text:
Philip P. Barbour

Philip Pendleton Barbour (May 25, 1783 – February 25, 1841) was the tenth speaker of the United States House of Representatives and an associate justice of the Supreme Court of the United States. He is the only individual to serve in both positions.

Born in Gordonsville, Virginia, Barbour established a legal career in Gordonsville after studying at the College of William & Mary. Several members of Barbour's family, including his brother, James Barbour, went on to hold prominent political office. Barbour won election to the House of Representatives in 1814 as a member of the Democratic-Republican Party. He served a single term as Speaker from 1821 to 1823 and declined to seek re-election to Congress in 1824. Barbour returned to Congress in 1827 as an ally of Andrew Jackson.

Barbour served in Congress until 1830, when he accepted appointment as a judge of the United States District Court for the Eastern District of Virginia. President Jackson appointed Barbour to the Supreme Court in 1835 to fill a vacancy caused by the resignation in 1835 of Gabriel Duvall. Barbour served on the Court until his death in 1841. On the Court, Barbour generally supported Jacksonian principles and states' rights.

Early and family life
Barbour was born near Gordonsville, Orange County, Virginia, as the son of a planter, Thomas Barbour, who was a legislator, neighbor and early political sponsor of James Madison. He was named for his ancestor Philip Pendleton, through whom he was related to Edmund Pendleton, a politician and judge. The family was one of the First Families of Virginia, descended from a Scottish merchant who married a Miss Taliaferro and made his home in nearby Culpeper County, Virginia.

Like his brother James Barbour, Philip attended common and private schools before beginning formal legal studies under jurist St. George Tucker in Williamsburg, Virginia, but financial circumstances forced Tucker to end this arrangement in 1799.

He soon moved to Kentucky to make his fortune, where after a year reading law, he was admitted to the bar, and began practicing law in Bardstown. After another year, friends persuaded him to return to Virginia and resume his studies at the College of William & Mary, so in 1802, he began practicing law near his family home in Gordonsville.

In 1804, Barbour married a local planter's daughter, Frances Johnson, with whom he had one son named Sextus Barbour. Barbour was a slave owner.

Political and early judicial career
Barbour practiced law for eight years before he started his public life as a member of the Virginia House of Delegates from 1812 to 1814. When U.S. Representative John Dawson died, Barbour won the special election to fill the seat, and served as a Jeffersonian Republican in the U.S. House of Representatives from September 19, 1814 to March 4, 1825, reaching the office of Speaker from 1821 to 1823. Barbour entered politics as the nation witnessed a political shift in which former state's rights activists such as current President James Madison, Henry Clay, and his brother James, now a U.S. Senator, began supporting nationalistic policies. Throughout this shift in power, Philip Barbour remained a strong advocate of Jeffersonian "Old Republican" principles of states' rights and maintaining a strict construction of the Constitution.

First term in Congress
Barbour's reputation for constitutional conservatism grew with his opposition to the Bonus Bill of 1817. The Bill permitted the federal funding of internal improvement projects such as building roads like that being constructed to connect Buffalo, New York to New Orleans, Louisiana, through Washington. Barbour viewed federally funded internal projects as outside the sphere of Congress' powers and therefore unconstitutional and undermining state sovereignty. Barbour viewed states as sovereign, political communities, independent of an overarching political dynasty and free to secede from the Union if the federal government infringed on the rights of the states, an argument that he employed when countering restrictions to Missouri's admission to the Union as a slave state.

Barbour also defended Missouri's ban on free Black Americans entering the state. To those who argued that this ban was a violation of Article IV of the Constitution, he replied that banning free Black Americans was no different than banning destitute white men who would become a burden on the state. He argued that the term "citizen" did not apply to Black Americans, whether free or not.

His opposition to national restrictions on slave states served to foment his passion for states' rights but also develop his pro-slavery argument in politics. As a Congressman, Barbour was the first prominent politician to openly contest the constitutionality of protective tariffs.

Cohens v. Virginia
In Cohens v. Virginia (1821), Congressman Barbour represented the Commonwealth of Virginia to argue the issue of the Supreme Court's jurisdiction to hear the case, in which two men from Baltimore were convicted for selling D.C. lottery tickets in Virginia. Barbour unsuccessfully argued that the Supreme Court lacked jurisdiction, since the law banning the sale of foreign lottery tickets was not meant to affect Virginia, rendering this a purely local issue. He also maintained that the suit was barred by the Eleventh Amendment, which prohibits suit against a state without its consent. However, Chief Justice Marshall held that the Court had jurisdiction based on the Supremacy Clause, Art. VI, cl. 2. This case strengthened Barbour's reputation as an Old Republican leader in a political system in which Virginian influence was waning and power was shifting between parties with the election of Andrew Jackson as the seventh President of the United States.

Jacksonian Democratic-Republican Party
Andrew Jackson's election in 1828 led to the bifurcation of the Old Republican Party into the Jacksonian Democratic Republicans and the opposing National Republicans. Jackson formed the Democratic party on the foundation of Old Republican principles, such as Jefferson's displeasure with Hamilton's National Bank. During his two terms, President Jackson destroyed the Second Bank of the United States, and advocated for individual liberty, states' rights, and slavery.

State judge and second term in Congress
Barbour declined to run for re-election in 1824 and turned down an offer from Thomas Jefferson to become the professor of law in the University of Virginia in 1825. Instead, he accepted election by Virginia legislature as a judge of the General Court of Virginia succeeding the late Hugh Holmes. Barbour served for two years as a state judge.

In 1827, Barbour returned to his seat in the House of Representatives as a Jacksonian. For the first two years of his second stint in the House, he was Chairman of the Judiciary Committee.

In 1829, Barbour became one of the first Jeffersonian Old Republicans to join the Jacksonian Democrats in opposition to the National Bank. He fought to expose the Second Bank of the United States as a private enterprise, endowed with federal funds while only masquerading as a government institution. Although his anti-Bank campaign did not take hold, Barbour's advocacy for state sovereignty, the removal of the National Bank, and the legalization of slavery in territories such as Missouri earned him favor with President Andrew Jackson.

Also in 1829, while continuing to serve as a U.S. Representative, Barbour became a delegate for the Virginia Constitutional Convention of 1829-1830, and the Convention elected him their second president, after the Convention's first president, James Monroe, had to withdraw due to failing health on December 8. As such, Barbour (with distinguished Virginians such as Monroe, James Madison, and John Marshall) helped restrict discussion of slavery's role in the Commonwealth, and limited the rancorous assembly's debates to issues of representation and suffrage (Virginia had been one of the last states to allow only landowners to vote, and slaveholders had disproportionate power). The resulting constitution was adopted in 1830, despite the votes against it from the state's northern and western areas (much of which ultimately split off to become West Virginia during the American Civil War decades after Barbour's death).

Federal district judge and the 1832 campaign season
Barbour also turned down offers of a chancellorship and the post of U.S. Attorney General before finally resigning his congressional seat October 15, 1830 to accept President Jackson's appointment to become judge of the United States District Court for the Eastern District of Virginia. Jackson appointed Barbour by recess appointment on October 8, 1830, to a seat on that court vacated by George Hay. Barbour was formally nominated on December 14, 1830, and two days later he was confirmed by the Senate, and received his commission, serving thereafter until March 17, 1836.

In 1832, Democrats unhappy with the selection of Martin Van Buren as their party's vice-presidential nominee held a convention in Virginia, at which they nominated Jackson for president and Barbour for vice president. Barbour eventually withdrew his candidacy and endorsed the Jackson-Van Buren ticket, but the alternative Democratic ticket still appeared on the ballot in several Southern states. Barbour also refused nominations for judge of the court of appeals, for Governor, and for United States Senator.

Although it was unknown whether Barbour could gain favor with voters outside Virginia, Barbour's campaigning on the Democratic ticket illuminated the similarities in parties and gained favor for the Democratic party. Voters reasoned that, if a man like Barbour, loyal to his party even when his fellow Virginians chose different principles, could switch to the Democratic party, then the Democrats must hold the same values. By joining the Jacksonian Democratic Party, Barbour entrenched Old Republican principles into a new political dynasty, therefore continuing the legacy of Jefferson and further validating the strength of Democratic principles. This was similar to Lincoln's argument that secession should not occur due to the state of perpetual Union that had existed since the first draft of the Constitution before the term "Union" was first used to describe the North during the Civil War. Therefore, Barbour's resignation allowed the second party system to coalesce by unifying the Democratic Party on the ideologies of war in the American system through the national reform retrenchment and economy, and a restoration of republican constitutionalism.

Appointment
In 1835, Chief Justice Marshall's death and Justice Gabriel Duvall's resignation created two vacancies on the Supreme Court. President Jackson, at the end of his second Presidential term, nominated Judge Barbour to fill Duvall's vacancy. Nationalists feared Jackson's appointment of Barbour because Barbour's anti-administration Congressional legacy and Democratic beliefs suggested that he would attempt to undermine the federal supremacy achieved during the Marshall Court. This fear made the finalization of the decision an arduous process with two attempts at delaying the Senate's decision. On March 15, 1836, the Senate approved the appointment of Barbour by a vote of 30-11.

Tenure
Barbour served on the Supreme Court for five years. He heard 155 cases, for which he authored one major opinion and two dissents. His passion for states' rights, strict constructionism, and limits on federal power helped shape the legacy of the Taney Court.

During Barbour's first term (1837), he heard three cases that mitigated Marshall's accomplishment of judicial nationalism, Briscoe v. Bank of the Commonwealth of Kentucky, Charles River Bridge v. Warren Bridge, and New York v. Miln. Justice Barbour authored the majority opinion in New York v. Miln. In 1824, the state of New York passed a law that required all ship masters to provide a report delineating personal information of passengers in order to prevent smuggling and immigration of the impoverished for whom the state could not provide. Ship master Miln refused to comply with the law and was therefore jailed and fined. The case went to the Court on the issue of whether the statute violated the Commerce Clause, U.S. Const., Art. 1, § 8. Barbour held that the New York statute did not violate the Commerce Clause, because it was an exercise of the power granted to the state to "regulate their internal police and to take care that no detriment comes to the commonwealth." People were "not the subject of commerce, and not being imported goods, cannot fall within a train of reasoning founded upon the construction of a power given to Congress to regulate commerce and the prohibition to the states from imposing a duty on imported goods." Justice Barbour argued that the statute was valid as an act of police power to protect the health and welfare of the community. Because it is within the powers of the state to have jurisdiction over its people and things within its territorial boundaries, then "the authority of a state is complete, unqualified, and exclusive."

