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Ninety-five Theses

The Ninety-five Theses or Disputation on the Power and Efficacy of Indulgences is a list of propositions for an academic disputation written in 1517 by Martin Luther, then a professor of moral theology at the University of Wittenberg, Germany. The Theses is retrospectively considered to have launched the Protestant Reformation and the birth of Protestantism, despite various proto-Protestant groups having existed previously. It detailed Luther's opposition to what he saw as the Roman Catholic Church's abuse and corruption by Catholic clergy, who were selling plenary indulgences, which were certificates supposed to reduce the temporal punishment in purgatory for sins committed by the purchasers or their loved ones.

In the Theses, Luther claimed that the repentance required by Christ in order for sins to be forgiven involves inner spiritual repentance rather than merely external sacramental confession. He argued that indulgences led Christians to avoid true repentance and sorrow for sin, believing that they could forgo it by obtaining an indulgence. These indulgences, according to Luther, discouraged Christians from giving to the poor and performing other acts of mercy, which he attributed to a belief that indulgence certificates were more spiritually valuable. Though Luther claimed that his positions on indulgences accorded with those of Pope Leo X, the Theses challenge a 14th-century papal bull stating that the pope could use the treasury of merit and the good deeds of past saints to forgive temporal punishment for sins. The Theses are framed as propositions to be argued in debate rather than necessarily representing Luther's opinions, but Luther later clarified his views in the Explanations of the Disputation Concerning the Value of Indulgences.

Luther sent the Theses enclosed with a letter to Albert of Brandenburg, Archbishop of Mainz, on 31 October 1517, a date now considered the start of the Reformation and commemorated annually as Reformation Day. Luther may have also posted the Ninety-five Theses on the door of All Saints' Church and other churches in Wittenberg, in accordance with University custom, at some point between 31 October and mid-November. The Theses were quickly reprinted and translated, and distributed throughout Germany and Europe. They initiated a pamphlet war with the indulgence preacher Johann Tetzel, which spread Luther's fame even further. Luther's ecclesiastical superiors had him tried for heresy, which culminated in his excommunication in 1521. Though the Theses were the start of the Reformation, Luther did not consider indulgences to be as important as other theological matters which would divide the church, such as justification by faith alone and the bondage of the will. His breakthrough on these issues would come later, and he did not see the writing of the Theses as the point at which his beliefs diverged from those of the Roman Catholic Church.

Background
Martin Luther, professor of moral theology at the University of Wittenberg and town preacher, wrote the Ninety-five Theses against the contemporary practice of the church with respect to indulgences. In the Roman Catholic Church, which was practically the only Christian church in Western Europe at the time, indulgences were part of the economy of salvation. In this system, when Christians sin and confess, they are forgiven and no longer stand to receive eternal punishment in hell, but may still be liable to temporal punishment. This punishment could be satisfied by the penitent's performing works of mercy. If the temporal punishment is not satisfied during life, it needs to be satisfied in Purgatory, a place believed by Catholics to exist between Heaven and Hell. By indulgence (which may be understood in the sense of "kindness"), this temporal punishment could be lessened. Under abuses of the system of indulgences, clergy benefited by selling indulgences and the pope gave official sanction in exchange for a fee.

Popes are empowered to grant plenary indulgences, which provide complete satisfaction for any remaining temporal punishment due to sins, and these were purchased on behalf of people believed to be in purgatory. This led to the popular saying, "As soon as the coin in the coffer rings, the soul from purgatory springs". Theologians at the University of Paris criticized this saying late in the 15th century. Earlier critics of indulgences included John Wycliffe, who denied that the pope had jurisdiction over Purgatory. Jan Hus and his followers had advocated a more severe system of penance, in which indulgences were not available. Johannes von Wesel had also attacked indulgences late in the 15th century. Political rulers had an interest in controlling indulgences because local economies suffered when the money for indulgences left a given territory. Rulers often sought to receive a portion of the proceeds or prohibited indulgences altogether, as Duke George did in Luther's Electoral Saxony.

In 1515, Pope Leo X granted a plenary indulgence intended to finance the construction of St. Peter's Basilica in Roma. It would apply to almost any sin, including adultery and theft. All other indulgence preaching was to cease for the eight years in which it was offered. Indulgence preachers were given strict instructions on how the indulgence was to be preached, and they were much more laudatory of the indulgence than those of earlier indulgences. Johann Tetzel was commissioned to preach and offer the indulgence in 1517, and his campaign in cities near Wittenberg drew many Wittenbergers to travel to these cities and purchase them, since sales had been prohibited in Wittenberg and other Saxon cities.

Luther also had a rather negative experience and idea with the indulgences connected to All Saints' Church, Wittenberg. By venerating the large collection of relics at the church, one could receive an indulgence. He had preached as early as 1514 against the abuse of indulgences and the way they cheapened grace rather than requiring true repentance. Luther became especially concerned in 1517 when his parishioners, returning from purchasing Tetzel's indulgences, claimed that they no longer needed to repent and change their lives in order to be forgiven of sin. After hearing what Tetzel had said about indulgences in his sermons, Luther began to study the issue more carefully, and contacted experts on the subject. He preached about indulgences several times in 1517, explaining that true repentance was better than purchasing an indulgence. He taught that receiving an indulgence presupposed that the penitent had confessed and repented, otherwise it was worthless. A truly repentant sinner would also not seek an indulgence, because they loved God's righteousness and desired the inward punishment of their sin. These sermons seem to have ceased from April to October 1517, presumably while Luther was writing the Ninety-five Theses. He composed a Treatise on Indulgences, apparently in early autumn 1517. It is a cautious and searching examination of the subject. He contacted church leaders on the subject by letter, including his superior, Bishop of Brandenburg, sometime on or before 31 October, when he sent the Theses to Archbishop Albert of Brandenburg.

Content
The first thesis states, "When our Lord and Master Jesus Christ said, 'Repent,' he willed the entire life of believers to be one of repentance." In the first few theses Luther develops the idea of repentance as the Christian's inner struggle with sin rather than the external system of sacramental confession. Theses 5–7 then state that the pope who Luther called the Vicar of Christ on earth can only release people from the punishments he has administered himself or through the church's system of penance, not the guilt of sin. The pope can only announce God's forgiveness of the guilt of sin in his name. In theses 14–29, Luther challenged common beliefs about purgatory. Theses 14–16 discuss the idea that the punishment of purgatory can be likened to the fear and despair felt by dying people. In theses 17–24 he asserts that nothing can be definitively said about the spiritual state of people in purgatory. He denies that the pope has any power over people in purgatory in theses 25 and 26. In theses 27–29, he attacks the idea that as soon as payment is made, the payer's loved one is released from purgatory. He sees it as encouraging sinful greed, and says it is impossible to be certain because only God has ultimate power in forgiving punishments in purgatory.

Theses 30–34 deal with the false certainty Luther believed the indulgence preachers offered Christians. Since no one knows whether a person is truly repentant, a letter assuring a person of his forgiveness is dangerous. In theses 35 and 36, he attacks the idea that an indulgence makes repentance unnecessary. This leads to the conclusion that the truly repentant person, who alone may benefit from the indulgence, has already received the only benefit the indulgence provides. Truly repentant Christians have already, according to Luther, been forgiven of the penalty as well as the guilt of sin. In thesis 37, he states that indulgences are not necessary for Christians to receive all the benefits provided by Christ. Theses 39 and 40 argue that indulgences make true repentance more difficult. True repentance desires God's punishment of sin, but indulgences teach one to avoid punishment, since that is the purpose of purchasing the indulgence.

In theses 41–47 Luther criticizes indulgences on the basis that they discourage works of mercy by those who purchase them. Here he begins to use the phrase, "Christians are to be taught..." to state how he thinks people should be instructed on the value of indulgences. They should be taught that giving to the poor is incomparably more important than buying indulgences, that buying an indulgence rather than giving to the poor invites God's wrath, and that doing good works makes a person better while buying indulgences does not. In theses 48–52 Luther takes the side of the pope, saying that if the pope knew what was being preached in his name he would rather St. Peter's Basilica be burned down than "built up with the skin, flesh, and bones of his sheep". Theses 53–55 complain about the restrictions on preaching while the indulgence was being offered.

In theses 56–66, Martin Luther criticizes the doctrine of the treasury of merit on which the doctrine of indulgences is based. He states that everyday Christians do not understand the doctrine and are being misled. For Luther, the true treasure of the church is the gospel of Jesus Christ. This treasure tends to be hated because it makes "the first last", in the words of Matthew 19:30 and 20:16. Luther uses metaphor and wordplay to describe the treasures of the gospel as nets to catch wealthy people, whereas the treasures of indulgences are nets to catch the wealth of men.

In theses 67–80, Luther discusses further the problems with the way indulgences are being preached, as he had done in the letter to Archbishop Albert. The preachers have been promoting indulgences as the greatest of the graces available from the church, but they actually only promote greed. He points out that bishops have been commanded to offer reverence to indulgence preachers who enter their jurisdiction, but bishops are also charged with protecting their people from preachers who preach contrary to the pope's intention. He then attacks the belief allegedly propagated by the preachers that the indulgence could forgive one who had violated the Virgin Mary. Luther states that indulgences cannot take away the guilt of even the lightest of venial sins. He labels several other alleged statements of the indulgence preachers as blasphemy: that Saint Peter could not have granted a greater indulgence than the current one, and that the indulgence cross with the papal arms is as worthy as the cross of Christ.

Luther lists several criticisms advanced by laypeople against indulgences in theses 81–91. He presents these as difficult objections his congregants are bringing rather than his own criticisms. How should he answer those who ask why the pope does not simply empty purgatory if it is in his power? What should he say to those who ask why anniversary masses for the dead, which were for the sake of those in purgatory, continued for those who had been redeemed by an indulgence? Luther claimed that it seemed strange to some that pious people in purgatory could be redeemed by living impious people. Luther also mentions the question of why the pope, who is very rich, requires money from poor believers to build St. Peter's Basilica. Luther claims that ignoring these questions risks allowing people to ridicule the pope. He appeals to the pope's financial interest, saying that if the preachers limited their preaching in accordance with Luther's positions on indulgences (which he claimed was also the pope's position), the objections would cease to be relevant. Luther closes the Theses by exhorting Christians to imitate Christ even if it brings pain and suffering. Enduring punishment and entering heaven is preferable to false security.

Luther's intent
The Theses are written as propositions to be argued in a formal academic disputation, though there is no evidence that such an event ever took place. In the heading of the Theses, Luther invited interested scholars from other cities to participate. Holding such a debate was a privilege Luther held as a doctor, and it was not an unusual form of academic inquiry. Luther prepared twenty sets of theses for disputation at Wittenberg between 1516 and 1521. Andreas Karlstadt had written a set of such theses in April 1517, and these were more radical in theological terms than Luther's. He posted them on the door of All Saints' Church, as Luther was alleged to have done with the Ninety-five Theses. Karlstadt posted his theses at a time when the relics of the church were placed on display, and this may have been considered a provocative gesture. Similarly, Luther posted the Ninety-five Theses on the eve of All Saints' Day, the most important day of the year for the display of relics at All Saints' Church.

