_{n=0}^\infty a_n x^n$$
 * }
 * $$\sum_{n=0}^\infty a_n x^n$$
 * }
 * $$\sum_{n=0}^\infty a_n x^n$$
 * }

in which the $$a_n = \frac{1}{n!}f^{(n)}(0)$$ are the exact weights.

If a function $$f(x)$$ is assumed to be continuous and differentiable and we assume that it's derivatives $$f^{(n)}(0)$$ are zero or of negligible magnitude for increasing $$n$$, it is a good idea to approximate the function with a polynomial.

Given $$n$$ distinct nodes $$x_i$$, $$i=1 \dots n$$ at which the function values $$f_i = f(x_i)$$ are known, we can construct an interpolating polynomial $$g(x)$$ such that $$g(x_i) = f_i$$ for all $$i=1 \dots n$$. Such an interpolating polynomial with degree $$\le n$$ is unique. However infinitely many such polynomials can be found with degree $$>n\;$$.

 * Any nice way of deriving the interpolation error?

The Vandermonde Matrix
By definition as given above, our polynomial

 * $$g(x) = \sum_{i=0}^{n-1} a_i x^i$$

must interpolate the function $$f(x)$$ at the $$n$$ nodes $$x_i$$. This leads to the following system of $$n$$ linear equations in the coefficients $$a_i$$:

 * $$f(x_1)$$
 * $$a_0 + a_1x_1 + a_2 x_1^2 + \dots + a_{n-1} x_1^{n-1}$$
 * $$f(x_2)$$
 * $$a_0 + a_1x_2 + a_2 x_2^2 + \dots + a_{n-1} x_2^{n-1}$$
 * $$\vdots$$
 * $$f(x_n)$$
 * $$a_0 + a_1x_n + a_2 x_n^2 + \dots + a_{n-1} x_n^{n-1}$$
 * }
 * $$\vdots$$
 * $$f(x_n)$$
 * $$a_0 + a_1x_n + a_2 x_n^2 + \dots + a_{n-1} x_n^{n-1}$$
 * }
 * $$f(x_n)$$
 * $$a_0 + a_1x_n + a_2 x_n^2 + \dots + a_{n-1} x_n^{n-1}$$
 * }
 * }

We can re-write this system of linear equation in matrix notation as

 * $$\mathbf M \mathbf a = \mathbf f$$

where $$\mathbf a$$ is the vector of the $$a_i$$, $$i=0\dots n-1$$ coefficients and $$\mathbf M$$ is the so-called moment matrix or Vandermonde matrix with

 * $$\mathbf M = \begin{bmatrix}

1 & x_1 & x_1^2 & \dots & x_1^{n-1} \\ 1 & x_2 & x_2^2 & \dots & x_2^{n-1} \\ \vdots & \vdots & \vdots & \ddots & \vdots \\ 1 & x_n & x_n^2 & \dots & x_n^{n-1} \end{bmatrix}$$

or

 * $$\mathbf M_{i,j} = x_i^{j-1}$$

This linear system of equations can be solved for $$\mathbf a$$ using Gauss elimination or other methods.

The following shows how this can be done in Matlab or GNU Octave.

% declare our function f f = inline('sin(pi*2*x)','x')

% order of the interpolation? n = 5

% declare the nodes x_i as random in [0,1] x = rand(n,1)

% create the moment matrix M = zeros(n) for i=1:n M(:,i) = x.^(i-1); end

% solve for the coefficients a a = M \ f(x)

% compute g(x) g = ones(n,1) * a(1) for i=2:n g = g + x.^(i-1)*a(i); end;

% how good was the approximation? g - f(x)

However practical it may seem, the Vandermonde matrix is not especially suited for more than just a few nodes. Due to it's special structure, the Condition Number of the Vandermode matrix increases with $$n$$.

If in the above example we set $$n=10$$ and compute $$\mathbf a$$ with

% solve for the coefficients a a = inv(M) * f(x)

the approximation is only good up to 10 digits. For $$n=20$$ it is accurate only to one digit.

We must therefore consider other means of computing and/or representing $$g(x)$$.

Lagrange Interpolation
Given a set of $$n$$ nodes $$x_i$$, $$i=1 \dots n$$, we define the $$k$$th Lagrange Polynomial as the polynomial of degree $$n-1$$ that satisifies

 * $$\ell_k(x_i) = \begin{cases}0\quad & i \neq k \\ 1 & i = k\end{cases}$$

Maybe add a nice plot of a Lagrange polynomial over a few nodes?