Justice Barbour's holding in Miln was supported by Taney's opinion in Charles River Bridge that the people have rights and it is the duty of both the state and the nation to preserve those rights in order to ensure the happiness and welfare of every citizen. Miln helped Barbour develop a states' rights constitutional vision for the Supreme Court, by narrowing the scope of federal commerce power while expanding state policing power. For both Briscoe v. Bank of the Commonwealth of Kentucky and Charles River Bridge v. Warren Bridge, Barbour voted with the majority, simultaneously gaining more power for states and weakening Marshall Court nationalism.

While Barbour did not spend enough time on the court to amass a large body of judicial opinions, he authored dissents in ''Kendall v. United States ex rel. Stokes (1838) and Holmes v. Jennison'' (1840). These two dissents sought to diminish federal authority by supporting Jacksonian political aspirations and opposing restrictions to state sovereignty. Kendall dealt with judicial supervision of executive acts. In 1835, President Jackson appointed Amos Kendall the Postmaster General for the United States. A firm, Stockton and Stokes, had had a contract with the previous Postmaster General, and demanded payment of outstanding debts thereunder, which Kendall declined, in favor of the debt-ridden U.S. Postal Service's other creditors.

The Court viewed Kendall as a proceeding against an Executive Branch official who acted within the scope of his powers. The Court dealt with the issues of whether it had jurisdiction to hear the case under Section 25 of the Judiciary Act of 1789 and whether it had the power to issue a writ of mandamus under Section 13 of the Judiciary Act of 1789 to an official of the Executive Branch. The majority held that the Supreme Court could issue a writ of mandamus to "compel the Postmaster General to perform any ministerial duty devolved on him by law." This issue and holding is similar to that in Marbury v. Madison (1803), which also involved writs of mandamus to an executive officer and held that the Supremacy Clause in Article VI and the notion of popular sovereignty granted the Court jurisdiction over state court cases and the power of judicial review to make legitimate and final rulings on constitutional questions.

Justices Taney and Catron concurred with Barbour's opinion that it was never within the scope of judicial power to control executive actions. Although Barbour believed that "Congress has the constitutional power to give to the federal judiciary …authority to issue the writ of mandamus," Barbour did not believe that the lower court had the "power to issue the writ in question". Even though the Postmaster General was subject to direction and control of the President with respect of the duties imposed by law, when the law is 'ministerial,' Congress can limit and regulate the executive officials. Because Congress created the executive office, then Congress could monitor executive decisions, but the President is not controlled by the federal courts. While the majority opinion served to further define separation of powers by holding acts of the executive branch as subject to the rulings of the Supreme Court, Barbour's dissenting opinion sought to discourage judicial supervision of executive acts by applying President Jackson's departmental theory, the notion that the executive branch has the right to interpret the Constitution for itself. Barbour's opinion in Kendall demonstrated his loyalty to President Jackson's political agenda.

Barbour made his most powerful argument in favor of states' rights in Holmes v. Jennison (1840), which focused on the extradition of a fugitive from Vermont to Canada. In 1838, George Holmes, a resident of Quebec, was convicted of murdering Louis Paschal Achille Tache in Canada. Holmes escaped to the United States where he was detained under issue of warrant in Vermont. Silas H. Jennison, the governor of Vermont, issued the warrant stating that Holmes, being a citizen of the lower province of Canada, would be arrested and returned to suffer prosecution according to the Canadian justice system, even though the United States had no extradition treaty with Canada. Because the Vermont Supreme Court refused to issue a writ of habeas corpus, Holmes petitioned to the Supreme Court on grounds that he was unlawfully imprisoned and deprived of his personal liberties.

The case became a contentious debate further polarizing the Court between nationalists and states' rights Justices. Holmes focused on whether the Court had the authority to review the case based on Section 25 of the Judiciary Act of 1789 and whether the governor's warrant violated the Extradition Clause of Article IV, section 2 of the Constitution, which gave the federal government power to surrender a fugitive to a foreign government. Chief Justice Taney believed that the case fell within the Court's jurisdiction and that the federal government had the exclusive power to engage in foreign relations and so believed that the governor had violated the Extradition Clause.

However, as the Court divided 4-4 over the issue of jurisdiction, the Court dismissed the petition. The Vermont Supreme Court subsequently ordered Holmes released in light of the fact that five of the eight Justices expressed the opinion that the governor had violated the Extradition Clause, an expression of the principle that the Constitution gives state officers no power to take independent actions concerned with foreign governments. Barbour was one of the four Justices who disagreed with the Chief Justice. Barbour believed that, because "there is no treaty on the subject of surrendering fugitives," between Vermont and Canada, then the returning of fugitives to Canada did not violate a power granted to the federal government by the Constitution, and therefore the "authority, exercised by the Governor of Vermont, is not repugnant to the power of making treaties in its dormant state, because, in the language of the Chief Justice before cited, it is not the mere existence of the power but its exercise which is incompatible with the exercise of the same power by the states." Barbour opined that, because the Constitution did not explicitly define the affairs of states with foreign countries, Governor Jennison was completely within his rights to order the extradition.

Barbour's opinion in Holmes accorded with his opinion in New York v. Miln that the state has the duty to maintain the welfare of its people. Holmes v. Jennison provides an example of Barbour's strict reading of the Constitution, which allowed him to read a more pronounced states' rights view into the text.

Death and legacy
Barbour died of a coronary thrombosis on February 25, 1841, while asleep in his bed, and partway through the arguments of John Quincy Adams, who sought freedom for African captives in the Amistad Case. Justice Story (although opposing slavery and personally more nationalist than Barbour) eulogized Barbour as earning the respect of his colleagues by his commitment to personal values, persistence in fighting for his beliefs, and legal acumen.

Barbour owned fifty-four slaves at the time of the 1840 census.

An Episcopalian throughout his life, Philip Pendleton Barbour was buried in the Congressional Cemetery, Washington, D.C. Barbour's long-time friend and fellow Virginian, Peter V. Daniel, succeeded him on the U.S. Supreme Court, and continued Barbour's legacy of maintaining Jacksonian principles, states' rights, and strict constructionist reading of the Constitution.

Locations named after him include Barbour County, West Virginia, Philippi, West Virginia and its Philip Barbour High School.

Barbour's tenure on the Court demonstrated his loyalty to President Jackson's national vision while applying a narrowed reading of state's rights into the Constitution. Barbour's decisions in major Court cases created an enduring Jacksonian legacy on the Taney Court. Barbour's furtherance of Jacksonian principles of departmental theory in his Kendall dissent, his states' rights advocacy in his majority opinion in New York v. Miln, and textualist reading of the Constitution in order to distinguish state from Congressional power in his dissent in Holmes, all served in this regard.

Barbour's opinions began to unravel the work of Marshall's Court, and set a precedent for future cases as the country became more polarized. Barbour's arguments for the authority of the President to interpret the Constitution in Kendall, and those in defense of the states' police power in Cohens v. Virginia, allowed Chief Justice Taney to rule that slaves were not citizens in Dred Scott v. Sanford (1857). Ironically, they were also used by President Abraham Lincoln to issue a suspension of habeas corpus in 1861.

title: Philip P. Barbour


text:
Talk:Convex hull

Computational complexity of finding the convex hull over a finite set of points
The following paragraph was in the convex article, but since it's about convex hulls it would be better suited to this convex hull article. I'm leaving it on the Talk page for now, however, as I don't think it would add anything useful to this article either. --Zundark 10:43, 16 Dec 2003 (UTC)

 * One application of convex hulls is found in efficiency frontier analysis. Efficiency is assumed to be a monotonic function of each of finitely many real variables. Each one of finitely many data points is in exactly one hull, and is considered more efficient than all data points in hulls contained within its own hull. A particle whose velocity vector has a value of a for all coordinates representing maximized variables, and a value less than a for all minimized variables, will pass through the hulls in increasing order of efficiency.

The Convex Hull article is inaccurate. Convex Hulls of 2D polygons are clearly Omega(n log n) by reduction to sorting: pick values x_i, compute convex hull of (x_i, x_i^2). Find point with smallest x, output the rest in order. Since a parabola is convex, the convex hull of the subset of the points will have all of them. For that to be the case, the output permutation will be such that points are output in order. If convex hulls were possible in Omega(n), then it would be possible to sort points in Omega(n). By a decision tree model, sorting points is Omega(n log n), and so is the convex hull.
 * You better read more carefully. First, The O(n) is not for 2D polygons, but for 2D simple polygons. Second, how do you make a polygon from points (x_i, x_i^2)? mikka (t) 02:10, 20 July 2005 (UTC)

 * Connect (x_1, x_1^2) to (x_n, x_n^2), and you'll have a simple convex polygon. And for every non-simple polygon, there is a simple polygon with the same vertex set, so the simple/non-simple polygon distinction is pointless (because convex hull really only cares about the vertex set)
 * You are wrong. Sorry, I have no intentions to teach you math. get yourself a book in computational geometry. mikka (t)
 * So, while mikka is correct, the article could certainly use some explanation of how the algorithm for finding the convex hull of a simple polygon (or simple polyline) works. Simply stating that the problem has an O(n) solution isn't very interesting (though it does imply that constructing a simple polygon from a set of points is Omega(n log n)).  A good web resource on some algorithms is at http://cgm.cs.mcgill.ca/~athens/cs601/ Cgray4 11:51, 2005 August 8 (UTC)

A more up-to-date reference is: http://www.cs.umd.edu/~mount/754/Lects/754lects.pdf (Lecture 4)69.216.96.64 14:50, 15 September 2005 (UTC)

I don't think I understand the purpose of this parenthetical after the first sentence: "(Note that X may be the union of any set of objects made of points)." Even if there is a reason for this sentiment, we should try to find a better way to express it. Dchudz 16:53, 2 August 2006 (UTC)

Too technical
I would like to thank anyone that has had a part in creating this article. The abundant use of terms and explanations that could only be understood by experts, with a complete disregard for the common man is excellent. I came here to try to understand convex hull approximations, as it could potentially be needed for an interactive project I'm currently working on. But it came as absolutely no surprise that, as most articles, it was explained in such a way where only individuals who already have somewhat of an idea about the subject could make good use of it. Fine work, experts. I shall crawl back to the cave of despair from which I came, miserable and hopeless as before. 90.229.248.197 (talk) 06:14, 11 June 2011 (UTC)