Luther's theses were intended to begin a debate among academics, not a popular revolution, but there are indications that he saw his action as prophetic and significant. Around this time, he began using the name "Luther" and sometimes "Eleutherius", Greek for "free", rather than "Luder". This seems to refer to his being free from the scholastic theology which he had argued against earlier that year. Luther later claimed not to have desired the Theses to be widely distributed. Elizabeth Eisenstein has argued that his claimed surprise at their success may have involved self-deception and Hans Hillerbrand has claimed that Luther was certainly intending to instigate a large controversy. At times, Luther seems to use the academic nature of the Theses as a cover to allow him to attack established beliefs while being able to deny that he intended to attack church teaching. Since writing a set of theses for a disputation does not necessarily commit the author to those views, Luther could deny that he held the most incendiary ideas in the Theses.

Distribution and publication
On 31 October 1517, Luther sent a letter to the Archbishop of Mainz, Albert of Brandenburg, under whose authority the indulgences were being sold. In the letter, Luther addresses the archbishop out of a loyal desire to alert him to the pastoral problems created by the indulgence sermons. He assumes that Albert is unaware of what is being preached under his authority, and speaks out of concern that the people are being led away from the gospel, and that the indulgence preaching may bring shame to Albert's name. Luther does not condemn indulgences or the current doctrine regarding them, nor even the sermons which had been preached themselves, as he had not seen them firsthand. Instead he states his concern regarding the misunderstandings of the people about indulgences which have been fostered by the preaching, such as the belief that any sin could be forgiven by indulgences or that the guilt as well as the punishment for sin could be forgiven by an indulgence. In a postscript, Luther wrote that Albert could find some theses on the matter enclosed with his letter, so that he could see the uncertainty surrounding the doctrine of indulgences in contrast to the preachers who spoke so confidently of the benefits of indulgences.

It was customary when proposing a disputation to have the theses printed by the university press and publicly posted. No copies of a Wittenberg printing of the Ninety-five Theses have survived, but this is not surprising as Luther was not famous and the importance of the document was not recognized. In Wittenberg, the university statutes demand that theses be posted on every church door in the city, but Philip Melanchthon, who first mentioned the posting of the Theses, only mentioned the door of All Saints' Church. Melanchthon also claimed that Luther posted the Theses on 31 October, but this conflicts with several of Luther's statements about the course of events, and Luther always claimed that he brought his objections through proper channels rather than inciting a public controversy. It is possible that while Luther later saw the 31 October letter to Albert as the beginning of the Reformation, he did not post the Theses to the church door until mid-November, but he may not have posted them on the door at all. Regardless, the Theses were well known among the Wittenberg intellectual elite soon after Luther sent them to Albert.

The Theses were copied and distributed to interested parties soon after Luther sent the letter to Archbishop Albert. The Latin Theses were printed in a four-page pamphlet in Basel, and as placards in Leipzig and Nuremberg. In all, several hundred copies of the Latin Theses were printed in Germany in 1517. in Nuremberg translated them into German later that year, and copies of this translation were sent to several interested parties across Germany, but it was not necessarily printed.

Reaction
Albert seems to have received Luther's letter with the Theses around the end of November. He requested the opinion of theologians at the University of Mainz and conferred with his advisers. His advisers recommended he have Luther prohibited from preaching against indulgences in accordance with the indulgence bull. Albert requested such action from the Roman Curia. In Rome, Luther was immediately perceived as a threat. In February 1518, Pope Leo asked the head of the Augustinian Hermits, Luther's religious order, to convince him to stop spreading his ideas about indulgences. Sylvester Mazzolini was also appointed to write an opinion which would be used in the trial against him. Mazzolini wrote A Dialogue against Martin Luther's Presumptuous Theses concerning the Power of the Pope, which focused on Luther's questioning of the pope's authority rather than his complaints about indulgence preaching. Luther received a summons to Rome in August 1518. He responded with Explanations of the Disputation Concerning the Value of Indulgences, in which he attempted to clear himself of the charge that he was attacking the pope. As he set down his views more extensively, Luther seems to have recognized that the implications of his beliefs set him further from official teaching than he initially knew. He later said he might not have begun the controversy had he known where it would lead. The Explanations have been called Luther's first Reformation work.

Johann Tetzel responded to the Theses by calling for Luther to be burnt for heresy and having theologian Konrad Wimpina write 106 theses against Luther's work. Tetzel defended these in a disputation before the University of Frankfurt on the Oder in January 1518. 800 copies of the printed disputation were sent to be sold in Wittenberg, but students of the university seized them from the bookseller and burned them. Luther became increasingly fearful that the situation was out of hand and that he would be in danger. To placate his opponents, he published a Sermon on Indulgences and Grace, which did not challenge the pope's authority. This pamphlet, written in German, was very short and easy for laypeople to understand. Luther's first widely successful work, it was reprinted twenty times. Tetzel responded with a point-by-point refutation, citing heavily from the Bible and important theologians. His pamphlet was not nearly as popular as Luther's. Luther's reply to Tetzel's pamphlet, on the other hand, was another publishing success for Luther.

Another prominent opponent of the Theses was Johann Eck, Luther's friend and a theologian at the University of Ingolstadt. Eck wrote a refutation, intended for the Bishop of Eichstätt, entitled the Obelisks. This was in reference to the obelisks used to mark heretical passages in texts in the Middle Ages. It was a harsh and unexpected personal attack, charging Luther with heresy and stupidity. Luther responded privately with the Asterisks, titled after the asterisk marks then used to highlight important texts. Luther's response was angry and he expressed the opinion that Eck did not understand the matter on which he wrote. The dispute between Luther and Eck would become public in the 1519 Leipzig Debate.

Luther was summoned by authority of the pope to defend himself against charges of heresy before Thomas Cajetan at Augsburg in October 1518. Cajetan did not allow Luther to argue with him over his alleged heresies, but he did identify two points of controversy. The first was against the 58th thesis, which stated that the pope could not use the treasury of merit to forgive temporal punishment of sin. This contradicted the papal bull Unigenitus promulgated by Clement VI in 1343. The second point was whether one could be assured that one had been forgiven when one's sin had been absolved by a priest. Luther's Explanations on thesis seven asserted that one could based on God's promise, but Cajetan argued that the humble Christian should never presume to be certain of their standing before God. Luther refused to recant and requested that the case be reviewed by university theologians. This request was denied, so Luther appealed to the pope before leaving Augsburg. Luther was finally excommunicated in 1521 after he burned the papal bull threatening him to recant or face excommunication.

Legacy
The indulgence controversy set off by the Theses was the beginning of the Reformation, a schism in the Roman Catholic Church which initiated profound and lasting social and political change in Europe. Luther later stated that the issue of indulgences was insignificant relative to controversies which he would enter into later, such as his debate with Erasmus over the bondage of the will, nor did he see the controversy as important to his intellectual breakthrough regarding the gospel. Luther later wrote that at the time that he wrote the Theses, he remained a "papist", and he did not seem to think the Theses represented a break with established Roman Catholic doctrine. But it was out of the indulgences controversy that the movement which would be called the Reformation began, and the controversy propelled Luther to the leadership position he would hold in that movement. The Theses also made evident that Luther believed the church was not preaching properly and that this put the laity in serious danger. Further, the Theses contradicted the decree of Pope Clement VI, in 1343, that indulgences are the treasury of the church. This disregard for papal authority presaged later conflicts.

31 October 1517, the day Luther sent the Theses to Albert, was commemorated as the beginning of the Reformation as early as 1527, when Luther and his friends raised a glass of beer to commemorate the "trampling out of indulgences". The posting of the Theses was established in the historiography of the Reformation as the beginning of the movement by Philip Melanchthon in his 1548 Historia de vita et actis Lutheri. During the 1617 Reformation Jubilee, the centenary of 31 October was celebrated by a procession to the Wittenberg Church where Luther was believed to have posted the Theses. An engraving was made showing Luther writing the Theses on the door of the church with a gigantic quill. The quill penetrates the head of a lion symbolizing Pope Leo X. In 1668, 31 October was made Reformation Day, an annual holiday in Electoral Saxony, which spread to other Lutheran lands. 31 October 2017, the 500th Anniversary of Reformation Day, was celebrated with a national public holiday throughout Germany.

title: Ninety-five Theses


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Talk:Geometric algebra

Intro sentence is a barrage of jargon
I appreciate the effort that's gone into the article, and the desire for precision, but this intro paragraph is just not suitable for the first paragraph in a Wikipedia article as per MOS:INTRO. It's completely impenetrable to a non-expert.

 * In mathematics, the geometric algebra (GA) of a vector space with a quadratic form (usually the Euclidean metric or the Lorentz metric) is an algebra over a field, the Clifford algebra of a vector space with a quadratic form with its multiplication operation called the geometric product. The algebra elements are called multivectors, which contains both the scalars F and the vector space V.

I think this info could even make an appearance in paragraph 2, but paragraph 1 needs to be especially accessible to readers with no advanced mathematical training. It needs to be at a level more like the following, which could perhaps serve as a starting point for us to develop a better intro paragraph here:

 * In mathematics, a geometric algebra is a framework for describing properties of geometric objects in space, based on the central notions of the multivector and the geometric product. It provides an alternative to more widely-used approaches based on linear algebra or quaternions.

(Please excuse me if this isn't right; take it as a starting point for further refinement. I'm not an expert—only an amateur who has been learning about geometric algebra for the last couple of days.) --Doradus (talk) 13:43, 12 August 2021 (UTC)

 * Looking at the page's history, I notice that a year ago the intro was much more accessible. We seem to have injected additional jargon over the last few months.

 * The geometric algebra (GA) of a vector space is an algebra over a field, noted for its multiplication operation called the geometric product on a space of elements called multivectors, which contains both the scalars F and the vector space V.