The first condition, namely that $$\ell_k(x_i)=0$$ for $$i \neq k$$ can be satisfied by construction. Since every polynomial of degree $$n-1$$ can be represented as the product

 * $$g(x) = c\prod_{i=1}^{n-1}(x - \xi_i)$$

where the $$\xi_i$$ are the roots of $$g(x)$$ and $$c$$ is some constant, we can construct $$\ell_k^\star(x)$$ as

 * $$\ell_k^\star(x) = \prod_{i=1,i \neq k}^{n}(x - x_i)$$.

The polynomial $$\ell_k^\star(x)$$ is of order $$n-1$$ and satisifies the first condition, namely that $$\ell_k^\star(x_i)=0$$ for $$i \neq k$$.

Since, by construction, the $$n-1$$ roots of $$\ell_k^\star(x)$$ are at the nodes $$x_i$$, $$i \neq k$$, we know that the value of $$\ell_k^\star(x_k)$$ cannot be zero. This value, however, should be $$1$$ by definition. We can enforce this by scaling $$\ell_k^\star(x)$$ by $$\ell_k^\star(x_k)^{-1}$$:

 * {|cellpadding=2

 * $$\ell_k(x)$$
 * $$\frac{\ell_k^\star(x)}{\ell_k^\star(x_k)}$$
 * $$\frac{\prod_{i=1,i \neq k}^{n}(x - x_i)}{\prod_{i=1,i \neq k}^{n}(x_k - x_i)}$$
 * }
 * $$\frac{\prod_{i=1,i \neq k}^{n}(x - x_i)}{\prod_{i=1,i \neq k}^{n}(x_k - x_i)}$$
 * }
 * $$\frac{\prod_{i=1,i \neq k}^{n}(x - x_i)}{\prod_{i=1,i \neq k}^{n}(x_k - x_i)}$$
 * }

If we insert any $$x_i$$, $$i \neq k$$ into the above equation, the nominator becomes $$0$$ and the first condition is satisified. If we insert $$x_k$$, the nominator and the denominator are the same and we get $$1$$, which means that the second condition is also satisfied.

We can now use the Lagrange polynomials $$\ell_k(x)$$ to construct a polynomial $$g(x)$$ of degree $$n-1$$ which interpolates the $$n$$ function values $$f_i$$ at the points $$x_i$$.

Consider that, given the definition of $$\ell_k(x)$$,

 * $$f_k\ell_k(x_i) = \begin{cases}f_k\quad & i = k \\ 0 & i \neq k\end{cases}$$.

Therefore, if we define $$g(x)$$ as

 * $$g(x) = \sum_{k=1}^{n} f_k\ell_k(x)$$

then $$g(x_i) = f_i$$ for all $$i=1 \dots n$$. Since the $$\ell_k(x)$$ are all of degree $$n-1$$, the weighted sum of these polynomials is also of degree $$n-1$$.

Therefore, $$g(x)$$ is the polynomial of degree $$n-1$$ which interpolates the $$n$$ values $$f_i$$ at the nodes $$x_i$$.

The representation with Lagrange polynomials has some advantages over the monomial representation $$g(x)=\sum_{i=0}^{n-1}a_ix^i$$ described in the previous section.

First of all, once the Lagrange polynomials have been computed over a set of nodes $$x_i$$, computing the interpolating polynomial for a new set of function values $$f_i$$ is trivial, since these only need to be multiplied with the Lagrange polynomials, which are independent of the $$f_i$$.

Another advantage is that the representation can easily be extended if additional points are added. The Lagrange polynomial $$\ell_k^+(x)$$, obtained by adding a point $$x_{n+1}$$ to the interpolation, is

 * $$\ell_k^+(x) = \ell_k(x) \frac{x - x_{n+1}}{x_k - x_{n+1}}$$.

Only the new polynomial $$\ell_{n+1}^+(x)$$ would need to be re-computed from scratch.

In the monomial representation, adding a point would involve adding an extra line and column to the Vandermonde matrix and re-computing the solution.

 * Add a word on Barycentric interpolation to facilitate adding points.