 * Sarcasm is unhelpful. Where did you run into trouble? Kiefer .Wolfowitz 16:08, 11 June 2011 (UTC)

 * There was a misuse of "convex hull" for the boundary; this misuse may be an understandable convention in computational geometry, but its inclusion in the lead was confusing.
 * I moved the elastic band picture below, to the computational geometry section, because it focuses too much attention on the boundary of the convex hull.
 * I also removed an unreferenced self-labeled "intuitive" discussion, perhaps written under the influence of the ghosts of Fenchel, Busemann, and Alexandrov, but somewhat underdeveloped.
 * Readers should first read the articles on convex set and convex combination before reading this article. Kiefer .Wolfowitz 16:36, 11 June 2011 (UTC)

Infinite dimensional?
A change today added a mention of convex hulls in infinite dimensional vector spaces. But, if one has a convex hull of infinitely many points in an infinite dimensional space, does one take all convex combinations for which the set of weights forms a series summing to one, or only those convex combinations with finite support? That is, is (1/2,1/4,1/8,...) a member of the convex hull of (1,0,0,...), (0,1,0,...), (0,0,1,...), ...? The definition of a convex hull as the minimal convex set containing a set of points, and the definition of a convex set as containing the line segment connecting any two of its points, leads to the finite support version. But, on the other hand, the definition of convex combination and of a convex hull as the set of all convex combinations seems to be stated in a way that would imply the other version. Perhaps this should be stated here more explicitly? —David Eppstein (talk) 00:12, 24 May 2008 (UTC)
 * I see no bigger problem with a vector space of infinite dimension than with a vector space of finite dimension. In each case there is an infinite number of points, and the convex hull is the set of sums of convex combinations of finite number of points. The number of points in a convex combination is not tied in any way to the dimension of the space. Oleg Alexandrov (talk) 04:53, 24 May 2008 (UTC)
 * I agree that's the right definition. But our convex combination article doesn't clearly state that it's a combination of only finitely many; one could read it as allowing infinitely-supported combinations. —David Eppstein (talk) 06:45, 24 May 2008 (UTC)
 * Well, there is the number n there, which implies that the number of points is finite. I clarified that more there. Also, the possibility of an infinite amount of points is ruled out by the fact that it is impossible to talk about an infinite sum unless you have some kind of norm/topology which is not always the case in real vector spaces. Oleg Alexandrov (talk) 14:55, 24 May 2008 (UTC)
 * Much better. I still have a quibble: now convex combinations are defined only for finite sets of points, while here we say that the convex hull is the set of convex combinations of all of the points, so we can only define convex hulls of finitely many points. Two possible fixes: (1) in the convex combination article, define a convex combination of infinitely many points to be a weighted sum with finite support, or (2) here, define the convex hull as the set of convex combinations of finite subsets of the points. I think (1) would be preferable, but I'm not sure about it. —David Eppstein (talk) 15:34, 24 May 2008 (UTC)
 * David, I reverted your edit since I believe a definition using finite support convex combinations of an infinite number of points is not that usual (I think). I understand your point after I read this convex hull article. The recent changes to it made the definition unclear. The convex hull is not the convex combination of all points in the space, but rather the set of all possible convex combinations of finite tuples of points. I hope after my revert to the text this is more clear. Oleg Alexandrov (talk) 04:05, 25 May 2008 (UTC)

 * Convexity is a special case of sequential convexity, which is a special case of measure convexity; all of these inclusions are strict (and important). For sequential convexity, see Topology and Normed Spaces by G[raham]. J[ames]. O[scar] Jameson for sequential convexity. For measure convexity (c.f., Choquet theory), see Choquet order and simplices: with applications in probabilistic models by Gerhard Winkler (Springer Verlag, Lecture notes in mathematics ; 1145). Kiefer.Wolfowitz (talk) 17:32, 26 November 2009 (UTC)

Copyright violation?
Forgive me (and correct me) if i'm not following appropriate protocol, however, i've noticed that the text in the "Applications" section, starting with the words "For example, consider the problem" and continuing through to "from one hull vertex to another", is word-for-word identical to a passage in the book, The Algorithm Design Manual by Steven Skiena (1998, Springer-Verlag New York), page 351 of the hardcover edition (section 8.6.2, "Convex Hull").

This text first appeared (with an additional sentence of quoted text from the book) in this revision, dating back to mid-2006. I've removed the content for the moment as a quick fix. Please advise if this is the incorrect course of action. Jmelesky (talk) 23:42, 22 June 2008 (UTC)

 * Thanks for spotting this! And it wasn't exactly a perfect formulation anyway, since the careless first sentence suggested that the diameter is a pair of points, not their distance. For lack of context it wasn't particularly clear either, and it may be best to drop this particular aspect altogether. --Hans Adler (talk) 00:13, 23 June 2008 (UTC)

 * I think it's an important aspect of the problem, and have added back a sentence that states it again without being a copyvio. Thanks for catching this. —David Eppstein (talk) 00:31, 23 June 2008 (UTC)

Carathéodory's theorem
Why do editors keep removing the reference to Carathéodory's theorem, without offering reasons or seeking consensus (at least since I've started watching this page)?

Of course, Carathéodory's theorem (Farkas, Steinitz, etc.) exemplifies Stigler's "law of eponymy".

Kiefer.Wolfowitz (talk) 14:57, 31 January 2010 (UTC)

No article on concave hull (more specifically, on algorithms or methods for finding one)
I don't know the proper place to put this, so please feel free to delete / move / change this as necessary. I'm no expert on geometry, but it seems strange that I couldn't find an article on concave hulls, the associated challenges, or any algorithms or methods involved. A few searches turned up a publication, a query for general info , another query for info, and a java application for showcasing some algorithms. I don't know enough about geometry to know if I should create this page or if there is some other generalization where this type of information is located. If there is a page for this information, I wanted to request better linking to that data from this page, so that someone searching for concave hull information might find it easier than I have. If there is not, perhaps it should be created.

Crabpot8 (talk) 15:10, 5 May 2011 (UTC)
 * Yes this is an important and interesting problem. For example, computing the non-convex hull may be needed for pattern recognition (e.g. in OCR, or more generally when converting any rasterized image, or photography into a vectorized representation.
 * One majour problem is that the non-convex hull of a finite set of points is almost never unique. The first intuitive approach, which consists in minimizing the surface covered by the hull will not work and can bring an extremely large (combinatorial) number of solutions.
 * Generally the solutions try instead to minimize the surface covered by the bordering triangles, these triangles being defined by triplets of consecutive points on the hull. Another approach is to try to minimize the perimeter of the hull and this generally brings another solution. In all cases, you also need to define a maximum radius of search of candidate points to connect, because otherwise you will get the convex hull (which already has the smallest perimeter, but not the smallest area).
 * For the case of sets of infinitely many points, there's simply no solution, except if you define a maximum local radius of search, and if the density of nearby points within that radius is finite for every point of the infinite set; for example this case occurs:
 * if you try to define the "best" non-convex 2D hull of a fractal curve of the plane (with dimension more than 1 but still less than 2), such as the Koch flake.
 * in cartography, this case occurs when you try to define the non-convex boundary of the coast of Britanny or Norway: there's no limit to search candidate points, and at best you can only select points within a maximum search radius, so that all land will fall within that boundary, but you'll necessarily include parts of the sea. IF your search radius goes very low, the total perimeter of the non-convex hull may grow indefinitely (that's why it's simply impossible to reliably define the length of coasts of Britanny or Norway).
 * Searching such non-convex hull over a finite set of points is a np-complete problem (with combinatorial complexity). On the opposite, finding the convex hull has a MUCH lower complexity in O(n²), using an intuitive approach, where n is the number of points in the set, but in most cases an efficient algorithm can reduce this complexity to O(n · log2 n), provided that n is not too large, because space may be limited (for example not all points can fit in memory, they must be splitted into subsets that have to be paged out, with a huge time cost; in general the solution is to subdivide the set using tiled squares, and this solution is used in cartographic applications, such as OpenStreetMap, Bing Maps, Google Maps/Google Earth).
 * verdy_p (talk) 10:07, 27 July 2011 (UTC)

Kallay?
There is a mention of Kallay's incremental algorithm, with no citation. I've looked for this algorithm for over an hour, and I can't find it. Is there a mistake or do I suck at finding things? — Preceding unsigned comment added by 67.80.148.73 (talk) 10:27, 13 March 2012 (UTC)
 * Try Gil Kalai, and fix the typo if my guess is correct, please!  Kiefer .Wolfowitz 11:01, 13 March 2012 (UTC)

lower, upper convex hull
I miss the definition of the lower and upper convex hull. The term is used for example in David Gross: Basic Structures of Function Field Arithmetic p. 39 def. 2.7. A definition I found in http://citeseerx.ist.psu.edu/viewdoc/download?doi=10.1.1.69.1152&rep=rep1&type=pdf But I know no texbook as a source. I would be very thankfull if somebody could add this. --Flegmon (talk) 11:36, 16 April 2012 (UTC)
 * Oh and it ist used in Newton_polygon --Flegmon (talk) 12:41, 16 April 2012 (UTC)
 * Do you know of an encyclopedia article that discusses such "convex hulls"? Are they hull operators, convexity systems, antimatroids? Kiefer .Wolfowitz 16:21, 16 April 2012 (UTC)
 * I don't know how you want to abstract them, but they're very standard in computational geometry. I'll see if I can find a source in the computational geometry texts I have. —David Eppstein (talk) 16:48, 16 April 2012 (UTC)

Equivalence of definitions
It appears to me that the 4 given definitions of the convex hull are not all equivalent. Conditions 1, 2 and 4 are obviously equivalent, but condition 3 is distinct. Consider {(x,y):y>0} union {(0,0)} in the plane. This is convex and hence equals its convex hull. But it is not the intersection of a family of half-planes. GrantCairns (talk) 12:25, 20 August 2012 (UTC)

 * This comment looks right to me. What's the correct statement?  Closed convex sets are the intersections of their halfspaces?  Open?  Something else?  This characterization is obviously right and important in a large number of cases; what's the defining feature of those cases?  --JBL (talk) 12:37, 7 September 2012 (UTC)

 * It seems that the editors of this article had in mind the convex hull of finite sets. I think that the correct assertions are the following ones:
 * The convex hull of a closed compact set (in particular of a finite set) is closed.
 * The convex hull of a closed compact is the intersection of the closed half hyperplanes containing it.
 * In any case, the given definition in term of intersection of half hyperplanes is meaningless without indicating it the half hyperplanes are open or closed. D.Lazard (talk) 13:32, 7 September 2012 (UTC)
 * I agree, this was wrong. I've refactored that part of the article to take this discussion into account. —David Eppstein (talk) 15:24, 7 September 2012 (UTC)

Many thanks to David Eppstein to have corrected the article and the mistake of my previous post. D.Lazard (talk) 09:16, 8 September 2012 (UTC)

"Hull" as a container
The definition of complex hull given in the first sentence of the article implies (at least for those who understand the definition of convex set) that a convex hull is not a boundary, but a solid object.