 * This is still a bit dense, but if the non-expert glosses over such jargon as "an algebra over a field", you immediately find out that GA is noted for is "geometric product" that operates on multivectors. This was a much better intro for the non-expert. --Doradus (talk) 13:53, 12 August 2021 (UTC)
 * Go ahead and move stuff around, just try not to lose any info in the process. You are right in principle, the "experts" do have a tendency to "jargonize" the articles. With some justification they will say that it is "math" and it is up to the casual user to learn it. The Clifford page (a GA is a CliffordA viewed more geometrically and less algebraically) is even worse.Selfstudier (talk) 14:13, 12 August 2021 (UTC)
 * The problem is not jargon, but vagueness and inaccuracy: there is no usable definition in the whole article. your suggestion is better than the current first paragraph, but not correct since an algebraic structure is not a framework. I would suggest the following first paragraph, but I am unable to certify its correctness. If it is correct, be free to use it in the article.
 * In mathematics, the geometric algebra (GA) of a quadratic space (a vector space with a non-degenerate quadratic form) is an associative algebra, more precisely a Clifford algebra, that is built from the quadratic space, and solves the universal problem of maps from vector spaces to Clifford algebras. Its operation is called the geometric product, and the GA contains the vector space and its exterior algebra as subspaces. The geometric algebra allows carrying all operations of linear and multilinear algebra in a single algebraic structure (scalar product, exterior product, tensor product, determinant, tensor calculus, etc.).
 * D.Lazard (talk) 17:08, 12 August 2021 (UTC)
 * I've decided to be bold and craft an intro sentence much like the one from a year ago. I tried to retain all the info in the intro section, as per Selfstudier, but took a little of it out of that first sentence so it would be less daunting. I'm open to suggestions if anyone would like to make further changes. --Doradus (talk) 19:37, 14 August 2021 (UTC)

Reversion notation
Hi HongGong, in https://en.wikipedia.org/w/index.php?title=Geometric_algebra&diff=1016190290&oldid=1016055619 (reverted) and then in https://en.wikipedia.org/w/index.php?title=Geometric_algebra&diff=1030284754&oldid=1018780264 you changed the notation for reversion from dagger to tilde. I searched the talk page for an explanation, but could not find any. Your second edit comment merely says "The notation is correct." Notation is a convention. Since the dagger notation was defined in the article itself (just as the tilde notation now is), it was just as correct as the tilde notation (as long as it does not clash with other notation). I noticed that you've also changed a different article in a similar way (https://en.wikipedia.org/w/index.php?title=Rotor_(mathematics)&diff=1016188882&oldid=1001315838), with an edit comment of similar quality ("General cleanup"). Can you please explain what makes tilde better than dagger here? --RainerBlome (talk) 21:49, 3 December 2021 (UTC)

Meet
In the article the Grassmann exterior product is - be it between quotes - referred to as the "meet". Allthough both concepts use the same symbol, in my opinion there is no relation between the two. Madyno (talk) 16:46, 2 December 2022 (UTC)
 * It says that the meet is the dual of the Grassmann exterior product. -Bryan Rutherford (talk) 17:44, 2 December 2022 (UTC)

Universal/general algebra
I undid a change by, relating to defining the algebra as what Vaz&daRocha and Lounesto appear to term "universal". I'm not objecting to the idea that the properties as stated do not necessarily define a universal Clifford algebra in this sense (and we do want the universal case), but we should provide a clearer definition, rather than some wording that someone may only understand if they are familiar with universal properties. Lounesto does this by requiring that Cl(V, g) is not generated by any proper subspace of V, while it is by the whole of V (Lounesto 2001 Clifford Algebras and Spinors p. 190). This seems to be more understandable to a reader. One possible shortfall in this is that he does not seem to cover the case of a degenerate quadratic form in this claim (though I suspect that it still applies). Vaz&al prove that requiring that dim(Cl(V, g)) = 2dim V is sufficient for it to be universal (Vaz & da Rocha 2016 p. 58). Maybe we can use these ideas? —Quondum 14:46, 2 March 2024 (UTC)
 * My point with those edits is that just giving those properties is not a definition in itself. I'm perfectly fine if there's a better yet still elementary way to word it because most casual readers won't understand abstract algebra here. I suggest adding the "not generated by a proper subspace but by the whole space condition" and the sentence "It can be shown that these conditions uniquely characterize the geometric product".--Jasper Deng (talk) 19:38, 2 March 2024 (UTC)
 * I'll spend a bit of time on it. I'll model it on your suggestion initially, which I like.  I might include footnotes that may need trimming/rework.  —Quondum 21:33, 2 March 2024 (UTC)
 * I've tried to do this. It turned out that the condition that I gave above was sufficient only in the case that the quadratic form is nondegenerate, which is rather unsatisfying: some useful GAs have degenerate quadratic forms.  To keep the less abstract part uncomplicated, I've chosen to not call it "axioms", only "properties", and hence not needing them to definitively define the geometric product.  The result is a bit clumsy; feel free to refine.  —Quondum 01:05, 3 March 2024 (UTC)

Unhelpful example?
The lead currently contains a statement "... pseudovector quantities of vector calculus normally defined using a cross product, such as ... the magnetic field". I am not familiar with the magnetic field "normally" being defined in this way, although I'm aware if the Biot–Savart law, which is not only a cross product. The point is that few readers will find this helpful; examples such as this are meant to be familiar. Maybe this particular example (magnetic field) might be better removed? —Quondum 02:04, 13 March 2024 (UTC)

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

title: Talk:Geometric algebra


text:
Talk:Tiger I tank

Why can't think be at Tiger I (from where it was just moved)? Is there something else of that name? If not, I think that's the better title. (if, by the way, it does stay here, the redirects need to be fixed, because they all point to Tiger I and are hence broken). --Camembert

title: Talk:Tiger I tank


text:
Tiger II

The Tiger II was a German heavy tank of the Second World War. The final official German designation was 'Panzerkampfwagen Tiger Ausf''. B, often shortened to Tiger B'''. The ordnance inventory designation was Sd.Kfz. 182. (Sd.Kfz. 267 and 268 for command vehicles). It was also known informally as the Königstiger (German for Bengal tiger, lit. 'King Tiger'). Contemporaneous Allied soldiers usually called it the King Tiger or Royal Tiger.

The Tiger II was the successor to the Tiger I, combining the latter's thick armour with the armour sloping used on the Panther medium tank. It was the costliest German tank to produce at the time. The tank weighed almost 70 tonnes, and was protected by 100 to 185 mm of armour to the front. It was armed with the long barrelled (71 calibres) 8.8 cm KwK 43 anti-tank cannon. The chassis was also the basis for the Jagdtiger turretless Jagdpanzer anti-tank vehicle.

The Tiger II was issued to heavy tank battalions of the Army and the Waffen-SS. It was first used in combat by 503rd Heavy Panzer Battalion during the Allied invasion of Normandy on 11 July 1944; on the Eastern Front, the first unit to be outfitted with the Tiger II was the 501st Heavy Panzer Battalion. Due to heavy Allied bombing, only 492 were produced.

Development
Development started in 1937 with a design contract awarded to Henschel. Another design contract followed in 1939, given to Porsche. Both prototypes used the same turret design from Krupp. The main differences were in the hull, transmission, suspension and automotive features.

The Henschel version used a conventional hull design with sloped armour resembling the layout of the Panther tank. It had a rear-mounted engine and used nine steel-tired, eighty-centimetre-diameter overlapping road wheels per side with internal springing, mounted on transverse torsion bars, in a similar manner to the original Henschel-designed Tiger I. To simplify maintenance, however, the wheels were only overlapping without being interleaved—the full Schachtellaufwerk rubber-rimmed road-wheel system that had been in use on nearly all German half-tracks used the interleaved design, later inherited by the Tiger I and Panther.

The Porsche hull designs included a rear-mounted turret and a mid-mounted engine. The suspension was the same as on the Elefant tank destroyer. This had six road wheels per side mounted in paired bogies sprung with short longitudinal torsion bars that were integral to the wheel pair; this saved internal space and facilitated repairs. One Porsche version had a gasoline-electric drive (fundamentally identical to a Diesel-electric transmission, only using a gasoline-fueled engine as the prime mover), similar to a gasoline-electric hybrid but without a storage battery; two separate drivetrains in parallel, one per side of the tank, each consisting of a hybrid drive train; gasoline engine–electric generator–electric motor–drive sprocket. This method of propulsion had been used on the rejected Tiger (P) design, which had been rebuilt as Elefant, and in some US designs and was put into production in the French World War I era Saint-Chamond tank and post-World War I Char 2C. The Porsche suspension components were later used on a few of the later Jagdtiger tank destroyers. Another proposal was to use hydraulic drives; Dr. Porsche's unorthodox designs gathered little favour.

Design

Henschel won the design contract, and all Tiger IIs were produced by the firm. Two turret designs were used in production vehicles. The initial design is often misleadingly called the "Porsche" turret due to the misbelief that it was designed by Porsche for their Tiger II prototype; in fact it was the initial Krupp design for both prototypes. This turret had a rounded front and steeply sloped sides, with a difficult-to-manufacture curved bulge on the turret's left side to accommodate the commander's cupola. Fifty early turrets were mounted to Henschel hulls and used in action. In December 1943 the more common "production" turret, sometimes erroneously called the "Henschel" turret, was simplified with a significantly thicker flat face (which eliminated the shot trap caused by the curved face of the earlier turret), and less-steeply sloped sides, which avoided the need for a bulge for the commander's cupola, and added additional room for ammunition storage.

The turrets were designed to mount the 8.8 cm KwK 43 L/71 gun. Combined with the Turmzielfernrohr 9d (German "turret telescopic sight") monocular sight by Leitz, which all but a few early Tiger IIs used, it was a very accurate and deadly weapon. During practice, the estimated probability of a first-round hit on a 2 m high, 2.5 m wide target was 100 percent at 1000 m, 95–97 percent at 1500 m and 85–87 percent at 2000 m, depending on ammunition type. Recorded combat performance was lower, but still over 80 percent at 1,000 m, in the 60s at 1,500 m and the 40s at 2,000 m. Penetration of armoured plate inclined at 30 degrees was 202 and 132 mm at 100 m and 2000 m respectively for the Panzergranate 39/43 projectile (PzGr – armour-piercing shell), and 238 and 153 mm for the PzGr. 40/43 projectile between the same ranges. The Sprenggranate 43 (SpGr) high-explosive round was available for soft targets, or the Hohlgranate or Hohlgeschoss 39 (HlGr – HEAT or High-explosive anti-tank warhead) round, which had 90 mm penetration at any range, could be used as a dual-purpose munition against soft or armoured targets.

Powered turret traverse was provided by the variable speed Boehringer-Sturm L4S hydraulic motor, which was driven from the main engine by a secondary drive shaft. A high and a low speed setting was available to the gunner via a lever on his right. The turret could be rotated 360 degrees at 6º/second in low gear independent of engine rpm, at 19º/second – the same as with the Tiger I – with the high speed setting and engine at 2000 rpm, and over 36º/second at the maximum allowable engine speed of 3,000 rpm. The direction and speed of traverse was controlled by the gunner through foot pedals, whilst a high torque low speed (useful when on slopes) or low torque high speed final gearing could be selected via a control lever near his left arm. This system allowed for very precise control of powered traverse, a light touch on the pedal resulting in a minimum traverse speed of 0.1 deg/sec (360 degrees in 60 min), unlike in most other tanks of the time (e.g. US M4 Sherman or Soviet T-34 medium tanks) this allowed for fine laying of the gun without the gunner needing to use his traverse handwheel. If power was lost, such as when the tank ran out of fuel, the turret could be slowly traversed by hand, assisted by the loader who had an additional wheel, which could manually rotate the turret at a rate of one-half a degree per each revolution of the hand crank; a 20° turret rotation required 40 full cranks of the handwheel, and to turn the turret a full 360° the gunner would be required to crank the handwheel 720 full revolutions.