Newton Interpolation
Given a set of $$n$$ function values $$f_i$$ evaluated at the nodes $$x_i$$, the Newton polynomial is defined as the sum

 * $$g(x) = \sum_{i=1}^{n} a_in_i(x)$$

where the $$n_i(x)$$ are the $$n$$ Newton basis polynomials defined by

 * {|cellpadding=2

An interpolation polynomial of degree n+1 can be easily obtained from that of degree n by just adding one more node point $$x_{n+1}$$ and adding a polynomial of degree n+1 to $$g(x)$$.
 * $$n_1(x)$$
 * $$1$$
 * $$n_i(x)$$
 * $$\prod_{k=1}^{i-1} (x - x_k)\quad \mbox{for } i > 1$$.
 * }
 * $$\prod_{k=1}^{i-1} (x - x_k)\quad \mbox{for } i > 1$$.
 * }
 * }

The Newton form of the interpolating polynomial is particularly suited to computations by hand, and underlies Neville's algorithm for polynomial interpolation. It is also directly related to the exact formula for the error term $$f_i - g(x_i)$$. Any good text in numerical analysis will prove this formula and fully specify Neville's algorithm, usually doing both via divided differences.

(Should link to error formula, divided differences and Neville's algorithm, adding articles where they don't exist)

Interpolation error
When interpolating a given function f by a polynomial of degree n at the nodes x0,...,xn we get the error

 * $$f(x) - p_n(x) = f[x_0,\ldots,x_n,x] \prod_{i=0}^n (x-x_i) $$

where
 * $$f[x_0,\ldots,x_n,x]$$

is the notation for divided differences.

If f is n + 1 times continuously differentiable on a closed interval I and $$p_n(x)$$ be a polynomial of degree at most n that interpolates f at n + 1 distinct points {xi} (i=0,1,...,n) in that interval. Then for each x in the interval there exists $$\xi$$ in that interval such that

 * $$ f(x) - p_n(x) = \frac{f^{(n+1)}(\xi)}{(n+1)!} \prod_{i=0}^n (x-x_i) $$

The above error bound suggests choosing the interpolation points xi such that the product | Π (x − xi) | is as small as possible.

Proof
Let's set the error term is

$$ R_n(x) = f(x) - p_n(x) $$

and set up a auxiliary function $$Y(t)$$ and the function is

$$ Y(t) = R_n(t) - \frac{R_n(x)}{W(x)} \ W(t) $$

where $$ W(t) = \prod_{i=0}^n (t-x_i) $$ and

$$ W(x) = \prod_{i=0}^n (x-x_i) $$

Since $$ x_i $$ are roots of function f and $$ p_n(x) $$, so we will have

$$ Y(x) = R_n(x) - \frac{R_n(x)}{W(x)} \ W(x) = 0 $$

and

$$ Y(x_i) = R_n(x_i) - \frac{R_n(x)}{W(x)} \ W(x_i) = 0 $$

Then $$Y(t)$$ has n+2 roots. From Rolle's theorem, $$Y^\prime(t)$$ has n+1 roots, then $$Y^{(n+1)}(t)$$ has one root $$\xi$$, where $$\xi$$ is in the interval I.

So we can get

$$ Y^{(n+1)}(t) = R_n^{(n+1)}(t) - \frac{R_n(x)}{W(x)} \ (n+1)! $$

Since $$p_n(x)$$ is a polynomial of degree at most n, then

$$ R_n^{(n+1)}(t) = f^{(n+1)}(t) $$

Thus

$$ Y^{(n+1)}(t) = f^{(n+1)}(t) - \frac{R_n(x)}{W(x)} \ (n+1)! $$

Since $$\xi$$ is the root of $$Y^{(n+1)}(t)$$, so

$$ Y^{(n+1)}(\xi) = f^{(n+1)}(\xi) - \frac{R_n(x)}{W(x)} \ (n+1)! = 0 $$

Therefore

$$ R_n(x) = f(x) - p_n(x) = \frac{f^{(n+1)}(\xi)}{(n+1)!} \prod_{i=0}^n (x-x_i) $$.

Piecewise Interpolation / Splines
B Splines

Extrapolation
Interpolation is the technique of estimating the value of a function for any intermediate value of the independent variable while the process of computing the value of the function outside the given range is called extrapolation.

Caution must be used when extrapolating, as assumptions outside the data region (linearization, general shape and slope) may breakdown.

title: Interpolation and Extrapolation


text:
User:Dr. Roy Schneemann

Roy Schneemann (born 27 Mai 1965) is a German visual artist. living in France. Roy Schneemann has created Abstract as well as Photorealistic Paintings, and also Photographs and Sculptures.

title: User:Dr. Roy Schneemann


text:
Wikipedia:Reference desk/Archives/Entertainment/2020 August 9

= August 9 =

Colin and Charles Farrell, actors
Were the Colin Farrell (not that Colin Farrell) and the Charles Farrell who were both in the film Oh! What a Lovely War related? Thank you, DuncanHill (talk) 16:03, 9 August 2020 (UTC)
 * Their IMDB biography pages  don't mention them being related.  Charles was born in Dublin but had moved to London by the time Colin was born in London, so it is conceivable that they were related and the short bios just don't mention it. --<IP_ADDRESS> (talk) 05:43, 10 August 2020 (UTC)

Phantom question
I saw a strip of the comic The Phantom in a Finnish newspaper. The entire strip was one single panel. I have a photograph of it but can't upload it here as it would violate copyright.