Since "hulls" and "envelopes" are kinds of hollow containers in plain English, it is quite difficult to accept that in mathematics a convex "hull" or "envelope" is a solid (non-hollow) object, rather than an external surface or boundary. This is made even more difficult by the rubber-band example given in the introduction ("the convex hull may be visualized as the shape formed by a rubber band stretched around X"), which is not compatible with the above mentioned definition. According to that definition, the covex hull would be the space bounded by the rubber band, rather than "the shape formed by" it.

Are you sure that the reliable literature consistently defines a convex hull as a convex set (rather than its boundary)? If this is true, then the introduction should warn readers that in mathematics a hull is not a container... Otherwise, the introduction should say that according to some (reliable) authors the hull is just a boundary (similar to an elastic band), and according to some others it is a convex set.

In this context, it may be also useful for editors to notice that in English, whatever is inside a container is simply "contained in" it. However, the expressions "contained in" or "included in" are used in set theory to mean "member of", or "part of" the set. Therefore, if a container (such as a bottle or the hull of an airplane) is modeled as a set of particles, whatever is inside the container (a liquid or the passengers of an airplane) is not "contained in" it, as it is not a part of it. Paolo.dL (talk) 15:04, 7 January 2013 (UTC)
 * The word "hull" in mathematics can be used with very abstract meanings — see e.g. injective hull. —David Eppstein (talk) 15:37, 7 January 2013 (UTC)

simplices

 * The union of all simplices with vertices in X.

So there can't be a pathological point set such that the union of simplices has a hole? —Tamfang (talk) 03:31, 1 March 2013 (UTC)

 * Keep reading. In the paragraph that follows you'll find a link to Carathéodory's_theorem_(convex_hull).  --JBL (talk) 04:08, 1 March 2013 (UTC)
 * Which seems obvious enough that I now wonder what prompted my question. —Tamfang (talk) 07:28, 10 February 2024 (UTC)

Definition ambiguity
The sentence "In fact, according to Carathéodory's theorem, if X is a subset of an N-dimensional vector space, convex combinations of at most N + 1 points are sufficient in the definition above" is misleading, as it appears to suggest that there exists set of $n+1$ vectors, such that convex combinations of them give the convex hull of the original set. Yet, this only gives a simplex and it is the union of many of these that give the complex hull of the original set, which implies that we need more than $n+1$ vectors. Rereading the sentence, perhaps misleading is too generous? 130.95.80.94 (talk) 02:49, 24 October 2014 (UTC)

No citations in the Applications section
Some of these sound very interesting, but they are unsupported. Because this section is about applications, rather than finding citations that quote an author saying something like "convex hulls are useful for ", it might be more helpful and interesting to the reader to link to, say, a paper that actually uses a convex hull for the listed application. Just an idea to consider. If I remember, I'll help add citations later. --166.20.224.10 (talk) 19:49, 24 November 2014 (UTC)

 * I've added a specific application for home range with citation. —Mrwojo (talk) 23:07, 7 March 2015 (UTC)

In materials science
I don't see how it's OR to include the use in materials science when this is cited to book published by Cambridge University Press and Springer. A quick search would show that this is a well established topic in science, hence I'm wondering if you actually read the sources or instinctively lumped my edits in with the recent edits by another user. Pieceofmetalwork (talk) 08:48, 22 June 2022 (UTC)

Convex hull of a compact set
This article claims that the convex hull of a compact set is compact, but this appears to be false without assuming some extra conditions: https://math.stackexchange.com/questions/2017113/is-the-convex-hull-of-a-compact-set-compact 196.3.50.248 (talk) 10:16, 22 December 2022 (UTC)
 * This article is primarily about convex hulls in finite dimensional Euclidean spaces. In more general kinds of spaces like the one of that example, more general kinds of things can happen. —David Eppstein (talk) 07:50, 23 December 2022 (UTC)

Convex closure
The terminology convex closure given in the introduction was added by an anonymous user almost 6 years ago, without any reference, and seems to have been unchallenged since.

However, I think that terminology is wrong and confusing, because a convex hull is not necessarily closed (in fact, as the article points out, the convex hull of an open set is always open) and thus can hardly be considered a "closure"... In fact, to me convex closure is a synonym of closed convex hull — which is a related but different notion.

Given the obvious nature of the problem and the way the term was added to the article, I was tempted to "be bold" and just remove it from the introduction. However, given that it has survived in the article for almost 6 years, I thought I'd start a discussion in case someone (@David Eppstein? @JBL? @D.Lazard?) has a better suggestion; maybe a detailed remark along the lines of "in some communities convex closure is used for convex hull, but that this is incorrect in general because", etc?

Best, Malparti (talk) 17:42, 8 January 2024 (UTC)

 * Google Scholar easily finds good sources for this term, such as by Hermann Weyl: . So it is in use. As for whether it is "correct": closure is used in mathematics in lots of senses that do not mean topological closure (see for instance the closure operations of a matroid, or algebraic closure). We cannot write in our article that this terminology is somehow incorrect without reliable sources that make the same statement. —David Eppstein (talk) 18:12, 8 January 2024 (UTC)
 * (ec) Thanks for the ping. To address something that is not your main point: the convex hull is closed with respect to a certain operation (namely, taking points on the segment connecting two points in the set), just as the algebraic closure of a field is closed with respect to a certain operation (taking roots of polynomials with coefficients in the field) and the topological closure is closed with respect to a certain operation (taking limit points of sequences of points in the set).  The algebraic closure of the rational numbers is not a closed set in the sense of topology (as a subset of the reals or complexes), and that is definitionally fine (it just requires authors to be a bit careful sometimes).  So I don't think there's any issue of correctness here.  --JBL (talk) 18:39, 8 January 2024 (UTC)
 * @David Eppstein @JBL thanks for the prompt reply.
 * I agree that "closure" can refer to other types of closures than topological ones. So incorrect wasn't the right word, misleading would have been better suited.
 * More to the point: my main concern is that, as I mentioned, convex closure can have the meaning of closed convex closure — a fairly common notion. And I suspect that most occurrences of convex closure actually refer to the closed convex closure, not to the convex hull; I'll do a quick literature search tomorrow to see if that claim actually holds.
 * Regarding David Eppstein's comment that we would need to base ourself on a reliable source if we want to discuss the whether the term convex closure is misleading: just by typing  in Google Books, the 6th result I get is Convex sets and their applications, Ky Fan (1959), where it's written: The reader is reminded to distinguish the two terms "convex hull" and "convex closure" (and there, convex closure does indeed mean the closure of the convex hull). So I don't think finding sources to backup the idea that one should be careful about the terminology should be a problem.
 * Best, Malparti (talk) 22:47, 8 January 2024 (UTC)
 * @David Eppstein @JBL Here are the results of my little experiment:
 * I searched for  on Google Books (I used Books instead of Scholar because I think textbooks are more relevant than research articles for a Wikipedia page). I looked at the first 4 pages (= 40 results), in the order in which Google Books listed them. I was able to access all these links from my institution, but not from my home; so some of the links below may not work for everybody.
 * For each of these results, I determined whether convex closure referred to the convex hull, to the close convex hull, or to both (meaning that the authors are working in a setting where the convex hull is always closed). I made a special category for cases where convex closure was used exclusively to refer to the convex closure of a function (i.e. the closed convex hull of its epigraph), but those results should actually be counted in the category closed convex hull (the reason why I listed them separately is that it is a bit trickier for someone not familiar with the terminology to see what's going on). I discarded results for which I wasn't immediately sure what was going on, or where no definition was given; and, in a separate category, results or that seemed to be talking about something extremely specific (boolean vectors, networks, etc) that is likely not relevant for this Wikipedia article.
 * {| class="wikitable"