Like all German tanks, the Tiger II had a petrol engine; in this case the same 700 PS (690 hp, 515 kW) V-12 Maybach HL 230 P30 which powered the much lighter Panther and Tiger I tanks. The Tiger II was under-powered, like many other heavy tanks of World War II, and consumed a lot of fuel, which was in short supply for the Germans. The transmission was the Maybach OLVAR OG 40 12 16 Model B, giving eight forward gears and four reverse, which drove the steering gear. This was the Henschel L 801, a double radius design which proved susceptible to failure. Transverse torsion bar suspension supported the hull on nine axles per side. Overlapped 800 mm diameter road wheels with rubber cushions and steel tyres rode inside the tracks. Late production Tiger Is received the same wheels, which were one of the few interchangeable parts between the two tanks.

Like the Tiger I, each tank was issued with two sets of tracks: a normal "battle track" and a narrower "transport" version used during rail movement. The transport tracks reduced the overall width of the load and could be used to drive the tank short distances on firm ground. The crew were expected to change to normal battle tracks as soon as the tank was unloaded. Ground pressure was 0.76 kg/cm2 (10.8 psi).

Command variant
The command variant of the Tiger II was designated Panzerbefehlswagen Tiger ''Ausf. B''. It had two versions, Sd.Kfz. 267 and Sd.Kfz. 268. These had reduced ammunition capacity (only 63 rounds of 8.8 cm ammunition) to provide room for the extra radios and equipment, and had additional armour on the engine compartment. The Sd.Kfz. 267 was to have used FuG 8 and FuG 5 radio sets, with the most notable external changes being a 2 m rod antenna mounted on the turret roof and a Sternantenne D ("Star antenna D"), mounted on an insulated base (the 105 mm Antennenfuß Nr. 1), which was protected by a large armoured cylinder. This equipment was located on the rear decking in a position originally used for deep-wading equipment. The Sd.Kfz. 268 used FuG 7 and FuG 5 radios with a two-metre rod antenna mounted on the turret roof and a 1.4 metre rod antenna mounted on the rear deck.

Production
The Tiger II was developed late in the war and built in relatively small numbers. Orders were placed for 1,500 Tiger IIs—slightly more than the 1,347 Tiger I tanks produced—but production was heavily disrupted by Allied bombing raids. Among others, five raids between 22 September and 7 October 1944 destroyed 95 percent of the floor area of the Henschel plant. It is estimated that this caused the loss in production of 657 Tiger IIs. Only 492 units were produced: one in 1943, 379 in 1944, and 112 in 1945. Full production ran from mid-1944 to the end of the war. Each Tiger II cost 321 500 Reichsmark. The vehicle was the costliest German tank to produce at the time.

The Tiger II served as the basis for one production variant, the Jagdtiger casemated tank destroyer, and a proposed Grille 17/21/30/42 self-propelled mount for heavy guns which never reached production.

Proposed upgrades
The Maybach HL234, an engine born from attempting to convert the Maybach HL230 to fuel injection, would have increased the power from 700 to at least 800 PS (hp). In January 1945 the Entwicklungskommission Panzer unanimously decided that HL234 be immediately included in the engine design and procurement program. The ZF AK-7-200 gearbox was also explored as an alternative to the Maybach Olvar-B semi-automatic gearbox, but Waffenamt research and development department Wa Prüf 6 found that it offered inferior driving characteristics and so the Maybach Olvar-B was retained. There was also a program using the Simmering-Graz-Pauker Sla.16-cylinder diesel engine, but the war's constraint on supplies and Germany's capitulation resulted in the cancellation of this program. Krupp proposed mounting a new main weapon, the 10.5 cm KwK L/68. Wa Prüf 6 did not support this as the Heer had not accepted the cannon. Other suggested improvements included stabilised sights, a stabilised main gun, an automatic ammunition feed, a Carl Zeiss AG stereoscopic rangefinder, heated crew compartment, stowage for an additional 12 rounds, and an overpressure and air filtration system to protect against poison gas. However, these also never got beyond the proposal stage or did not enter production before the war ended.

Specifications

 * Gearbox: Maybach OLVAR OG 40 12 16 B (eight forward and four reverse)
 * Radio: FuG 5, Befehlswagen (command tank) version: FuG 8 (Sd.Kfz. 267), FuG 7 (Sd.Kfz. 268)
 * Ammunition:
 * 8.8 cm – 80 rounds (early turret), 86 rounds (main production turret), usually 50% PzGr 39/43 and 50% SprGr 43, sometimes with a limited number of PzGr 40/43, or with the SprGr replaced by HlGr
 * 7.92mm – up to 5,850 rounds
 * Gun Sight: Turmzielfernrohr 9b/1 (TZF 9b/1) binocular to May 1944, then the 9d (TZF 9d) monocular.

Organisation
Apart from research, training, and a five-tank attachment to the Panzer Lehr, the Tiger II was only issued to heavy tank battalions (schwere Panzer-Abteilungen) of the German Army (Heer), or Waffen-SS.

A standard battalion (Abteilung) comprised 45 tanks:

Units that used the Tiger II were as follows:
 * Heer: (s.H.Pz.Abt) 501, 502, 503, 504, 505, 506, 507, 508, 509, 510, 511
 * SS: (s.SS.Pz.Abt) 501, 502, 503

Reliability and mobility

Early Tiger IIs proved unreliable, owing principally to leaking seals and gaskets, an overburdened drive train originally intended for a lighter vehicle, and teething problems with the final drive and steering unit, both of which had been newly designed for the Tiger II. The final drive unit and the double radius steering gear were initially particularly prone to failures.

The new double-link track proved to be vulnerable to sideways stresses when the tank was driving on uneven terrain, as well as causing only every other sprocket tooth to engage with the track, leading to their rapid wear and potentially damaging the final drive. The inspector general of panzer troops, Wolfgang Thomale, said in a briefing on November 4, 1944, "These complaints could be traced back to the new track, which, although a considerable production simplification, on the other hand entails a greater susceptibility of the Tiger." The engagement of only every second sprocket tooth was causing “sudden jerks in the final drive, which cannot withstand these blows".

Henschel's chief designer, Erwin Aders, wrote, "The failure occurred because the Tiger II went into production without considering the test results." Lack of crew training could amplify this problem; drivers originally given only limited training on other tanks were often sent directly to operational units already on their way to the front.

The Schwere Heeres Panzer Abteilung 501 arrived on the Eastern Front with only eight out of 45 tanks operational; these faults were mostly due to final drive failures. The first five Tiger IIs delivered to the Panzer Lehr Division broke down before they could be used in combat, and were destroyed to prevent capture.

Henschel worked closely with crews to solve the problems, and with the introduction of modified seals, gaskets, drive train components and a new track and sprocket wheel design, as well as improved driver training and sufficient maintenance, the Tiger II could be maintained in a satisfactory operational condition. Statistics from 15 March 1945 show reliability rates of 59 percent for the Tiger, almost equal to the 62 percent of the Panzer IV and better than the 48 percent of the Panther that were operational by this period.

The s.H.Pz.Abt 503 noted in an after-action report during operations in Hungary, November 1944:

"...The battalion went into action in two battle groups with two different divisions on two different days. Provided the assault was successful in penetrating into the enemy rear, the battalion would then reunite. Both groups were extraordinarily successful. From 19-23 October 1944, 120 anti-tank guns and 19 guns were destroyed. The extremely tough and steadfast enemy (penal battalions) was shaken to the core by the energetic assault and his communications to the rear thrown into total confusion by the destruction of various columns and a transport train which, in the final analysis, forced the Russian Sixth Army from the Debrecen area. The total distance of about 250 kilometers covered during the operation was accomplished essentially without mechanical failure. The Tiger II proved itself extremely well, both in its armor and from a mechanical perspective. Vehicles which received up to twenty hits without becoming disabled were not uncommon ... In summary, the Tiger II has proven itself in every way and is a weapon that the enemy fears. When the formation is used as a single, unified entity and is employed in accordance with proper tactics, it always brings decisive success..."

Notwithstanding its initial reliability problems, the Tiger II was remarkably agile for such a heavy vehicle. Contemporary German records and testing results indicate that its tactical mobility was as good as or better than most German or Allied tanks.

Lt Col H.A. Shields of the 66th Armored Regiment reported in 1945:

"Wherever we have seen Tiger or Panther tanks, they have not demonstrated any inferior maneuverability. Near Puttendorf several Royal Tiger tanks were encountered. These Royal Tigers were able to negotiate very soft ground and their tracks did not sink in soft ground as did our own."

Combat history
The first combat use of the Tiger II was by the 1st Company of the 503rd Heavy Panzer Battalion (s.H.Pz.Abt. 503) during the Battle of Normandy, opposing the Canadian offensive Operation Atlantic between Troarn and Demouville on 18 July 1944. Two were lost in combat, while the company commander's tank became irrecoverably trapped after falling into a bomb crater created during Operation Goodwood.

On the Eastern Front, it was first used on 12 August 1944 by the 501st Heavy Panzer Battalion (s.H.Pz.Abt. 501) resisting the Lvov–Sandomierz Offensive. It attacked the Soviet bridgehead over the Vistula River near Baranów Sandomierski. On the road to Oględów, three Tiger IIs were destroyed in an ambush by a few T-34-85s. Because these German tanks suffered ammunition explosions, which caused many crew fatalities, main gun rounds were no longer allowed to be stowed within the turret, reducing capacity to 68. Up to fourteen Tiger IIs of the 501st were destroyed or captured in the area between 11 and 14 August to ambushes and flank attacks by both Soviet T-34-85 and IS-2 tanks, and ISU-122 assault guns in inconvenient sandy terrain. The capture of three operational Tiger IIs allowed the Soviets to conduct tests at Kubinka and to evaluate its strengths and weaknesses

On 15 October 1944, Tiger IIs of 503rd Heavy Panzer Battalion played a crucial role during Operation Panzerfaust, supporting Otto Skorzeny's troops in taking the Hungarian capital of Budapest, which ensured that the country remained with the Axis until the end of the war. The 503rd then took part in the Battle of Debrecen. The 503rd remained in the Hungarian theater of operations for 166 days, during which time it accounted for at least 121 Soviet tanks, 244 anti-tank guns and artillery pieces, five aircraft and a train. This was set against the loss of 25 Tiger IIs; ten were knocked out by Soviet troops and burned out, two were sent back to Vienna for a factory overhaul, while thirteen were blown up by their crews for various reasons, usually to prevent them from falling into enemy hands.