Anyway, here's a description. A woman is saying to a man: "You think you can play with Lamanda Luaga? Nomad, you don't know what you are doing!" There are, inexplicably to me, pictures of skulls on the edges of the panel.

What story is this panel from? J I P | Talk 16:43, 9 August 2020 (UTC)
 * You should upload the image to a file hosting site such as imgur and post the link here. --Viennese Waltz 09:14, 10 August 2020 (UTC)
 * Here you go: https://imgur.com/zp3yH9W . The strip is in Finnish, I have provided an English translation in this post. Ignore the top and bottom comics, they're gag-a-day strips from Zits and Viivi & Wagner. It's the middle one I'm asking about. J I P  | Talk 09:51, 10 August 2020 (UTC)
 * For what it's worth, the panel appears in this forum, and it seems the Portuguese title of the story is "ACERTO DE CONTAS COM O NÔMADE" and the English title should be A Reckoning with the Nomad, from 2018. --Wrongfilter (talk) 11:36, 10 August 2020 (UTC)
 * Thanks for the answers. It would be nice to know what the skulls mean. J I P  | Talk 11:52, 10 August 2020 (UTC)
 * Perhaps a reference to Skull Cave, or to the skull of the murderer of Christopher Walker's father? DuncanHill (talk) 16:07, 10 August 2020 (UTC)


text:
Fleming Blanchard McCurdy

Fleming Blanchard McCurdy, (February 17, 1875 – August 29, 1952) was a Canadian politician.

Born in Old Barns, Nova Scotia, he was elected to the House of Commons of Canada for the Nova Scotia riding of Shelburne and Queen's in the 1911 election as a Conservative. He was re-elected in the 1917 election for the riding of Colchester as a supporter of Sir Robert Laird Borden's Unionist government.

In 1916, he was one of the first parliamentarians to be appointed a Parliamentary Secretary, when he was appointed Parliamentary Secretary of Militia and Defence for Sam Hughes. He was also the Parliamentary Secretary of Soldiers' Civil Re-establishment. Upon his appointment to Borden's Cabinet in 1920 as Minister of Public Works he was required by the custom of the time to resign his seat and run in a by-election. By this point it was customary for Cabinet ministers running in by-elections to be acclaimed however, the newly formed United Farmers party contested the by-election with a United-Farmers/Labour candidate. McCurdy opted to face this challenge by running as a Nationalist Liberal rather than as a Conservative and was re-elected, though narrowly. It is possible he chose this banner as the Unionist Party had formally changed its name to the National Liberal and Conservative Party by this time or as a means of facing down the threat from a left-wing candidate. In any case, Blanchard ran the following year in the 1921 election as a Conservative and was defeated.

title: Fleming Blanchard McCurdy


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Erik López

Erik Nicolás López Samaniego (born 27 November 2001) is a Paraguayan professional footballer who plays as a forward for Olimpia in the Paraguayan Primera División.

Olimpia
Born in Asunción, López began his career in youth system of Olimpia. On 25 August 2019, López made his professional debut for Olimpia in the Primera División against Deportivo Santaní. He started and also scored his first goal in the 28th minute as Olimpia won 4–0. In the following two matches, López scored another two goals, one each against Deportivo Capiatá and San Lorenzo.

López finished his first professional season at Olimpia with 4 goals in 15 matches.

Atlanta United
On 18 July 2020, López signed with Major League Soccer club Atlanta United on a contract starting prior to the 2021 season. For the 2020 season, López would join Atlanta United 2, the reserve side of Atlanta United, in the USL Championship.

Loan to Banfield
On 22 February 2022, López was loaned to Banfield for the 2022 season.

Mutual termination
On August 4, 2023, Atlanta United and López agreed to a mutual termination of his contract.

International career
In 2020, López was called-in as part of the Paraguay squad for the CONMEBOL Pre-Olympic Tournament. He made his debut for the Paraguay under-23s on 19 January 2020 against Uruguay, starting in a 1–0 defeat.

Honours
Olimpia
 * Primera División: 2019 Torneo Clausura

title: Erik López