! Meaning !! Counts !! Links
 * convex hull || 5 || 6, 16, 26, 27, 34
 * closed convex hull ||  5  ||  1, 5, 19, 25, 40
 * both     ||  1 || 33; also includes the example given by David Eppstein, since Weyl explicitsly considers closed sets.
 * used only for functions || 6 || 2, 7, 10, 15, 21, 36
 * discarded (no access) || 0 || —
 * discarded (unsure) || 3 || 3, 12, 14, 22, 24, 28, 32, 35, 38
 * discarded (too restricted) || 12 || 4 8, 11, 13, 17, 18, 20, 23, 29, 30, 31, 37, 39
 * }
 * Here are a few comments on these limited data:
 * Some people do indeed use convex closure as a synonym of convex hull. Since, as pointed out above, the "convex-hull" operator is a closure operator, this makes sense.
 * However, most of the occurrences of that term refer to something different. Usually, that would be either:
 * the closed convex hull;
 * the closed convex hull of the epigraph of a function (in that case, a distinction is usually made between the convex closure and the convex hull [which is just the convex hull of the epigraph]).
 * a related notion with a more restrictive definition (usually in a specific context: discrete mathematics, computer science, logic...)
 * At least one very influential mathematician (Ky Fan) felt the need to point out that one should not confuse convex hull and convex closure.
 * The example of use by Hermann Weyl given above cannot really be used to support the use of convex closure as a synonym for convex hull rather than closed convex hull, since only closed sets are considered and so the convex hull and the closed convex hull coincide.
 * Having that in mind, I do not think that listing convex closure as a synonym of convex hull in the introduction without some additional explanation is a great idea. Not sure what is the best way to solve the problem, though. Here is a suggestion:
 * Remove convex closure from the introduction
 * In the section Closure operator, add something saying that the fact that the convex-hull operator is a closure operator leads some authors to refer to the convex hull has the convex closure; but that it should not be confused with the closed convex hull, which is can also be called convex closure (a reference to Ky Fan can be given here).
 * In the section Closed and open hulls, mention that the closed open hull is sometimes simply called the convex closure. Ky Fan could be used again as a reference, but 1 is perhaps a bit nicer, as it's better typeset and has some pictures, etc.
 * Unless someone disagrees, I can take care of implementing those changes later this week.
 * Best, Malparti (talk) 16:13, 9 January 2024 (UTC)
 * Personally it seems to me that the natural thing to do in the lead would be to put a footnote (using template:efn) following the words "convex closure" observing that this phrase is also used for another operation, together with relevant citations, rather than removing a valid alternate term. Since the closed convex hull is almost certainly never going to have its own article, I agree that including the information about that operation in this article is very sensible.  --JBL (talk) 19:26, 9 January 2024 (UTC)
 * @JBL The footnote in the lead works for me too. I'll let a bit of time pass to give other people a chance to chime in. Thanks for your input. Cheers, Malparti (talk) 22:24, 9 January 2024 (UTC)
 * Remove convex closure from the introduction
 * In the section Closure operator, add something saying that the fact that the convex-hull operator is a closure operator leads some authors to refer to the convex hull has the convex closure; but that it should not be confused with the closed convex hull, which is can also be called convex closure (a reference to Ky Fan can be given here).
 * In the section Closed and open hulls, mention that the closed open hull is sometimes simply called the convex closure. Ky Fan could be used again as a reference, but 1 is perhaps a bit nicer, as it's better typeset and has some pictures, etc.
 * Unless someone disagrees, I can take care of implementing those changes later this week.
 * Best, Malparti (talk) 16:13, 9 January 2024 (UTC)
 * Personally it seems to me that the natural thing to do in the lead would be to put a footnote (using template:efn) following the words "convex closure" observing that this phrase is also used for another operation, together with relevant citations, rather than removing a valid alternate term. Since the closed convex hull is almost certainly never going to have its own article, I agree that including the information about that operation in this article is very sensible.  --JBL (talk) 19:26, 9 January 2024 (UTC)
 * @JBL The footnote in the lead works for me too. I'll let a bit of time pass to give other people a chance to chime in. Thanks for your input. Cheers, Malparti (talk) 22:24, 9 January 2024 (UTC)

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

title: Talk:Convex hull


text:
Talk:Amazon River

Possible misleading translation
I suspect this sentence is misleading, but I want to be sure.

"In this journey, Orellana baptised some of the affluents of the Amazonas like Rio Negro, Napo and Jurua."

In my first reading of this, I took it to be an inelegant way to say that Orellana introduced some of the wealthy residents ("affluents") of the region to Christianity, including three specific regions. On my second reading I don't think this was intended. Does the following sentence capture what the author intended?

"In this journey, Orellana named some of the tributaries of the Amazon River such as the Rio Negro, Napo, and Jurua."

hydropower potential
he mean flow of Amazonas currently is 200.000m3/s. I guess it was much more in history.

How much Hydropower is that?

Answer: 2GW per 1meter dam.

50m, 100GW Hydro. Wikistallion (talk) 05:46, 11 August 2020 (UTC)

Consistent capitalization?
Should it be "Amazon River" or "Amazon river"? The format seems to change throughout the article. — Preceding unsigned comment added by Hatehowobvious (talk • contribs) 17:49, 31 March 2021 (UTC)

 * Good catch. CactiStaccingCrane (talk) 09:21, 20 August 2022 (UTC)

A Commons file used on this page or its Wikidata item has been nominated for speedy deletion
The following Wikimedia Commons file used on this page or its Wikidata item has been nominated for speedy deletion: You can see the reason for deletion at the file description page linked above. —Community Tech bot (talk) 10:37, 23 January 2023 (UTC)
 * Amazonas und Reliefkarte.png

A Commons file used on this page or its Wikidata item has been nominated for deletion
The following Wikimedia Commons file used on this page or its Wikidata item has been nominated for deletion: Participate in the deletion discussion at the nomination page. —Community Tech bot (talk) 12:10, 23 January 2023 (UTC)
 * Amazonas und Reliefkarte.png

title: Talk:Amazon River


text:
Saavik

Saavik is a fictional character in the Star Trek universe. She first appeared in the film Star Trek II: The Wrath of Khan (1982) played by Kirstie Alley. Robin Curtis took over the role for Star Trek III: The Search for Spock (1984) and Star Trek IV: The Voyage Home (1986).

Fictional biography
Saavik's background was never explored on screen. It has, however, been fleshed out in novels and comic books, though none of these sources is considered canon. According to the novels and comics, Saavik was born on Hellguard, an abandoned Romulan colony, and is half Vulcan and half Romulan.

A line of dialogue that would have revealed this in The Wrath of Khan was edited out prior to the film's release and never restored; as a result, the canonicity of this piece of information has been debated for more than two decades. Saavik's mixed parentage is referenced often in her appearances in Star Trek novels. However, if Saavik's mixed ancestry were to be made canon, it would violate the continuity created by the Star Trek: The Original Series episode "Balance of Terror" (which takes place after Saavik's birth) in which Starfleet learns for the first time that Romulans resemble Vulcans, a fact that appears to be unknown to Vulcans (or at least the extremely knowledgeable Mr. Spock) as well.

Some non-canon novels, however, hold that at least some Vulcans were fully aware of the Romulans' heritage, but deliberately concealed that knowledge from the Federation, considering it an embarrassing internal affair that should not be revealed to their allies. The TV series Star Trek: Enterprise established in canon that some factions of the Vulcan government were aware of the connection as early as the 22nd century. (There has also been some debate about whether Spock rescued the child Saavik before or after the events that occurred during "Balance of Terror". A rescue occurring after the episode would not be in conflict with the Vulcans' knowledge of Romulans.)

A few sources have her (non-canon) origin story aligned to original material found in the film's novelization, as follows: she was rescued from the colony, along with other children, by Spock, and she was cared for by his parents Ambassador Sarek and Amanda Grayson. Following in the footsteps of her mentor, Spock, she entered Starfleet Academy.

In the non-canon 1990 novel The Pandora Principle, written by Carolyn Clowes, it is established that four Vulcan research ships were captured by Romulans. Their Vulcan crews were abducted by Romulan scientists and their fertility was manipulated to produce half-Romulan, half-Vulcan children such as Saavik to use in mind control experiments. Vulcan scientists learned of the experiments and mounted a secret rescue of Saavik and other child survivors on Hellguard. Spock threatened to reveal the story to Federation authorities and along with it the secret of the Vulcan mating cycle pon farr if the survivors were denied Vulcan citizenship. Other members of the party wanted to educate them elsewhere and send the children to live on worlds other than Vulcan. Clowes writes that Saavik's name is of Romulan origin and translates as "little cat". In The Pandora Principle, Saavik, unlike the other half-Vulcan, half-Romulan child survivors, refuses a DNA test that would identify her Vulcan relatives. Instead, Spock, who has established a bond with her, takes a year of personal leave to "civilize" and educate the 9- or 10-year-old Saavik. She then lives off Vulcan with foster families or at boarding schools chosen by Spock until she is accepted into the Starfleet Academy as a teenager. This agrees with the Star Trek III: The Search for Spock novelization which said Saavik has never been to Vulcan until then. After graduating, as a fresh Lieutenant Saavik was on her cadet cruise on the USS Enterprise with Admiral James T. Kirk and Captain Spock when Kirk's old enemy Khan Noonien Singh sought revenge for the failure of the Ceti Alpha V colony and the death of his wife, Marla McGivers, and attacked the Enterprise.

Spock died while saving the Enterprise during the events of Wrath of Khan, but before his death transferred his katra to Dr. Leonard McCoy. His coffin was fired from the Enterprise in orbit around the Genesis Planet and was believed to have been destroyed in the atmosphere. A rare expression of emotion by a Vulcan is displayed when Saavik is seen shedding a tear during the eulogy for Spock by Kirk. Saavik and David Marcus (son of Admiral James T. Kirk), subsequently were assigned to the research vessel USS Grissom to study the newly formed Genesis Planet. During this mission, Saavik discovered that Spock had somehow been regenerated, and was rapidly aging. As the new Spock entered his teenage years, he began experiencing the mating drive known as pon farr, and Saavik helped Spock through this difficult time. When the Klingon commander Kruge and his men captured the landing party the next day, David sacrificed his life to save Saavik from being executed. Saavik helped Admiral Kirk return Spock to Vulcan, where his body and katra were reunited. Afterwards, she remained on Vulcan with Spock's family for reasons never explained on screen; the film's writers intended that this was because she was pregnant with Spock's child as a result of the pon farr, but no references to her pregnancy made it into the finished movie and it was never followed up, thereby once again placing this development into a grey area in terms of canon. Before the Enterprise crew departed Vulcan, Saavik told Captain Kirk how his son had died bravely, sacrificing himself to save both Spock and herself.

Unrealized concepts
The role of Saavik in Star Trek III went to Robin Curtis.

Saavik was at one point to appear in the Star Trek: The Next Generation episode, "Cause and Effect" in a scene in which the Enterprise-D encounters a starship that had been trapped in a time anomaly for some 80 years. The idea was dropped when Kirstie Alley insisted on being paid more for a nonspeaking cameo part than the episode budget could supply. (Saavik was to have been shown standing alongside a character played by Kelsey Grammer, Alley's Cheers co-star.)

The character of Saavik was originally intended to appear in Star Trek VI: The Undiscovered Country, which would have revealed her as a traitor to the Federation. The idea of using an established character was dropped and instead a new character, Valeris, was created, whom Douglas Brode described as "a dark doppelgänger of the heroic Saavik". According to director Nicholas Meyer, writing in his autobiography, The View from the Bridge, Saavik was dropped from the film and Valeris created when Kirstie Alley proved unwilling to reprise the role and Meyer didn't like Curtis's portrayal of the character, while Leonard Nimoy, in his autobiography I Am Spock, said there were also second thoughts about casting a popular, established character as a villain. Saavik, however, does appear in the novelization of the film, as a recruiting officer who inspires Valeris to join Starfleet, and offers some insights on how to deal with a dual heritage.