The Tiger II was also used in significant numbers, distributed into four heavy panzer battalions, during the Ardennes Offensive (also known as the 'Battle of the Bulge') of December 1944. At least 150 Tiger IIs were present, nearly a third of total production; most were lost over the course of the offensive.

Some Tiger IIs were also present during the Soviet Vistula–Oder and East Prussian Offensives in January 1945, as well as the German Lake Balaton Offensive in Hungary in March 1945, the Battle of the Seelow Heights in April 1945, and the Battle of Berlin at the end of the war.

The 103rd SS Heavy Panzer Battalion (s.SS Pz.Abt. 503) claimed approximately 500 kills in the period from January to April 1945 on the Eastern Front for the loss of 45 Tiger IIs (most of which were abandoned and destroyed by their own crews after mechanical breakdowns or for lack of fuel).

Gun and armour performance

The heavy armour and powerful long-range gun gave the Tiger II an advantage against all opposing Western Allied and Soviet tanks attempting to engage it from head on. This was especially true on the Western Front where, until the arrival of the few M26 Pershings in 1945 and the few M4A3E2 Sherman "Jumbo" assault tanks with additional armour that were scattered around Europe after D-Day, as well as a few late Churchill models, neither the British nor US forces brought heavy tanks into service. A Wa Prüf 1 report estimated that the Tiger II's frontal aspect was impervious to the Soviet 122 mm D-25T, one of the largest calibre tank guns of the war. Soviet testing found that the frontal glacis could be destroyed only by firing 3–4 shots at the weld joints from the ranges of 500–600m. Weld joints were found to be inferior quality to the Tiger I and Panther. An R.A.C 3.d. document of February 1945 estimated that the British (76.2 mm) QF 17-pounder gun, using armour-piercing discarding sabot shot was theoretically capable of penetrating the front of the Tiger II's turret and nose (lower front hull) at 1100 and 1200 yd respectively although, given the lack of a stated angle, this was presumably at the ideal 90 degrees and in combat the Tiger II was never penetrated frontally by the QF 17-Pounder.

As a result of its thick frontal armour, flanking manoeuvres were most often used against the Tiger II to attempt a shot at the thinner side and rear armour, giving a tactical advantage to the Tiger II in most engagements. Moreover, the main armament of the Tiger II was capable of knocking out any Allied tank frontally at ranges exceeding 2.5 km, well beyond the effective range of Allied tank guns.

Soviet wartime testing
During August 1944, two Tiger Ausf B tanks were captured by the Soviets near Sandomierz, and were soon moved to the testing grounds at Kubinka. During the transfer, the two tanks suffered from mechanical breakdowns. The cooling system was insufficient for the excessively hot weather, causing overheated engines and gearbox failure. The right suspension of one of the tanks had to be completely replaced, and its full functionality could not be re-established. The tank broke down again every 10–15 km. The 8.8 cm KwK 43 gave positive results in penetration and accuracy, which were on par with the 122 mm D-25T. It proved capable of passing completely through its "colleague", a Tiger Ausf B's turret at a range of 400 m. The armour of one vehicle was tested by firing at it with shells between 100 and 152 mm calibre. The welding was, despite careful workmanship, significantly worse than on similar designs. As a result, even when shells did not penetrate the armour, there was often a large amount of spalling from the inside of the plates, which damaged the transmission and rendered the tank inoperable. Further testing showed that the armour plate was inferior quality to earlier German tanks such as the Tiger I and Panther. Lab testing found the plates lacked molybdenum (ascribed to a loss of supply, being replaced by vanadium), resulting in low malleability.

The expanded firing test states that the АР projectiles from the 100 mm BS-3 and 122 mm A-19 gun penetrated a Tiger Ausf B's turret at ranges of 1000–1500 metres. However, the firing test against the turret front was conducted after removal of the gun and mantlet, and penetrations were close to openings such as vision slits and the gun location. The penetrations to the right gun opening occurred after previous 100 mm projectile penetration hits or armour damage. The 100 mm BS-3 and 122 mm A-19 could also penetrate the weld joints of the front hull at ranges of 500–600 metres after 3–4 shots.

Surviving vehicles

The only working example is displayed at the Musée des Blindés, Saumur, France. It has the production turret and is accessible to the public. This tank belonged to the 1st Company, 101st SS Heavy Panzer Battalion. It was believed to have been abandoned by its crew on 23 August 1944, due to engine problems, at Brueil-en-Vexin, near Mantes-la-Jolie. It was salvaged by the French Army in September 1944 and then stored in a factory in Satory before being transferred to the museum in 1975. It was believed to have had turret number 123, but Colonel Michel Aubry, the founder of the museum, decided to put 233 on the turret in honour of the Tiger II that destroyed his Sherman tank at the end of the war. Unlike other captured German vehicles, this Tiger II was never used by the French Army. Other survivors include:

 * The Tank Museum, Dorset, UK: Tiger II with early production turret is on display. This vehicle was the second soft steel prototype made and did not see active service.
 * Defence Academy of the United Kingdom, Shrivenham, UK: Tiger II (production turret). This vehicle was from s.SS Pz.Abt. 501, with hull number 280093, turret number 104, and has a comprehensive coating of Zimmerit. It was claimed by Sergeant Roberts of A Squadron, 23rd Hussars, 11th Armoured Division in a Sherman tank near Beauvais, although it had already been disabled and abandoned by its crew following damage to its tracks and final drive. This item is currently on display at The Tank Museum, in Dorset, UK.
 * The Wheatcroft Collection, Leicestershire, UK. A private collector, Kevin Wheatcroft, is about to start a restoration/rebuild of a complete Tiger II. The project will include parts from many individual Tiger IIs, but many parts will be of new manufacture. Wheatcroft has stated that he has 70–80% of the original parts needed for a reconstruction and more parts are sourced continuously. Known and shown parts are a complete front glacis plate, 8.8 cm KwK 43 main armament, engine deck plates, approx. 1/3 hull (rear) in one part, a set of tracks, and approx. 2/3 of the left-side hull plate in two parts. The aim of the project is a complete Tiger II in running order.
 * Deutsches Panzermuseum, Munster, Germany: Tiger II (production turret), hull number 280101. Originally bearing turret number 121 from s.SS.Pz.Abt 501, it was restored with a different number for unknown reasons.
 * Mantes-la-Jolie, France. A more or less complete, but wrecked, Tiger II (production turret) is buried under regional road 913. Parts of the turret were recovered in a limited exploratory excavation in 2001. Further excavation halted for financial reasons. There are plans to fully excavate and restore this Tiger II for a Vexin battle memorial.
 * Kubinka Tank Museum, Russia: Tiger II (production turret) with turret number 002 (502) captured at Oględów by the Red Army.
 * December 44 Museum, La Gleize, Belgium: A cosmetically restored Tiger II (production turret), hull number 280273, built in October 1944. Turret number 213 from s.SS Pz.Abt 501. Displayed at the entrance to December 44 Museum Collections, a museum devoted entirely to the Battle of the Bulge. This tank was abandoned in La Gleize on 24 December 1944, where the advance of Kampfgruppe Peiper was halted. The front part, about 1/3, of the gun barrel is restored with a Panther gun barrel and muzzle brake. It also has restored mudguards. It is stripped of exterior and internal fittings and most of the torsion bars are broken, but it still has its gearbox and engine in place.
 * U.S. Army Armor & Cavalry Collection, Fort Moore, Georgia, United States: Tiger II (production turret), hull number 280243, built in September 1944. Turret number 332 from s.SS Pz.Abt. 501. Captured during the Battle of the Bulge by Sgt. Glenn D. George of the 740th Tank Battalion of the 1st US Army on December 24, 1944. The left side was cut open for educational purposes at the Aberdeen Proving Ground in the late 1940s. Was on display at the former "Patton Museum of Cavalry & Armor, Fort Knox KY, then under BRAC transferred to Fort Benning as Fort Moore was then known.
 * Schweizerisches Militärmuseum Full, Switzerland. This Tiger II (production turret) was previously displayed in the Thun Tank Museum, and was loaned to the Schweizerisches Militärmuseum Full in September 2006). This tank was given to Switzerland by France after the war. Hull number 280215 from s.H.Pz.Abt 506. As of 2021, it is in the process of being restored to working order.

Tanks of comparable role, performance and era

 * Soviet IS-3 heavy tank - entered service in 1945
 * United States T26E4 "Super Pershing" heavy tank
 * French ARL 44 - produced and served in limited numbers in the late 1940s and early 1950s
 * French AMX-50 - several prototypes produced in the late 1940s and early 1950s

title: Tiger II


text:
Talk:Celestial Legend Ceres

What is it? A comic book? -- Zoe

I have no clue. Sounds like it might be an anime or manga series tho. Can anyone elaborate??? KJ

It's a manga, sorry for the unclear stuff. I'll edit accordingly. Nikki

title: Talk:Celestial Legend Ceres


text:
Kara-Khanid Khanate

The Kara-Khanid Khanate, also known as the Karakhanids, Qarakhanids, Ilek Khanids or the Afrasiabids , was a Karluk Turkic khanate that ruled Central Asia from the 9th to the early 13th century. The dynastic names of Karakhanids and Ilek Khanids refer to royal titles with Kara Khagan being the most important Turkic title up until the end of the dynasty.

The Khanate conquered Transoxiana in Central Asia and ruled it independently between 999 and 1089. Their arrival in Transoxiana signaled a definitive shift from Iranic to Turkic predominance in Central Asia, yet the Kara-khanids gradually assimilated the Perso-Arab Muslim culture, while retaining some of their native Turkic culture. The Khanate split into the Eastern and Western Khanates in the 1040s. In the late 11th century, they came under the suzerainty of the Seljuk Empire followed by the Qara Khitai (Western Liao dynasty) who defeated the Seljuks in the Battle of Qatwan in 1141. The Eastern Khanate ended in 1211, and the Western Khanate was extinguished by the Khwarazmian Empire in 1212.

The capitals of the Kara-Khanid Khanate included Kashgar, Balasagun, Uzgen and Samarkand. The history of the Kara-Khanid Khanate is reconstructed from fragmentary and often contradictory written sources, as well as studies on their coinage.

Names
The term Karakhanid was derived from Qara Khan or Qara Khaqan, the foremost title of the rulers of the dynasty. The word "Kara" means "black" and also "courageous" from Old Turkic (𐰴𐰺𐰀) and khan means ruler. The term was devised by European Orientalists in the 19th century to describe both the dynasty and the Turks ruled by it.
 * Arabic Muslim sources called this dynasty al-Khaqaniya ("That of the Khaqans") or al Muluk al-Khaniyya al-Atrak (The Khanal kings of the Turks).
 * In his linguistic treatise Dīwān Lughāt al-Turk, Mahmud al-Kashgari, a native-born Karakhanid, listed two endonyms: "Khāqānī Turks" or just "Turks", the latter he also used to denote Turkic peoples in general.
 * Persian sources often used the term Al-i Afrasiyab  based on a supposed link to the legendary though actually unrelated King Afrasiab of pre-Islamic Transoxania. Kashgari refers to him as Alp Er Tunga.
 * They are also referred to as Ilek Khanids or Ilak Khanids in Persian.
 * Chinese sources refer to this dynasty as Kalahan  or Heihan  (, literally "Black Khan") or Dashi (, a term for Arabs that extends to Muslims in general).

Origin
The Kara-Khanid Khanate originated from a confederation formed some time in the 9th century by Karluks, Yagmas, Chigils, Tuhsi, and other peoples living in Zhetysu, Western Tian Shan (modern Kyrgyzstan), and Western Xinjiang around Kashgar. 10th-century Arab historian Al-Masudi listed two "Khagan of Khagans" of the Karluk horde: Sanah, a possible rendition of Ashina (compare Śaya (also by al-Masudi), Aś(i)nas (al-Tabari), Ānsa (Hudud al-'Alam), and Śaba (Ibn Khordadbeh) ), and Afrasiab, whom 11th-century Karakhanid scholar Mahmud al-Kashgari identified with Turkic king Alp Er Tunga, the legendary progenitor of the Karakhanid ruling dynasty. Furthermore, Kara-khanid heads of state claimed the title khagan, which indicates that they may have been descended from the Ashina. Even so, the tribal origin of Bilge Kul Qadir Khan, the first Kara-Khan, is still unknown: if Bilge Kul Qadir descended from the Karluk Yabghus, then he indeed belonged to the Ashina dynasty as they did; if Bilge Kul Qadir descended from the Yagma (as suggested by Vasily Bartold), then he did not, considering that the Hudud al-'Alam stated that "Their [Yagmas'] king is from the family of the Toġuzġuz kings", that Ashina tribe was not listed among the Toquz Oghuz (Ch. 九姓 Jĭu Xìng "Nine Surnames") in Chinese-language sources and that early Uyghur khagans belonged to the Yaglakar clan of Toquz Oghuz and later Uyghur khagans belonged to the Ädiz clan. Alternatively, Bilge Kul Qadir might belong to the Eðgiş or Chigils.

Early history
The Karluks were a nomadic people from the western Altai Mountains who moved to Zhetysu (Semirechye). In 742, the Karluks were part of an alliance led by the Basmyl and Uyghurs that rebelled against the Göktürks and led to the demise of the Second Turkic Khaganate (682–744). In the realignment of power that followed, the Karluks were elevated from a tribe led by an Elteber to one led by a yabghu, which was one of the highest Turkic dignitaries and also implies membership in the Ashina clan in whom the "heaven-mandated" right to rule resided. The Karluks and Uyghurs later allied themselves against the Basmyl, and within two years they toppled the Basmyl khagan. The Uyghur yabghu became khagan and the Karluk leader yabghu. This arrangement lasted less than a year. Hostilities between the Uyghur and Karluk forced the Karluk to migrate westward into the western Turgesh lands.

By 766 the Karluks had forced the submission of the Turgesh and they established their capital at Suyab on the Chu River. The Karluk confederation by now included the Chigil and Tukshi tribes who may have been Türgesh tribes incorporated into the Karluk union. The Karluks converted to Nestorian Christianity at the end of the 8th century CE, about 15 years after they established themselves in the Semerich'e region. This was the first time the Church of the East received such major sponsorship by an eastern power. Remains of a Nestorian church have been found in the Karluk capital of Suyab, as well as hundreds of tomstones with Nestorian Syriac inscriptions in the Semerich'e region.

By the mid-9th century, the Karluk confederation had gained control of the sacred lands of the Western Türks after the destruction of the Uyghur Khaganate by the Old Kirghiz. Control of sacred lands, together with their affiliation with the Ashina clan, allowed the Khaganate to be passed on to the Karluks along with domination of the steppes after the previous Khagan was killed in a revolt.

During the 9th century southern Central Asia was under the rule of the Samanids, while the Central Asian steppe was dominated by Turkic nomads such as the Pechenegs, the Oghuz Turks, and the Karluks. The domain of the Karluks reached as far north as the Irtysh and the Kimek confederation, with encampments extending to the Chi and Ili rivers, where the Chigil and Tukshi tribes lived, and east to the Ferghana valley and beyond. The area to the south and east of the Karluks was inhabited by the Yagma. The Karluk center in the 9th and 10th centuries appears to have been at Balasagun on the Chu River. In the late 9th century the Samanids marched into the steppes and captured Taraz, one of the headquarters of the Karluk khagan, and a large church was transformed into a mosque.

Formation of the Kara-Khanid Khanate (840 CE)
During the 9th century, the Karluk confederation (including three chief tribes: the Bulaq (Mouluo 謀落 / Moula 謀剌), Taşlïk (Tashili 踏實力), and Sebek (Suofu 娑匐), along with Chigils, Charuks, Barskhans, Khalajes, Azkishi and Tuhsis (the last three being possibly remnants of Türgesh  ) and the Yaghma, possible descendants of the Toquz Oghuz, joined forces and formed the first Karluk-Karakhanid khaganate. The Chigils appear to have formed the nucleus of the Karakhanid army. The date of its foundation and the name of its first khan is uncertain, but according to one reconstruction, the first Karakhanid ruler was Bilge Kul Qadir Khan.

The rulers of the Karakhanids were likely to be from the Chigil and Yaghma tribes – the Eastern Khagan bore the title Arslan Qara Khaqan (Arslan "lion" was the totem of the Chigil) and the Western Khagan the title Bughra Qara Khaqan (Bughra "male camel" was the totem of the Yaghma). The names of animals were a regular element in the Turkic titles of the Karakhanids: thus Aslan (lion), Bughra (camel), Toghan (falcon), Böri (wolf), and Toghrul or Toghrïl (a bird of prey). Under the Khagans were four rulers with the titles Arslan Ilig, Bughra Ilig, Arslan Tegin and Bughra Tegin. The titles of the members of the dynasty changed with their position, normally upwards, in the dynastic hierarchy.

Conversion to Islam (c. 934 CE)
In the mid-10th century the Kara-Khanids converted to Islam and adopted Muslim names and honorifics, but retained Turkic regnal titles such as Khan, Khagan, Ilek (Ilig) and Tegin. Later they adopted the Arab titles sultan and sultān al-salātīn ("Sultan of Sultans"). According to the Ottoman historian known as Munajjim-bashi, a Karakhanid prince named Sultan Satuq Bughra Khan was the first of the khans to convert. After conversion, he obtained a fatwa which permitted him in effect to kill his presumably-still-pagan father, after which he conquered Kashgar (of the old Shule Kingdom). Later, in 960, according to Muslim historians Ibn Miskawaih and Ibn al-Athir, there was a mass conversion of the Turks (reportedly "200,000 tents of the Turks"), and circumstantial evidence suggests these were the Karakhanids.

Conquest of Transoxiana
The grandson of Satuk Bughra Khan, Hasan b. Sulayman (or Harun) (title: Bughra Khan) attacked the Samanids in the late 10th century. Between 990 and 992, Hasan took Isfijab, Ferghana, Ilaq, Samarkand, and the Samanid capital Bukhara. However, Hasan Bughra Khan died in 992 due to an illness, and the Samanids returned to Bukhara.

Hasan's cousin Ali b. Musa (title: Kara Khan or Arslan Khan) resumed the campaign against the Samanids, and by 999 Ali's son Nasr had taken Chach, Samarkand, and Bukhara. The Samanid domains were divided between the Ghaznavids, who gained Khorasan and Afghanistan, and the Karakhanids, who received Transoxiana. The Oxus River thus became the boundary between the two rival empires.

The Karakhanid state was divided into appanages (Ülüş system), as was common of Turkic and Mongol nomads. The Karakhanid appanages were associated with four principal urban centers, Balasagun (then the capital of the Karakhanid state) in Zhetysu, Kashgar in Xinjiang, Uzgen in Fergana, and Samarkand in Transoxiana. The dynasty's original domains of Zhetysu and Kasgar and their khans retained an implicit seniority over those who ruled in Transoxiana and Fergana. The four sons of Ali (Ahmad, Nasr, Mansur, Muhammad) each held their own independent appanage within the Karakhanid state. Nasr, the conqueror of Transoxiana, held the large central area of Transoxiana (Samarkand and Bukhara), Fergana (Uzgen) and other areas, although after his death his appanage was further divided. Ahmad held Zhetysu and Chach and became the head of the dynasty after the death of Ali. The brothers Ahmad and Nasr conducted different policies towards the Ghaznavids in the south – while Ahmad tried to form an alliance with Mahmud of Ghazna, Nasr attempted to expand unsuccessfully into Ghaznavid territory.

Ahmad was succeeded by Mansur, and after the death of Mansur, the Hasan Bughra Khan branch of the Karakhanids became dominant. Hasan's sons Muhammad Toghan Khan II, and Yusuf Kadir Khan who held Kashgar, became in turn the head of the Karakhanid dynasty. The two families, i.e., the descendants of Ali Arslan Khan and Hasan Bughra Khan, would eventually split the Karakhanid Khanate in two.

In 1017–1018, the Karakhanids repelled an attack by a large mass of nomadic Turkic tribes in what was described in Muslim sources as a great victory. Around the same time, the Kara-Khanid ruler Ilig Khan reached an agreement with Mahmud of Ghazni, in which they agreed to partition former Samanid territory along the Oxus river.

Conquest of western Tarim Basin
The Islamic conquest of the Buddhist cities east of Kashgar began when the Karakhanid Sultan Satuq Bughra Khan converted to Islam in 934 and then captured Kashgar. He and his son directed endeavors to proselytize Islam among the Turks and engage in military conquests. In the mid-10th century, Satuq's son Musa began to put pressure on Khotan, and a long period of war between Kashgar and the Kingdom of Khotan ensued. Satok Bughra Khan's nephew or grandson Ali Arslan was said to have been killed by Buddhists during the war; during the reign of Ahmad b. Ali, the Karakhanids also engaged in wars against non-Muslims to the east and northeast.

Muslim accounts tell the tale of the four imams from Mada'in city (possibly now in Iraq) who travelled to help Yusuf Qadir Khan, the Qarakhanid leader, in his conquest of Khotan, Yarkend, and Kashgar. The "infidels" were said to have been driven towards Khotan, but the four Imams were killed. In 1006, Yusuf Qadir Khan of Kashgar conquered the Kingdom of Khotan, ending Khotan's existence as an independent state.