Other appearances and Next Generation continuity
In the novel Vulcan's Heart, which takes place some years after Undiscovered Country, an older Saavik marries Spock. Saavik appears again in the Vulcan's Soul trilogy of novels published from 2004. In this continuity, the character has risen to the rank of captain. In the Titan novel, Taking Wing, it is clearly stated that Spock and Saavik are married, as she sends greetings through Tuvok. Star Trek books are not considered part of the established canon.

In the "Mirror Universe Saga" trilogy of novels written by William Shatner, it is revealed that the Mirror Universe's Intendant Spock had a daughter named T'Val with Mirror Saavik.

Kirstie Alley did play Saavik one other time, in a play that was set between The Wrath of Khan and The Search for Spock, "The Machiavellian Principle" written by Walter Koenig for the ambitious "Ultimate Fantasy" convention. It also starred James Doohan, Mark Lenard (not as Sarek), Walter Koenig, Nichelle Nichols and George Takei, with a walk-on role by William Shatner as "the Admiral". The short script was eventually published by Creation Conventions in a booklet about Koenig's career, called "Through the Looking Glass". It misspells the name in the cast list as "Savik".

Early reference
Samuel A. Peeples' unused script, Worlds That Never Were, for the second Star Trek film, had a male character called "Doctor Savik", who eventually was morphed into the female Lieutenant Saavik.

Reception
Her character has been discussed by a number of scholars in the context of changing the representation of women characters in the Star Trek franchise. Mary Ann Tetreault noted how her story has marked the change in the style of how females are portrayed in Star Trek, noting that "she is not conventionally pretty", nor is she "subordinate to the men in the story", and that she "is shown to be much more capable" than many of them. Anne Cranny-Francis, discussing her character's background as revealed in a 1990 novel, The Pandora Principle, by Carolyn Clowes, described her as one of the "strong and courageous" women in early Star Trek stories. Likewise, Gary Westfahl called her "a strong and independent character", also noting that Saavik's character was "effectively destroyed when the producers refused to meet Alley's salary demands and recast the role in the next two films with a spectacularly untalented and vacuous actress, Robyn Curtis, transforming Saavik from a woman warrior to a wallflower". Sociologist Bärbel Schomers similarly characterized Saavik as an important character and strong female role, and listed her among several such figures that were conspicuously removed from the Star Trek franchise shortly after their introduction.

Donald E. Palumbo stated that the Star Trek movies closely conform to the structure of the monomyth as described by Joseph Campbell. In this view, Saavik provides the "supernatural aid" to Kirk in The Wrath of Khan. She is also the "navigator" in this and the following two films. In The Search for Spock, "the reborn Spock appears to have at least a mystical marriage on Genesis with Saavik", who here takes the role of "the goddess as ’good mother’ who helps him survive pon farr".

title: Saavik


text:
Ata'ollah Mohajerani

Sayyid Ata'ollah Mohajerani (, also Romanized as Atā'ollāh Mohājerāni; born 24 July 1954) is an Iranian journalist, author, and reformist politician. Mohajerani served as Minister of Culture and Islamic Guidance of Iran under President Mohammad Khatami from 1997 until 2000 when he was fired from office for alleged "permissiveness". He is living as a UK citizen.

Education
Mohajerani received his bachelor's degree in history from University of Isfahan, his master's degree in history and Iranian culture from Shiraz University and his PhD in history from Tarbiat Modares University.

Career
Mohajerani's political career began in 1980 after the Iranian Revolution, when he won the first round of the parliamentary elections to become a representative of Shiraz and the youngest member of the majlis. Later, he became the Parliamentary Deputy to the Prime Minister Mir-Hossein Mousavi, when he started to write the weekly column Naghd-e Haal in the Ettela'at newspaper, and then Vice President of Parliamentary Affairs under Ali Akbar Hashemi Rafsanjani.

As minister of culture and Islamic guidance, he officially announced and pursued a policy of "leniency" towards the field of culture and arts and removed many restrictions. He earned the wrath of conservatives by allowing hundreds of new publications to start up, the release of fifty-some Persian pop music albums, and the screening of the controversial movie Two Women.

He survived impeachment by the 5th Majlis which was dominated by the conservatives in part with a "daring" speech defending the principle of freedom of speech in Islamic rather than Western terms.

"Why does the Quran carry the harshest criticism of the Prophet? ... It was not in the nature of the Prophet to stifle discussion of opposing points of view."

In April 2000, however, he resigned due to heavy criticisms by the Iranian Supreme Leader, Ayatollah Khamenei, because of his "liberal" policies. He also served as the speaker of the cabinet during that time. He later became the president of the Iranian International Centre for Dialogue among Civilizations, but resigned from the post.

He was a member and a founder of Executives of Construction Party, which is considered a backer of Ali Akbar Hashemi Rafsanjani.

Mohajerani participated in the funeral and burial of former revolutionary Prime Minister Mehdi Bazargan, when few Iranian officials dared doing so because of Bazargan's very unpopular status among the higher ranks of the Islamic Republic government.

Works
Of the books Mohajerani has written, most famous are a "learned critique" of the Salman Rushdie novel Satanic Verses, a book in support of Ferdowsi (and against attacks by Ahmad Shamlou), and a book on Zaynab bint Ali's role in and after Aashurah. His other publications/works include:
 * Gray heaven/paradise, 2007.

Personal life
Mohajerani is married to Jamileh Kadivar, who is also a reformist politician and a former member of parliament.

Mohajerani left Iran and as of 2009 lives in England with his wife. They launched a website called www.maktoub.ir. Mohajerani is "a vocal supporter of the pro-democracy Green Movement," and opposes violence against the Iranian government saying "If we answer violence with violence, we are no different from them."

Advocating Khomeini's order to kill British author
After Ruhollah Khomeini issued a fatwa ordering Muslims to kill Salman Rushdie because of his novel The Satanic Verses, Mohajerani published a book called Critique of the Satanic Verses Conspiracy in 1989. Mohajarani quoted Khomeini's fatwa at the beginning of his book and approved and justified the fatwa. In 1995, Mohajerani wrote a short story gleefully satirising this British writer's fear of being attacked. Responding to Khomeini's Fatwa, on July 2, 1993, unknown assailants set fire to a hotel in the Turkish city of Sivas that was hosting a speech by Aziz Nesin, a renowned humorist who had translated the book into Turkish. A total of 35 people plus two perpetrators were killed in the blaze, and 145 people were injured. Mohajirani insisted that the massacre was a proud moment in what he called the glorious Islamic reawakening and wrote that Khomeini's fatwa had worked like a vaccine preventing further criticism of the prophet of Islam. So far, no proper study has been conducted into the role of Mohajerani and his book in promoting this massacre of intellectuals, translators and publishers worldwide.

In January 2023, The Guardian reported that the Metropolitan Police was reviewing a legal dossier filed in August 2022 that accused Mohajerani of encouraging terrorism contrary to the Terrorism Act 2006.

title: Ata'ollah Mohajerani


text:
Mohammad-Ali Abtahi

Seyed Mohammad-Ali Abtahi (born January 28, 1960, in Mashhad) is an Iranian theologian, scholar, pro-democracy activist and chairman of the Institute for Interreligious Dialogue. During the 1980s, he worked as the head of IRIB broadcasting in Mashhad, Bushehr, and Shiraz, and between 2001 and 2004 he worked as the vice-president for legal affairs in Majlis (Islamic Parliament of Iran) and was the advisor to the president between 2004 and 2005.

After three years of living in Lebanon he joined the presidential election campaign as an IRIB broadcasting representative. He also took the position of the head of the president's office at the time of the 7th government ( Seyed Mohammad Khatami). He served served as the deputy for legal affairs for the Islamic Consultative Assembly between 2001 and 2004.

Biography
Mohammad Ali Abtahi, born January 28, 1960, in Mashhad, was the eldest child of Seyed Hassan Abtahi and Seyedeh Zahra Hashemi. His father being from Mashhad and his mother being from Behshahr (Abdolkarim Hashemi Nejad's sister), he pursued his educations in religious studies as a family tradition and in 1976 he accomplished Dars-Kharij-Fiqh. In late 1978, he married his cousin, Fahimeh Mousavi Nejad, the daughter of Mohammad Mousavi Nejad and had three daughters, Faezeh, Fatemeh and Farideh.

He has three brothers, Mohammad Taghi, Hossein, and Reza and two sisters, Hourieh and Narges.

Positions in the Islamic Republic
Due to his background in supporting the Islamic Revolution, and his amateur activities in arts and culture before the Islamic Revolution in 1979, he was elected as the director of Mashhad Broadcasting programs. After a two-year-old residence in Qom dedicated to his studies, he became the chief executive director of Boushehr and Shiraz Broadcasting. Abtahi was transferred to Tehran in 1983 and was assigned as Radio Iran's director. He remained in the same position until 1988, when he became the deputy of IRIB Broadcasting overseas department, and while Mohammad Reza Khatami was the minister of Islamic Guidance, Abtahi became the deputy of the international affairs of this ministry, responsible for community centers (Khane-ye-Farhang) and cultural discussions all over the world. After Mohammad Reza Khatami resignation in 1992, he resigned as well and returned to IRIB Broadcasting as the adviser to the president (Mohammad Hashemi Rafsanjani) consultant. While Ali Larijani worked as the head of IRIB, he started his work at IRIB Broadcasting in Beirut. In the 1997 presidential election, he left Beirut and joining Seyyed Mohammad Khatami's campaign, he became the head of the president's office on July 10, 1997. After the presidential election in 2001, he became the deputy for legal affairs in the Islamic Parliament of Iran. After the 7th Parliament poll, and after three resignations, he was accepted to resign on October 12, 2004, and became the adviser president consultant. He has been a member of the Founders’ Council and Central Council of Combatant Clergy Association ever since they have been established. Together with his wife, Fahimeh Mousavi Nejad, he established the Religions’ Dialogue NGO and has given speeches at dozens of international inter-religion conferences.