The conquest of the western Tarim Basin which includes Khotan and Kashgar is significant in the eventual Turkification and Islamification of the Tarim Basin, and modern Uyghurs identify with the Karakhanids even though the name Uyghur was taken from the Manichaean Uyghur Khaganate and the Buddhist state of Qocho.

Division of the Kara-Khanid Khanate
Early in the 11th century the unity of the Karakhanid dynasty was fractured by frequent internal warfare that eventually resulted in the formation of two independent Karakhanid states. A son of Hasan Bughra Khan, Ali Tegin, seized control of Bukhara and other towns. He expanded his territory further after the death of Mansur. The son of Nasr, Böritigin, later waged war against the sons of Ali Tegin, and won control of a large part of Transoxiana, making Samarkand the capital. In 1041, another son of Nasr b. Ali, Muhammad 'Ayn ad-Dawlah (reigned 1041–52) took over the administration of the western branch of the family that eventually led to a formal separation of the Khara-Khanid Khanate. Ibrahim Tamghach Khan was considered by Muslim historians as a great ruler, and he brought some stability to the Western Karakhanids by limiting the appanage system that caused much of the internal strife in the Kara-Khanid Khanate.

The Hasan family remained in control of the Eastern Khanate. The Eastern Khanate had its capital at Balasaghun and later Kashgar. The Fergana-Zhetysu areas became the border between the two states and were frequently contested. When the two states were formed, Fergana fell into realm of the Eastern Khanate, but was later captured by Ibrahim and became part of the Western Khanate.

Seljuk suzerainty
In 1040, the Seljuk Empire defeated the Ghaznavids at the Battle of Dandanaqan and entered Iran. Conflict with the Karakhanids broke out, but the Karakhanids were able to withstand attacks by the Seljuks initially, even briefly taking control of Seljuk towns in Greater Khorasan. The Karakhanids, however, developed serious conflicts with the religious classes (the ulama), and the ulama of Transoxiana then requested the intervention of the Seljuks. In 1089, during the reign of Ibrahim's grandson Ahmad b. Khidr, the Seljuks entered and took control of Samarkand, together with the domains belonging to the Western Khanate. For half a century, the Western Karakhanid Khanate was a vassal of the Seljuks, who largely controlled the appointment of the Khanate's rulers in that time. Ahmad b. Khidr was returned to power by the Seljuks, but in 1095, the ulama accused Ahmad of heresy and managed to secure his execution.

The Karakhanids of Kashgar also declared their submission following a Seljuk campaign into Talas and Zhetysu, but the Eastern Khanate was a Seljuk vassal for only a short time. At the beginning of the 12th century the Eastern Khanate invaded Transoxiana and briefly occupied the Seljuk town of Termez.

Qara Khitai invasion
The Qara Khitai (Western Liao dynasty) host which invaded Central Asia was composed of remnants from the defunct Liao dynasty which was annihilated by the Jin dynasty in 1125. The Liao noble Yelü Dashi recruited warriors from various tribes and formed a horde that moved westward to rebuild the Liao dynasty. Yelü occupied Balasagun on the Chu River, then defeated the Western Karakhanids in Khujand in 1137. In 1141 Qara Khitai became the dominant force in the region after they dealt a devastating blow to the Seljuk Sultan Ahmad Sanjar and the Kara-Khanids at the Battle of Qatwan near Samarkand. Several military commanders of Karakhanid lineages such as the father of Osman of Khwarazm fled from Karakhanid lands in the wake of the Qara Khitai invasion.

Despite losing to the Qara Khitai, the Karakhanid dynasty remained in power as their vassals. The Qara Khitai themselves stayed at Zhetysu near Balasagun, and allowed some of the Karakhanids to continue to rule as their tax collectors in Samarkand and Kashgar. Under the Qara Khitai the Karakhanids functioned as administrators for sedentary Muslim populations. While the Qara Khitai were Buddhists ruling over a largely Muslim population, they were considered fair-minded rulers whose reign was marked by religious tolerance. Islamic religious life continued uninterrupted and Islamic authority persevered under the Qara Khitai. Kashgar became a Nestorian metropolitan see and Christian gravestones in the Chu River Valley appeared beginning in this period. However, Kuchlug, a Naiman who usurped the throne of the Qara Khitai dynasty, instituted anti-Islamic policies on the local populations under his rule.

Downfall
The decline of the Seljuks following their defeat by the Qara Khitais at the Battle of Qatwan (1141) allowed the Khwarazmian dynasty, then a vassal of the Qara Khitai, to expand into former Seljuk territory, where they became independent rulers circa 1190. In 1207, the citizens of Bukhara revolted against the sadrs (leaders of the religious classes), which the Khwarazmshah 'Ala' ad-Din Muhammad used as a pretext to conquer Bukhara. Muhammad then formed an alliance with the Western Karakhanid ruler Uthman ibn Ibrahim (who later married Muhammad's daughter) against the Qara Khitai. In 1210, the Khwarezm-Shah took Samarkand after the Qara Khitai retreated to deal with the rebellion from the Naiman Kuchlug, who had seized the Qara Khitans' treasury at Uzgen. The Khwarezm-Shah then defeated the Qara Khitai near Talas. Muhammad and Kuchlug had, apparently, agreed to divide up the Qara Khitan's empire. In 1212, the population of Samarkand staged a revolt against the Khwarezmians, a revolt which Uthman supported, and massacred them. The Khwarezm-Shah returned, recaptured Samarkand and executed Uthman. He demanded the submission of all leading Karakhanids, and finally extinguished the Western Karakhanid state.

In 1204, a rebellion of the Eastern Kara-Khanid in Kashgar was suppressed by the Kara-Khitai who took the prince Yusuf hostage to Balasagun. The prince was later released but he was killed in Kashgar by rebels in 1211, effectively ending the Eastern Kara-Khanid. In 1214, the rebels in Kashgar surrendered to Kuchlug, who had usurped the Kara-Khitai throne. In 1218, Kuchlug was killed by the Mongol army. Some of the Kara-Khitai's eastern vassals including Eastern Kara-Khanids then joined the Mongol forces to conquer the Khwarezmian Empire.

Culture
The takeover by the Karakhanids did not change the essentially Iranian character of Central Asia, though it set into motion a demographic and ethnolinguistic shift. During the Karakhanid era, the local population began using Turkic in speech – initially the shift was linguistic with the local people adopting the Turkic language. While Central Asia became Turkicized over the centuries, culturally the Turks came close to being Persianized or, in certain respects, Arabicized. Nevertheless, the official or court language used in Kashgar and other Karakhanid centers, referred to as "Khaqani" (royal), remained Turkic. The language was partly based on dialects spoken by the Turkic tribes that made up the Karakhanids and possessed qualities of linear descent from Kök and Karluk Turkic. The Turkic script was also used for all documents and correspondence of the khaqans, according to Dīwānu l-Luġat al-Turk.

The Dīwānu l-Luġat al-Turk (Dictionary of Languages of the Turks) was written by a prominent Karakhanid historian, Mahmud al-Kashgari, who may have lived for some time in Kashgar at the Karakhanid court. He wrote this first comprehensive dictionary of Turkic languages in Arabic for the Caliphs of Baghdad in 1072–76. Another famous Karakhanid writer was Yusuf Balasaghuni, who wrote Kutadgu Bilig (The Wisdom of Felicity), the only known literary work written in Turkic from the Karakhanid period. Kutadgu Bilig is a form of advice literature known as mirrors for princes. The Turkic identity is evident in both of these pieces of work, but they also showed the influences of Persian and Islamic culture. However, the court culture of the Karakhanids remained almost entirely Persian. The two last western khaqans also wrote poetry in Persian.

The Cambridge World History describes the Kara-Khanid state as the first of the Islamic Turco-Iranian states.

Islam and its civilization flourished under the Karakhanids. The earliest example of madrasas in Central Asia was founded in Samarkand by Ibrahim Tamghach Khan. Ibrahim also founded a hospital to care for the sick as well as providing shelter for the poor. His son Shams al-Mulk Nasr built ribats for the caravanserais on the route between Bukhara and Samarkand, as well as a palace near Bukhara. Some of the buildings constructed by the Karakhanids still survive today, including the Kalyan minaret built by Mohammad Arslan Khan beside the main mosque in Bukhara, and three mausolea in Uzgend. The early Karakhanid rulers, as nomads, lived not in the city but in an army encampment outside the capital, and while by the time of Ibrahim the Karakhanids still maintained a nomadic tradition, their extensive religious and civil constructions showed that they had assimilated the culture and traditions of the settled population of Transoxiana. During the excavations of the citadel of Samarkand, the ruins of the palace of the Karakhanid ruler Ibrahim ibn Hussein (1178–1202) were found. The palace was decorated with wall paintings.

Legacy
Kara-Khanid is arguably the most enduring cultural heritage among coexisting cultures in Central Asia from the 9th to the 13th centuries. The Karluk-Uyghur dialect spoken by the nomadic tribes and Turkified sedentary populations under Kara-Khanid rule formed two major branches of the Turkic language family, the Chagatay and the Kypchak. The Kara-Khanid cultural model that combined nomadic Turkic culture with Islamic, sedentary institutions spread east into former Kara-Khoja and Tangut territories and west and south into the subcontinent, Khorasan (Turkmenistan, Afghanistan, and Northern Iran), Golden Horde territories (Tataristan), and Turkey. The Chagatay, Timurid, and Uzbek states and societies inherited most of the cultures of the Kara-Khanids and the Khwarezmians without much interruption.

The Kara-Khanids translated the Quran into Middle Turkic. There are four surviving copies of the Quran translations found in various collections and a Middle Turkic excerpt of Al-Fatiha, which supposedly belong to the Kara-Khanid period.

Identification with China
Kara-Khanid monarchs adopted Tamghaj Khan (Turkic for "Khan of China"; 桃花石汗) or Malik al-Mashriq wa-l’Sin (Arabic for "King of the East and China"; 東方與秦之主) as their title, and minted coins bearing these titles. Another title they used was Sulṭān al-Sharq wa al-Ṣīn (Sultan of the East and China). Early period "proto-Qarakhanid" coinage featured Chinese-style square-holed coins, combined with Arabic writing.

Much of the realm of the Kara-Khanid Khanate, including Transoxiana and the western Tarim Basin, had been under the rule of the Tang dynasty prior to the Battle of Talas in 751, and the Kara-Khanid rulers continued to identify their dynasty with China several centuries later. Yusuf Qadir Khan sent the first Kara-Khanid envoy to the Song dynasty, Boyla Saghun, to request the Song to send an official envoy who would help 'pacify' Khotan, apparently seeking to use the prestige of the Chinese court to strengthen the Kara-Khanids' local status.

The Kara-Khanid rulers also formed marriage relations with the Liao dynasty and addressed the Song emperors as "maternal uncle", in possible imitation of Uyghur and Tibetan rulers who had marital relations with the previous Tang dynasty.

In an account, the Kara-Khanid scholar Mahmud al-Kashgari referred to his homeland, around Kashgar, then part of the Kara-Khanid Khanate, as "Lower China".

Genetics

A genetic study published in Nature in May 2018 examined the remains of three Khara-Khanid individuals. They were found to be carrying the maternal haplogroups G2a2, A and J1c. The Kara-Khanid were found to have more East Asian ancestry than the preceding Goktürks.

Monarchs

 * Bilge Kul Qadir Khan (840–893)
 * Bazir Arslan Khan (893–920)
 * Oghulcak Khan (893–940)
 * Satuk Bughra Khan 920–955, in 932 adopted Islam, in 940 took power over Karluks
 * Musa Bughra Khan 955–958
 * Suleyman Arslan Khan 958–970
 * Ali Arslan Khan 970–998, Great Qaghan
 * Ahmad Arslan Qara Khan 998–1017, son of Ali Arslan
 * Mansur Arslan Khan 1017–1024, son of Ali Arslan
 * Muhammad Toghan Khan 1024–1026, son of Hasan b. Sulayman
 * Yusuf Qadir Khan 1026–1032, son of Hasan b. Sulayman
 * Ali Tigin Bughra Khan (1020–1034), Great Qaghan in Samarkand, son of Hasan b. Sulayman
 * Abu Shuja’ Sulayman 1034–1042

Western Karakhanids

 * Tamghach Khan Ibrahim (also known as Böritigin) c. 1040–1068
 * Shams al-Mulk Nasr 1068–1080: married Aisha, daughter of Alp Arslan.
 * Khidr 1080–1081
 * Ahmad 1081–1089
 * Ya'qub Qadir Khan 1089–1095
 * Mas'ud 1095–1097
 * Sulayman Qadir Tamghach 1097
 * Mahmud Arslan Khan 1097–1099
 * Jibrail Arslan Khan 1099–1102
 * Muhammad Arslan Khan 1102–1129
 * Nasr 1129
 * Ahmad Qadir Khan 1129–1130
 * Hasan Jalal ad-Dunya 1130–1132
 * Ibrahim Rukn ad-Dunya 1132
 * Mahmud 1132–1141
 * Ibrahim Tabghach Khan 1141–1156
 * Ali Chaghri Khan 1156–1161
 * Mas'ud Tabghach Khan 1161–1171
 * Muhammad Tabghach Khan 1171–1178
 * Ibrahim Arslan Khan 1178–1202
 * Uthman ibn Ibrahim 1202–1212

Eastern Karakhanids

 * Ebu Shuca Sulayman 1042–1056
 * Muhammad bin Yusuph 1056–1057
 * İbrahim bin Muhammad Khan 1057–1059
 * Mahmud 1059–1075
 * Umar (Kara-Khanid) 1075
 * Ebu Ali el-Hasan 1075–1102
 * Ahmad Khan 1102–1128
 * İbrahim bin Ahmad 1128–1158
 * Muhammad bin İbrahim 1158–?
 * Yusuph bin Muhammad ?–1205
 * Ebul Feth Muhammad 1205–1211

title: Kara-Khanid Khanate


text:
Liaison aircraft

A liaison aircraft (also called an army cooperation aircraft) is a small, usually unarmed aircraft primarily used by military forces for artillery observation or transporting commanders and messages.

Operation
The concept developed before World War II and included also battlefield reconnaissance, air ambulance, column control, light cargo delivery and similar duties. Able to operate from small, unimproved fields under primitive conditions, with STOL capabilities, most liaison aircraft were developed from, or were later used as general aviation aircraft. Both fixed-wing aircraft and helicopters can perform liaison duties.

Argentina
(Fuerza Aérea Argentina)
 * Piper Chincul PA-28 Dakota
 * Piper Chincul PA-34 Seneca
 * Cessna C-182
 * Beechcraft TC-12B Huron

Bulgaria

 * Kaproni Bulgarski KB-11 Fazan

Germany
Nazi period:
 * Fieseler Fi 156 Storch
 * Messerschmitt Bf 108 Taifun
 * Focke-Wulf Fw 189 Uhu

Japan
Imperial period: Postwar period:
 * Kokusai Ki-76 (Imperial Japanese Army Air Force, 1942–1945)
 * Tachikawa Ki-36 (Imperial Japanese Army Air Force, 1938–1945)
 * LR-1 (Japan Ground Self-Defense Force, 1967–2016)
 * LC-90 (Japan Maritime Self Defense Force, 1974–)

Poland

 * Lublin R-XIII
 * RWD-14 Czapla
 * PZL Ł.2

Portugal

 * Piper L-21 Super Cub (Portuguese Army, 1952–1957 and Portuguese Air Force, 1957–1976)
 * Auster D.5/160 (Portuguese Air Force, 1961–1974)
 * Dornier Do 27 (Portuguese Air Force, 1961–1979)
 * Reims-Cessna FTB-337, (Portuguese Air Force, 1974–2007)

Soviet Union

 * Polikarpov Po-2 Kukuruznik ("Crop Duster")

Sweden

 * Piper PA-18-150 Super Cub as Flygplan 51, 1958–1974
 * Dornier Do 27 as Flygplan 53, 1962–1991
 * Scottish Aviation Bulldog as Flygplan 61C, 1972–1989

Switzerland

 * Pilatus PC-6

United Kingdom

 * de Havilland Dominie
 * Westland Lysander
 * Taylorcraft Auster AOP

title: Liaison aircraft


text:
8.8 cm KwK 43

The 8.8 cm KwK 43 (Kampfwagenkanone —"fighting vehicle cannon") was an 88 mm 71-calibre-length tank gun designed by Krupp and used by the German Wehrmacht during the Second World War. It was mounted as the primary armament on the Panzerkampfwagen VI Ausf. B Tiger II. The 8.8 cm Pak 43, an anti-tank gun, was very similar in design but mounted on tank destroyers or deployed stand-alone on the field.

Design and development
At 6.24 m, the length of the KwK 43's barrel was over 1.3 metres longer than of that of the 8.8 cm KwK 36 used for the Tiger I. The cartridge of the KwK 43's shell was also considerably longer (at 82.2 cm) and wider than that of the KwK 36's, meaning that the KwK 43 allows for more room for a heavier propellant charge in its cartridge case than the KwK 36 could. All guns of the PaK/KwK 43 series could use the same ammunition interchangeably.

The KwK 43 and PaK 43 were initially manufactured with monobloc barrels, meaning the barrel was made from one piece. However, due to the weapons' extremely high muzzle velocity and operating pressures when fired, the weapon suffered from accelerated barrel wear. As a result, the change was made to manufacture the PaK/KwK 43 with a two-piece barrel instead of a monobloc barrel. This had minimal to no effect on the performance of the gun, but made replacing a worn-out barrel much faster and easier than before.

In addition, the massively increased operating pressures of the new gun also required a new armour-piercing shell to be designed. The result of this was the PzGr.39/43 APCBC-HE projectile, which was similar to the older 10.2 kg PzGr.39-1 APCBC-HE projectile used by the 8.8 cm KwK 36 and PaK 43 guns except for the addition of much wider driving bands. The wider driving bands of the PzGr.39/43 increased the weight of the shell to 10.4 kg as a result. However, as the full transition to the newer PzGr.39/43 rounds was slow to take place, the older PzGr.39-1 rounds were instead allowed to be used for the KwK 43 & PaK 43 provided the gun had fired no more than 500 rounds. Above that set amount, the expected barrel wear combined with the narrower driving bands of the PzGr.39-1 would lead to a loss of pressure and therefore muzzle velocity in the gun. The new PzGr.39/43 could be fired without loss of pressure until the barrel was worn out, thus requiring no restriction.

PzGr.39-1 FES & Al all up weight: 10.2 kg (9.87 kg without fuse & bursting charge) PzGr.39/43 FES & Al all up weight: 10.4 kg (10.06 kg without fuse & bursting charge)

The same 278 gram BdZ 5127 fuse and 59 gram Amatol bursting charge were used for both types of projectile (PzGr.39-1 & PzGr.39/43), requiring armoured targets of 30 mm or thicker to ignite after penetration for maximum behind-armour effects.

PzGr. 39/43 (APCBC-HE)

 * Type: Armour-piercing, capped, ballistic cap - high explosive
 * Projectile weight: 10.40 kg
 * Muzzle velocity: 1000 m/s

PzGr. 40/43 (APCR)

 * Type: Armour-piercing, composite rigid
 * Projectile weight: 7.30 kg
 * Muzzle velocity: 1130 m/s

Gr. 39/43 HL (HEAT)

 * Type: High explosive anti-tank
 * Projectile weight: 7.65 kg
 * Muzzle velocity: 600 m/s
 * Penetration: 90 mm (30 degrees)

Sprgr. 43 (HE)

 * Type: High explosive
 * Projectile weight: 21 lb
 * Explosive Charge: 2.25 lb Amatol (4,270 Kilojoules)

Anti-tank gun
The anti-tank gun version of the 8.8 cm KwK 43 was known as the 8.8 cm PaK 43. This name was also applied to versions of this weapon mounted in various armored vehicles designed to hunt tanks, such as the Jagdpanther, Hornisse/Nashorn and Ferdinand/Elefant Panzerjäger tank destroyers. The Nashorn was the first vehicle to carry the KwK/PaK 43 series of guns. The series included: PaK 43 (cruciform mount), PaK 43/41 (two-wheel split-trail carriage), PaK 43/1 (Nashorn), and PaK 43/2 (Ferdinand/Elefant), all with monobloc (one-piece) barrels; PaK 43/3 and 43/4 (Jagdpanther) with two-piece barrels, and KwK 43 (Tiger II) with a two-piece barrel.

Weapons of comparable role, performance and era

 * British Ordnance QF 17 pounder
 * Soviet 100 mm D-10T
 * United States 90 mm T15E1/T15E2

title: 8.8 cm KwK 43


text:
Talk:Norman Schwarzkopf

Is number 2 the father of number 1? -- Zoe

 * Cool, I didn't know that - even typed in New Jersey twice, but the remarkable coincidence never occurred to me. Wikipedia wins again! Stan Shebs 03:55 Feb 25, 2003 (UTC)

 * They're both H. Norman Schwarzkopf, too, so I'll stick that in -- Someone else 04:14 Feb 25, 2003 (UTC)

redirect
Should this page be a redirect too Norman Schwarzkopf, Jr.? He's certainly the more famous one, and just about anyone searching for "Norman Schwarzkopf" is looking for him rather than his father (whose main claim to fame involves a not terribly significant connection to the Lindburgh kidnapping). A disambiguation header at the top of Jr's article would take care of the few people looking for his father. -R. fiend 19:30, 8 Mar 2005 (UTC)

title: Talk:Norman Schwarzkopf