The Election of 2009 and detention
In the 10th election, unlike Khatami who supported MirHossein Mousavi, he joined Karroubi’s campaign and was arrested on June 16, 2009. Following the post-election struggles, he was arrested together with several other reformists. He was arrested by the order of Saeed Mortazavi issued before the election. His wife states (regarding his arrest):"I met my husband 43 days after he had been arrested, while he had lost about 43 kilos. and said they had been giving him a tablet during the last few days which had calmed him down against all the excitements of the world." Though Abtahi denied receiving any tablets in an interview broadcast on August 2, in Bist-o-Si, he attended the first trial session of suspects in the meeting hall of the Tehran General Department of Justice. A few years after he was released, he had an interview with Hossein Dehbashi in Khesht-e-Kham in which Abtahi explained his reasons for what he had said on the trial session.

Statements on the Trial Session
On August 1, 2009, in a court presided over by Judge Salavati and without the presence of independent journalists, the jury, the defendants' lawyer (Saleh Nikbakht) and the defendants' family.

Only the reporters of IRIB new Agency, IRNA and Fars News were present at the court. Also, the camera team of Press TV was not allowed to take pictures. Abtahi was trialed along with 100 other people.

He appeared in a news conference together with Mohammad Atrianfar and considered Mirhossein Mousavi to be under the illusion of fraud and called Seyyed Mohammad Khatami's association with Mousavi treacherous. He also accused Akbar Hashemi Rafsanjani of taking revenge on Mahmoud Ahmadinejad and Seyedali Khamenei.

The Secretariat of Expediency Discernment Council issued a statement rejecting the remarks of Abtahi, calling them completely false, claiming the uncertainty of the conditions and considerations under which these remarks were made.

On November 21, 2009, Abtahi was sentenced to six years of penal servitude, and on November 22, 2009, he was released from prison after 160 days on bail. After his release, Zahra Rahnoord, Mirhossein Mousavi, Seyed Mohammad Khatami, Mehdi Karroubi and Hassan Khomeini visited him at his home.

The assault and attack
On June 20, 2010, after a memorial for Mirza Javad Tehrani, some plainclothesmen attacked him and beat him severely."“I passed there and turned into the side boulevard; I was chased by some motorcycle riders when suddenly the driver of a Pride took his colt out and blocked my way. First, they kicked my car widely in a way that even the side mirror of the car was smashed. Then one of the cycle riders took a knife out of his shirt and as he was approaching me, he shouted “get out of the car” several times. He hit the car with his knife and at the same time, another cycle rider approached me with a thick cable in his hand, and hit the rear window so severely that the whole glass was smashed, making a loud sound. Suddenly I noticed another man who had entered my car through the broken window and when I tried to push him out, he sprayed tear gas directly into my eyes. My clothes were completely covered with pieces of broken glass, and I could see nothing due to the tear gas; yet, I tried to get out of the car and could pass from the side of their car. At the same time as they were still busy, I tried my best to get away from there. Then, I saw a man cycling in front of them all. He was talking on the phone and signaled them to stop. I managed to escape that catastrophic condition with that car. There were no police officers around, and they were not worried about the arrival of any police officer, either.”"

Attending the leader's Ramadan Breakfast Ceremony
On May 23, 2018, Abtahi, together with several other members of the government was invited to the leader’s Ramadan breakfast ceremony, at the leader’s Beyt after many years.

Government positions
1969: Mashhad Broadcasting Director

1972: General Director of Boushehr and Shiraz Broadcasting

1973: Radio Iran Director

1978: Deputy of IRIB Broadcasting overseas department

1978: Deputy of the International Affairs of the Islamic Guidance Ministry

1994: IRIB Representative in Beirut

1997: Head of the President’s office

2001: Deputy of the Presidents’ Legal and Parliament Affairs

2004: Advisor to the President

Blogs
He is the first Iranian politician to use Internet to write blogs. In a rare event, from November 2003 to June 13, 2009, he wrote in the “Webnevesht” blog series without even a single interval, for six unremitting years. After Abtahi was imprisoned for 70 days, his weblog was updated for a week, from somewhere located inside the prison. This was met with the blog writers’ uncertainty, and the reformists never believed that Abtahi himself had written them.

Books
1- The assassination of a President (Translation)

2- A Dialogue with Christian Thinkers (Religion in the Contemporary World) 1990 Tarh-e-No Publication

3- Prudence and Tolerance, 2004, Loh-e-Fekr Publication

4- A comic book; Al-Ahghar to Be Sacrificed for You, 2004, Loh-e-Fekr Publication

5- For My Heart 2005, Chalesh Publication

6- Without a Mask, 2005, Chalesh Publication

7- We Lost (A study of the political losses since 2005) 2017, Rouzegar Publication

8- Nuclear Halo, 2017, Sales Publication

9- I Have Come for Your Smile 2017, Aban Publication

10- From Corona and Other Evils 2021, Rozaneh Publication

11- Khan Alley, a Novel, 2023 Ghoghnous Publication

12- No One Believes Here 2011 Morvarid Publication, (It has not yet received the publication permission.)

Articles and interviews
Dozens of his articles have been published in Iranian and foreign newspapers, and many of his interviews with international broadcasts have been released so far.

He has interviewed in Arabic, in several TV programs with Aljazirah, Al-Arabia, and Arabic B.B.C.

A friendly conversation between Siavash Ardalan with Mohammad Ali Abtahi grabbed many people's attention in 2017.

title: Mohammad-Ali Abtahi


text:
Antarctic toothfish

The Antarctic toothfish (Dissostichus mawsoni), also known as the Antarctic cod, is a large, black or brown fish found in very cold (subzero) waters of the Southern Ocean near Antarctica. It is the largest fish in the Southern Ocean, feeding on shrimp and smaller fish, and preyed on by whales, orcas, and seals. It is caught for food and marketed as Chilean sea bass together with its sister species, the more northerly Patagonian toothfish (D. eliginoides). Often mistakenly called "Antarctic cod", the Antarctic toothfish belongs to the notothen family (Nototheniidae), a family of fish genera that are abundant near Antarctica.

Name and taxonomy
The common name "toothfish" refers to the two rows of teeth in the upper jaw, thought to give it a shark-like appearance.

The genus name Dissostichus is from the Greek dissos (twofold) and stichus (line) and refers to the presence of two long lateral lines that enable the fish to sense prey. The species name, mawsoni, honors the Australian geologist Douglas Mawson who led the 1911-1914 Australasian Antarctic Expedition that explored the Antarctic coast and obtained the species' type specimen.

The Antarctic toothfish was first formally described in 1937 by the English ichthyologist John Roxborough Norman with the type locality given as off MacRobertson Land at 66°45'S, 62°03'E in Antarctica.

Description
Fully grown, these fish (and their warmer-water relative, the Patagonian toothfish, D. eleginoides) can grow to more than 1.7 m in length and 135 kg in weight, twice as large as the next-largest Antarctic fish. Being large, and consistent with the unstructured food webs of the ocean (i.e., big fish eat little fish regardless of identity, even eating their own offspring), the Antarctic toothfish has been characterized as a voracious predator. Furthermore, by being by far the largest midwater fish in the Southern Ocean, it is thought to fill the ecological role that sharks play in other oceans. Aiding in that role, the Antarctic toothfish is one of only five notothenioid species that, as adults, are neutrally buoyant. This buoyancy is attained at 100–120 cm in length  and enables them to spend time above the bottom without expending extra energy. Both bottom-dwelling and mid-water prey are, therefore, available to them. Most other notothenioid fish and the majority of all Antarctic fishes, including smaller toothfish, are confined to the bottom. Coloring is black to olive brown, sometimes lighter on the undersides, with a mottled pattern on body and fins. Small fish blend in very well among the benthic sponges and corals. The species has a broad head, an elongated body, long dorsal and anal fins, large pectoral fins, and a rudder-like caudal fin. They typically move slowly, but are capable of speed bursts that can elude predatory seals.

Feeding ecology
Over the continental shelf, Antarctic toothfish feed on shrimp (Nauticaris spp.) and small fish, principally another neutrally buoyant nototheniid, the Antarctic silverfish (Pleuragramma antarcticum). This loosely schooling species is also a major prey of Adélie (Pygoscelis adeliae) and emperor penguins (Aptenodytes forsteri), Weddell seals (Leptonychotes weddellii) and Antarctic minke whales (Balaenoptera bonaerensis). Therefore, competition for prey among toothfish and these other mesopredators (middle trophic level predators) could be very important. The large Antarctic toothfish are eaten by sperm whales (Physeter macrocephalus), killer whales (Orcinus orca), Weddell seals, and possibly colossal squid (Mesonychoteuthis hamiltoni). Toothfish that are dwelling on the bottom, particularly those caught during the summer on the continental slope, eat mainly grenadiers (Macrouridae), but also feed on other smaller fish species and skates (Raja spp.). They also feed on the colossal squid. Antarctic toothfish have been caught to depths of 2200 m, though based on commercial fishing effort, few occur that deep.

Aging and reproduction
Aging data indicate Antarctic toothfish are relatively fast-growing when young, but then growth slows later in life. They reach about one-third of maximum size after 5 years, and half maximum by 10 years, after which growth slows considerably. To grow fast when small is an adaptation of most predatory fish, e.g., sharks, so as not to be small for very long. The maximum age recorded so far has been 48 years. Antarctic toothfish take a long time to mature (13 years for males, 17 years for females) and once mature may not spawn every year, though the actual spawning interval is unknown. Only a few Antarctic toothfish with mature eggs have ever been caught, meaning knowledge is sparse about fecundity. They spawn sometime during winter. Large, mature, older fish have been caught among the seamounts of the Pacific-Antarctic Ridge, a location thus thought to be important for spawning. Smaller, subadult Antarctic toothfish tend to concentrate in shallower waters on the continental shelf, while a large portion of the older fish are found on in the continental slope. This sequestering by size and age could be another adaptation for small fish to avoid being eaten by large ones. The recruitment potential of Antarctic toothfish, a measure of both fecundity and survival to spawning age, is not known.

Anatomy and physiology
The Antarctic toothfish has a lightweight, partially cartilaginous skeleton, lacks a swim bladder, and has fatty deposits which act as a stored energy source, particularly during spawning. This fat also makes large toothfish neutrally buoyant. Many toothfish caught over the seamounts are very depleted of fat, and this is thought perhaps to be related to spawning and spawning migration, which are energy-demanding activities. It is not known what happens to these fat-depleted fish, including whether they reach, or how long it takes them to reach, breeding condition again; this ostensibly occurs upon returning to continental-slope waters. Antarctic toothfish have vision and lateral line systems well adapted to find prey in low light levels. Since ice covers the surface of the ocean where Antarctic toothfish occur even in summer, these sensory specializations likely evolved to enable survival in the reduced light levels found under ice and in the Antarctic winter, as well as at deep depths. Antarctic toothfish also have a very well developed sense of smell, which is why they are easily caught by baited hooks and also scavenge the remains of penguins killed by other predators.

Cold adaptation
The Antarctic toothfish lives in subzero degree water below latitude 60°S. It is noteworthy, like most other Antarctic notothenioids, for producing antifreeze glycoproteins, a feature not seen in its closest relative, the Patagonian toothfish, which typically inhabits slightly warmer waters. The presence of antifreeze glycoproteins allows the Antarctic toothfish (and other notothenioids) to thrive in subzero waters of the Southern Ocean surrounding Antarctica. The Antarctic toothfish's voracious appetite also is important in coping with cold water. It is mainly caught in the Ross Sea in the austral summer, but has also been recorded from Antarctic coastal waters south of the Indian Ocean sector, in the vicinity of the Antarctic Peninsula, and near the South Sandwich Islands.

Fishery and associated ecosystem
A fishery for Antarctic toothfish, managed by the Convention for the Conservation of Antarctic Marine Living Resources (CCAMLR), has existed since 1997. The existence of this fishery in the Ross Sea, the area where most Antarctic toothfish are caught, is very contentious - the main argument proposed for this is the lack of accurate population parameters, such as original stock size, fecundity, and recruitment. Moreover, the main fishing grounds are presumed by some researchers to cover the area through which the entire stock of Antarctic toothfish pass. Typically, the fishing season has finished in the area by the end of February and for the remainder of the year, much of the area is covered by sea ice, providing a natural impediment to fishing. This fishery is characterised by opponents as being a challenge to manage owing to the nature of benthic longline fishing. The bycatch of other fish can also be significant, with the ratio of toothfish caught ranging from 4.5% to 17.9% and averaging 9.3% from the 1999/2000 fishing season to 2013/14 in CCAMLR Subarea 88.1 when the toothfish catch first exceeded 50 tonnes and from 2.3% to 24.5% averaging 12.4% in CCAMLR Subarea 88.2 up to the latest publicly available figure from 2013/14. The bycatch of other fish species is also regulated to a maximum amount annually by CCAMLR. CCAMLR decision rules are based on determining the catch level that will ensure that the median estimated spawning stock biomass (not total biomass) is greater than or equal to 50% of the average pre-exploitation spawning biomass after a further 35 years of fishing (i.e. 35 years from each year of assessment), with the additional condition that the probability is less than a 10% that the spawning biomass will decline below 20% of the pre-exploitation level at any time during this period. Current spawning stock biomass for Antarctic toothfish in the Ross Sea Region is estimated to be at 75% of the pre-exploitation level (95% Bayesian probability interval 71–78%), well above the 50% target reference point.

An independent study was reported to have detected the disappearance of large fish at the southern periphery of its range in the McMurdo Sound and was postulated to be consistent with this apparent loss of large fish. However, more recent work has shown this was not the case in 2014. Some studies have reported that the prevalence of fish-eating killer whales has been apparently decreasing in the southern Ross Sea, foraging efficiency of Weddell seals is decreasing, and numbers of Adélie penguins (competitors for Antarctic silverfish) have been increasing. More recent studies have confirmed visual sightings of Weddell seals and Type-C killer whales holding and consuming large toothfish in the McMurdo Sound area and raise questions over the previously assumed importance of assumed dominance of Antarctic silverfish (Pleuragramma antarcticum) in the diet of Weddell seal and Type-C killer whales. These reports highlight the importance of managing this fishery in the best interests of the ecosystem by continuing to collect information on both Antarctic toothfish life history and the interaction of that species with predators and prey. An important research programme in this regard is the annual 'Shelf' survey carried out annually since 2012, which is designed to monitor the abundance of subadult Antarctic toothfish in areas where subadult-sized fish have been regularly found (e.g., in the southern Ross Sea) has been designed provide data to better estimate recruitment variability and provide an important early-warning signal of changes in toothfish recruitment. The project also is used for additional targeted data collection to better understand the lifecycle and ecosystem role of Antarctic toothfish.

Research has provided evidence for long-distance migrations of type-C killer whales between the Ross Sea and New Zealand waters, indicating a much wider range that had been postulated by a number of scientists. One adult female type-C killer whale has been seen in both New Zealand waters and McMurdo Sound, Antarctica, and a high large proportion of type-C killer whales sighted in McMurdo Sound have scars caused by cookiecutter sharks that are currently assumed to be limited to north of 50°S. At the same time as this study was occurring, Italian whale experts at Terra Nova Bay, about 360 km north of Scott Base, deployed satellite transmitters on type-C killer whales to determine the whales' movements. Their results independently verified that type-C killer whales were commuting between Scott Base and the waters off Northland.

The total catch of Antarctic toothfish in 2013–14 was 3820 tonnes; 3,320 tonnes of this were taken from the Ross Sea (FAO Statistical Divisions 88.1 and 88.2), with the remainder taken from other high seas areas within the CCAMLR convention area.

Management
The ecosystem approach to fishing is encapsulated in Article II of the CAMLR Convention. The ecosystem approach uses decision rules based on both population status targets and limit reference points, and incorporates uncertainty and ecosystem status in the calculation of these targets. Different reference points to account for the needs of dependent predators in the ecosystem are used depending on the location of the species in the food web. The ecosystem fisheries management approach by CCAMLR involves use of move-on rules to protect trophic interactions, and limit direct effects of fishing on fish bycatch, seabirds, and vulnerable marine ecosystems. Annually reviewed mitigation measures such as line weighting and streamer lines minimize seabird bycatch, which have resulted in a substantial reduction in accidental seabird mortalities in the CAMLR Convention Area. The 50% (target) and 20% (limit) reference points used by the CCAMLR decision rules exceed the requirements for target and limit reference points set by almost all national and international fisheries management organizations, even for species longer lived than toothfish. A wide study of many fisheries generally indicated that most reach maximum sustainable yield at 30–35% of their pre-exploitation abundances. CCAMLR uses a more conservative reference level to allow exploitation at a level where toothfish recruitment and the ecosystem in general is not appreciably impacted. This is required by Article II of the CAMLR Convention. A common misunderstanding of the CCAMLR decision rules is an assumption that the decline in population size will follow a clear trajectory from the starting year to a point 35 years later when the stock size will reach 50% of pre-exploitation levels and an assumption that no feedback occurs during each assessment. The catch limit, though, is recalculated based on all updated or revised data at each annual or biennial assessment. This approach is used to ensure that the 50% level will be approached slowly and enables an ongoing readjustment of catch levels as knowledge improves.

Environment and bycatch
CCAMLR imposes stringent environmental protection and bycatch mitigation measures to Antarctic toothfish fisheries, including:
 * Monitoring of daytime setting and movement of vessels from the fishery should any vessel catch more than three seabirds
 * Use of streamer lines during setting to keep birds away from baited hooks
 * Weighting of lines to ensure fast sink rates to prevent seabirds from accessing baited hooks
 * The use of bird exclusion devices to prevent birds from accessing hooks whilst lines are being hauled
 * Limitations on the release of fish offal overboard at the same time as setting and hauling of lines to avoid attracting seabirds: An additional requirement prohibits the dumping of all offal south of 60°S, the region where Antarctic toothfish are caught
 * Prohibition on the dumping of oil, plastic, garbage, food waste, poultry, eggs or eggshells, sewage, and ash by fishing vessels
 * Prohibition of the use of plastic packaging bands on fishing vessels

Incidental mortality of seabirds as a result of fishing has fallen to near-zero levels in the CCAMLR convention area. No mortality of seabirds or marine mammals was recorded as a result of fishing for Antarctic toothfish in 2011–12 and only two seabirds (southern giant petrels Macronectes giganteus) have been killed as a result of fishing in the Ross Sea since 1996/97.

Compliance
Compliance measures adopted by CCAMLR apply to all Antarctic toothfish fisheries. These include:
 * At-sea inspections of fishing vessels
 * Vessel licensing
 * Port inspections of fishing vessels
 * Continuous reporting of fishing vessel positions via satellite-linked vessel monitoring systems
 * Catch documentation scheme for toothfish, which tracks toothfish from the point of landing through to the final point of sale and requires verification and authorisation by government authorities at each step
 * The requirement to carry two scientific observers on each licensed vessel – including one from a member state other than the vessel flag

Sustainability
In November 2010, the Marine Stewardship Council (MSC) certified the Ross Sea Antarctic toothfish fishery as a sustainable and well-managed fishery. The certification is contentious, with many conservation groups protesting the certification due to the paucity of information needed to reliably manage the fishery, and that only eight of the 19 vessels in the fishery during the latest year for which data are publicly available were certified. During the 2013–14 season, vessels operating under the Marine Stewardship Certification landed 51.3% of all Antarctic toothfish from the Ross Sea Region (CCAMLR Subarea 88.1) and 64.7% of Antarctic toothfish from the Amundsen Sea sector (CCAMLR Subarea 88.2).

The argument that only a portion of Antarctic toothfish is certified, the high price it commands, and the remote areas where a large proportion of the fish are caught have been advanced as an encouragement to illegal, unreported, and unregulated (IUU) fishing and mislabeling. A 2011 genetic study of MSC-labeled Antarctic toothfish found in markets revealed a significant proportion was not from the MSC-certified stock, and many were not toothfish at all. The MSC had conducted its own internal study, which found no evidence of mislabeling. The MSC conducts an annual audit of the fishery which includes sampling of certified product.

Due to the challenges that faced toothfish management in the 1990s and early 2000s (e.g., IUU fishing, mislabeling, and inadequate data for management), consumer seafood guides such as Seafood Watch placed toothfish of both species (Chilean seabass) on their red, or “avoid”, list; however, in light of up-to-date, internationally peer-reviewed scientific information, in April 2013, Seafood Watch upgraded the Ross Sea Antarctic toothfish fishery to a "good alternative". Following a comprehensive review in 2012, the Monterey Bay Aquarium revised its rating of Antarctic toothfish to 'good alternative'.

Greenpeace International added the Antarctic toothfish to its seafood red list in 2010. This approach is at variance with the high score given the fishery when it was granted certification by the MSC.

title: Antarctic toothfish